From cube-lovers-errors@mc.lcs.mit.edu Thu Sep 17 17:18:28 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id RAA12950; Thu, 17 Sep 1998 17:18:27 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 14 Sep 1998 14:14:22 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Re: Weak Local Maxima, 6f from Start In-Reply-To: <14Sep1998.111621.Hoey@AIC.NRL.Navy.Mil> To: Cube Lovers Message-Id: > It turns out that 6f is indeed the shortest. There are two such positions > unique to symmetry which are 6f from Start, the Pons and one other. The > other one is quite pretty: > > L2 R2 D2 U2 B' F (6f*) > I didn't notice it originally, but this position is in the slice subgroup, and is only one slice move from Pons. Half turns such as L2 can be written equally well as either LL or as L'L', so we can write (L2 R2) as (L'R)(L'R) and (D2 U2) as (D'U)(D'U). Thus, the weak local maximum 6f from Start can be written as five slices, one slice short of Pons. L'R L'R D'U D'U B'F All we would have to do to get the Pons would be to add one more B'F slice. ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Thu Sep 17 20:27:13 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id UAA14346; Thu, 17 Sep 1998 20:27:13 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Chris and Kori Pelley" To: "Cube Lovers" Subject: DOGIC solution Date: Mon, 14 Sep 1998 18:01:56 -0400 Message-Id: <000a01bde02b$49b5aae0$da460318@CC623255-A.srst1.fl.home.com> Using Noel Dillabough's PUZZLER program for MS Windows, I was able to verify the basic moves needed to solve the new DOGIC puzzle. SPOILER WARNING! If you wish to solve the puzzle yourself, read no further. What seems fairly obvious is that the DOGIC is essentially a superset of Impossi-Ball, which is basically the corners of MegaMinx. On DOGIC, however, these corners have been flattened and could more properly be called "centers." Using classic 3x3x3 techniques, you can position and orient these pieces using the following moves: Center 3-cycle: (R' U L U') (R U L' U') Center orientation (pair): (R' D R) (F D F') U' (F D' F') (R' D' R) U Note that these faces refer to the large pentagons and must be "translated" to fit the dodecahedral nature of DOGIC. R, U, and L form a horseshoe, and F intersects all three. The D face is not really D, in fact it touches the U face at one point. The remaining triangular pieces turn out to be fairly trivial, and any two can be swapped with the simple sequence: R u R' u' In this case, R is a large pentagon and u is any intersecting smaller pentagon. A general strategy would be to manually place the top "centers" followed by their adjacent centers (if you have solved ImpossiBall this should not be difficult). Then apply the first two moves above to complete the remaining centers. Finally, place all the smaller triangles with the third move. Despite having more permutations than most magic puzzles, DOGIC seems to be fairly easy to solve. Chris Pelley ck1@home.com http://www.chrisandkori.com From cube-lovers-errors@mc.lcs.mit.edu Fri Sep 18 14:29:06 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA20307; Fri, 18 Sep 1998 14:29:05 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 15 Sep 1998 12:21:58 -0400 (EDT) From: der Mouse Message-Id: <199809151621.MAA19286@Twig.Rodents.Montreal.QC.CA> To: cube-lovers@ai.mit.edu Subject: Two-face and three-face subgroups I've been playing with the two-face subgroup [%] of the 3-Cube and got to wondering - how much work has been done on the two-face and three-face subgroups? Certainly the two-face subgroup "feels" like a much smaller object than even the 2-Cube (though perhaps more tedious for human solution), perhaps about the size of the Pyraminx. [%] Okay, strictly speaking there are two different two-face subgroups, but one of them is not even the least bit interesting. And what about the three-face subgroups? Certainly the three- and four-face subgroups are smaller than the whole Cube group, though ISTR that the five-face (sub)group is actually the whole thing. But how much smaller, and how difficult of human solution? I'd expect one of the three-face groups (the one involving two opposite faces - call it the L-F-R one) to be more tedious but no more difficult than the two-face group, whereas the other one (involving one face from each pair of opposite faces - U-F-R, say) should have more interest. In particular, the two-face subgroup is smaller than the set of all position that leave unchanged the cubies that the two-face subgroup never touches. (To put it another way, I'm saying that the subgroup generated by {R,F} is smaller than the set of positions of the full group that leaves unmoved the 11 cubies that don't touch either of those two faces - 7 if you don't count face cubies.) I can see a factor of 128 smaller, since it's not possible to flip edge cubies in the two-face group, but I haven't thought about the corners, so it may be even smaller than that. What about the three-face subgroups? The L-F-R subgroup is also smaller, if for no other reason than an inability to flip edge cubies, like the two-face group. But is the U-F-R subgroup the same as the subset of the full group that leaves untouched the 7 (4 if you don't count face centers) cubies in the DBL corner? What about human solvability? I've taught myself to solve the two-face group, and with the tools I developed (largely powers, reorientations, and inverses of F' R' F R) I feel confident I can handle the L-F-R three-face group or even the L-F-R-B four-face group. Can anyone comment on how humanly difficult the U-F-R group, or for that matter the U-F-R-L four-face group, is? der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Tue Sep 22 16:10:10 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id QAA17882; Tue, 22 Sep 1998 16:10:10 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 18 Sep 1998 15:52:33 -0400 (EDT) From: Nicholas Bodley To: Hana Bizek Cc: cube-lovers@ai.mit.edu Subject: Re: Rubik's cube kingdom In-Reply-To: <35F350B1.626F@ameritech.net> Message-Id: My apologies for a delayed reply. Hana's essay was rather philosophical, and contained some uncommon points of view; it was appropriate, in my opinion. One aspect of the Cube (and related puzzles) that seemed to be ignored is the remarkable ingenuity of their internal mechanisms. I maintain that the mechanism of the original (i.e., 3^3) Rubik's Cube is one of the most ingenious ever invented. I recall being very fatigued, riding the West Side IRT subway in NYC about 2 AM, perhaps, and catching sight of someone manipulating what must have been one of the very first Cubes, probably from Hungary*. I was fairly sure I wasn't hallucinating, but was very troubled that what I'd seen simply appeared impossible. I've been a somewhat-casual student of mechanisms all my life. *This was probably several weeks, or more, before the Scientific American article, and the later explosion of its popularity. My regards to all, |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Tue Sep 22 18:09:16 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA18211; Tue, 22 Sep 1998 18:09:15 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 17 Sep 1998 00:03:47 -0400 (EDT) From: Jerry Bryan Subject: More on Calculating Weak Local Maxima To: Cube-Lovers Message-Id: In the process of adding the code to my God's Algorithm program to calculate weak local maxima in the face turn metric, I realized that the algorithm I posted previously to do so was incomplete in one subtle but very important respect. This message will provide the missing piece to the algorithm. I have posted much of this before, but my program is in general jumping ahead by more than one move at a time. For example, suppose we can store all the positions up to five moves from Start. Then, we can determine all the positions which are eight move s from Start by calculating all the products xy where x is a position of length five and y is a position of length three. Obviously, just because the length of x is five and the length of y is three does not mean that the length of xy is eight. In fact, the length of xy could be anywhere from two through eight. To determine the true length of xy, we compare xy to the stored positions of length two, three, four, and five. In addition, we compare xy to the calculated positions of length six and seven, which are calculated in the same manner as is xy. If xy fails to match all such shorter positions, then its length is indeed eight. Next we focus on the quarter turn metric. For some fixed q in Q, the set of twelve quarter turns, what is the length of xyq if the length of xy is eight with the length of x equal to five and the length of y equal to three? First of all, it must be either seven or nine. Second of all, the length of yq must be either two or four. If the length of yq is two, then we know that the length of xyq must be seven. But if the length of yq is four, then we are still not sure. The reason is that there might be some u not equal to x of length five and some v not equal to y of length three such that xy=uv, but where the length of vq is two. If so, then the length of xyq is the same as the length of uvq which is seven. The basic idea is that if z=xy where the length of x is five and the length of y is three, then there may be many, many x and y pairs of length five and three respectively whose product yields z. The length of zq is nine only if for every such y the length of yq is four. Even if all but one yq is of length four, it only takes one yq of length two to spoil the pudding, as it were. The mechanism which I have posted previously to capture this concept is the Ends-with function E(z). E(z) is defined to the be set of all moves with which a minimal maneuver for z can end. So in the case at hand, since the length of z is eight, the length of zq is nine only if E(z) does not contain q'. E(z) can be calculated in the case at hand as the union of E(y) taken over all the y values of length three which can be composed with an x of length five to create z. Therefore, to say that E(z) does not contain q' is the same thing as saying that none of the E(y) contain q'. So far, so good and there is nothing new here which I haven't posted before. But let's consider the exact same issue in the face turn metric. If the length of x is five and the length of y is three, then the length of xy can be in the range of two through eight as before. And as before, if we compare xy with all positions of length two through seven without finding a match, then the length of xy is indeed eight. But this time we need to consider xyf, where f is some fixed face turn in the set Q+H of twelve quarter turns and six half turns. What is the length of xyf? For starters, it is either seven or eight or nine. Also, the length of yf is two or three or four. If the length of yf is two, then the length of xyf is guaranteed to be seven. If the length of yf is three, then the length of xyf is guaranteed to be no more than eight. But the length nevertheless might be seven, because as in the quarter turn case, there may be some u of length five and some v of length three such that uv=xy, but such that the length of vf is only two. If so, the length of xyf is the same as the length of uvf which is guaranteed to be seven. The definition of Ends-with is the same in the face turn case as in the quarter turn case, namely E(z) is the set of all face turns with which a minimal maneuver for z can end. If z=xy then E(z) can be calculated as the union of E(y) over all the y value s of length three which can be combined with an x value of length five to form z. To say that the length of zf is at least eight is the same thing is saying that E(z) does not contain f' which is the same thing as saying that none of the E(y) contain f'. Next, let's suppose that indeed E(z) does not contain f'. We are still left with the issue of whether the length of z is eight or nine, having eliminated seven as a possibility. The test is still the length of all the yf, with a length of two having been eliminated as a possibility. If all of the yf are of length 4, then xyf is of length nine. But if even so many as one of the yf are of length three, then xyf is of length 8. The mechanism I have posted before to capture this concept is the Ends-with2 function. E2(z) is a little tricky to describe. Informally, we might say that E2(z) is the set of all f in Q+H with which z can end without changing it's length. It is probably better to say that E2(z) is the set of all f in Q+H such that the length of zf' is the same as the length of z. The technique which I have posted before (and which I must now correct) to calculate E2(z) is to form the union of E2(y) over all y values of length three which can be combined with an x value of length five to form z. If the length of zf is eight or nine, then this mechanism is fine. But if the length of zf turns out to be seven, there is a problem. That is, there may be one y where the length of yf is two and where E(y) contains f, and there may be another y where the length of yf is is three and where E2(y) contains f. In such a case, both E(z) and E2(z) would contain f. Hence, we must always calculate E(z) prior to calculating E2(z), and we must omit from E2(z) any f values which are already contained in E(z). With this correction, everything works. A local maximum is a position z for which |E(z)|+|E2(z)|=18, a strong local maximum is a local maximum z for which |E(z)|=18 and |E2(z)|=0, and a weak local maximum is a local maximum z for which |E(z)| < 18 and |E 2(z)| > 0. All my examples have been specific to y values of length 3 for clarity of exposition, but the calculation of E(z) and E2(z) is totally general, and is the union of E(y) and E2(y), respectively, over all y values which can be used to form a z of the form z=xy, and with any values which are in E(z) omitted from E2(z). Finally, my programs also calculate a Starts-with and a Starts-with2 function, which are defined analogously. The same correction must be made to the Starts-with2 function as was made for the Ends-with2 function. Equivalently, we can define S(z)=E'(z') and S2(z)=E2'(z'), where E' and E2' are the set of all inverses of the elements of E and E2, respectively. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990 From cube-lovers-errors@mc.lcs.mit.edu Tue Sep 22 19:05:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA18829; Tue, 22 Sep 1998 19:05:00 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sat, 19 Sep 1998 09:13:58 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Re: Two-face and three-face subgroups In-Reply-To: <199809151621.MAA19286@Twig.Rodents.Montreal.QC.CA> To: der Mouse Cc: Cube Lovers Message-Id: On Tue, 15 Sep 1998 12:21:58 -0400 (EDT) der Mouse wrote: > I've been playing with the two-face subgroup [%] of the 3-Cube and got > to wondering - how much work has been done on the two-face and > three-face subgroups? Certainly the two-face subgroup "feels" like a > much smaller object than even the 2-Cube (though perhaps more tedious > for human solution), perhaps about the size of the Pyraminx. > The subgroup has been explored fairly thoroughly. For example, look in the archives 8/31/1994 for a summary of the first complete God's Algorithm search of this particular subgroup. There are a number of articles in the archives thereafter. has been searched in both the quarter turn metric and the face turn metric, and local maxima have been investigated as a part of the search. has a very small branching factor and a corresponding large diameter of 25 in the quarter turn metric, at least I think it's a large diameter for such a small group. Until Mike Reid recently showed that the diameter of G in the quarter turn metric was at least 26, the diameter of was the largest known for the 3x3x3 cube or any of its subgroups. Frey and Singmaster's book discusses both two face and three face subgroups, among other things giving their sizes. To my knowledge, no God's Algorithm searches have been performed for the three face subgroups. We have ||=73483200, so is slightly smaller than the corners group at 88179840. The 2x2x2 is 24 times smaller than the corners group, at 3674160. However, I am of the school of thought that tends not to equate the size of the group (or search space, for problems that are not actually groups) with the difficulty of the problem. ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Tue Sep 22 19:50:07 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA19137; Tue, 22 Sep 1998 19:50:02 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 21 Sep 1998 16:34:29 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Local Maxima which Fix the Corners, 12q from Start To: Cube Lovers Message-Id: I am making a run to calculate God's Algorithm out to 12 moves from Start in the quarter turn metric. It has been running several weeks, and will probably run several more. I have made some changes to my program to make it easier to extract the positions for local maxima, and to checkpoint the local maxima data. As a part of the checkpointing, I can actually see the local maxima as they are generated without having to wait for the program to end. It is becoming apparent that there are a *lot* of local maxima 12q from Start. It is already known that there are only four (unique to symmetry) which are 10q from Start (the shortest ones in the quarter turn metric), and that there are none 11q from Start. So I am a little surprised that I am seeing so many. I have looked at quite a few of them, and most of them are not all that interesting. But the ones which fix the corners are all quite pretty. Because the positions are being produced in lexicographic order, and because I am sorting by corners first, edges second, the positions which fix the corners are the first ones to appear. There are eight of them as follows. 1. F2 L2 F2 B2 R2 B2 2. F B' U2 D2 F' B R2 L2 3. F B R2 F' B' U D L2 U' D' 4. D' F B' R F R' F' B U F' U' D 5. F B R2 L2 F B U2 D2 6. R L' F2 B2 R L' F2 B2 7. F2 B2 U2 D2 R2 L2 8. R L' U D' F B' R2 L2 U D' #1 is a 2-H pattern (only four edge cubies are moved). #2 is a 4-H. #3 moves four edge cubies, leaving eight of the nine facelets the same color on four faces, and a solid color on the other two faces. #4 moves three edge cubies, leaving eight of the nine facelets the same color on all six faces. #5 has 2 H's, 2 checkerboards, and 2 solid faces -- with the respective H's, checkerboards, and solid faces opposing each other. #6 has 4 H's and 2 checkerboards, with the 2 checkerboards opposing each other. #7 is the Pons Asinorum, and is included only for completeness because we already knew that the Pons was a local maximum of length 12q. #8 has all six faces being sort of a "three colored checkerboard". Some of these positions may have appeared on Cube-Lovers in some other context, but the only one I recognize for sure is the Pons. In some ways, #4 is the most interesting to me, because it a simple 3-cycle on the edges, and who would have thought that such a position would turn out to be a local maximum? #1 and #3 both consist of two 2-cycles on the edges, and are about as striking to me as is #4. ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Wed Sep 23 12:37:03 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id MAA22987; Wed, 23 Sep 1998 12:37:03 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19980922204717.20206.rocketmail@web1.rocketmail.com> Date: Tue, 22 Sep 1998 13:47:17 -0700 (PDT) From: "Jorge E. Jaramillo" Subject: Moves to this pattern To: Cube-Lovers@ai.mit.edu Hi I just joined the list! I was wondering if someone could help me with a pattern that has been bugging me for a while. I have been able to solve the cube to this pattern so i know it is a valid one. I used one of those on-line solvers entered the pattern and then reversed the sequence the solver gave me and it indeed gets the pattern i want but somehow it seemed too many moves for me for such a simple pattern. the pattern I am talking about is: the 4 cubelets that make the vertex formed by FDR are exchanged with the vertex from BDL Can any one give me the set of moves to get to this pattern from a solved cube? Does this pattern have a name? [Here is a] set of moves (they work but I am sure there is a shorter way): D2 F B- L2 F- B D- F B- L F- B D2 F B- L2 F- B D F B- L- F- B F B- L- F- B D2 F B- L- F- B D2 R- D- R D- R- D2 R D2 L- D- L B D- B- L- D L2 D L- D- F- D- F D B- D- B D R D R- D F- B D B- F R D- R- T B- T- B- D- B- This long set of moves reminds me of something else: There are many Rubik cube annimations that you move the faces with either the keypad or the mouse. Does anyone know of one that follows sets of orders you write? It would be neat to try this long patterns in one of those simulators. Thanks === Jorge E Jaramillo From cube-lovers-errors@mc.lcs.mit.edu Wed Sep 23 19:54:38 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA26229; Wed, 23 Sep 1998 19:54:38 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19980922213222.29513.rocketmail@web1.rocketmail.com> Date: Tue, 22 Sep 1998 14:32:21 -0700 (PDT) From: "Jorge E. Jaramillo" Subject: Is it only mine? To: cube In order to solve the cube faster I developed a method that would turn a lot the middle faces. I don't know how you call them in this list I am talking about the face between Top and Bottom, the face between Right and Left and even the face between Front and Back. Well after twisting it a few times my cube came undone, fell apart and I thought "Damn made in Taiwan cubes" (although the ones I can buy here do not say where are they made). I was going through my second cube in a short while (I just regained interest in the cube a short while ago after say 15 years) and it fell apart again. I took off the plastic color of the center cubelet that came apart and found a screw and a spring that keeps the screw tight. I re screwed it but did not have any glue at hand so I kept on playing without the color of the center cubelet I was doing one of these center face moves and saw how the screw was turning counterclockwise in other words the way that makes the cube fall apart. Needless to say I had to re design my method. This long story is to ask if all the cubes are built this way or only the ordinary ones I can buy here? Thanks. === Jorge E Jaramillo From cube-lovers-errors@mc.lcs.mit.edu Fri Sep 25 18:05:43 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA07121; Fri, 25 Sep 1998 18:05:42 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <360964EA.D07A79F8@t-online.de> Date: Wed, 23 Sep 1998 23:15:22 +0200 Reply-To: Rainer.adS.BERA_GmbH@t-online.de Organization: BERA Softwaretechnik GmbH To: "Jorge E. Jaramillo" Cc: Cube-Lovers@ai.mit.edu Subject: Re: Moves to this pattern References: <19980922204717.20206.rocketmail@web1.rocketmail.com> From: Rainer.adS.BERA_GmbH@t-online.de (Rainer aus dem Spring) Jorge E. Jaramillo wrote: > the pattern I am talking about is: the 4 cubelets > that make the vertex formed by FDR are exchanged with > the vertex from BDL. R2 U R2 U2 B2 D L2 U2 L2 B2 D' B2 U2 Rainer adS PS If you have a WINTEL system you should download Herbert Kociemba's cube program. [ Moderator's note: Jerry Bryan provides another 13f process, R2 U' B2 R2 U2 R2 U' B2 U2 R2 U' B2 U2, which hasn't been proven optimal. Steve LoBasso has a longer one. ] From cube-lovers-errors@mc.lcs.mit.edu Sat Sep 26 00:05:04 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id AAA07745; Sat, 26 Sep 1998 00:05:03 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 25 Sep 1998 08:36:22 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Summary of Local Maxima, Face Turn Metric To: Cube Lovers Message-Id: I have posted maneuvers for a number of specific strong and weak local maximal positions (the strong local maxima at 9f and 10f, and the weak local maxima at 6f) , but I haven't really posted a summary of the numbers. Here are the numbers I have so far. In order to complete the table through 10f from Start for weak local maxima, I would have to repeat a rather long run. As might be expected, it appears that the number of weak local maxima will greatly exceed the number of strong local maxima. As is the usual case, patterns are M-conjugacy classes (symmetry classes), and represent the number of positions which are unique up to symmetry. Distance Strong Strong Weak Weak from Lclmax Lclmax Lclmax Lclmax Start Patterns Positions Patterns Positions 0f 0 0 0 0 1f 0 0 0 0 2f 0 0 0 0 3f 0 0 0 0 4f 0 0 0 0 5f 0 0 0 0 6f 0 0 2 7 7f 0 0 1 6 8f 0 0 37 739 9f 2 32 327 13014 10f 6 107 ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 6 15:05:42 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id PAA07299; Tue, 6 Oct 1998 15:05:41 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 27 Sep 1998 20:35:33 -0400 (EDT) From: Jerry Bryan Subject: Corners Only, Ignoring Twist To: Cube-Lovers Reply-To: Jerry Bryan Message-Id: I have been playing around with the idea of trying to calculate God's Algorithm all the way to the bitter end for the group which results from ignoring all twists of the corners and flips of the edges. It's a pretty big group. The order is |G|/(3^7)/(2^11), which is about 9.7*10^12, call it about 10^13 to make it a round number. (Another way to calculate it is 8!12!/2.) This is probably right at the bare edge, maybe even slightly past the bare edge, of the size of problem I can handle right now, which makes it a worthy endeavor. Also, it would provide a lower limit on the diameter of G (although the limit might not be any better than the ones we already have), which again makes it a worthy endeavor. Such a result might be suitable as the estimator function required by IDA* searches. The distance from Start in the no-twist, no-flip group would certainly be a lower bound for every position where twist and flip *are* considered. My only hesitation about suggesting this group as a suitable IDA* estimator function is that there are obvious pathological cases such as the superflip where this function would be a very poor estimator. In developing a no-twist, no-flip version of the program, I decided to try it out on the corners only case. Here are the results. Distance from Patterns Positions Start 0q 1 1 1q 1 12 2q 5 114 3q 24 876 4q 119 4931 5q 301 12972 6q 364 15066 7q 166 6300 8q 3 48 Distance from Patterns Positions Start 0f 1 1 1f 2 18 2f 9 243 3f 68 2646 4f 302 12516 5f 418 17624 6f 170 7080 7f 14 192 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990 From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 6 16:52:26 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id QAA08831; Tue, 6 Oct 1998 16:52:24 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 2 Oct 1998 23:18:37 +0200 (METDST) From: Martin Moller Pedersen Message-Id: <199810022118.XAA19053@stargazer.daimi.aau.dk> To: cube-lovers@ai.mit.edu Subject: cubes at spielmessen in Essen There will soon be a big gathering for games in Germany - Essen a so-called Spielmessen. I am attending this gathering for the first time in three years so I am looking for companies who will came to the spielmessen and who sells cubes. The places is big so it would be nice for me to have same names to look for. and hopefully I will have a real 4x4x4 and 5x5x5 cube to play with in a few weeks :-) /Martin From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 6 18:38:32 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA10776; Tue, 6 Oct 1998 18:38:31 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: Date: Sun, 4 Oct 1998 11:12:27 -0600 To: cube-lovers@ai.mit.edu From: Steve LoBasso Subject: Cube Solver for Macintosh I just wrote a Macintosh port to Dik T. Winter's cube solving code. I put it on my web page at the link below. I haven't had a chance to make an info page for it so the link below is just the application. It will run on both 68k and PPC Native. Be warned the 68k version runs fairly slow and the initialization phase takes quite a while. Cube Solver By Steve LoBasso slobasso@dtint.com Written using algorithm code by Dik T. Winter based on algorithm described by Herbert Kociemba. http://members.tripod.com/~slobasso/downloads/Cube_Solver.hqx -- Steve LoBasso mailto:slobasso@dtint.com Digital Technology International or mailto:slobasso@hotmail.com 500 West 1200 South, Orem, UT, 84058 http://members.tripod.com/~slobasso (801)226-6142 ext.265 FAX (801)221-9254 From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 6 20:00:34 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id UAA12380; Tue, 6 Oct 1998 20:00:34 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Chris and Kori Pelley" To: Subject: That's Incredible! Date: Sun, 4 Oct 1998 22:37:28 -0400 Message-Id: <002701bdf009$180cb5e0$da460318@CC623255-A.srst1.fl.home.com> I recently obtained (courtesy of Peter Beck) the Rubik's Cube-a-Thon video from the TV show "THAT'S INCREDIBLE" and digitized it in RealVideo format. The file is rather large (18.1 megabytes) but it's worth a download if you're into cubic nostalgia. Eleven and a half minutes long, it features Minh Thai, Jeff Varasano, Kris Wunderlich, and others that may be on this list. Here's the URL: http://www.chrisandkori.com/incredible.htm It requires the RealPlayer 5.0 or later to view it. Note that you must download the file, then view it. I do not have a streaming video server. If anyone would like to host the file on a streaming server, please contact me. Chris Pelley ck1@home.com From cube-lovers-errors@mc.lcs.mit.edu Thu Oct 8 19:04:05 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA24808; Thu, 8 Oct 1998 19:04:04 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 8 Oct 1998 15:11:54 +0100 From: David Singmaster To: cube-lovers@ai.mit.edu Message-Id: <009CD656.72A81016.35@ice.sbu.ac.uk> Subject: Davenport's pattern The pattern given by Jacob Davenport is what I called a cube in a cube in a cube. I discovered this in 1979 or 1980 and was very pleased with it. Indeed, I used the cube in a cube as the logo of the late and much lamented David Singmaster Ltd. in 1980-1982 (approx. dates since I'm not where my records are). The pattern is in my Notes. There are various ways to generate the pattern, but the one that I can remember uses what Roger Penrose called the Y-commutator, which has the form FR'F'R. The reason this is the Y-commutator is that it affect the three edges adjacent to a corner and the corner and its three adjacent corners. I.e. the affected pieces form a Y, while the pieces affected by the ordinary commutator FRF'R' form a Z. Combining three Y-commutators as follows: FR'F'R RU'R'U UF'U'F gives a process that twists the corner and the three adjacent edges as a unit and twists an adjacent corner the opposite direction. NOTE - I'm doing this from memory and I have a suspicion that the middle group may need to be inverted?? By moving the odd corner to the right place adjacent to the opposite corner and applying the inverse of the above, one gets the same sort of pattern at the opposite corner and the odd corner has been restored. Now one 3-cycles the centers, as is easily done by a commutator of slice moves, and one has the cube in a cube. Now one can twist the two opposite corners to get the cube in a cube in a cube, though I find this not as visually dramatic as the cube in a cube. Someone - Mike Reid ? - sent me a minimal method for one of these patterns, but it's not very memorable. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Thu Oct 8 19:47:11 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA24896; Thu, 8 Oct 1998 19:47:10 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 8 Oct 1998 16:45:31 +0100 From: David Singmaster To: cube-lovers@ai.mit.edu Message-Id: <009CD663.86DEF2D6.16@ice.sbu.ac.uk> Subject: Nicholas Bodley's message of 22 Sep 1998. Nicholas Bodley's message reminds me of when I wrote about the Cube in 1978 or early 1979, I think in the Observer, which seems to have been the first article outside Hungary. I mentioned that the mechanical problem seemed even harder than the mathematical problem and this led to about six submissions of mechanisms from readers. All but one of these were clearly impossible, but the last was Rubik's mechanism with slight differences - e.g. he had the undersides of the centers rounded. The submitter of this was a UK patent agent with obvious mechanical aptitude. However, one of my students, who had bought a cube from me, told me that a friend rang her up and asked if she had seen the hoax article about a cube that moved in all directions. The friend had just proven that such an object was impossible. My student had to disabuse her. When the cubes first came out of Hungary, we didn't know what the mechanism was and they were too precious to fiddle with. Roger Penrose said he had one face center piece come undone and he carefully wrapped thread around the exposed part of the screw and worked the screw into place and pulled on the thread to screw the screw back into the central piece. Sometime in late 1978, a friend had trouble with his cube and took a screwdriver to it and discovered the cover plates and the screw heads inside! Enough for now. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Fri Oct 9 18:40:38 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA02313; Fri, 9 Oct 1998 18:40:37 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <361E8D3F.6597@ameritech.net> Date: Fri, 09 Oct 1998 17:25:03 -0500 From: Hana Bizek Reply-To: hbizek@ameritech.net To: cube-lovers@ai.mit.edu Subject: comments on "davenport's pattern" David Singmaster claims to have discovered this pattern in 1979 or 1980, so it should be credited to him. In my own book I present a number of patterns, but I would never dare to claim authorship to any of them. Singmaster's comments prompted me to look at my own books. In CUBE GAMES (Taylor and Rylands} this pattern appears on the top of page 37.I have a strong suspicion this pattern could be a combination of the two cyclicity-three patterns on page 36 therein. One may use this pattern as a corner in a 3-color design. Design-construction is a step beyond pattern-construction. My question has not yet been satisfactorily answered. Has anyone seen construction of 3-dimensional "sculpture-like" designs? People referred me to Davenport's creations, but my own designs are quite different. Hana From cube-lovers-errors@mc.lcs.mit.edu Fri Oct 30 13:56:08 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id NAA17979; Fri, 30 Oct 1998 13:56:07 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Thu Oct 15 11:02:13 1998 Message-Id: <19981015145704.8314.rocketmail@attach1.rocketmail.com> Date: Thu, 15 Oct 1998 07:57:04 -0700 (PDT) From: "Jorge E. Jaramillo" Subject: Moves to this other pattern To: cube Please if this is not one of the purposes of this list someone let me know I don't meant to be rude. Could someone please tell me the moves to get from a solved cube to the following pattern: The top and bottom faces keep their colors. The 4 columns in the middle of every side face stay with their color. The left column on the front face moves to the right and the right column moves to the left. The left column on the back face moves to the right and the right column moves to the left. Thanks === Jorge E Jaramillo [ Moderator's note: We have a lot of requests for processes for various and have got a lot of optimal processes. Maybe the hard part is figuring out how to look them up. This is one of the "4-" patterns, and probably appears among the quasi-continuous partial isoglyphs. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Fri Oct 30 14:17:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA18032; Fri, 30 Oct 1998 14:16:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 26 Oct 1998 23:58:27 -0400 (EDT) From: Jerry Bryan Subject: 12q From Start To: Cube-Lovers Message-Id: |x| Patterns Lcl Positions Lcl Branching Max Max Factor 0q 1 0 1 0 1q 1 0 12 0 12 2q 5 0 114 0 9.5 3q 25 0 1068 0 9.368 4q 219 0 10011 0 9.374 5q 1978 0 93840 0 9.374 6q 18395 0 878880 0 9.366 7q 171529 0 8221632 0 9.355 8q 1601725 0 76843595 0 9.347 9q 14956266 0 717789576 0 9.341 10q 139629194 4 6701836858 42 9.337 11q 1303138445 0 62549615248 0 9.333 12q 12157779067 103 583570100997 2913 9.330 The last time a new level was calculated for the quarter turn metric was 4 February 1995. The cumulative number of positions now identified is 653625391832, or about 6.5*10^11. This is well past the "geometric halfway point" of sqrt(|G|), which is about 6.5*10^9. However, it is known that the diameter of G is at least 26q, strongly indicating that there is a bit of a tail to the distribution of positions by length. Of the 103 local maxima of length 12q, 70 of them also have their inverse as local maxima. For the other 33, the inverse is not a local maximum. For one of them, the inverse has 11 moves which go closer to Start. For seven of them, the inverse has 10 moves which go closer to Start. For eleven of them, the inverse has 8 moves which go closer to Start. For six of them, the inverse has 6 moves which go closer to Start. For two of them, the inverse has 4 moves which go closer to Start. And for six of them, the inverse has only 2 moves which go closer to Start. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 2 09:40:50 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id JAA29402; Mon, 2 Nov 1998 09:40:48 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <363B1799.3534@hrz1.hrz.tu-darmstadt.de> Date: Sat, 31 Oct 1998 14:58:49 +0100 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: cube-lovers@ai.mit.edu Subject: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks? About 2 weeks ago I received the following message and it seems to me that it might be interesting for you too: > Subject: > Use of RUBIK'S mark > Date: > Sun, 18 Oct 1998 21:05:31 EDT > From: > CK4IPLAW@aol.com > To: > kociemba@hrz1.hrz.tu-darmstadt.de > > > CLEARY, KOMEN & LEWIS, LLP > 600 Pennsylvania, Avenue, S.E. > Suite 200 > Washington, D.C. 20003-4316 > Telephone: 202 675-4700 > Telecopier: 202 675-4716 > E-Mail: ck4iplaw@aol.com > > > October 18, 1998 > > Via Electronic Mail > > Herbert Kociemba > kociemba@hrz1.hrz.th-darmstadt.de > > Re: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks > > Dear Mr. Kociemba: > > This firm is intellectual property counsel to Seven Towns Limited ("Seven > Towns"), the manufacturer and worldwide distributor of the RUBIK'S CUBE three- > dimensional puzzle and provider of an electronic version of the puzzle via its > official web site, which is located at http://rubiks.com. > > The RUBIK'S CUBE mark is famous throughout the world. The distinctive > overall appearance of the RUBIK'S CUBE puzzle also is a famous trademark owned > by Seven Towns. These marks are registered or are the subject of pending > trademark applications in most of the major countries of the world. > > It has come to our attention that your web site features a program under the > name of Rubik's Cube Explorer. I must advise that your unauthorized use of > the RUBIK'S CUBE mark owned by Seven Towns constitutes trademark infringement. > Specifically, the use of this mark in designating the origin of your program > confuses the public into believing mistakenly that it derives from, is > associated with, or is endorsed or sponsored by the owner of this commercial > symbol (i.e., Seven Towns). Moreover, apart from causing consumer confusion, > your use of the well-known mark dilutes its distinctive value in violation of > the federal and state anti-dilution laws. > > Seven Towns appreciates your interest in the RUBIK'S CUBE puzzle, and it > certainly does not wish to inhibit legitimate discussion of the puzzle on the > Internet or in any other medium. However, it also must be vigilant in > maintaining the value and integrity of its intellectual property. It cannot > afford to lose control over its commercial reputation, or damage to its > substantial goodwill, by permitting another party to use its trademarks or > trade dress in a manner that causes source confusion or otherwise dilutes > their selling power. Thus, Seven Towns requests that you remove from your web > site the electronic version of the RUBIK'S CUBE manipulative puzzle, and that > you discontinue any further use of the term RUBIK'S CUBE or any similar > designation in the prominent, source-indicating manner of a trademark. > > I hope that you are understanding of our client's position, and I thank you > in advance on behalf of Seven Towns for your prompt attention to this matter. > > Sincerely yours, > > //sjm// > > Scott J. Major Indeed the headline of my homepage at http://home.t-online.de/home/kociemba/cube.htm was "Rubik's Cube Explorer 1.5". So I removed the word "Rubik's" and added some note at the bottom of the page (...blah blah is not derived from, is not associated with blah blah...). I definitely will not remove the program from my homepage. This seems ridiculous. I know, that other cube fans received similar mail because they have some similar statements on their homepages now. What do you think about that? Herbert Kociemba From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 2 14:41:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA00366; Mon, 2 Nov 1998 14:41:00 -0500 (EST) Precedence: bulk Date: Sat, 31 Oct 1998 23:06:34 -0400 (EDT) From: Jerry Bryan Subject: All the Local Maxima at 12q To: Cube-Lovers Message-Id: I had originally decided not to post all the 12q local maxima because there are so many and because not all of them look all that interesting. But I have been looking at them a bit more, and I think it's worth the effort. Some of them will be very familiar and some of them not. I would highlight the following ones. #9 is a partial isoglyph -- four short T's (or four short U's). #57 is the well-known four spot. #68 is one of the more striking of several pseudo two spots. #80 is worthy of some study. It's the only one where the maximality of the inverse is 11 -- almost but not quite a local maximum. #97 along with #98 and #99 are very striking pseudo six spots. #97 and #99 are almost the same pattern, and it took me a while to see how they differ. In the table below, the right most column gives the maximality of the inverse of the pattern, where the maximality is the number of moves which go closer to Start. The maximality of the inverse gives an indication of how close the inverse comes to being a local maximum, with 12 indicating a local maximum. (The maximality of the pattern itself is not given, since it is 12 by definition.) The table gives the 103 local maxima of length 12q which are unique up to symmetry. 1. F F L L F F B B R R B B 12 2. F B' U U D D F' B R R L L 12 3. F B R R F' B' U D L L U' D' 12 4. U' R' L B L B' R L' D L' U D' 12 5. F B R R L L F B U U D D 12 6. R L' F F B B R L' F F B B 12 7. F F B B U U D D R R L L 12 8. R L' U' D F' B R R L L U' D 12 9. F B U U D D F' B R R L L 12 10. U B' D F D' B' D F' D' B B U' 12 11. L B B R D D R' L B B L L 12 12. U R' U L' U' R' U L U' R R U' 12 13. F F U' D R R U D D B B D' 12 14. F B D D F B' L L U U F F 12 15. U D' F U D R' L' U D F U D' 12 16. U U R L F' B' U D' R R L L 10 17. R R U D F' B U' D F B' U' D 8 18. U U D D F B' R R L L B B 12 19. R' L F' B U U F F B B U' D' 12 20. U D' F F U' D R L F B' U' D 12 21. F B R' L D D F B' R' L U' D 12 22. L L U D' B B R L U' D B B 12 23. F L L F' D D F B' L L B B 12 24. F' R R F' U U F' B L L B B 12 25. F B U U L L B B L L U U 8 26. U' D' R L' F F B B L L U' D 4 27. U D R L' F F B B L L U D' 4 28. F B' U U B B L L B B U U 12 29. F' B U D L L B B R R U D 12 30. F' B U D R R F F L L U D 12 31. F B' U U F F R R F F U U 12 32. F B' U U L L B B L L U U 12 33. F B' U U R R F F R R U U 12 34. L L U D L L F' B R L U U 10 35. F' R R F U U F B' R R B B 12 36. L L F' B D D R R F F B B 12 37. L L F' B D D F F B B L L 12 38. D D F' B U D' F F B B U D' 10 39. F F R' L F B' U' D F F L L 12 40. U R' L F U D' R' L F F B B 8 41. U D R L F B' U D' R' L F F 12 42. U D F F U' D R L F B' U' D 12 43. U D B B U' D R' L' F B' U' D 12 44. F F R L' F B' U D' F F L L 12 45. U D F' B R L U' D B B U' D 12 46. U D F' B R' L' U' D F F U' D 12 47. F B' D R' L' U U R L D B B 8 48. B' U' D R' L B' U' D R R L L 6 49. B' U D' R L' F U D' R R L L 6 50. U D F' B' U' D L L F B' U' D' 8 51. U' F' U' D F B' U' D R R L L 2 52. U' F F B R' L U' D F F B B 8 53. D R R L F' B U' D R R L L 2 54. R U' F' B R L' U D' F F U D' 2 55. L F F B R L' F B' R R L L 2 56. L F F B U D' R' L F F B B 8 57. F B' U U D D F B' R R L L 12 58. F B' R L' U' D F' B' R L' U' D' 12 59. F B R L U D' F B R' L' U D' 12 60. F B' U U D D F' B U U D D 12 61. R L' U' D F' B L L U' D F F 12 62. R L B B U D' R R F B U D' 12 63. F B' U D' R L' F F B B U D' 12 64. F B R R L L U D' R' L' U D' 12 65. F B' U D' R L' B B U D' L L 12 66. F F U' D R R U D F F U U 12 67. F L L B U U F' B L L F F 12 68. B R L F F R' L' B U U L L 12 69. U' F B' L' U D' R L' F F B B 2 70. F B R' L' U D' F' B' R' L' U' D' 12 71. F B R L U D' F B R' L' U' D' 12 72. U' R L' U' D F B' R R L L U' 12 73. F' B R' L U' D B R' L U' D D 12 74. U' R' L F B' U' D F B B U' D 6 75. U R' L F' B U D' B F F U D' 6 76. F B U D R' L F F R' L U' D 12 77. R' L' F' B R R L L U D B B 12 78. R L F B' R R L L U' D' F F 12 79. F F R R F' B' U' D' L L U D 8 80. U U R' L F' B' U' D R R L L 11 81. U U D R L' B U D' R R L L 6 82. U D F' B U' D F B' U' D R R 12 83. F B' U D R L' B B R L' U' D 12 84. U D' F F U D' R' L' F B' U' D 12 85. B R L' D' F B' U D' R R L L 2 86. F' R' L U' F B' R' L U D' B B 12 87. F' R' L U' F' B R' L U' D B B 12 88. R' L F B' U D R R L L D D 12 89. F B R L' F' B R L' U D' F F 12 90. U' D' R L' F F U D' R R L L 12 91. F F R' L F' B' U' D' L L B B 10 92. F U D B B U' D' F R L U D' 10 93. R L U D' F B' R' L' F B' U' D 8 94. F B' U' D L L F B' U' D' F F 10 95. F B' U U D D F B' R' L' U D' 10 96. R' L L F' B U R L' F F B B 6 97. F B' U' D R L F' B U U B B 12 98. F B U' D R' L F' B D D B B 12 99. F B' U' D R L F B' D D F F 12 100. U' D F B' U D' F F B B U D' 12 101. U R L' F' U D' R L' F F B B 8 102. U D' R L' F' B U D' F F B B 12 103. F' B' L L U' D F B U' D R R 8 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990 From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 2 18:00:09 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA01157; Mon, 2 Nov 1998 18:00:08 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19981102164235.0094e100@mail.spc.nl> Date: Mon, 02 Nov 1998 16:42:36 +0100 To: cube-lovers@ai.mit.edu From: Christ van Willegen Subject: Re: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks? At 14:58 31-10-1998 +0100, you wrote: >About 2 weeks ago I received the following message and it seems to me >that it might be interesting for you too: [Message deleted for brevity] > >Indeed the headline of my homepage at > >http://home.t-online.de/home/kociemba/cube.htm > >was "Rubik's Cube Explorer 1.5". So I removed the word "Rubik's" and >added some note at the bottom of the page (...blah blah is not derived >from, is not associated with blah blah...). > >I definitely will not remove the program from my homepage. This seems >ridiculous. I know, that other cube fans received similar mail because >they have some similar statements on their homepages now. > >What do you think about that? > I had the same 'problem' a couple of months ago. A handheld computer users group I was active in, once published a program that could be described as 'well, it looks a bit like Tetris ((R), if those lawyers are reading this, as well :-), but it's a long way off the mark'. The program was published in our magazine, and was also placed on a web-page. A couple of months ago, I received a letter from a Belgian lawyer firm, addressed to the user's group. This user's group, by the way, died about 5 years (!) ago. They told us to 'cease and decist' (a couple of things), including publishing this article on 'our web-page'. Well, since this was someone else's web- page, there was nothing we could do about it. We told them (in friendly terms) that the user's group no longer existed, that we were not affiliated to the user having the article on his web-page, and that we nover sold the program. We haven't heard from them (not even a letter stating that they received our reply!) since. It's kinda sad: The program was for an HP28S. I would have _loved_ to see those lawyers type the program in (a couple of kilobytes, via the keyboard!), only to find out that it was 'almost, but not quite, entirely unlike Tetris' (Douglas, if you're reading this, quotes are ok, no?). Just tell them you will take down the name, and they will probably be off your back. Christ van Willegen From cube-lovers-errors@mc.lcs.mit.edu Tue Nov 3 06:37:22 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id GAA02996; Tue, 3 Nov 1998 06:37:21 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 2 Nov 1998 15:32:29 -0500 From: michael reid Message-Id: <199811022032.PAA24281@euclid.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks? Cc: kociemba@hrz1.hrz.tu-darmstadt.de > > Re: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks > > > > Dear Mr. Kociemba: [ ... ] > What do you think about that? i think it's not good business strategy to attack the people who are the biggest fans of their product! to claim ownership of "the distinctive overall appearance of the RUBIK'S CUBE puzzle" is ludicrous! the changes you've described to your web page seem quite reasonable and appropriate (given the circumstances), without compromising too much. i hope you have no further trouble with seven towns. but if you do, please let me know about it. to make this situation even more ridiculous, i just checked out their "official" website, which features a java cube (http://rubiks.com/VRCUBE.html). their applet is stolen from karl ho"rnell! (http://www.tdb.uu.se/~karl/java/rubik.html) mike From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 9 17:39:21 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id RAA01496; Mon, 9 Nov 1998 17:39:20 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981104032938.14284.rocketmail@send102.yahoomail.com> Date: Tue, 3 Nov 1998 19:29:38 -0800 (PST) From: Han Wen Subject: Query for Corners-First Method Rubik Solution To: cube-lovers@ai.mit.edu Hi, Does anyone know of any websites that describe the Corners-first method of the solving the rubik's cube? I know of many layer-first methods such as Jiri Fridrich's (for which I have spent many hours learning), but I really haven't seen a comprehensive explanation of the corners-first method. I'm really curious to understand how anyone can solve the cube under 30secs by solving the corners first. -Han- From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 9 18:35:15 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA01664; Mon, 9 Nov 1998 18:35:13 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 04 Nov 1998 16:41:26 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Local Maxima Whose Inverses are not Local Maxima To: Cube Lovers Message-Id: On 30 June 1997 I reported that if you could find a local maximum whose inverse was not a local maximum, then you could also find a longer local maximum. For example, suppose x is a local maximum in the quarter turn metric and x' is not. Then, there exists q in Q such that |x'q| = |x'| + 1 = |x| + 1. But we know that q'x is a local maximum and we also know that |q'x| = |x| + 1 because |q'x| is the same as |x'q|. Because we now have at 12q a good number of local maxima whose inverses are not local maxima as specimens, I have begun to wonder if the same process might be able to be repeated several times to yield progressively longer local maxima. For example, if x is a local maximum and (q1)x is a local maximum, might also (q2)(q1)x be a local maximum and also (q3)(q2)(q1)x etc. It seems to me that good candidates to investigate in this regard might be those local maxima at 12q whose inverses have a very small maximality. For example, if x is a local maximum where the maximality of x' is 2 (and there are several such cases), then we know that there are 10 local maxima of the form qx. I am not sure if I have time to investigate this question further, but I certainly would love to hear from anyone who has the time and the computing resources to do so. ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Tue Nov 10 06:10:31 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id GAA04442; Tue, 10 Nov 1998 06:10:31 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Sender: bosch@sgi.com Message-Id: <36477CAE.446B@sgi.com> Date: Mon, 09 Nov 1998 15:37:18 -0800 From: Derek Bosch To: Han Wen Cc: cube-lovers@ai.mit.edu Subject: Re: Query for Corners-First Method Rubik Solution References: <19981104032938.14284.rocketmail@send102.yahoomail.com> Here's the method I use to solve Rubik's Cube in 30 seconds or less. My notation is as follows: F = turn front face clockwise 90 degrees. F' = turn front face counter-clockwise 90 degrees. F" = turn front face 180 degrees. U = turn top face clockwise 90 degrees. R = turn right face " " " L = turn left face " " " B = turn back face " " " D = turn bottom face " " " ^ = move middle slice 90 degrees up. v = move middle slice 90 degrees down. OK. Now the order I do things is corners, edges on two OPPOSITE sides (Right and Left), followed by the middle slice edges. (1) Corners: I solve my corners a bit wierdly, but I find it is really fast. I position any four corners of the same color on a side. I don't care what colors are on the adjoining faces right now, as I fix them later. (1a) Once I have the 4 corners of the same color, I turn the cube so that those colors are on the down face. Now there are a few combinations that can occur on the top face: All corners on top face same color: Goto (1b) Three corners need to rotate clockwise (position like below o=no rotate) (+ = needs clockwise rotation) (- = needs counter-clkwise rot.) + + Move: R'U"RUR'UR and goto (1b) + o Three corners need counter-clockwise rotate: - o Move: RU"R'U'RU'R' and goto (1b) - - One corner needs clockwise rotate, One needs counter-clockwise rotate: 3 cases: + - Move: RU"RU"RUR" and goto (1b) o o - + Move: RUR'U'F'U'F and goto (1b) o o o - Move: R'URUBU'B' and goto (1b) + o Two corners need clockwise rotate, Two need counter clockwise: 2 cases: + - Move R"U"RU"R" and goto (1b) - + - + Move RUR"F'R"UR' and goto (1b) - + (1b) Now, you should have two opposite sides, with the corners of those two sides the proper color. We have to correct the 4 remaining sides to get corners in the right place, before we can move onto edges. To do this, count the number of sides that have the upper pair of corners the same color. Also counter the number of sides that have the lower pair of corners the same color. All four sides (upper and lower) corner pairs match. Goto (2) No sides' corner pairs match. Do Move R"F"R". Goto (2) One Bottom corner pair matches. Move that corner pair to the Down-Left position. Move R"UR"U'R"UR"U'R. Goto (2) One Top corner pair matches. Turn Cube over, and do previous moves. One Top and one Bottom pair matches. Move both corner pairs to the front face. Move R"UR"U"F"UF". Goto (2) All Bottom pairs match. Move R"UR"U"F"UF"U"L"UL". Goto (2) All Top pairs match. Turn Cube over, and do previous move. All Bottom pairs match. One Top pair match. Move Top Pair to Left-Upper position. Move R"UR"U'R"F"U'F"UF". Goto(2) All Top pairs match. One Bottom pair match. Turn Cube over, and do prev. (2) Solving two Opposite Sides. Now, all the corners should be solved. You should move the center of each cube to its respective corners, to get an X on each side (at least on two opposite sides). From now on orient the cube so that the two opposite sides are right and left. (2a) Solve three edges on the left face with the following moves. U'^U - moves the edge piece in the Front-Down position to the Up-Left position. UvU' - moves the edge piece in the Back-Down position to the Up-Left position. This is easier done with a cube in your hand, and try and see how this works. This will mess up the centers and edges in the middle slice, as well as the Up-Right edge. Don't worry about this. As long as you keep this orientation, and rotate the left face to get ready for a new edge to be moved you can solve three out of four of the edges on the left face. (2b) Solve four edges on the right face: First, rotate the left face, so that the unsolved edge is in the Up-Left position. Then, using the following moves, solve all four edges (similarly to step 2a). U^U' - moves the edge piece in the Front-Down position to the Up-Right position. U'vU - moves the edge piece in the Back-Down position to the Up-Right position. (2c) Solve remaining edge on left face: 2 cases (other than already solved): edge in place, needs to be flipped: Use U'vUvUvU' otherwise, move edge to Down-Front position, using v or ^. if the front color (of the DF edge) is the same as the left face color, Use U'vU"vU' else Use vU^U"^U (3) Solve middle slice edges. First use ^ or v to position middle slice centers in proper faces. (3a) Position edges: 3 cases (other than all in place): only three edges out of place: position cube such that DF needs to go to UB and UB needs to go to UF. Use ^U"vU". all four edges need to move: if UF needs to go to DB, Use ^F"B"vF"B". otherwise, position so that UF needs to go to UB, Use U'^^U'^^. (3b) Flip required edges: 3 cases (other than no flips needed). all four need flipping, use FR'F'^U^U^U^UFRF' two edges need flipping, both on same face. Turn cube so that these edges are the UF and UB edges. use ^U^U^U"vUvUvU" otherwise, turn cube so UB and DF need flipping, use F"^U^U^U"vUvUvU"F" That should do it. I apologize for the roughness of this solution. I think diagrams would help it a lot. If you have any criticism or ideas that could help this solution become more readable, let me know. Note, this solution is very close to Jeff Verasano (sp) and Minh Thai's methods... D -- Derek Bosch "A little nonsense now and then (650) 933-2115 is relished by the wisest men"... W.Wonka bosch@sgi.com From cube-lovers-errors@mc.lcs.mit.edu Tue Nov 10 07:33:39 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id HAA04496; Tue, 10 Nov 1998 07:33:37 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 9 Nov 1998 19:15:58 -0500 (EST) From: Alchemist Matt Reply-To: Alchemist Matt To: Han Wen Cc: cube-lovers@ai.mit.edu Subject: Re: Query for Corners-First Method Rubik Solution In-Reply-To: <19981104032938.14284.rocketmail@send102.yahoomail.com> Message-Id: My page at http://www.unc.edu/~monroem/rubik.html describes a method that is sort of "corners first". Although, in my first step I say to solve the first layer before going on, one could effectively simply place only the four corners in the top layer, then move on to the four corners in the bottom layer (specified in steps 2 and 3), then begin filling in the gaps on the top and bottom layers (steps 4 and 5), and lastly finish the middle layer. In fact, a chemistry professor at my current school, Holden Thorp, competed in one of the Rubik's cube playoff contests that was aired on the TV show That's Incredible. Someone posted the video of it about a month ago (and mentioned it in this discussion list), and he saw it here at my school after I downloaded it. He then looked at my page and mentioned that the winner of the contest actually used the solution shown on my page (probably modified slightly). I can only solve a well-scrambled cube in 2 to 3 minutes using the solution, but I'm sure someone quite adept, nimble, and fast could push it to under one minute. (Please note this isn't "my" solution; I simply learned it from a book many years ago. Further, I have never been in a cube solving competition). Matt ----------------------------------------------------------------------- Matthew Monroe Monroem@UNC.Edu Analytical Chemistry http://www.unc.edu/~monroem/ UNC - Chapel Hill, NC This tagline is umop apisdn From cube-lovers-errors@mc.lcs.mit.edu Thu Nov 12 14:18:47 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA24676; Thu, 12 Nov 1998 14:18:45 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981111170341.14375.rocketmail@send105.yahoomail.com> Date: Wed, 11 Nov 1998 09:03:41 -0800 (PST) From: Han Wen Subject: RE: Query for Corners-First Method Rubik Solution To: Noel Dillabough Cc: cube-lovers@ai.mit.edu Hi, Thanks for the link to your Puzzler program. You're not going to believe this, but you can still purchase the Professor's Cube (5x5x5) and the Megaminx! Since it's difficult... no, impossible to find anyone that sell these puzzles, I think it's worth mentioning. You can get them from Meffert's site: http://ue.net/mefferts-puzzles/ Your Puzzler program is a tremendously useful tool to develop moves. I've got 11/12 sides of the Megaminx solved. But for the last side, I need to figure out corner/edge twisting/permuting moves. You're Puzzler program's great for that. I'm surprised how many of my Rubik's cube moves can be applied with minor modifications to the Megaminx. -Han- ---Noel Dillabough wrote: > I actually solve all the cubes this way (or at least centers -> > corners -> edges for larger cubes) I just find it more logical and > easier to memorize than other methods. > You can check out my solution at > http://www.mud.ca/puzzler/puzzler.html. Its in the puzzler help > file under "solving the cube". I will be adding other solutions > soon that are clearer, let me know if you would like them I could > mail them to you. > -Noel. From cube-lovers-errors@mc.lcs.mit.edu Thu Nov 12 15:00:46 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id PAA26362; Thu, 12 Nov 1998 15:00:45 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 12 Nov 1998 15:01:40 +0000 From: David Singmaster To: cube-lovers@ai.mit.edu Message-Id: <009CF1D5.D1348312.50@ice.sbu.ac.uk> Subject: Use of the name Rubik's Cube The lawyers are being obsessively zealous as the name is certainly well on its way to becoming a common noun. It was included in the Oxford English Dictionary in the mid-1980s. Other examples are Kleenex and Aspirin, which were both originally tradenames and their owners fought to retain them but eventually lost. Xerox is fighting a rear-guard action on its name. If you don't want to get involved in legal hassle, I suggest that you use the name Magic Cube which was the original name and is such a common term that they can't claim it is a trademark. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk [ Moderator's note: I am still dropping messages that consist mainly of generic comments on intellectual property issues. There a great variety of individualistic and contentious debate on these topics that you may follow in dedicated fora such as the Usenet group misc.int-property. I am not yet persnickety enough to elide the third and fourth sentences from the above, but they are on the edge. I will also note that the term "Magic Cube" is also used to refer to a cubical array of natural numbers whose orthogonal and diagonal rows sum to the same number, as a generalization of "Magic Square", so it is advisable to include context such as "The geometrical puzzle originally known as the Hungarian Magic Cube." ] From cube-lovers-errors@mc.lcs.mit.edu Wed Nov 18 12:52:47 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA28044 for ; Wed, 18 Nov 1998 12:52:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 12 Nov 1998 17:05:37 -0500 (EST) From: Nicholas Bodley To: Han Wen Cc: Noel Dillabough , cube-lovers@ai.mit.edu Subject: Solutions (Was: RE: Query for Corners-First Method Rubik Solution) In-Reply-To: <19981111170341.14375.rocketmail@send105.yahoomail.com> Message-Id: On Wed, 11 Nov 1998, Han Wen wrote: {snips} }mentioning. You can get them from Meffert's site: }http://ue.net/mefferts-puzzles/ It might be of interest to mention that Meffert has solutions to many puzzles at his Web site. The Contributors section gives generous credit to a number of experts; they wrote the solutions. Best, |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Wed Nov 18 13:27:34 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA28426 for ; Wed, 18 Nov 1998 13:27:29 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19981113091853.00948790@mail.spc.nl> Date: Fri, 13 Nov 1998 09:18:55 +0100 To: cube-lovers@ai.mit.edu From: Christ van Willegen Subject: MegaMinx/5^3 (Was: RE: Query for Corners-First Method Rubik Solution) At 09:03 11-11-1998 -0800, you wrote: >Hi, > >Thanks for the link to your Puzzler program. > >You're not going to believe this, but you can still purchase the >Professor's Cube (5x5x5) and the Megaminx! Since it's difficult... no, >impossible to find anyone that sell these puzzles, I think it's worth >mentioning. You can get them from Meffert's site: >http://ue.net/mefferts-puzzles/ Also, a store in The Netherlands sells these! Last time I was there (last saturday), they had; - a couple of 3^3's - a couple of 5^3's - skewb I can't recall if they had a Megaminx at that time. The store is based in Eindhoven. If anybody wants some, I can buy them and send them out. 5^3 costs F. 50 (about $25). 3^3 costs F. 10 (about $5). Before anybody gets this wrong: - I do not work for them, I'm a happy customer - I don't get paid to do this - I make no money out of this You can call them at: +31-40-2461376 Business hours are 0900 to 1800. The Netherlands is at CET (differs +6 hours with NY, +9 with CA) Christ van Willegen From cube-lovers-errors@mc.lcs.mit.edu Wed Nov 18 17:23:08 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA29198 for ; Wed, 18 Nov 1998 17:23:06 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981114070437.9789.rocketmail@attach1.rocketmail.com> Date: Fri, 13 Nov 1998 23:04:37 -0800 (PST) From: "Jorge E. Jaramillo" Subject: RE: Moves to this other pattern To: David Singmaster , Maybe (although I don't think so since some people already answered what I was asking) I made a mistake when describing the position I wanted to accomplish. What I wanted was: L B R L B R L B R F F F T T T F F F D D D L L L T T T R R R D D D B B B T T T B B B D D D L F R L F R L F R And until now the best solution is: F B L F2 T D- L2 B- T- D- F2 R- T- D L- R D === Jorge E Jaramillo From cube-lovers-errors@mc.lcs.mit.edu Wed Nov 18 18:05:42 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA29431 for ; Wed, 18 Nov 1998 18:05:41 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <365115AC.22369936@erco.com> Date: Tue, 17 Nov 1998 07:20:28 +0100 From: "michael ehrt" Reply-To: m.ehrt@erco.org To: Cube Lovers Mail Subject: Getting 2x2x2 cubes If anyone is interested in getting 2x2x2 cubes, during my holiday in the UK two weeks ago I found a shop in Sheffield which has them in stock. It's called "The Puzzle Shop" and in situated in Meadowhall shopping centre. The cubes are GBP 5 each, and they have a few other things like keyring 3x3x3s etc. Michael From cube-lovers-errors@mc.lcs.mit.edu Thu Nov 19 13:41:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA03513 for ; Thu, 19 Nov 1998 13:40:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981117105414.18936.rocketmail@attach1.rocketmail.com> Date: Tue, 17 Nov 1998 02:54:14 -0800 (PST) From: "Jorge E. Jaramillo" Subject: The Cylinder To: cube I was checking the Rubik official website and I was surprised not to find one product that I seem to find here (I live in Colombia South America) fairly easily. I am talking about the cylinder. When I first saw it I bought it and thought it was going to be some amazing and tricky to solve puzzle, it ended up being a 3x3 cube with the corners cut, so corner cubelets only have 2 colors and there are two types of borders, 8 borders with the usual two colors and 4 with only one. Does it mean that this cube was "invented" by some manufacturer other than Mr Rubik and that is not so common? === Jorge E Jaramillo [Moderator's note: I own such a puzzle, but I would call its shape an octagonal prism, rather than a cylinder. On mine, the solved position is not an octagonal prism because one beveled face is rotated 90 degrees, forming a decahedron whose faces are six rectangles and four irregular hexagons. I don't remember whether it was originally manufactured this way or whether I altered the color tabs. ] From cube-lovers-errors@mc.lcs.mit.edu Thu Nov 19 17:36:55 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA04360 for ; Thu, 19 Nov 1998 17:36:54 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 19 Nov 1998 15:00:06 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Re : The Cylinder In-Reply-To: <19981117105414.18936.rocketmail@attach1.rocketmail.com> To: "Jorge E. Jaramillo" Cc: cube Message-Id: Jorge E. Jaramillo's message of 17 Nov 1998 included: >[Moderator's note: I own such a puzzle, but I would call its shape > an octagonal prism, rather than a cylinder. On mine, the solved > position is not an octagonal prism because one beveled face is > rotated 90 degrees, forming a decahedron whose faces are six > rectangles and four irregular hexagons. I don't remember whether > it was originally manufactured this way or whether I altered the > color tabs. ] I also own such a puzzle, although I have never seen one in a store. I got mine at a garage sale for $0.25. I haven't played with it in a long time. But my best recollection is that it can be solved basically the same way as a 3x3x3 cube, except that *I think* (don't remember for sure) that the color scheme permits invisible swaps of identically colored pieces which can make the puzzle seem "impossible" to solve unless you realize that the identically colored pieces must be swapped. It is also my best recollection that such a puzzle is mentioned briefly and is pictured in one of Douglas Hofstadters's cube articles in Scientific American back in the early 80's. So I don't think it is any kind of new invention. ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us Pellissippi State Technical Community College From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 20 11:11:16 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA07158 for ; Fri, 20 Nov 1998 11:11:15 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981117070139.11901.rocketmail@send103.yahoomail.com> Date: Mon, 16 Nov 1998 23:01:39 -0800 (PST) From: Han Wen Subject: Fwd: Re: HOW TO SOLVE THE PROBLEM OF THE PROFESSOR CUBE To: cube-lovers@ai.mit.edu I thought this would be of value to Rubik fans out there with Professor Cubes (5x5x5)... note: forwarded msgs attached. _________________________________________________________ ---Uwe Meffert wrote: [reprinted here with his permission] > Dear Mr. Wen > Thank you for your interest in my puzzles, I am sorry to hear that > you are having problems with the Prof. Cube. > You received one of the last ones from the last production batch and > the next production is not for another month. > What unfortunately happened is that when gluing the center small > caps excess glue fixed the screw to the plastic centre piece that it > should turn in. So when you turn these sections it will tighten / > loosen that one screw. > If you are skilful enough you can try and carefully remove the > centre label and then pry open and remove the centre cap of the blue > and orange side. Then try to remove the excess glue from around the > screw with a sharp object and try turning the screw with a > screwdriver firmly holding the plastic piece so you can break the > glue bond. Once the screw can freely turn inside the plastic part, > re-tighten it to the same tension as it was originally, so as to > allow smooth turning without any pieces falling out during play. > Then carefully using only very little glue fix the centre cap back > into place and re-attach the color label. > Good Luck and Happy Puzzeling. > Please let me know the outcome of this recommended procedure. > With warm regards > Uwe Meffert ________________________________________________________________ Date: Mon, 16 Nov 1998 22:57:20 -0800 (PST) From: Han Wen Subject: Re: HOW TO SOLVE THE PROBLEM OF THE PROFESSOR CUBE To: Uwe Meffert Cc: Jing Meffert Hi, My cube is all fixed. Thank you for your prompt reply. You were right, the glue used to fix the caps also fixed the spindle screw! Actually, your instructions gave me the perfect excuse to take your cube apart. I was dying to find out how the heck all these pieces are held together. Anyways, I popped of the caps carefully using a razor blade, scraped off all the excess glue, greased the screw head and before screwing it back together, I took all the pieces for one face out just to see and understand the engineering holding all the pieces together. Wow, what an amazing bit of engineering. It's like a cube spindle inside another cube spindle! Amazing. Actually, the center caps don't really need glue. They fit nice and snug, and it also leaves me the option to adjust the screw again in case it becomes loose. Now that I understand the mechanism, I've decided to only rotate faces clockwise to minimize the possibility that a counter-clockwise rotation will actually loosen one of the spindle screws. I still haven't messed the faces up though. I'm so close to finishing the Megaminx. I just have two edge pieces to swap on the last face! The other 11 sides were fairly straightforward to solve. I also got the corners of the last face fairly quickly by using Sune's move to twist corner pieces (a standard Rubik's cube move). However, getting those edge pieces was a different story. I had to develop quite a few moves to rotate and twist the edge pieces around. I'm close... so close..! :) I hope you keep inventing and making new puzzles. I eagerly click on your new releases on your web page quite regularly, hoping to find a worthy successor to the Megaminx or the Professor's Cube. Maybe a 7x7x7?!! Or a Buckyball? One can only imagine... -Han- From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 20 14:44:20 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA08578 for ; Fri, 20 Nov 1998 14:44:17 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3654ED01.E6D38EE8@hurstlinks.com> Date: Thu, 19 Nov 1998 23:16:01 -0500 From: "Guy N. Hurst" Organization: HurstLinks Sites On the Internet To: "Jorge E. Jaramillo" Cc: cube Subject: Re: The Cylinder References: <19981117105414.18936.rocketmail@attach1.rocketmail.com> I have seen one or both of these puzzles, and they were very different from each other. The cylinder, or prism, was actually the first cube I learned to solve, when my cousin from Luxembourg visited back in 1981. I have pleasant memories of it, because it was very well made and pleasing to view. It is harder to solve than the cube since the four of the edges are "cut", so it is impossible to match edges to centers - leaving the possibility of having to backtrack later and figure out which "corner" (and matching edge) is in the wrong place! But I had it down and could quickly readjust (usually had to swap corners diagonally in the top two layers if I found a single flipped edge left in the bottom layer when almost done solving it, if I remember). I liked it so much, I requested and obtained 4 more after my cousin returned to Europe! I would take them to school, one at a time, until (unfortunately) they all eventually disappeared. At least two were stolen out of my (locked) locker on different occasions. Someone else liked them, too. Anyway, I never found that puzzle in the US, and could only get it from my cousin in Europe. (Who I think may have gotten them from England). But the other puzzle, as described by the moderator, was available in the US back then, I think in the following year or so after my cousin visited, since one of my friends had one. But it wasn't as nice looking or well made. So I didn't care for it. It was more like the cube with its corners cut, forming rectangles and triangles in a spherical symmetry, as opposed to the prism from Europe which has four of its 3-piece-edges cut, forming only rectangles and having a cylindrical symmetry. Guy N. Hurst From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 20 15:16:19 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA08664 for ; Fri, 20 Nov 1998 15:16:18 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: Date: Fri, 20 Nov 1998 08:46:30 +0100 (CET) From: Bas de Bakker To: Cube-Lovers@ai.mit.edu In-Reply-To: (message from Jerry Bryan on Thu, 19 Nov 1998 15:00:06 -0500 (Eastern Standard Time)) Subject: Re: The Cylinder References: >>>>> "Jerry" == Jerry Bryan writes: [About the octagonal "cube"] Jerry> I haven't played with it in a long time. But my best Jerry> recollection is that it can be solved basically the same Jerry> way as a 3x3x3 cube, except that *I think* (don't remember Jerry> for sure) that the color scheme permits invisible swaps of Jerry> identically colored pieces which can make the puzzle seem Jerry> "impossible" to solve unless you realize that the Jerry> identically colored pieces must be swapped. Your recollection is not exact. There are no identically colored pieces to swap, but you can swap complete columns consisting of two "corners" (what would have been corners on the cube) and one "edge" without noticing. In fact, if you create an even permutation of those columns, there is no problem. But if you create an odd permutation, it will become impossible to solve the upper layer. Presuming you solve cubes in layers, the easiest way out is to not start at one of the octagonal layers (which seems the most natural way), but to start with a "side" layer. If you do it this way, it will always be possible to solve the last layer. I hope I'm making myself at least somewhat clear, Bas. From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 20 17:41:06 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA09316 for ; Fri, 20 Nov 1998 17:41:05 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.1.32.19981120105340.009ac040@icex5.cc.ic.ac.uk> Date: Fri, 20 Nov 1998 10:53:40 +0000 To: jbryan@pstcc.cc.tn.us From: "Andrew R. Southern" Subject: Space Shuttle. Cc: Cube-Lovers@ai.mit.edu, kingeorge@rocketmail.com I got a similar puzzle in the same way. Mine was called the "Space Shuttle". The lack of the name Rubik probably meant it wasn't from Rubiks. But since they only have a patent in Hungary, and everywhere else they are protected by copyrights on the name and the external appearence, this is probably legally legitimate. The colour scheme allowed the puzzle to be solved in more ways than the cube and so I reckon its easier. Each of the chamfered sides was coloured in a colour which did not relate to the rest of the puzzle, and so these were (within the boundaries of a 2-swap) possible to position ("correctly") in a few different positions. The mid-edges of the chamfered edges were rotationally symmetrical every 180 degreees and so, since they were all one colour, it was possible to have one (or three) of them rotated, and hence one of the other mid edges rotated and it would look majorly FUBAR'd. Once you'd realised what happened, the puzzle was easier than the cube though. -Andy Southern. From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 23 13:45:28 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA18663 for ; Mon, 23 Nov 1998 13:45:28 -0500 (EST) Message-Id: <199811231845.NAA18663@mc.lcs.mit.edu> Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Fri Nov 20 22:15:27 1998 Date: Fri, 20 Nov 1998 22:13:38 -0500 (EST) From: Nicholas Bodley To: Jerry Bryan Cc: "Jorge E. Jaramillo" , cube Subject: Re: Re : The Cylinder In-Reply-To: Uwe Meffert had a printed color catalogue around 1985 that showed some very interesting moving-piece "group theory" puzzles (is that a proper term?). Although I have a copy safely stashed somewhere, I don't know where. I'm just about sure that one was a cylinder, possibly in three layers like layer cake; it also, iirc, had maybe three more "cutting planes" that were spherical sectors bounded by the cylinder. Rotating the pieces would exchange top and bottom. |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 23 16:35:08 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA19314 for ; Mon, 23 Nov 1998 16:35:06 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <001e01be155b$9a456940$6bc4b0c2@home.icl.web> From: roger.broadie@iclweb.com (Roger Broadie) To: "cube" Cc: "Jorge E. Jaramillo" Subject: Re: The Cylinder Date: Sat, 21 Nov 1998 14:29:22 -0000 I was given a cylinder here in England in 1981. I no longer have the packaging, but I suspect it was Taiwanese, unless the Hungarians made this variant. It was my first cube puzzle, and its shape was so unappealing when disturbed that I put it on one side and got a genuine cube to learn on - well, almost genuine: it came from a street trader in Regent Street. The apparently impossible state is a monoflip of a top or bottom edge piece. There will be a matching flip of a middle-layer edge piece, but that will be invisible, since the piece has only one face. I wondered if it would be possible to get the puzzle into the solved shape and then restore the positions of the pieces without losing the shape, that is, only allowing turns from the group , where S and A are slice and anti-slice moves of the middle layers (I needed them). In fact it is not. There may always be a hidden flip in the middle layer and you can't correct that without moving the piece out of the middle layer, which needs a turn like F, and that destroys the shape. But if you cheat a little and make sure the flips are got right before the shape is finally restored, then it can be done. Andy Southern has already made the point about the flips. He also pointed out that the configuration is not unique because columns corresponding to the vertical edges on a normal cube can be swapped. As a rider to that point, the pretty pattern stripes on the normal cube is not distinguishable on the octagonal prism, because it's striped already. It should be possible to work out whether our moderator's puzzle came in the form he now has by counting stickers. The octagonal prism has 2 sets of 9 (the top and bottom) and 8 of 3 (the side columns). If I've grasped his configuration correctly, if it came in that form originally it should have 4 sets of 6 and 6 of 3. Roger Broadie [ Yes, my decahedron's stickers are incompatible with an octagonal prism solution. I just can't remember whether I replaced some of the stickers to make this new shape. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 23 18:13:16 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA19716 for ; Mon, 23 Nov 1998 18:13:15 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981123071931.2655.rocketmail@send105.yahoomail.com> Date: Sun, 22 Nov 1998 23:19:31 -0800 (PST) From: Han Wen Subject: Method for Solving the Megaminx To: Cube-Lovers@ai.mit.edu Hi, Well, it took me a 2-3 days, but I finally solved the Megaminx. Whew. I know, big deal. It's been done.. many many times... over a decade ago. But, I thought some of the moves I found may of interest to some of the Megaminx aficionados out there. So, here it is, I apologize for its length: Solving the Megaminx faces 1-11 are fairly straightforward. Ironically, the larger number of faces makes it easier to solve than the Rubik's cube, because they provide a lot more "free lanes" to move pieces around. There's actually just one move you need to remember to solve these faces. It's the same move when solving the middle layer of the Rubik's cube, when you want to move edge pieces from the bottom layer to their respective position in the middle layer. Namely, D'R'DRF'RFR' Solving the last face, however, is another matter. The general strategy I followed is the same as some of the standard methods for solving the bottom layer of the Rubik's cube. Namely, I first solve the 5 corners, then I solve the 5 edge pieces. To solve the corners, I simply used Sune's move applied with slight modification to the Megaminx. For the remaining edge pieces, I had to develop moves that only moved the edge pieces around, while leaving the corners unchanged. Noel Dillabough's Puzzler program was an invaluable tool for helping me experiment with various edge moves. Anyways, the following are my notes describing some of the more useful moves I've found. I'm pretty sure they're not the most efficient method for solving the Megaminx, but they're the best I could come up with. ___________________________________________ Notation for Solving the Last Face corner pieces: F=Front Face, D=Lower Face, L=Left Face, R=Right Face The F and D faces are adjacent The last layer containing the corners you need to flip/permute should be positioned at the D-face ____________________________________________ Move for Solving the Last Face corner pieces: Name: Sune's Double-Swap Description: Sune's Rubik's Cube move applied to the Megaminx Number of pairs of corners swapped: 2 Number of corners twisted counterclockwise: 3 Move: R'D'RD'R'D'3R ____________________________________________ Strategy for Solving the Last Face corner pieces: - Position the corners - Twist the corners in place by applying Sune's Double-Swap move twice ============================================ Notation for Solving the Last Face edge pieces: F=Front Face, U=Upper Face, L=Left Face, R=Right Face The F and U faces are adjacent X= L'R U2 LR' F2 X'=L'R U'2 LR' F'2 X2= X X = (L'R U2 LR' F2) (L'R U2 LR' F2) Xa= L'R U2 LR' F'2 Y= LR' F2 L'R U2 The last layer containing the edges you need to flip/permute should be positioned as the F-face or the U-face depending on the move described below: _____________________________________________ Moves for Solving the Last Face edge pieces: Name: F Tricycle 1 Description: Permutes 3 adjacent edges clockwise on the lower left of the F-face No. Edges permuted: 3 No. Edges flipped: 2 Move: (Xa3 X'2)^2 Name: F Tricycle 2 Description: Permutes 3 adjacent edges clockwise on the upper half of the F-face No. Edges permuted: 3 No. Edges flipped: 2 Move: (Xa3 X2)^2 Name: U Tricycle 1 Description: Permutes 3 edges clockwise on the U-face No. Edges permuted: 3 No. Edges flipped: 2 Move: F' X2 Y'2 F Name: U Tricycle 2 Description: Permutes 3 edges counterclockwise on the U-face No. Edges permuted: 3 No. Edges flipped: 2 Move: F X'2 Y2 F' Name: Cross-country Tricycle Description: Permutes 3 edges across the U and F faces No. Edges permuted: 3 No. Edges flipped: 1 Move: (X2 X'2)^4 Name: U Bi-Flip 1 Description: Flips two opposite edges on the U-face No. Edges permuted: 0 No. Edges flipped: 2 Move: (Xa3 X'2)^3 Name: U Bi-Flip 2 Description: Flips two adjacent edges on the U-face No. Edges permuted: 0 No. Edges flipped: 2 Move: (X2 X2 X'2)^5 Name: Cross-country Bi-Flip Description: Flips two edges, one on the U-face, one on the F-face No. Edges permuted: 0 No. Edges flipped: 2 Move: (Xa3 X2)^3 Name: "W"-Cycle Description: Permutes all edges on the F-face in a "W" pattern No. Edges permuted: 5 No. Edges flipped: 2 Move: (X2 X2 X'2)^2 Name: "Figure 8"-Cycle Description: Permutes all edges on the F-face in a "Figure 8" pattern No. Edges permuted: 5 No. Edges flipped: 4 Move: (X2 X2 X'2)^4 ____________________________________________ Strategy for Solving the Last Face edge pieces: - You should only need to use F Tricycle and the Bi-Flip moves to completely solve the edges. The F Tricycle move usually needs to be applied twice. If anything is vague/unclear please feel free to request clarification. -Han Wen- From cube-lovers-errors@mc.lcs.mit.edu Tue Nov 24 16:09:26 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA24075 for ; Tue, 24 Nov 1998 16:09:26 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: The Cylinder Date: 24 Nov 1998 18:53:56 GMT Organization: California Institute of Technology, Pasadena Message-Id: <73evc4$cq0@gap.cco.caltech.edu> References: roger.broadie@iclweb.com (Roger Broadie) writes: >I was given a cylinder here in England in 1981. I no longer have the >packaging, but I suspect it was Taiwanese, unless the Hungarians made >this variant. It was my first cube puzzle, and its shape was so >unappealing when disturbed that I put it on one side and got a genuine >cube to learn on - well, almost genuine: it came from a street trader >in Regent Street. There is a Taiwanese manufacture of the octagonal prism. I have part of one in my collection. (Got it when I was 10, and many cubies have disappeared since then.) I also have one of the "truncated cubes" mentioned earlier in this thread. I find the discussion on these two quite strange, since I always thought of these as cubes with weird cubies -- no more special than, say, that spherical "cube" they had a few years back. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- StethoPHONE, not stethoSCOPE. What do doctors SEE in those things anyway? From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 1 14:27:08 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA18757 for ; Tue, 1 Dec 1998 14:27:07 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: Cube-Lovers@ai.mit.edu From: "Andrew R. Southern" Subject: Uwe Meffert's Re-issueing of Prof. Cube Message-Id: Date: Mon, 30 Nov 1998 22:48:11 +0000 Dear Cube Lovers, I have written a website for Uwe Meffert (with input from both W. David Joyner and David Byrden) that can be found at: http://www.ue.net/mefferts-puzzles/ and was speaking with him earlier today. Uwe is going to make another batch of Professor Cubes (5x5x5) in the next week or so, and is taking orders through his site. This is a subject that is often raised on the newsgroup, and I hope people don't think of this as taking too much of a liberty. The website contains a credit card order page, information about the puzzles (including a solution to all of his popular puzzles) and multiple links to other pages. Whilst I am not involved with the day to day running of the website, if people would like their pages added to the links, please forward the URL to this address WITH A SHORT SUMMARY that will appear with the link. Puzzle available include some of the more recent ones (Orbix, Pyramorphix, Megaminx, Prof Cube). I am told that orders *may* still be on time for delivery before Chirstmas. I hope this has been of use to you guys, Andy Southern. a.southern@ic.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 1 15:45:22 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA19069 for ; Tue, 1 Dec 1998 15:45:21 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981201060918.6975.rocketmail@send104.yahoomail.com> Date: Mon, 30 Nov 1998 22:09:18 -0800 (PST) From: Han Wen Subject: Method for Solving the Professor's Cube (5x5x5) To: Cube Lovers Cc: Charles Lin , Keith Miller Hi, Okay, another so what, big deal. I finally solved the Professor's Cube. For those who may not be familiar, the Professor's Cube is a 5x5x5 Rubik's cube. Whew that was hard. It took me a good 4 days to figure out all the moves. Gees, it made the Megaminx seem like child's play in comparison. Once again, Noel Dillabough's Puzzler program was an invaluable tool to visualize and experiment with various moves. Thanks Noel! For those brave souls who would like to conquer this beast, the following solution may provide some enlightenment. It's a layers solution, in contrast to the corners-first solution that I have seen posted on various web sites. Good luck to you. The Professor's Cube is a truly challenging puzzle. ______________________________________________________ Method for Solving the Professor's Cube (5x5x5) I will use Noel Dillabough's system for referring to various slices or layers, as described in his Puzzler's F1 help. ________________________________________ Notation: U - The upper slice u - One slice away from the upper slice e - The equator slice d - One slice away from the lower slice D - The lower slice L - The leftmost slice l - One slice away from the leftmost slice m - The middle slice r - One slice away from the rightmost slice R - The rightmost slice F - The facing slice f - Once slice away from the facing slice M - The facing middle slice b - One slice away from the back face B - The back slice I will use the words "slice" and "layer" synonymously. A "face" is one of the six outer slices; namely, U, D, L, R, F or B. Rotations of the middle slices e, m or M will be in the same direction as the U, R and F faces, respectively. Let y denote one of the slices. y - represents a clockwise 1/4 turn of the y-slice y' - represents a counterclockwise 1/4 turn of the y-slice y2 - represents a clockwise 1/2 turn of the y-slice (For example, Rrm represents clockwise 1/4 turns using the RIGHT-hand of the R, r and m slices. Ll represents clockwise 1/4 turns using the LEFT-hand of the L and l slices.) Finally, let's consider the pieces or cubelets on any given face. There are four types of cubelets: corners, edges, centrals and a center. For a given face, there are 4 corners, 12 edges, 8 centrals and 1 center. With these four types and the intersection of any two slices using Dillabough's notation, we can specify the location of any cubelet. For example, consider the F-face: LU-corner: the corner cubelet on the upper left-hand corner of the F-face re-central: the central cubelet adjacent and to the right of the center cubelet of the F-face _______________________________________ First Layer (U slice): Solving the first layer is fairly straightforward. Basically the same as solving the Rubik's cube. The central pieces are the only thing really different. _______________________________________ Second Layer (u slice): 1. First, solve for the mid-central pieces (F-face mu, B-face mu, L-face Mu, R-face Mu). Get one of the mid-central piece on the same color face, and then rotate it into position by using the "free lane" from the opposite face. For example, let's say we want have a mid-central piece at the re position of the F-face. Use the D-"free lane" of the B face to position the mid-central piece without affecting your newly completed U slice, by moving: B2 U2 F' U2 B2. 2. Now, solve for the left and right central pieces (F-face lu, ru, L-face bu, fu, etc). Here's where we'll use a genuinely new move. Position one of the left/right central pieces on the D-face so that it and the position you want to move the cubelet into lie in the save vertical slice. For example, let's say we want to move the left central cubelet into the F-face lu position. Position the left central cubelet at the D-face lb position and perform the following u-layer DF Swing move: >From the D-face lb position: l d' l' d' l d2 l' See how that works? The corresponding move at the D-face rb position is: >From the D-face rb position: r' d r d r' d2 r This same concept is used to move the left/right central pieces into position for both the Second (u-slice) and Fourth (d-slice) layers. "Hey, what if my left/right central piece is on the F face? How do I move the piece to the D face so that I can apply this move?" Good question. Position the piece on the F-face ld or rd position and apply the corresponding move described above. That should move the cubelet to the D face where you can then apply the move again to move it into the correct left/right central position. 3. Finally, solve for the left and right edges (F-face and B-face Lu, Ru). Use the classic Rubik's cube move to rotate an D-edge piece into one of the middle layer edge positions. Namely, if the cubelet is at the F-face rD or lD position and the destination position is F-face Ru or Lu then perform the following: F-Edge Swing Moves: Destination position F-face Ru: D' R' D R F' R F R' Destination position F-face Lu: D L D' L' F L' F' L _______________________________________ Third Layer (e slice): 1. Solve for the left/right central pieces (F-face le, re, L-face be, fe, etc). You'll notice that the DF Swing moves will not work here. Darn. Instead, we'll use the F-Edge Swing move adapted for the l and r slices. Position the cubelet at the F-face md position then perform the following: F-Central Swing Moves: Destination position F-face Re: d'r'dD rR f'F' r fF r'R' Destination position F-face Le: d l d'D' l'L' fF l' f'F' lL "Hey, what if my left/right central piece is on the D face? How do I move the piece to the F face so that I can apply this move?" Same problem. Position the cubelet at the D-face rM position then apply the Re F-Central Swing move. 2. Solve for the left and right edges (F-face and B-face Le, Re). Again, a slight variation of the F-Edge Swing move will do. Position the edge piece on the F-face mD position and perform the following: e-Layer F-edge Swing Moves: Destination position F-face Re: D' R' D rR F' R F r'R' Destination position F-face Le: D L D' L'l' F L' F' Ll ______________________________________ Fourth Layer (d slice): 1. First, solve for the mid-central pieces (F-face md, B-face md, L-face Md, R-face Md). This is one of the most difficult steps. The mid-central pieces will be on either the d-slice or on the D-face. To move them into there correct positions, you'll need to use a few modified Rubik's cube moves: Place the D-face as the U-face when applying these moves: The following sets of cubelets are affected by these moves: cL = (central L-face Lu, edge U-face LM and central U-face lM) cR = (central R-face Ru, edge U-face RM and central U-face rM) cF = (central F-face mu, edge U-face mF and central U-face mf) Mid-central Tricycle: move: T2(U) = F2 f2 Uu Ll r'R' F2 f2 L'l' rR Uu F2 f2 action: Permutes the three sets of cubelets (cL, cR, cF) clockwise: Mid-central Bi-Flip Tricycle: move: S2(B) = L'l' rR bB Ll r'R' U2u2 L'l' rR Bb Ll r'R' action: Permutes the three sets of cubelets (cL, cR, cF) clockwise and flips the cR and cF sets. Let's clarify "flipping". Let's say for the cR set you have the colors: blue, (blue, yellow), yellow corresponding to the three cubelets. After flipping the cR set you'll have the colors: yellow, (yellow, blue), blue. Use these two moves to position all the mid-central pieces for the Fourth Layer. Now, if you're lucky, and Murphy's Law says that you will be, you may end up in a configuration where you'll have three of the mid-central pieces positioned properly, but the fourth mid-central position will be on the D-face. Okay, now we're going to start having fun. Position the central cubelet at the D-face lM position (i.e. on the left-hand side). Place the D-face as the U-face and then apply the following sequence of moves: S2(B) T2(U') U2 T2(U) S2(B') U' S2(B') Yes, all that trouble just to move one mid-central cubelet from the U-face to the F-face. 2. Whew, congratulate yourself if you've made it this far. Now, solve for the left/right central cubelets, (F-face ld, rd, L-face bd, fd, etc). Position the left central cubelet at the D-face lf or rf position and perform the following d-layer DF Swing move: >From the D-face lf position: l d l' d l d2 l' >From the D-face rf position: r' d' r d' r' d2 r 3. Solve for the left and right edges (F-face and B-face Ld, Rd). Again, a slight variation of the F-Edge Swing move will do. Position the edge piece on the F-face lD or rD position and perform the following: d-Layer F-edge Swing Moves: Destination position F-face Rd: D' R' D mrR F' R F m'r'R' Destination position F-face Ld: D L D' L'l'm F L' F' Llm' ______________________________________ Fifth Layer (D slice): 1. Solve for the corner cubelets using standard Rubik's cube moves. First, position the corners in their correct locations using the usual corner swappers: Adjacent corners swap: R' D' R F D F' R' D R D2 Diagonal corners swap: R' D' R F D2 F' R' D R D And then rotate or twist the corners in position using Sune's move: Sune's 3-corner twister: : R' D' R D' R' D2 R D2 2. Solve for the mid-edges (mF, RM, mB, LM) using a slight modification to the Tricycle moves. Place the D-face as the U-face when applying these moves: Mid-edge Tricycle: move: F2 U Ll r'R' F2 L'l' rR U F2 action: Permutes the three edges (LM, RM, mF) clockwise: Mid-edge Bi-Flip Tricycle: move: L'l' rR B Ll r'R' U2 L'l' rR B Ll r'R' action: Permutes the three edges (LM, RM, mF) clockwise and flips the RM and mF. 3. Solve for the left/right edges (lF,rF, Rf, Rb, lB, rB, Lf, Lb). Now, we're going to have some serious fun. The hardest part of this step is not getting lost while performing the long sequence of moves. Also while spinning all these slices, another difficulty is preventing the cube from exploding and keeping the central pieces from twisting around. Again, place the D-face as the U-face with applying these collection of moves: LR-edge Tricycle: move: F2 U Lm'R' F2 L'mR U F2 action: Permutes the three pairs of edges ((Lf,Lb), (Rf,Rb), (lF,rF)) clockwise: LR-edge Bi-Flip Tricycle: move: L'mR B Lm'R' U2 L'mR B Lm'R' action: Permutes the three pairs of edges ((Lf,Lb), (Rf,Rb), (lF,rF)) clockwise and flips the Rf, Rb, lF and rF. To get those last remaining cubelets in place, a few more exotic moves are necessary: Definitions: T(x) = F2 U x F2 x' U F2 x1 = L r' R' x2 = L l R' x3 = L m' R' (T(x) is a generalized form of the Mid-edge Tricycle) X1 = T(x1) T(x1) T(x1) X2 = T(x2) T(x2) T(x2) X3 = T(x3) Name: Double pair F swap Description: Swap two pairs of edges: (lF - Lb) and (rF - Rb) Move: X2 X1 Name: Double pair F cross swap Description: Swap two pairs of edges: (lF -Lf ) and (rF -Rf ) Move: X1 X2 Name: Double pair R swap Description: Swap two pairs of edges: (Rb - Lf) and (Rf - lF) Move: X2 X1 X3 Name: Double pair R cross swap Decription: Swap two pairs of edges: (Rb - rF) and (Rf - Lb) Move: X1 X2 X3 Name: Double pair L swap Description: Swap two pairs of edges: (Lb - Rf) and (Lf - rF) Move: X3 X2 X1 Name: Double pair L cross swap Description: Swap two pairs of edges: (Lb - lF) and (Lf - Rb) Move: X3 X1 X2 Name: LRL-edge Bi-Flip Tricycle Description: Permutes (lF, Lf, Rf) edges clockwise and flip lF and Lf edges Move: X3 X1 Name: LLR-edge Bi-Flip Tricycle Description: Permutes (lF, Lb, Rb) edges clockwise and flip Lb and Rb edges Move: X1 X3 Name: RRL-edge Bi-Flip Tricycle Description: Permutes (rF, Lf, Rf) edges clockwise and flip Lf and Rf edges Move: X2 X3 Name: RLR-edge Bi-Flip Tricycle Description: Permutes (rF, Lb, Rb) edges clockwise and flip rF and Lb edges Move: X3 X2 With these collection of moves, you should be able to finish off the Professor's Cube! *Sigh* -Han- P.S. Thanks "Professor" Meffert. For those folks like myself who have wrestled and completed your 5x5x5 cube, we can only ask and plead, "What's Next?!!" :) From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 1 19:18:47 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA20686 for ; Tue, 1 Dec 1998 19:18:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 30 Nov 1998 23:13:51 -0500 From: michael reid Message-Id: <199812010413.XAA11878@euclid.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: new types of cyclic shifters a few months ago, i introduced the position superflip composed with four spot and showed that it had a new type of cyclic shifting property. i've now found some new ways to generalize cyclic shifting, and this in turn suggests some new positions to consider. first, some brief review. the position superflip is central, so it commutes with all turns. therefore, if x y produces superflip, so does y x . we can shift one turn at a time, removing the first turn of the sequence and shifting it to the end. in other words, if m produces superflip, then x m = m x for all turns x . clearly, any position m with the property that x m = m x for all turns x , is central, so the only such positions are superflip and start. i showed in an earlier message, that if x is any turn and m is superflip composed with four spot, then x m = m y , where y is x conjugated by the cube rotation C_U2 . more generally, we can ask for positions m such that for any turn x , there is another turn y satisfying x m = m y . for such a position, we can cyclically shift any maneuver, one turn at a time, by replacing the turn x^(-1) at the beginning with the corresponding y^(-1) at the end. some other positions with this property are: four spot, six spot, six spot composed with superflip. a new way to generalize this is to consider positions m such that for any turn x , we have x m = n x , where n is the same pattern as m , but perhaps in a different orientation. for such a position, we can cyclically shift any maneuver, by shifting the first turn to the end, and then conjugating by the appropriate cube symmetry. for example, consider the position in which the UFR corner is twisted clockwise, and the other seven corners are twisted counterclockwise. (i'll call this "1-7-twist" for now, but this pattern needs a better name.) this position is created by U F2 B' U B U D2 R2 U2 B U' D2 B U F2 B L2 B2 now, cyclically shift the U at the beginning to the end to get F2 B' U B U D2 R2 U2 B U' D2 B U F2 B L2 B2 U which produces a different orientation of the same position; this time, the ULF corner is twisted clockwise. now conjugate this maneuver by C_U to get R2 L' U L U D2 B2 U2 L U' D2 L U R2 L F2 L2 U which produces the original position, in its original orientation. actually, there are 3 cube symmetries by which one could conjugate, since the position has 3-fold symmetry. another position with this type of cyclic shifting property is 1-7-twist composed with superflip. we can combine both types of generalizations, and ask for positions m that have the property that for any turn x , we have x m = n y , where y is another turn, and n is the same pattern as m , but perhaps in a different orientation. for such positions, we can cyclically shift any maneuver by replacing x^(-1) at the beginning of the maneuver by the corresponding y^(-1) at the end, and then conjugating the whole maneuver by the appropriate cube symmetry. two such positions are: 1-7-twist composed with four spot, and 1-7-twist composed with four spot composed with superflip. here's all the examples of cyclic shifters that i know, along with minimal maneuvers: 1. central positions start (0q*, 0f*) superflip R' U2 B L' F U' B D F U D' L D2 F' R B' D F' U' B' U D' (24q*, 22f) F' B' D2 L' B2 L2 F2 U' D B' D2 R L D' F2 U' L2 D' F2 D' (20f*, 28q) 2. four spot F2 B2 U D' R2 L2 U D' (12q*, 8f*) six spot F B' U D' R L' F B' (8q*, 8f*) four spot composed with superflip U2 D2 L F2 U' D R2 B U' D' R L F2 R U D' R' L U F' B' (26q*, 21f) F U2 R L D F2 U R2 D F2 D F' B' U2 L F2 R2 B2 U' D (20f*, 28q) six spot composed with superflip R' U D R' U F' D R' B U' L' U' F' D F' B' D' R' F D F D' R2 (24q*, 23f) U2 F B' R F L2 F2 D B2 D2 R2 B' L2 F' D2 R2 D' B R B2 (20f*, 30q) 3. 1-7-twist F R' U' L' F' U' B' L' U' R2 F L' D' R' F' D' B' R' D' L2 (22q*, 20f) F R2 L' F L F B2 U2 F2 L F' B2 L F R2 L D2 L2 (18f*, 26q) 1-7-twist composed with superflip F R F' R U B L D B D' L' D L F B' R B D F R' (20q*, 20f) F R L' B L D F' L2 B D2 B' L' F2 B' D B U L B (19f*, 22q) 4. 1-7-twist composed with four spot F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' (22q*, 20f*) 1-7-twist composed with four spot composed with superflip F U' R' L F' U R L' U2 D' B R L F' R D' R' F2 L U' (22q*, 20f*) as usual, i give a maneuver which is minimal in both metrics whenever this is possible. i don't claim that i've found all positions in these categories, but these are all that i know. if you find any others, they'd be good candidates for positions far from start. mike From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 2 14:51:54 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA24883 for ; Wed, 2 Dec 1998 14:51:53 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 30 Nov 1998 23:39:25 -0500 From: michael reid Message-Id: <199812010439.XAA11918@euclid.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: asymmetric local maxima based on the previous analysis, i can now give 2 asymmetric positions that are local maxima, namely 1-7-twist composed with four spot, and 1-7-twist composed with four spot composed with superflip. all previous examples of local maxima had some symmetry (although jerry bryan recently gave a bunch of new local maxima at distance 12q; perhaps these contain some other examples.) to show that a position is locally maximal, i must give a minimal maneuver that ends with each possible quarter turn. bear in mind that F2 = F F = F' F'. 1-7-twist composed with four spot: F L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' F2 (22q*) U' R' D L F' U' L' B U' B' U F2 U' D F R' U' F' L R2 (22q*) D' L B' D' L' F B2 D' F' U B R' D' B' L D' L' D R2 U (22q*) F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' (22q*) R' U L' F B D' F L' D B' L F' L' F D' B D' B L' U R' B (22q*) U' F L' U' B' L D R' U' R L2 F' U' L' F U' D F2 U B' (22q*) U' R' D L F' U' L' B U' B' U F2 U' D F R' U' F' R2 L (22q*) U' F' L U' L' U R2 U' D R B' U' R' F B2 U' F' D B L' (22q*) F' U' F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D (22q*) L B' D' L' F B2 D' F' U B R' D' B' L D' L' D R2 U D' (22q*) 1-7-twist composed with four spot composed with superflip: R' D' R B' R L F U2 D' R L' U B' R' L U' B U' R F2 (22q*) B U' R U' F B' R' U F' B U2 D' L F B R' B D' B' R2 (22q*) B D R B R L' U F' B' L' F L D' B2 U R' B L B D' U (22q*) F U' R' L F' U R L' U2 D' B R L F' R D' R' F2 L U' (22q*) U' D2 L F B R' F U' F' R2 B D' L D' F B' L' D F' B (22q*) U' F L' F B R U' D2 F B' D L' F' B D' L D' F R2 B' (22q*) U' F L2 B' D' B L' F B R U2 D' F' B U L' F B' U' L (22q*) B' D R L' U' D2 F R L B' R U' R' B2 L D' F D' R L' (22q*) R L' D F' R' L D' F D' R B2 L' U' L B' R L F U' D2 (22q*) these positions are also strong local maxima in the face turn metric. 1-7-twist composed with four spot: U D' B2 D F' D' F R' D' B' R U L' D' R2 L F' D' R' F (20f*) F L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' F2 (20f*) U' R' B D F' U' F B2 L' U' B' L U' D L2 U R' U' R F' (20f*) F' U' L' B U' B' U F2 U' D F R' U' F' R2 L U' L' D R (20f*) D R' D' R B' D' L' B U F' D' F B2 R' D' B' R U D' R2 (20f*) F B2 D' F' U B R' D' B' L D' L' D R2 U D' R F' D' R' (20f*) D' L B' D' L' F B2 D' F' U B R' D' B' L D' L' D R2 U (20f*) D' B D F2 B R2 B2 D F2 B' D B D' R2 U2 B2 U2 D2 F' U2 (20f*) F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' (20f*) L2 U R2 B D2 B L2 U' F' B2 D F D' R2 L2 D2 B2 L2 D' B (20f*) B L2 U F' L2 U' F' B U F D' L2 U F2 D F2 D' R2 U2 B2 (20f*) U' F L' U' B' L D R' U' R L2 F' U' L' F U' D F2 U B' (20f*) U' R' D L F' U' L' B U' B' U F2 U' D F R' U' F' R2 L (20f*) D2 F2 U' L2 U L2 D B2 U' L D R L' D' B2 L' D B2 R L2 (20f*) U' F' L U' L' U R2 U' D R B' U' R' F B2 U' F' D B L' (20f*) F' U' F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D (20f*) F2 B R2 D F' R2 D' F' B D F U' R2 D F2 U F2 U' L2 D2 (20f*) L B' D' L' F B2 D' F' U B R' D' B' L D' L' D R2 U D' (20f*) 1-7-twist composed with four spot composed with superflip: R L F' L U' L' F2 R D' B D' R' L B' D R L' U' D2 F (20f*) R' D' R B' R L F U2 D' R L' U B' R' L U' B U' R F2 (20f*) R L F U' D2 R' L D B' R L' D' B D' L F2 R' U' R F' (20f*) R F' L U' L' F2 R D' B D' R' L B' D R L' U' D2 F R (20f*) B U' R U' F B' R' U F' B U2 D' L F B R' B D' B' R2 (20f*) F' B D' L D' F R2 B' U' B R' F B L U' D2 F' B D R' (20f*) F D' B' R2 D' F R U B' L D2 B R2 U2 B2 U' R L2 B U (20f*) R2 U' F B2 R U R D' L' B2 D' R B U L' F D2 L B2 U2 (20f*) F U' R' L F' U R L' U2 D' B R L F' R D' R' F2 L U' (20f*) U' D2 L F B R' F U' F' R2 B D' L D' F B' L' D F' B (20f*) B L U L D' R' F2 D' L F U R' B D2 R F2 U2 R2 U' B2 (20f*) U' F L' F B R U' D2 F B' D L' F' B D' L D' F R2 B' (20f*) U' F L2 B' D' B L' F B R U2 D' F' B U L' F B' U' L (20f*) D' F2 B R D R U' L' F2 U' R F D L' B U2 L F2 D2 L2 (20f*) B' D R L' U' D2 F R L B' R U' R' B2 L D' F D' R L' (20f*) R L' U' D2 F R L B' R U' R' B2 L D' F D' R L' F' D (20f*) R L' D F' R' L D' F D' R B2 L' U' L B' R L F U' D2 (20f*) F D' R B2 L' U' L B' R L F U' D2 R' L D B' R L' D' (20f*) mike From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 2 20:31:57 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA27103 for ; Wed, 2 Dec 1998 20:31:57 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 2 Dec 1998 00:49:45 -0500 Message-Id: <0008F2BF.C22092@scudder.com> From: Jacob_Davenport@scudder.com (Jacob Davenport) Subject: Re: Method for Solving the Professor's Cube (5x5x5) To: Cube Lovers It is difficult. I also took a long time to solve it, but I used a very different solution. Check out www.wunderland.com/WTS/Jake/5x5x5.html for my solution. Perhaps you can combine the best moves of both solutions to find a way of solving this interesting puzzle that you find most pleasing. If you do use my solution and have any comments about how I can make it better, either in my writing or my moves, please let me know. -Jacob From cube-lovers-errors@mc.lcs.mit.edu Thu Dec 3 15:12:43 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA02280 for ; Thu, 3 Dec 1998 15:12:42 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Method for Solving the Professor's Cube (5x5x5) Date: 2 Dec 1998 18:21:22 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7440f2$q5v@gap.cco.caltech.edu> References: Han Wen writes: >For those brave souls who would like to conquer this beast, the >following solution may provide some enlightenment. It's a layers >solution, in contrast to the corners-first solution that I have seen >posted on various web sites. Good luck to you. The Professor's Cube >is a truly challenging puzzle. >______________________________________________________ >Method for Solving the Professor's Cube (5x5x5) [snip] Well, since we're sharing solutions, here's my solution to the 5x5x5: First, a preliminary exercise that should be mastered before the solution is attempted: Let's ignore all the corners and all the cubies adjacent or diagonally adjacent to the corners. (In other words, ignore the "supercorners," where "super" is a prefix meaning "two layers deep.") Ignore the centers, too. Paint all of them black, if you want. :-) Now, all we have left are the 12 "superedges." Each superedge is composed of a normal edge piece and two attached edge centers. Or, in other words, each of the 24 edge centers are attached to an edge piece face. In a normal messed-up cube, these edge centers will not match their edge piece faces. Our goal in this exercise will be to match all the edge centers with their edge piece faces. Note that superface turns never destroy an edge center pairing. Now, consider the following sequence of moves: 1. Rotate any face (NOT superface) 180 degrees. 2. Turn any center slice (as much as you want). 3. Rotate the same face in step 1 180 degrees. (i.e., perform the inverse move of step 1.) Now, if you chose the center slice to be parallel to the face, obviously this sequence doesn't do anything. Ditto for when you turned the center slice some multiple of 360 degrees. In all other cases, this will essentially perform two swaps of edge centers. Step 1 swaps two pairs of edge centers all around the face, but one of those swaps gets undone by Step 3. Step 2 moves the other pair out of the way and puts another pair in its place to be swapped again. So, if you choose wisely, you can increase the number of correctly matched edge center pairs by this move. Many of these moves, interspersed with superface turns, will allow you to match all the edge center pairs. Practice this on your cube. Thus ends the preliminary exercise. Note that all the moves in the exercise do not disturb the individual supercorners (well, one move does for a bit, but then it undoes the damage) but does change their orientation with respect to each other. Now, the solution! Step 1. Ignore the superedges and the centers. You now have what is equivalent to a 4x4x4. Solve it. Step 2. Match the edge centers with the edges as detailed in the preliminary exercise. Step 3. You now have a cube with correct supercorners (as done in step 1) and correct superedges (as done is step 2). This means that your cube is equivalent to a 3x3x3, using only superface turns. Solve it. Step 4. Tada! Your 5x5x5 is now solved. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- O*e T*o: "Thre* *our fi*e s*x; se*en *ight *ine, *en!" From cube-lovers-errors@mc.lcs.mit.edu Thu Dec 3 16:32:04 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA02610 for ; Thu, 3 Dec 1998 16:32:04 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: In-Reply-To: <872566CD.007745CF.00@notes.dtint.com> Date: Wed, 2 Dec 1998 23:15:57 -0700 To: Cube Lovers From: Steve LoBasso Subject: Re: Method for Solving the Professor's Cube (5x5x5) Although I use a different method, centrals first, edge combinations, edge parity corrections, finish using 3x3x3 solution. I was playing with a layered solution last week also, amazing coincidence. Much of my solution is the same as Han's. Most of the differences are in the 4th and 5th layers. To move the 4th layer mid centrals into place: central D-face bm to central F-face dm: F l D l' D' F' If there are no central pieces in the bottom central area, simply move a bottom central up causing another central to go down. To move 4th layer edges into place: edge L-face Db to edge F-Rd: R' D' r D R D' r' edge R-face Db to edge F-Ld: L D l' D' L' D l My 5th layer edge moves are a bit different but I haven't had time to write them down with this terminology. -- Steve LoBasso mailto:slobasso@dtint.com Digital Technology International or mailto:slobasso@hotmail.com 500 West 1200 South, Orem, UT, 84058 http://members.tripod.com/~slobasso (801)226-6142 ext.265 FAX (801)221-9254 From cube-lovers-errors@mc.lcs.mit.edu Thu Dec 3 20:49:15 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA03518 for ; Thu, 3 Dec 1998 20:49:14 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 3 Dec 1998 17:47:33 -0500 Message-Id: <00096300.C22092@scudder.com> From: Jacob_Davenport@scudder.com (Jacob Davenport) Subject: (5x5x5) edge parity corrections To: Cube Lovers I don't like the edge parity correction move that I use in my solution, and I'm hoping that someone can give me a better one. The parity problem is found in 5x5x5 cubes (and 4x4x4 cubes, I understand) when two of the edges right next to the corners (which I call "wings") are switched. Some fairly simple moves can get all three edges in line with each other, but half the time two wings need to be switched. By the time I figure this out when doing a 5x5x5 cube, I've solved most of it, and my parity fixing move messes up many of the edges I've been working on. How do other people fix this problem? -Jacob From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 4 11:30:15 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA05048 for ; Fri, 4 Dec 1998 11:30:14 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981204043241.26555.rocketmail@send106.yahoomail.com> Date: Thu, 3 Dec 1998 20:32:41 -0800 (PST) From: Han Wen Subject: Re: Method for Solving the Professor's Cube (5x5x5) To: Steve LoBasso Cc: Cube-Lovers@ai.mit.edu Hi, > To move the 4th layer mid centrals into place: > > central D-face bm to central F-face dm: F l D l' D' F' > This is a stunningly elegant move. You've reduce the difficulty in solving the 4th layer by an order of magnitude. I tried this move out, actually it swaps two centrals: F-face md <-> D-face lM (mid central swap) F-face rd <-> D-face lf (right central swap) Beautiful move. There is one particular move that I haven't figured out yet. It pops up occasionally when I solve the edges of the D-layer. Sometimes I end up with every cubie in place except for two right centrals on adjacent faces. For example: F-face rD and L-face Lf. The two pieces only need to be swapped. No flipping is needed. Does anyone know how to perform this move? I've been beating the Puzzler program for a while, but I have been unsuccessful so far. ______________________________________________ Han Wen Applied Materials 3050 Bowers Ave, MS 1145 Santa Clara, CA 95054 e-mail: Han_Wen@amat.com / hansker@yahoo.com From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 4 13:17:06 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA05373 for ; Fri, 4 Dec 1998 13:17:05 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 3 Dec 1998 23:58:19 -0500 (EST) From: der Mouse Message-Id: <199812040458.XAA26116@Twig.Rodents.Montreal.QC.CA> To: Cube-Lovers@ai.mit.edu Subject: Re: (5x5x5) edge parity corrections > The parity problem is found in 5x5x5 cubes (and 4x4x4 cubes, I > understand) when two of the edges right next to the corners (which I > call "wings") are switched. Yes, it does occur equally on the 4-Cube. Though I have never seen one, I feel certain that similar parity problems will occur on all higher-order Cubes as well, though above order 5 there will be multiple distinct types of "wings", each of which will have its own comparable potential problem. Note that the problem goes away entirely if cube faces are marked such that symmetrically placed face cubies are not visually indistinguishable, because the parity problem in question always occurs in conjunction with a similar parity problem on face cubies, but the latter is invisible on most cubes. > [...] half the time two wings need to be switched. > How do other people fix this problem? Most briefly, how I do it is to make a single quarter-turn of a slice containing one of the wing pieces involved, then fix up the damage by moving wings back into place using commutators rather than slice moves. der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 4 14:26:23 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA05692 for ; Fri, 4 Dec 1998 14:26:23 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Method for Solving the 4x4x4 Date: 4 Dec 1998 17:26:00 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7495v8$3nv@gap.cco.caltech.edu> References: I have been told that my solution for the 5x5x5 includes knowing how to solve the 4x4x4, which is of course not trivial. With the post asking about the parity problem, I thought I might as well post my solution to the 4x4x4. Yes, the biggest barrier is the parity problem where two adjacent edge cubies are flipped. My earliest attempt at a 4x4x4 solution was the following: 1. Match all the centers. 2. Match all the edges. 3. You now have a 3x3x3. Solve. Unfortunately, with the parity problem you can often end up with an unsolvable 3x3x3 by the time you get to step 3. Any simple moves that fix the parity problem tend to mess up the rest of the cube quite badly -- I wrestled with this problem a long time until I realized one thing: Most solutions of the 3x3x3 treat the centers as static, using them as "anchors" for the entire cube. But this is entirely unnecessary! If you solve the 3x3x3 while IGNORING the centers, you will eventually get a solved cube where the centers are either in the "6 dots" or "4 dots" situation well known to cubists -- and these have rather simple solutions, essentially consisting of a slice turn conjugated with another slice turn. So, my most favorite 4x4x4 solution is now: 1. Match all the edges. 2. Solve the parity problem, if necessary (postpone until after step 3 if desired). 3. Ignore the centers and treat the cube as a 3x3x3. Solve. 4. Solve the centers. Okay. Now to qualify the solution. Part 1 is simple and can be done anyway you wish (the move rF2r'F2 will be rather useful in the later stages). Part 3 is simple, with the caveat that you may be treating the "centers" in the wrong manner! Part 2 stems from the fact that the cube apparently has an "even" permutation (a 2-cycle involving two edge pieces), an apparent paradox since 2-cycles should not exist (e.g., on the 3x3x3 it is impossible to swap exactly two edges). The reason this is only an "apparent" paradox, however, is because of the misassumption that the centers of the 4x4x4 are static, which they certainly are not! In fact, just rotate one slice incident on your 2-cycle, and you have magically turned the 2-cycle into a 5-cycle, which is perfectly solvable! Personally, I solve the 5-cycle by two or more 3-cycles, which generally take on the form: FR'F' r FRF' r' This move performs a cycle on the three edges fUR, FUr, and FDr, without disturbing the corners, but doing rather annoying things to the centers. (This move is an extension of the perhaps-not-so-well-known sequence for the 3x3x3: FR'F'LR'DRD'L'R that rotates 3 edges.) For FR'F' you may substitute any sequence of moves that brings your desired edge piece (in this case fUR) to the FUr position, as long as it does not disturb any other edges on the r slice (specifically, the edges FDr, BUr, and BDr). You will also have to substitute the inverse of your sequence for FRF'. As an example, the move F'L2F r F'L2F r' cycles BdL, FUr, and FDr. You may also use r2 instead of r and r', which means that BDr is affected instead of FDr. And finally, step 4: the centers. This is solved by a generalization of the "6-dots" rule. This move creates "6 dots": u'r'ur This permutes bUr, Fur, and buR, as well as their "opposites" fDl, Bdl, and fdL, while affecting no other cubies. This is two 3-cycles on 6 faces, which is rather unwieldy, so I conjugate (is that the right word?) it with a simple face turn to get u'r'ur F r'u'ru F' which permutes Fur, Fdr, and buR in a simple 3-cycle. Both Fur and Fdr are on the same face, which makes this move rather easy to deal with. Especially, if one of those is the right color already, it can be involved in the 3-cycle without "increasing error." I think I may have extended my personal jargon a bit more into this post -- if you wish to understand anything in this post or, conversely, would like to teach me more "Standard" jargon, please e-mail me. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- O*e T*o: "Thre* *our fi*e s*x; se*en *ight *ine, *en!" From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 4 15:28:52 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA05995 for ; Fri, 4 Dec 1998 15:28:52 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: From: Noel Dillabough To: "'Cube Lovers'" Cc: "'Jacob_Davenport@scudder.com'" , "'noel@mud.ca'" Subject: RE: (5x5x5) edge parity corrections Date: Fri, 4 Dec 1998 12:44:07 -0500 The parity problem can be solved on a 4x4x4 or 5x5x5 by using the following move (can be pasted into puzzler's move macro): r2D2l1D2l1D1l3r3d2l1r1D3l3r3d2B2r1B2l3B2l1B2r2 For the 4x4x4, this is all that is needed, but for the 5x5x5, two crosses (centre edges) are swapped. So you'll need to use the following to solve the crosses: First, get the crosses across from each other with: F2l3F2e1l2e3l2F2l1F2 Now swap the opposite crosses with: R2e1l2e3l2R2e1l2e3l2 Parity problem solved... If anyone has a better solution to this rather long one, let me know, I'm sure some moves could be shaved off. From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 4 16:11:19 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA06137 for ; Fri, 4 Dec 1998 16:11:18 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199812041806.NAA21024@pike.sover.net> Date: Fri, 04 Dec 1998 13:07:36 -0500 To: Jacob Davenport From: Nichael Lynn Cramer Subject: Re: (5x5x5) edge parity corrections Cc: Cube Lovers In-Reply-To: <00096300.C22092@scudder.com> Jacob Davenport wrote: >I don't like the edge parity correction move that I use in my solution, and >I'm hoping that someone can give me a better one. > >The parity problem is found in 5x5x5 cubes (and 4x4x4 cubes, I understand) >when two of the edges right next to the corners (which I call "wings") are >switched. Some fairly simple moves can get all three edges in line with >each other, but half the time two wings need to be switched. By the time I >figure this out when doing a 5x5x5 cube, I've solved most of it, and my >parity fixing move messes up many of the edges I've been working on. > >How do other people fix this problem? > >-Jacob Hi Jacob In both cases (4X and 5X) I solve this problem in the following way: 1] I solve the rest of the cube, leaving me with the two "switched wings" (in your terminology). 2] I then arrange things so both "wings" are on the same "off-center-slice". (Also it will always be the case that both of these winds are now on the same face.) This will be easy to do using the 3-wing swapping operators. 3] At this point I now rotate the "off-center-slice" containing the "switched wings" by a quarter turn. As a result of this move it will be the case that that the "off-center-slice" now has one of the previously "switched wings" in its "correct cubicle". The other three "wings" will be now be in a cyclic permutation. 4] Since --from your note above-- I assume you understand how to cycle three "wings", all you have to do now is put the "wings" in the right place and replace the damage to the off-center central faces that were messed up during that initial quarter-turn above. (And since they are in "paired" clusters, this should be pretty straightforward.) (In short, the quarter-turn of the non-central slice puts the cube back in the proper "orbit" for finishing up.) Now clearly this is far from maximal. And it's certainly not terribly fast. But I find it a very simple, and an easy (and easy-to-remember [and easy-to-explain]) way to clean up this potentially messy situation. Hope this helps Nichael -- Nichael Cramer nichael@sover.net deep autumn-- http://www.sover.net/~nichael/ my neighbor what does she do From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 4 16:49:43 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA06282 for ; Fri, 4 Dec 1998 16:49:43 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: In-Reply-To: <872566D0.000F48EF.00@notes.dtint.com> Date: Fri, 4 Dec 1998 11:26:10 -0700 To: Jacob_Davenport@scudder.com (Jacob Davenport) From: Steve LoBasso Subject: Re: (5x5x5) edge parity corrections Cc: Cube-Lovers@ai.mit.edu This should solve the edge parity problem by swapping the edge F-Ru and edge F-Rd pieces. R2 d L2 d L2 d' R2 u' F2 u2 F2 u' F2 L2 F l' F' L2 F l F This move swaps only these two pieces and some centrals, but only within their face. A variant of this move should be scalable to solve parity issues in any NxNxN cube. The only way I can think of to not have the parity problem, or at least not require such a long series, is to solve centrals last. Another other idea would be to spot the parity problem much earlier by counting edge flips. Not very easy for a person to do, but I have seen it done in software for normal 3x3x3 cubes. If it were were known very early in either the centers first or layered solution, it would be trivial to fix. >I don't like the edge parity correction move that I use in my solution, and >I'm hoping that someone can give me a better one. > >The parity problem is found in 5x5x5 cubes (and 4x4x4 cubes, I understand) >when two of the edges right next to the corners (which I call "wings") are >switched. Some fairly simple moves can get all three edges in line with >each other, but half the time two wings need to be switched. By the time I >figure this out when doing a 5x5x5 cube, I've solved most of it, and my >parity fixing move messes up many of the edges I've been working on. > >How do other people fix this problem? > >-Jacob -- Steve LoBasso Digital Technology International mailto:slobasso@dtint.com 500 West 1200 South or mailto:slobasso@hotmail.com Orem, UT 84058 http://members.tripod.com/~slobasso (801)226-6142 ext.265 FAX (801)221-9254 From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 4 17:13:44 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA06366 for ; Fri, 4 Dec 1998 17:13:43 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36683B51.A50833E4@switchview.com> Date: Fri, 04 Dec 1998 14:43:13 -0500 From: Michael Swart Organization: Switchview To: Cube-Lovers@ai.mit.edu Subject: Re: (5x5x5) edge parity corrections References: <199812040458.XAA26116@Twig.Rodents.Montreal.QC.CA> I got this from the archives, it may be relevant to repost it. It's a way of solving the parity problem: r2 U2 r l' U2 r' U2 r U2 r l U2 l U2 r U2 l r2 U2 I'm confident you can't do too much better than this. Mike From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 8 11:22:45 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA18601 for ; Tue, 8 Dec 1998 11:22:43 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199812042200.RAA02240@pike.sover.net> Date: Fri, 04 Dec 1998 16:40:51 -0500 To: der Mouse From: Nichael Lynn Cramer Subject: Re: (5x5x5) edge parity corrections Cc: Cube-Lovers@ai.mit.edu In-Reply-To: <199812040458.XAA26116@Twig.Rodents.Montreal.QC.CA> der Mouse wrote: >> The parity problem is found in 5x5x5 cubes (and 4x4x4 cubes, I >> understand) when two of the edges right next to the corners (which I >> call "wings") are switched. > >Yes, it does occur equally on the 4-Cube. [...] The appearance is particularly striking on the 4X cube. Especially in the situation where the two out-of-place "wings" are side-by-side. It looks very similar to a solved 3X cube with a single edge-cubie flipped. This is an interesting state to leave your cube in, when it is just lying around your office, for visitors to find. N From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 8 12:38:33 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA18817 for ; Tue, 8 Dec 1998 12:38:32 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199812051241.VAA08521@soda3.bekkoame.ne.jp> Date: Sat, 5 Dec 1998 21:47:39 +0900 To: Cube-Lovers@ai.mit.edu From: Ishihama Yoshiaki Subject: 4DRubik Cube I have simulated 4DRubikCube for Macintosh. It is madeup of 2x2x2x2 hypercubes. It is on my HomePage. //----------------------------------------// Ishihama Yoshiaki Tokyo Chofu E-mail: ishmnn@cap.bekkoame.or.jp (Until 1999/3/31) ishmnn@cap.bekkoame.ne.jp ( This is correct address) HomePage : http://www.asahi-net.or.jp/~hq8y-ishm/ //--------------------------------------// From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 8 13:31:28 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA19371 for ; Tue, 8 Dec 1998 13:31:28 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <366C1ED9.C11@hrz1.hrz.tu-darmstadt.de> Date: Mon, 07 Dec 1998 19:30:49 +0100 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: cube-lovers@ai.mit.edu Subject: Optimal Cube Solver New Optimal Cube Solver I wrote an optimal Cube Solver and experimented with coordinates different of those I use in my Cube Explorer program or of those in Mike Reid's Optimal Cube Solver. Its pruning tables are not very large (about 25MB), so the performance is relatively low (at least in comparison with Mike's program), but I think it is worth to give you some information about it. Some general considerations on the use of "coordinates" in cube solving algorithms first. Instead of representing a state of the cube by the positions of corners or edges, the use of coordinates not only increases the speed of computing a face-turn but also serves as an index for the pruning tables. If we have an arbitrary subgroup H of the Cube Group G, we map the right cosets Ha to natural numbers from 0 to ord(G)/ord(H)-1). A face-turn T (which also is an element from G) now induces a map on these numbers, which can be implemented as a simple lookup-table. For this to work we have to ensure that if x=h1*a and y=h2*a are in the same coset Ha, then x*T and y*T are in the same coset Hb. But this is true because (x*T)*(y*T)^-1 = (h1*a*T)*(h2*a*T)^-1 = h1*h2^-1 is in H. If we take for example H1={all g from G with corner orientations 0, corner permutations and edges arbitrary} the resulting coordinate (0<=x<2187) represents the orientation of the corners. It also should be possible to reduce the size of the coordinates by the 48 symmetries of the cube (or at least by a subgroup of the symmetry group M). This is done by defining equivalence classes on the cosets. Two cosets Ha and Hb are called equivalent, if there is an m from M with Hb = m*Ha*m^-1. But to make this definition work we have to ensure, that the elements of a coset Ha are really all mapped to the same coset Hb by the conjugation with m. This only is true, if (1) mHm^-1=H The subgroup H1 from above for example does have this property only for symmetries which do not change the UD-axis in the way the orientations of the corners are usually defined. So the corner orientation coordinate can only be reduced by 16 symmetries. Is it possible to define the corner orientations in another way, so that (1) holds for all 48 symmetries? I do not believe it, but I do not know how to prove this. For the analogous case of the edge orientations there is a possibility to define the orientations in a way (different to the way usually used) which allows reduction by all 48 symmetries: every quarter turn changes the orientation of any involved edge. In my program I use 3 coordinates. The first (let's call it the X2-coordinate) is defined by the subgroup, where the edges are arbitrary and the corners are generated by . There are 918540 different cosets. Because (1) holds for all m, they can be reduced by all 48 symmetries and we get 19926 equivalence classes. The second coordinate is the edge orientation defined by the subgroup {all g from G with edge orientations 0, edge permutations and corners arbitrary}. There are 2048 cosets. I do not reduce them by symmetries because the number is relative small. The third coordinate describes the edge permutation. Because there are 12! coordinate values, even reduction by 48 symmetries still gives too many coordinate values. So for use in a turntable we define two edge permutations a and b equivalent, if a=m1*b*m2, were m1 and m2 are in M. In this way we get 208816 equivalence classes c. If now m1*c*m2 is a (not necessarily unique) representation of an edge permutation applying a faceturn T is done like that: (m1*c*m2)*T = m1*c*[m2*T*m2^-1]*m2 = m1*[c*T']*m2= [m1*m1']*c'*[m2'*m2]=m1''*c'*m2'' The operations in square brackets are done by table lookups: [m2*T*m2^-1]:=T', [c*T']:=m1'*c'*m2', [m1*m1']:=m1'' and [m2'*m2]:= m2''. A cube, which has all three coordinates zero, is in a subgroup with 96 elements, were the edges are in place and the corner orientations are correct. To find such states, I use two pruning-tables. The first combines the X2-coordinate and the edge-orientation coordinate which takes 19926*2048/2=20404224Bytes of memory (we only need 4 bit per entry). The maximal table entry is 12, with an average of about 9.5. The second is a pruning table for the edge-permutation. It takes 208816*48/2=5011584Bytes, the maximal table entry is 10 (so it takes not more then 10 faceturns to position all edges ignoring the orientations). The program produces about 1 million nodes per second on a P350 and a depth 15 search is done in about 4 minutes (depending on the situation). So a complete depth 18 search will need a few days which of course is not very satisfying. A possible improvement could be to use the subgroup instead of for the first coordinate. The subgroup has only 4 elements, so the coset-space has 24 times the size. The pruning table will need about 480MB instead of 20MB which is above that what is possible for me in the moment. But a complete depth 18 search should be done in about 1/24 of the time which will be a few hours then. Herbert From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 8 14:34:56 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA19972 for ; Tue, 8 Dec 1998 14:34:56 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: jmb184@frontiernet.net (John Bailey) To: ishmnn@cap.bekkoame.or.jp (Ishihama Yoshiaki) Cc: Submissions Cube-Lovers Subject: Re: 4DRubikCube Date: Sat, 05 Dec 1998 13:10:10 GMT Message-Id: <36692f00.213266943@mail.frontiernet.net> References: On Sat, 05 Dec 1998 18:57:03 +0900, in rec.puzzles you wrote: >I have created 4Dimension Rubik Cube for Macintosh. >URL: http://www.asahi-net.or.jp/~hq8y-ishm/ I went there the instant I read your post. Unfortunately, I am running a Pentium based machine. Could you put a gif image of your cube on the page? Maybe even a screen copy bitmap of the user interface. We IBM-PC types can stare and drool. If you haven't checked out my 2x2x2x2 cube, it's at http://www.ggw.org/donorware/4D_Rubik John http://www.frontiernet.net/~jmb184 From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 8 16:03:32 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA20365 for ; Tue, 8 Dec 1998 16:03:31 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199812042200.RAA02263@pike.sover.net> Date: Fri, 04 Dec 1998 17:00:42 -0500 To: cube-lovers@ai.mit.edu From: Nichael Lynn Cramer Subject: Re: Method for Solving the Professor's Cube (5x5x5) In-Reply-To: <7440f2$q5v@gap.cco.caltech.edu> References: >>Method for Solving the Professor's Cube (5x5x5) > >[snip] This is not a formal solution, but --say when I want to kill some time-- I often find it entertaining to solve the 5X cube in "ascending spirals". By which I mean: Start with the center face on a particular color (I always start with blue). Next solve the non-center face cubies, one by one, in order moving clockwise around the "loop". When that loop is done, then solve one of the blue-faced corners and then solve the remaining blue-sided edge cubies (in order). Then move up, solving each parallel-to-the-blue-face internal slice in order; and so on. Needless to say, this is hardly an optimal solution (in either time or number of moves). But think of it as a way to "practice scales" (Or as I say, just a good way to kill some time. ;-) There are obvious variations on this. For example, solve the individual faces in "ascending spirals" like the above, but instead of starting on a center face cubie, start on a corner cubie and work your way diagonally, in slices, across the cube toward the opposite corner. Or, for the truly masochistic, solve the cube --again a cubie at a time-- in a checkboard pattern (i.e. the result of putting the 5X cube through the Pons Asinorum transformation) doing first the half of the cubies in the first "phase" and then the cubies in the other. -- Nichael Cramer work: ncramer@bbn.com home: nichael@sover.net http://www.sover.net/~nichael/ From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 8 19:08:13 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA22642 for ; Tue, 8 Dec 1998 19:08:13 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 8 Dec 1998 18:37:02 -0500 (EST) From: Alchemist Matt Reply-To: Alchemist Matt To: Herbert Kociemba Cc: cube-lovers@ai.mit.edu Subject: Re: Optimal Cube Solver In-Reply-To: <366C1ED9.C11@hrz1.hrz.tu-darmstadt.de> Message-Id: This question is directed to both Herbert and Mike Reid in case he's reading this list: With all this discussion of the "Professor Cube" lately, how hard would it be to extend either Optimal cube solving program to handle 4x4x4 and 5x5x5 cubes in addition to the traditional 3x3x3? Considering reasonable table files (50 - 100 mb), how much longer would the computation time be extended by. If either of you would find the time to implement this modification, I would be very interested in trying out the program. Matt ----------------------------------------------------------------------- Matthew Monroe Monroem@UNC.Edu Analytical Chemistry http://www.unc.edu/~monroem/ UNC - Chapel Hill, NC This tagline is umop apisdn ----------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 9 12:45:11 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA24863 for ; Wed, 9 Dec 1998 12:45:11 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 8 Dec 1998 23:24:09 -0500 From: michael reid Message-Id: <199812090424.XAA00740@euclid.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Optimal Cube Solver matt monroe asks > This question is directed to both Herbert and Mike Reid in case he's > reading this list: With all this discussion of the "Professor Cube" > lately, how hard would it be to extend either Optimal cube solving program > to handle 4x4x4 and 5x5x5 cubes in addition to the traditional 3x3x3? > Considering reasonable table files (50 - 100 mb), how much longer would > the computation time be extended by. If either of you would find the time > to implement this modification, I would be very interested in trying out > the program. i think it's reasonable to say that an optimal solver for the 4x4x4 (or 5x5x5) is currently far out of reach. one could write a program that theoretically finds optimal solutions after running for enough time. but it would be feasible only for positions a few turns from start; other positions would take years, centuries, millenia, ... on the other hand, a sub-optimal solver is certainly possible. just teach the computer your favorite method. this would be more "sub" than it is "optimal", so next we'd ask to make it as good as possible. the real question is: are computer methods superior to human methods for the larger cubes? so far, probably not, but not much work has been done on sub-optimal solvers for larger cubes. mike From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 9 15:20:18 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA26381 for ; Wed, 9 Dec 1998 15:20:17 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 8 Dec 1998 23:36:23 -0500 From: michael reid Message-Id: <199812090436.XAA00765@euclid.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: meffert's web site and puzzles i'm glad to hear that uwe effert is still making puzzles. i hope this means he'll make that master pyraminx (which was once planned) in which edges can also turn! and while i'm dreaming ... how about a higher order pyramid, preferably also of the edge-turning as well as peak-turning variety? david byrden's web site has some puzzles i'd like to see made: the icosahedron, the octahedral "oddity", ... any chance of making any of these? mike From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 9 16:00:55 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA26560 for ; Wed, 9 Dec 1998 16:00:53 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199812090645.BAA17397@terminus.idirect.com> From: "Mark Longridge" To: Subject: My rubik's cube webpage Date: Wed, 9 Dec 1998 01:49:33 -0500 Hello cube-lovers, My site has moved to: http://www.snipercade/com/cubeman/index.html the old site: http://web.idirect.com/~cubeman will be up for a few days still. web masters please update your links! Thanks, -> Mark From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 9 17:00:48 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA26848 for ; Wed, 9 Dec 1998 17:00:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Creative ways of solving the cube Date: 9 Dec 1998 15:48:18 GMT Organization: California Institute of Technology, Pasadena Message-Id: <74m642$lb5@gap.cco.caltech.edu> References: Nichael Lynn Cramer writes: >This is not a formal solution, but --say when I want to kill some time-- I >often find it entertaining to solve the 5X cube in "ascending spirals". Although I don't play with my 5x5x5 much, I do play with the 3x3x3 a lot and have entertained myself by solving it in many different ways. The canonical methods: 1. First level, second level, third level 2. Centers, corners, edges After much more understanding, however, I now try different techniques for entertainment. In order of approximate difficulty: 0. Solve to a particular state (pons asinorum, super-flip) 1. Corners, edges, centers 2. Edges, corners, centers (rather disorienting) 3. First level, third level, center slice 4. One face at a time, with no regard to correct cubie placement as long as the color is correct (this is fun) 5. Solve to a particular subgroup (half-turn group, anti-slice group) then stay in that subgroup -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- "I'd like to have the same quest again, sir." From cube-lovers-errors@mc.lcs.mit.edu Mon Dec 14 12:44:15 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA11438 for ; Mon, 14 Dec 1998 12:44:15 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199812111354.IAA18055@terminus.idirect.com> From: "Mark Longridge" To: Subject: New URL Correction Date: Fri, 11 Dec 1998 08:59:00 -0500 Hello folks... Sorry, but the URL I posted for my new web page is wrong. The correct URL is: http://www.snipercade.com/cubeman The old site http://web.idirect.com/~cubeman will be up for a few days yet. The virtual URL http://welcome.to/cubeman should always point to the current site! :-) More interesting stuff to follow -> Mark From cube-lovers-errors@mc.lcs.mit.edu Mon Dec 14 13:45:36 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA11697 for ; Mon, 14 Dec 1998 13:45:36 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199812111354.IAA18055@terminus.idirect.com> From: "Mark Longridge" To: Subject: New URL Correction Date: Fri, 11 Dec 1998 08:59:00 -0500 Hello folks... Sorry, but the URL I posted for my new web page is wrong. The correct URL is: http://www.snipercade.com/cubeman The old site http://web.idirect.com/~cubeman will be up for a few days yet. The virtual URL http://welcome.to/cubeman should always point to the current site! :-) More interesting stuff to follow -> Mark From cube-lovers-errors@mc.lcs.mit.edu Mon Dec 14 15:00:05 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA11876 for ; Mon, 14 Dec 1998 15:00:04 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 10 Dec 1998 23:04:10 -0500 From: michael reid Message-Id: <199812110404.XAA03343@cauchy.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: fixing edge parity on 4x4x4 several people have posted maneuvers for "fixing" the edge parity on rubik's revenge. i haven't seen any maneuvers as short as mine (although there might be some disagreement about "length"). recall that i am using the notation _R_ (R underscored) to mean turn the outer two layers together. to switch the two UF edges: _R2_ B2 L U2 l U2 r' U2 r U2 F2 r F2 _L'_ B2 _R2_ side effects: rotates the set of 4 U centers by 180 degrees. also makes a 4-cycle of internal (0 faces visible) cubies. if you're not concerned about moving centers, use _(R2 B)_ u _(B' D2 B)_ u' _B_ l _(B2 D2 R2)_ here, _( ... )_ means the whole thing inside the parentheses is underlined. the maneuver that i normally use, since it's appropriate for my solving method, is U2 (r U2)^5 which makes a 4-cycle of edges in the r-slice (and also rotates the set of 4 U centers by 180 degrees). this one is short and easy to remember! these maneuvers all work well on the 5x5x5 also. mike From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 15 08:40:06 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id IAA13901 for ; Tue, 15 Dec 1998 08:40:05 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Sender: bosch@sgi.com Message-Id: <3675637C.6231@sgi.com> Date: Mon, 14 Dec 1998 11:14:04 -0800 From: Derek Bosch To: Cube-Lovers@ai.mit.edu Subject: re-assembling a 2x2x2? Well, I accidentally managed to pop apart my Rubik's Mini-Cube, aka the 2x2x2... Are there any easy instructions on getting it back together? I'd rather not force it... D -- Derek Bosch "A little nonsense now and then (650) 933-2115 is relished by the wisest men"... W.Wonka bosch@sgi.com From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 15 10:30:58 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id KAA14077 for ; Tue, 15 Dec 1998 10:30:58 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 15 Dec 1998 17:30:24 +0900 (JST) Message-Id: <199812150830.RAA03209@soda2.bekkoame.ne.jp> To: cube-lovers@ai.mit.edu From: Ishihama Yoshiaki Subject: 4D Rubik Cube(2x2x2x2) Java I have converted my "4DRubikCube" (for Macintosh) to java applet. I have uploaded it to my java page. I have not yet added direct drag mode, only rotate cubes by buttons. Please check this applet. //----------------------------------------// Ishihama Yoshiaki ( Tokyo Japan) E-mail: ishmnn@cap.bekkoame.ne.jp HomePage : http://www.asahi-net.or.jp/~hq8y-ishm/ //----------------------------------------// From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 15 12:13:33 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA14336 for ; Tue, 15 Dec 1998 12:13:32 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 15 Dec 1998 11:35:13 -0500 (EST) From: Nicholas Bodley To: Derek Bosch Cc: Cube-Lovers@ai.mit.edu Subject: Re: re-assembling a 2x2x2? In-Reply-To: <3675637C.6231@sgi.com> Message-Id: I've pulled mine apart a *few* times. Imho, it's probably impossible to reassemble without some forcing. If it were made of cheap plastic, I very much doubt that it could be assembled. Study the structure, so you won't try to assemble it wrong; you probably wouldn't make such a mistake, though. Hope you didn't lose any pieces! (Be *sure* to match colors properly before assembling; of course, you know that, too.) My hopeful guess is that you'll succeed, but be rather amazed by the force it takes, and also that the plastic can take such stress. I have seen 2^3s on sale fairly recently, btw, so there has been a stock of them, possibly a new production run. I've been a mechanical tech. at times for several decades, so I'm reasonably sure of what I say. I've pulled apart many movable-part puzzles, and the 2^3 is surely the most intractable of all I've dealt with. Alexanders' Star and the 4^3 have some parts that are easy to break. I'd love to know how it's done at the factory. I hope it's not some subtle ultrasonic welding. (Maybe someone could ask Dr. Christoph Bandelow, Dr. Uwe Meffert, or (Dr.?*) David Singmaster.) *Sorry if I forget! Best regards, and good luck! |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 16 13:02:37 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA17548 for ; Wed, 16 Dec 1998 13:02:37 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: In-Reply-To: <3675637C.6231@sgi.com> Date: Tue, 15 Dec 1998 18:41:19 -0500 To: Cube-Lovers@ai.mit.edu From: Charlie Dickman Subject: Re: re-assembling a 2x2x2? >Well, I accidentally managed to pop apart my Rubik's Mini-Cube, >aka the 2x2x2... Are there any easy instructions on getting it >back together? I'd rather not force it... You should use a small Phillips screwdriver to remove one of the triangular flanges that forms the tracks that the "cubies" ride in. Then, put the "cubie" pieces in place and then g_e_n_t_l_y spread the space between the 4 "cubie" surfaces that hide the stump that holds the triangular flange and put the screw back in. Be careful not to break the shaft between the cubie face and its anchor. Charlie Dickman charlied@erols.com From cube-lovers-errors@mc.lcs.mit.edu Thu Dec 17 12:58:39 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA21072 for ; Thu, 17 Dec 1998 12:58:39 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 16 Dec 1998 23:46:46 -0500 (EST) From: Nicholas Bodley To: Charlie Dickman Cc: Cube-Lovers@ai.mit.edu Subject: Newer mechanism? (Was: Re: re-assembling a 2x2x2?) In-Reply-To: Message-Id: Charlie, I'm just about dead sure my 2^3s (from about 15 (?) years go) have no screws. I studied your description, and it seems that the mechanism has been redesigned! I described the mechanism of mine in considerable (if not painful!) detail, maybe a year and a half ago; it's probably in the archives. The keyword "jack" should help to locate the post. Perhaps a continuing market combined with the difficulty of assembling the original design created a need for a new one. Would really *love* to know whether there is a newer and different mechanism. As a somewhat casual student of these mechanisms, I've come to realize that for all "sizes", more than one mechanism is possible. I have great admiration for the designers who create these marvelous mechanisms. I love the 5^3 as much for its innards (which I regard as thoroughly astonishing) as for its essential function. I also admire the mathematicians, programmers, and practical users of group theory on this List; I have only a faint awareness of what they're talking about, but their amazing posts keep my mind properly stretched. I feel a bit like a dog listening to his human family discussing, say, a trip to Australia (the dog didn't go). However, that's perfectly OK with me! My mind is quite good, and to some degree it's circumstance that I'm not "with it". My regards to all, |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Thu Dec 17 14:01:55 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA21297 for ; Thu, 17 Dec 1998 14:01:50 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 17 Dec 1998 09:32:42 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Re : Optimal Cube Solver In-Reply-To: <366C1ED9.C11@hrz1.hrz.tu-darmstadt.de> To: kociemba@hrz1.hrz.tu-darmstadt.de Cc: Cube Lovers Message-Id: On Mon, 07 Dec 1998 19:30:49 +0100 Herbert Kociemba wrote: > > The third coordinate describes the edge permutation. Because there are > 12! coordinate values, even reduction by 48 symmetries still gives too > many coordinate values. So for use in a turntable we define two edge > permutations a and b equivalent, if a=m1*b*m2, were m1 and m2 are in M. > In this way we get 208816 equivalence classes c. If now m1*c*m2 is a > (not necessarily unique) representation of an edge permutation applying > a faceturn T is done like that: > > (m1*c*m2)*T = m1*c*[m2*T*m2^-1]*m2 = m1*[c*T']*m2= > [m1*m1']*c'*[m2'*m2]=m1''*c'*m2'' > This is remindful of a technique I used many years ago to reduce the size of the search space for the 2x2x2 problem, and the issue would apply to any cube such as the 4x4x4 with an even number of cubies per edge. That is, in the (2n)x(2n)x(2n) problem you can treat as equivalent any positions of the form (m1)*x*(m2) for m1 and m2 in M, provided only that both of m1 and m2 are rotations or that both of m1 and m2 are reflections. Another (and in some ways better) way to model a (2n)x(2n)x(2n) problem and to reduce the size of the search space is to fix one of the corners and to use the symmetry group which preserves the major diagonal axis which includes the corner which is fixed, but that is a different issue. Dan Hoey showed that (m1)*x*(m2) is equivalent to m'xmc for suitable choices of m and c, for m in M and for c in C (the set of 24 rotations). Requiring that m1 and m2 both be rotations or both be reflections is necessary because you really can't turn the corners inside out on a physical cube. Herbert does not impose the same restriction on both of m1 and m2 being rotations or reflections because his third coordinate applies only to the edges, and the edges can indeed be turned inside out on a physical cube, namely with the Pons Asinorum maneuver. So for this case, (m1)*x*(m2) is equivalent to m'xmc if m1 and m2 are both rotations or both reflections, and is equivalent to m'xmcv if they are not, where v is the central inversion of the edges (essentially, the Pons Asinorum applied to the edges). I used to talk about 1152-fold symmetry for the 2x2x2 (1152=24*48). Herbert's approach for the third coordinate yields a 2304-fold reduction in the search space (2304=48*48). However, the reductions in the search space in the two cases are not really dealing with quite the same issue. In the case of 1152-fold symmetry for the 2x2x2, there are (up to) 1152 equivalent positions which are the same distance from Start. If I am understanding Herbert's technique correctly, when positions are equivalent in the third coordinate, there are (up to) 2304 positions of the edges for which the distance from Start has the same lower bound. (Maybe I should say "the same non-trivial lower bound", because (for example) zero would be a lower bound for all positions.) ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us Pellissippi State Technical Community College From cube-lovers-errors@mc.lcs.mit.edu Thu Dec 17 15:55:31 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA21935 for ; Thu, 17 Dec 1998 15:55:29 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 17 Dec 1998 10:02:24 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Re : Re: Optimal Cube Solver In-Reply-To: To: Alchemist Matt Cc: Cube Lovers Message-Id: On Tue, 08 Dec 1998 18:37:02 -0500 (EST) Alchemist Matt wrote: > This question is directed to both Herbert and Mike Reid in case he's > reading this list: With all this discussion of the "Professor Cube" > lately, how hard would it be to extend either Optimal cube solving program > to handle 4x4x4 and 5x5x5 cubes in addition to the traditional 3x3x3? > Considering reasonable table files (50 - 100 mb), how much longer would > the computation time be extended by. If either of you would find the time > to implement this modification, I would be very interested in trying out > the program. Mike Reid has already answered this question in the negative with respect to optimal solvers, based on the huge size of the search spaces that would be involved. For several years, I have wondered about the same thing with respect to a God's Algorithm search of a Start rooted tree (how many positions are one move from Start, how many are two moves from Start, etc.). You could obviously get a few moves from Start, but I don't think you would get very far. For example, with my existing program, I think maybe I could get five or six moves from Start with the 4x4x4 or the 5x5x5. However, I have been reluctant to deal with either the 4x4x4 or the 5x5x5 for several reasons. One is that the programming is not quite as easy as it might seem, or at least not for my program the way it is written. In principle, all I would have to do is replace the existing tables for the permutations which generate the 3x3x3 with the corresponding tables for the 4x4x4 and the 5x5x5 and everything should just work. However, my program contains optimizations previously described on Cube-Lovers which are very dependent on the edge and corner structure of the 3x3x3. For the larger problems, I would have to add a bit (not a lot, but a bit) of new code to deal with new kinds of pieces. Secondly, in the case of the 4x4x4 I would have to deal with might be called rotational equivalences, for example that RrL'l' (capital letters denote moving the outer layers and lower case letters denote moving the inner layers) would normally treated as being equivalent to the Start state. Both ways I know how to do it would require some reprogramming, especially in light of the same existing optimizations I talked about before with respect to the 3x3x3. Namely, I could treat rotations as being equivalent, so that x is equivalent to all positions of the form xc for c in C. Or I could fix one of the corners. Thirdly, I would have to deal with what might be called invisible equivalences, where pieces can be moved without the movement being visible on a physical cube. In the case of the 4x4x4 (for example), the four "face center" facelets on each face can move with respect to each other (subject to parity constraints) without the movement being visible. I would think that you would want to treat such differences as being equivalent. Actually, I think that an optimal solver for the 4x4x4 or the 5x5x5 would need to deal with some of the same issues, in addition to the huge size of the search spaces that was pointed out by Mike Reid in his original response to this question. ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us Pellissippi State Technical Community College From cube-lovers-errors@mc.lcs.mit.edu Thu Dec 17 19:18:53 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA22644 for ; Thu, 17 Dec 1998 19:18:53 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36796BF2.5B57@hrz1.hrz.tu-darmstadt.de> Date: Thu, 17 Dec 1998 21:39:14 +0100 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: Jerry Bryan Cc: Cube Lovers Subject: Re: Optimal Cube Solver References: Jerry Bryan wrote: > > On Mon, 07 Dec 1998 19:30:49 +0100 Herbert Kociemba > wrote: > > > > > The third coordinate describes the edge permutation. Because there are > > 12! coordinate values, even reduction by 48 symmetries still gives too > > many coordinate values. So for use in a turntable we define two edge > > permutations a and b equivalent, if a=m1*b*m2, were m1 and m2 are in M. > > In this way we get 208816 equivalence classes c. If now m1*c*m2 is a > > (not necessarily unique) representation of an edge permutation applying > > a faceturn T is done like that: > > > > (m1*c*m2)*T = m1*c*[m2*T*m2^-1]*m2 = m1*[c*T']*m2= > > [m1*m1']*c'*[m2'*m2]=m1''*c'*m2'' > > > I used to talk about 1152-fold symmetry for the 2x2x2 > (1152=24*48). Herbert's approach for the third coordinate > yields a 2304-fold reduction in the search space > (2304=48*48). However, the reductions in the search space > in the two cases are not really dealing with quite the same > issue. In the case of 1152-fold symmetry for the 2x2x2, > there are (up to) 1152 equivalent positions which are the > same distance from Start. If I am understanding Herbert's > technique correctly, when positions are equivalent in the > third coordinate, there are (up to) 2304 positions of > the edges for which the distance from Start has the same > lower bound. (Maybe I should say "the same non-trivial > lower bound", because (for example) zero would be a lower > bound for all positions.) I do not use the equivalence in the third coordinate as an index in a pruning table. On the contrary, I have to "expand" the coordinate again by a factor of 48 to get equivalence classes, which have the same distance from start and from which I built the pruning table. But due to the large size (12!) of edge permutations, it seems a good way (and I see no other way) to keep track of the edge-permutation-coordinate with only a few table-lookups. I now have enough RAM (128MB) to implement a pruning table for all possible coordinates of the first phase of my Two-Phase-Algorithm, which brings the cube into the subgroup H=. This is what Mike Reid already did about one year ago and which seems powerful enough even to be used as an Optimal Solver (omitting phase 2, in which the edge- and cornerpermutations are restored). Due to this power I think of implementing a "static" phase 2 only with a table which stores the edge- and corner permutations of all positions up to maybe 5 face-turns in H from start. Using the approach for the edge permutation from above,the computation of the starting position of phase 2 should be very fast. In the implementation currently used, I have to switch back from the coordinate-representation of the cube in phase 1 to a more "physical" representation using edges and corners, apply the maneuver generated in phase 1 and then compute the starting coordinates of phase 2. In the new approach only coordinates could be uses. Herbert From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 18 11:33:50 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA24449 for ; Fri, 18 Dec 1998 11:33:50 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <002c01be2a01$f6ba7020$7ac4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: Cc: "Nicholas Bodley" , "Charlie Dickman" Subject: Re: Newer mechanism? (Was: Re: re-assembling a 2x2x2?) Date: Thu, 17 Dec 1998 21:11:22 -0000 Nicholas Bodley wrote (17 December 1998) > > Would really *love* to know whether there is a newer and different >mechanism. As a somewhat casual student of these mechanisms, I've >come to realize that for all "sizes", more than one mechanism is >possible. > According to the reports on the patent case brought against Ideal for infringement of the Nichols patent (Moleculon Research Corp v. CBS, Inc) there were two Ideal 2x2x2 cubes, both sold as the Rubik's Pocket Cube, but one from Taiwan and one from Japan. The Japanese version used an internal sphere, which could well be the version with the Philips screw referred to by Charlie Dickman, since it sounds like the inside of a 4x4x4. The Taiwanese version is less clearly described - the internal faces are said to form a tongue and groove mechanism - but probably also had an internal spider like the conventional 3x3x3 - is this Nicholas Bodley's version? Incidentally, by the time the case had been up and down to the Appeals court a couple of times, the final decision, in 1989, was that just these two forms infringed the patent. The 3x3x3 and 4x4x4 were held not to infringe. Roger Broadie From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 18 14:53:20 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA25180 for ; Fri, 18 Dec 1998 14:53:19 -0500 (EST) Precedence: bulk Mail-from: From cube-lovers-request@life.ai.mit.edu Thu Dec 17 22:07:25 1998 Date: Thu, 17 Dec 1998 22:06:01 -0500 From: michael reid Message-Id: <199812180306.WAA21451@cauchy.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Optimal Cube Solver herbert writes > I do not use the equivalence in the third coordinate as an index in a > pruning table. On the contrary, I have to "expand" the coordinate again > by a factor of 48 to get equivalence classes, which have the same > distance from start and from which I built the pruning table. But due to > the large size (12!) of edge permutations, it seems a good way (and I > see no other way) to keep track of the edge-permutation-coordinate with > only a few table-lookups. > I now have enough RAM (128MB) to implement a pruning table for all > possible coordinates of the first phase of my Two-Phase-Algorithm, which > brings the cube into the subgroup H=. This is what Mike > Reid already did about one year ago and which seems powerful enough even > to be used as an Optimal Solver (omitting phase 2, in which the edge- > and cornerpermutations are restored). Due to this power I think of > implementing a "static" phase 2 only with a table which stores the edge- > and corner permutations of all positions up to maybe 5 face-turns in H > from start. > Using the approach for the edge permutation from above,the computation > of the starting position of phase 2 should be very fast. In the > implementation currently used, I have to switch back from the > coordinate-representation of the cube in phase 1 to a more "physical" > representation using edges and corners, apply the maneuver generated in > phase 1 and then compute the starting coordinates of phase 2. In the new > approach only coordinates could be uses. herbert, you might be interested in what my sub-optimal program (the one based on your two-stage algorithm) does about edge permutations. i have this extra coordinate i call "sliceedge", (really this is just another coset space) which considers the locations of four distinguishable edges. there are 12*11*10*9 = 11880 possibilities for this coordinate. when the cube is entered, it calculates the corresponding coordinate for edges in the U-D slice, also for edges in the F-B slice, and also for the R-L slice. then i have lookup tables to tell me how this coordinate transforms under turns. this lookup table is 18 * 11880 shorts = 427680 bytes. when stage 2 is reached, i have a lookup table that maps this coordinate into permutations of the four U-D slice edges. actually, only 24 of the entries are valid, but only these occur, since we've reached stage 2. this lookup table is 11880 chars. there's also a lookup table to transform the "sliceedge" coordinate into another coordinate, which gives the locations of four distinguishable edges among the eight U and D edges. this coordinate has 8*7*6*5 = 1680 possibilities, and the lookup table is 11880 shorts. the big lookup table is the one that takes two of these last coordinates and transforms it into a permutation of the eight U and D edges. this table has 1680 * 1680 shorts = about 5.5 megabytes. most of the entries are garbage, only 40320 = 8! actually occur, since we've reached stage 2. so for about 6 megabytes of space, all the edge permutations are done with lookup tables. i haven't actually calculated how much of a speed up this is, but it's probably good. mike From cube-lovers-errors@mc.lcs.mit.edu Fri Dec 18 15:30:11 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA25304 for ; Fri, 18 Dec 1998 15:30:10 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <5B9619E72C59D211B22100A0C99CC4632EEE9E@www.evangel.edu> From: "CRAWFORD, SCOTT" To: Cube-Lovers@ai.mit.edu Subject: Snake Date: Thu, 17 Dec 1998 19:50:21 -0600 This may be a little off topic, but I've recently fell in love with the snake, making many shapes I'd never even thought of. Are there any websites or archives of different snake patterns? Thanks Scotte From cube-lovers-errors@mc.lcs.mit.edu Mon Dec 21 14:00:52 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA01463 for ; Mon, 21 Dec 1998 14:00:52 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <367BDD1D.DE6@hrz1.hrz.tu-darmstadt.de> Date: Sat, 19 Dec 1998 18:06:37 +0100 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: cube-lovers@ai.mit.edu Cc: michael reid Subject: Re: Optimal Cube Solver References: <199812180306.WAA21451@cauchy.math.brown.edu> michael reid wrote: > herbert, you might be interested in what my sub-optimal program > (the one based on your two-stage algorithm) does about edge > permutations. i have this extra coordinate i call "sliceedge", > (really this is just another coset space) which considers the > locations of four distinguishable edges. there are 12*11*10*9 = 11880 > possibilities for this coordinate. when the cube is entered, it > calculates the corresponding coordinate for edges in the U-D slice, > also for edges in the F-B slice, and also for the R-L slice. > then i have lookup tables to tell me how this coordinate transforms > under turns. this lookup table is 18 * 11880 shorts = 427680 bytes. > > when stage 2 is reached, i have a lookup table that maps this > coordinate into permutations of the four U-D slice edges. actually, > only 24 of the entries are valid, but only these occur, since we've > reached stage 2. this lookup table is 11880 chars. I already made some experience with the "sliceedge"-coordinate before. I built it in the way: 24*position of the 4 edges + permutation of the 4 edges, where the position range is from 0 to 494 and permutation ranges from 0 to 23. In this way when reaching stage 2, the "sliceedge"-coordinate automatically is in the range from 0 to 23 and you need no lookup table at all. > there's also a lookup table to transform the "sliceedge" coordinate > into another coordinate, which gives the locations of four > distinguishable edges among the eight U and D edges. this coordinate > has 8*7*6*5 = 1680 possibilities, and the lookup table is 11880 shorts. > > the big lookup table is the one that takes two of these last coordinates > and transforms it into a permutation of the eight U and D edges. > this table has 1680 * 1680 shorts = about 5.5 megabytes. most of > the entries are garbage, only 40320 = 8! actually occur, since we've > reached stage 2. This seems an interesting approach. Using the edge-permutation-coordinate in the way I described it before, I need about 20MB for the lookup-table which tells the coordinate-tranformation under turns, which is quite a lot. Maybe I also try your method. Herbert From cube-lovers-errors@mc.lcs.mit.edu Mon Dec 21 14:52:35 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA01635 for ; Mon, 21 Dec 1998 14:52:34 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 20 Dec 1998 16:41:43 -0500 (EST) From: Nicholas Bodley To: Roger Broadie Cc: Cube Mailing List , Charlie Dickman , Mark Glusker Subject: Re: Newer mechanism? (Was: Re: re-assembling a 2x2x2?) In-Reply-To: <002c01be2a01$f6ba7020$7ac4b0c2@home> Message-Id: On Thu, 17 Dec 1998, Roger Broadie wrote: (Interesting to read about the lawsuit...) }Nicholas Bodley wrote (17 December 1998) }inside of a 4x4x4. The Taiwanese version is less clearly described - }the internal faces are said to form a tongue and groove mechanism - }but probably also had an internal spider like the conventional 3x3x3 - }is this Nicholas Bodley's version? In the mechanism I know for a 2X2X2 Cube, at its center is a piece like a jack, that is, one of the pieces in the traditional game, but without the knobs at the ends. You could also think of it as three rods intersecting at a common point, and mutually orthogonal; it's as if you had plus and minus x, y, and z axes defined by the directions of the rods. These create the axes of revolution for one half relative to the other. The cubies are hollow, and their mating faces have curved cutaways. To keep the cubies from moving too far from each other, 12 "clips" extend from the center outward. If you think of a deeply-grooved pulley, cut pie-style into quarters, you have a general idea. The curved-cutout edges of the cubies fit between two curved, parallel sides of the "clips". Finally, the "clips" are kept engaged with the cubies either directly by square cross-section extensions of the center "jack", or by hollow square rods that pivot on (smaller) cylindrical extensions. Just as the ball in a 4^3 is locked to one half, the "jack" is, also. The big problem with this mechanism is that unless the parts can deform sufficiently without breaking (the actual case; they can do so), it's impossible to assemble or to disassemble as molded. If it were made of metal, it couldn't be assembled without design changes. Illustrations are really needed here; this mechanism is a challenge to describe understandably! I'd think that the internal ball uses a variant of the tongue and groove scheme, if it's like the 4^3. |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer indusztry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 22 12:31:20 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA03877 for ; Tue, 22 Dec 1998 12:31:18 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 20 Dec 1998 21:18:09 -0500 (EST) From: Nicholas Bodley To: "CRAWFORD, SCOTT" Cc: Cube-Lovers@ai.mit.edu Subject: Re: Snake In-Reply-To: <5B9619E72C59D211B22100A0C99CC4632EEE9E@www.evangel.edu> Message-Id: The Snake is delightful; you can do some interesting investigations by starting with a straight config., and twisting each consecutive joint according to a pattern. Just as long as you don't get physical interferencies, you see some modestly-interesting shapes. It's also worth a bit of casual effort to create a "ball". All of these things are, however, trivially easy to many of the subscribers to this list. The snake is for mental relaxation! |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 22 15:28:37 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA04251 for ; Tue, 22 Dec 1998 15:28:36 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 22 Dec 1998 16:40:58 +0900 (JST) Message-Id: <199812220740.QAA00692@soda3.bekkoame.ne.jp> To: cube-lovers@ai.mit.edu From: Ishihama Yoshiaki Subject: 5DRubikCube I have made simulation of 5D RubikCube(2x2x2x2x2). This is consisted of 2x2x2x2x2=32 5DCubes. This is for Macintosh only. I will not convert this program to java because it is too troublesome. It is on my HomePage. //----------------------------------------// Ishihama Yoshiaki (Tokyo Japan) E-mail: ishmnn@cap.bekkoame.ne.jp HomePage : http://www.asahi-net.or.jp/~hq8y-ishm/ //----------------------------------------// [Moderator's note: This is the third announcement of this website this month. For all further developments, check the website. ] From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 22 18:44:01 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA04933 for ; Tue, 22 Dec 1998 18:44:00 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 22 Dec 1998 18:37:57 -0500 From: michael reid Message-Id: <199812222337.SAA26516@adams.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Optimal Cube Solver i'm glad that herbert brought up this issue of edge transformations. because now that i think about this again, i realize that my tables can be reduced dramatically. i described my tables: > there's also a lookup table to transform the "sliceedge" coordinate > into another coordinate, which gives the locations of four > distinguishable edges among the eight U and D edges. this coordinate > has 8*7*6*5 = 1680 possibilities, and the lookup table is 11880 shorts. > > the big lookup table is the one that takes two of these last coordinates > and transforms it into a permutation of the eight U and D edges. > this table has 1680 * 1680 shorts = about 5.5 megabytes. most of > the entries are garbage, only 40320 = 8! actually occur, since we've > reached stage 2. since this big table is sparse, we don't need most of it. what i should do is have another table (11880 char's) to transform "sliceedges" into permutations of four edges. the location of the four R-L slice edges determines the location of the four F-B slice edges, so we only need to know how they're permuted. thus the big table can be replaced by one with 1680 * 24 shorts that gives the permutation of the eight U and D edges. it no longer would have error-checking (i.e. making sure we don't get an invalid entry in the big table), but that could be installed with another simple table lookup, if desired. with this new mechanism, only about 543K of tables would be needed, the largest being a lookup table which tells how "sliceedges" transform under face turns. this is much better than the 6 megabytes of tables i'm currently using. i don't know why i didn't think of this earlier! mike From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 23 17:40:01 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA08319 for ; Wed, 23 Dec 1998 17:40:01 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36816C59.1204@hrz1.hrz.tu-darmstadt.de> Date: Wed, 23 Dec 1998 23:19:05 +0100 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: cube-lovers@ai.mit.edu Cc: michael reid Subject: Re: Optimal Cube Solver References: <199812222337.SAA26516@adams.math.brown.edu> michael reid wrote: > since this big table is sparse, we don't need most of it. what i > should do is have another table (11880 char's) to transform "sliceedges" > into permutations of four edges. the location of the four R-L slice > edges determines the location of the four F-B slice edges, so we only > need to know how they're permuted. thus the big table can be replaced > by one with 1680 * 24 shorts that gives the permutation of the eight > U and D edges. it no longer would have error-checking (i.e. making > sure we don't get an invalid entry in the big table), but that could > be installed with another simple table lookup, if desired. > > with this new mechanism, only about 543K of tables would be needed, > the largest being a lookup table which tells how "sliceedges" > transform under face turns. this is much better than the 6 megabytes > of tables i'm currently using. i don't know why i didn't think of > this earlier! > > mike Is it necessary to use the table for the map from the "sliceedges" to the 1680 "4 out of 8"-coordinate at all? I think you constructed this "helper"-coordinate, because a 11880*11880 table-size was too big and 1680*1680 was reasonable. But 11880*24 also is small (just twice as much as the lookup table which tells how "sliceedges" transform under face turns). In the way I construct the sliceedge-coordinate x, the x mod 24 gives the permutation part, x/24 the location part. So I could compute the edge-coordinate at the start of phase 2 with M[x][y mod 24], where x and y are the RL- and FB-sliceedge coordinates and M is a table with 11880*24 shorts. So I need only one tablelookup to get the coordinate. Herbert From cube-lovers-errors@mc.lcs.mit.edu Thu Dec 24 11:35:18 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA09905 for ; Thu, 24 Dec 1998 11:35:17 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 23 Dec 1998 19:07:26 -0500 From: michael reid Message-Id: <199812240007.TAA28326@adams.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Optimal Cube Solver herbert writes > Is it necessary to use the table for the map from the "sliceedges" to > the 1680 "4 out of 8"-coordinate at all? no, i guess the "4 out of 8" coordinate is not really needed. good point. the tradeoff would be one extra table lookup versus having tables that are 455K larger. i don't know if there's a clear choice between these two options, but either is much better than the 6 megabytes i'm using now! mike From cube-lovers-errors@mc.lcs.mit.edu Mon Dec 28 12:21:48 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA17014 for ; Mon, 28 Dec 1998 12:21:48 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Sun Dec 27 13:14:59 1998 Message-Id: <003301be31c4$60a798e0$335755ca@Uwe.ue.net> From: uwe@ue.net (Uwe Meffert) To: "Cube-Lovers" Subject: ADDITIONAL FEATURES FOR OUR PUZZLE SITE Date: Mon, 28 Dec 1998 01:47:54 +0800 Requesting Help: For 1999 I will be adding a lot of additional interactive puzzles & games to the "Meffert's World of Puzzles" site in several puzzle categories enabling a person to challenge a friend or send an interactive puzzle greeting. Each Puzzle Challenge will be made available for 30 days, with actual time taken to solve it being relayed back to the challenger. After the Puzzle Challenge is received, the challenge can be accepted or rejected or a counter challenge made. Puzzle Games will also be available online. I am hoping to have a very large range of categories from very simple games & puzzles such as electronic tik tak toe (from single layer to triple layer) with some additional new features, the traditional 8 and 15 piece sliding puzzles with talking help function, the Orbix & Orbix Junior (12 & 6 lights in 3 colors) Electronic Reversy etc. etc. etc. to more complex puzzles & games. Whilst I have developed some of these already I will need a lot of help from puzzlers worldwide to make this the best FREE interactive really Great Puzzle and Games site for 1999. Please spread the word to anyone you know that can contribute and other puzzle site Web Editors that may let me use some of their existing puzzles. I hope to have very unique graphics and concepts to really popularize puzzles again, this time as a Free service over the Internet. To appeal to the majority of the people the puzzles must not be too hard, yet still be challenging. Also, I am presently looking for a new Web Editor for our site, our present Webmaster Andrew Southern is unfortunately fully tied up until July with his studies, please pass the word along to anyone you think my be suitable. Many Thanks Warm regards and a Very Happy New Year to All. Uwe Uwe Meffert P.O. Box 24455, Aberdeen, Hong Kong. Tel. 852-2518-3080, Fax. 852-2518-3282 Email:- uwe@ue.net Sites: www.bloodpressure.org, www.cmd-diagnostics.com www.ue.edu www.ue.net www.ue.net/mefferts-puzzles From cube-lovers-errors@mc.lcs.mit.edu Mon Dec 28 19:00:54 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA19705 for ; Mon, 28 Dec 1998 19:00:53 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3685267B.D1459EC7@geocities.com> Date: Sat, 26 Dec 1998 10:10:03 -0800 From: Jono Reply-To: BagelBoyJ@geocities.com Organization: Fine Finger Design To: cube-lovers@ai.mit.edu Subject: Other Cubes Hi, cube lovers. I have a few questions. Does anyone know if Erno Rubik is still alive? About 4 years I vaguely remember seeing a large star-shaped rubiks puzzle. Does anyone know where I can find one? I am also looking for a 4x4x4 and a 5x5x5 cube. Where can I find one? Thanks to all. -Jono [ Moderator's note: Cube-lovers-request gets a lot of requests for information on finding 4^3 and 5^3 puzzles. I'm pretty sure there is no source of 4^3 puzzles, except for the occasional auction. Last I heard Uwe Meffert sells 5^3 puzzles at http://www.ue.net/mefferts-puzzles/ --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 29 15:00:41 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA22498 for ; Tue, 29 Dec 1998 15:00:41 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 29 Dec 1998 02:22:08 -0500 (EST) From: Nicholas Bodley Reply-To: Nicholas Bodley To: Jono Cc: cube-lovers@ai.mit.edu Subject: Re: Other Cubes In-Reply-To: <3685267B.D1459EC7@geocities.com> Message-Id: On Sat, 26 Dec 1998, Jono wrote: }Hi, cube lovers. I have a few questions. }Does anyone know if Erno Rubik is still alive? Quite likely. There's a Website that might help you find out: http://www.rubiks.com Try a Web search (I like the meta-search engines; Metasearch and Metafind are a couple). }About 4 years I vaguely remember seeing a large star-shaped }rubiks puzzle. It might well have bees Alexander's Star. As to finding one, sorry to say, I can't help. Rather sure it wasn't a Rubik design, though. It was harder to manipulate mechanically than one might like. Not sure, but I think I've seen it it a store. You might try a Web puzzle dealer. (...Puzzletts.com ?) } Does anyone know where I can find one? I am also looking for a 4x4x4 }and a 5x5x5 cube. Where can I find one? For the 5^3, in addition to Meffert, as Dan said, Dr. Christoph Bandelow, in Germany, was selling them, as well, I'm almost certain. The store [The Games People Play] on Mass. Ave. in Cambridge, Mass., might have them in stock. Sorry, but I've lost track of Dr. Bandelow's address. My general impression is that there's enough interest in the 5^3 to have revived production, although it could have been just one big run. Fwiw, (honestly, not much!), my experience regarding the 4^3 agrees with Dan's comments. }[ Moderator's note: Cube-lovers-request gets a lot of requests for } information on finding 4^3 and 5^3 puzzles. I'm pretty sure there } is no source of 4^3 puzzles, except for the occasional auction. } Last I heard Uwe Meffert sells 5^3 puzzles at } http://www.ue.net/mefferts-puzzles/ --Dan ] } |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 29 20:15:59 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA23142 for ; Tue, 29 Dec 1998 20:15:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199812292316.SAA06321@life.ai.mit.edu> From: "Christoph Bandelow" To: cube-lovers@ai.mit.edu Date: Wed, 30 Dec 1998 00:14:50 +0000 Subject: Availability of 5x5x5 cubes and other Rubik type puzzles On Tue, 29 Dec 1998, Nicholas Bodley wrote about the availability of 5x5x5 cubes and other puzzles: > Sorry, but I've lost track of Dr. Bandelow's address. May I help without being too much vituperated for making an unseemly advertisement? Christoph Bandelow's email address is Christoph.Bandelow@ruhr-uni-bochum.de He does not only sell excellent 5x5x5 Magic Cubes (the good old ones made in Hong Kong, not in mainland China), but also Magic Dodecahedra, Skewbs, Pyraminxes, Impossiballs, various Puzzle Balls, Mach Balls and other Rubik type puzzles and books about those puzzles. It is a pleasure to deal with him for he is quick, absolutely reliable, fair and competent. Free mail order catalog. Christoph -- Christoph Bandelow mailto: Christoph.Bandelow@ruhr-uni-bochum.de http://www.ruhr-uni-bochum.de/mathematik3/bandelow.htm [ Objective testimonials written in the third person are always appreciated. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 29 21:21:03 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA23271 for ; Tue, 29 Dec 1998 21:21:03 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Douglas Zander Message-Id: <199812282147.PAA06517@solaria.sol.net> Subject: ADDITIONAL FEATURES FOR OUR PUZZLE SITE (fwd) To: cube-lovers@ai.mit.edu (cube) Date: Mon, 28 Dec 98 15:47:11 CST I would like to voice my concern over this site. The thing is that not everyone has the latest version of Netscape or IE installed. Many libraries (from which I myself access the WWW) do not allow Java to be installed on their machines nor do they allow sound. The highest browser versions I have access to in any library here in Milwaukee is 3.0 I had gone to this site and I could not play the puzzle that was supposed to be there; nothing showed up on the screen. I just wished to point this out to the creator of the site; in fact, to all creators of puzzle sites. There are, I believe, a significant number of people who use public browsers without Java or sound. Please keep this in mind when designing your sites. Thank you. -- Douglas Zander | dzander@solaria.sol.net | Shorewood, Wisconsin, USA | [Moderator's note: Cube-lovers is not really the place to debate the philosophy of web design. I must agree that for maximum usability, the text on a page should be displayed without requiring images, and that the static images should be displayed with requiring Java. Still, setting up a puzzle simulator without Java is more problematic than we can reasonably ask of a free server, and having a simulation that requires Java is certainly better than none. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 30 10:43:10 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id KAA24411 for ; Wed, 30 Dec 1998 10:43:09 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 29 Dec 1998 23:48:14 -0500 (EST) From: der Mouse Message-Id: <199812300448.XAA02148@Twig.Rodents.Montreal.QC.CA> To: cube-lovers@ai.mit.edu Subject: Re: Availability of 5x5x5 cubes and other Rubik type puzzles >> Sorry, but I've lost track of Dr. Bandelow's address. > Christoph Bandelow's email address is > Christoph.Bandelow@ruhr-uni-bochum.de > He does not only sell [...] but also [...]. It is a pleasure to deal > with him for he is quick, absolutely reliable, fair and competent. > Christoph Bandelow > mailto: Christoph.Bandelow@ruhr-uni-bochum.de > http://www.ruhr-uni-bochum.de/mathematik3/bandelow.htm Heehee! Had me going there until I saw the signature. :-) I have had only one experience dealing with Mr. Bandelow. In that one, I did indeed find him quick, reliable, fair, and competent. (I bought a 5x5x5 and the Cube-family puzzle whose name I forget based on the dodecahedron, the one that turns based on slices made parallel to the faces, passing through edge centres. Interestingly, my experience with the dodecahedral puzzle taught me enough that I can now solve a two-face scramble on the 3x3x3 without leaving the two-face subgroup, which I previously couldn't.) der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Tue Jan 5 17:17:11 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA18103 for ; Tue, 5 Jan 1999 17:17:10 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Wed Dec 30 20:17:39 1998 Message-Id: In-Reply-To: <3685267B.D1459EC7@geocities.com> Date: Wed, 30 Dec 1998 20:26:43 -0400 To: cube-lovers@ai.mit.edu From: Charlie Dickman Subject: Re: Other Cubes >[...]I am also looking for a 4x4x4 and a 5x5x5 cube. Where can I >find one? Jono, I recently saw a 4x4x4 for sale at auction at www.ebay.com. Check it out. Charlie Dickman charlied@erols.com From cube-lovers-errors@mc.lcs.mit.edu Tue Jan 5 17:47:44 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA18165 for ; Tue, 5 Jan 1999 17:47:44 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Chris and Kori Pelley" To: Subject: Rubik's old-timer Date: Fri, 1 Jan 1999 22:44:07 -0500 Message-Id: <001b01be3602$2685f3e0$da460318@CC623255-A.srst1.fl.home.com> Puducky@aol.com asked me to forward the following to this list: I have a 96 year old friend that can do the rubiks cube in less than five minutes, and near the end he doesn't even look at it! I thought this pretty amazing for a man of his age. Do you know anyone I can contact about him? Was wondering if there is a record for his age? Thank you. Puducky@aol.com From cube-lovers-errors@mc.lcs.mit.edu Tue Jan 5 19:10:03 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA18445 for ; Tue, 5 Jan 1999 19:10:02 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990102200254.8149.rocketmail@send104.yahoomail.com> Date: Sat, 2 Jan 1999 12:02:54 -0800 (PST) From: Han Wen Subject: Original Rubik's Cube Query To: Cube Lovers Hi, This may be inappropriate for this list, but I thought a few cube lovers may be interested in this. I was talking to my college buddy the other day, and he was telling me about a curious habit of his mom's of buying x-mas gifts and not giving them away. Instead, the gifts were stowed away in one of their closets like museum pieces. One of these "pieces" is a Rubik's cube. Hmm... Now I became interested. I asked him about it.. he thought it wasn't worth much, the packaging was pristine, looked new. I asked him to look carefully at the packaging. The manufacturer was Ideal, and it has a "1980" and a "Made in Hungary" stamped on it. (i.e. an Original Rubik's Cube, untouched in it's original packaging for almost two decades). I told him it was probably worth more than he thinks. Just curious. Does anyone know how much this little gem is worth? == _________________________________________________________ Han Wen Applied Materials 3050 Bowers Ave, MS 1145 Santa Clara, CA 95054 e-mail: Han_Wen@amat.com / hansker@yahoo.com [Moderator's note: For the past few years there have been rumors flying around the net, and perhaps the news services, about thousands of dollars being paid for vintage unopened cubes, either the Ideal "Rubik's cubes", or the earlier "Hungarian Magic Cube". Some of these rumors may even be true. However, I feel I should warn people against careless speculation, since the Internet is prone to fraud of various forms. ] From cube-lovers-errors@mc.lcs.mit.edu Tue Jan 5 19:59:00 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA18553 for ; Tue, 5 Jan 1999 19:59:00 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3692A126.3FA0@hrz1.hrz.tu-darmstadt.de> Date: Wed, 06 Jan 1999 00:32:54 +0100 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: cube-lovers@ai.mit.edu Cc: michael reid Subject: Your Optimal Solver Mike, I now have a Linux-partition on my PC and I compiled your optimal cube solver on it. It really runs fast, about 30%-40% faster than my own optimal solver which uses the same coordinates. I then compiled your source code with the Microsoft Visual C++ compiler with similar results. (By the way, if there other users of the Wintel platform who are interested in Mikes program I could send the program code to the Cube Lovers Archives, its only 50KB). The main reason for the different performance is the fact, that during the tree search I only hold one cube in memory and I do not use an array for the cube-coordinates. But then I had another idea, which was not implemented in my program and which does not seem to be implemented in yours and which significantly increased the performance of my program (about 20%) with a few lines of code (but I think it only works in face-turn-metric): You use the lines similar to if (p_node[1].remain_depth1 except at the very beginning of the search). In this case, if we for example had applied the move R, we need not to check R2 and R' any more but we can continue with another axis. In the case of the quarter-turn-metric, if we had applied R, we still had to check R' because the distance of the two resulting states from start can differ by 2. Herbert From cube-lovers-errors@mc.lcs.mit.edu Thu Jan 7 13:53:48 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA29288 for ; Thu, 7 Jan 1999 13:53:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 6 Jan 1999 23:02:32 -0500 From: michael reid Message-Id: <199901070402.XAA18140@cauchy.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Your Optimal Solver herbert writes > You use the lines similar to > > if (p_node[1].remain_depth > which means tree pruning and we apply the next move in this depth. > > An analysis shows, that the case (p_node[1].remain_depth happens quite often (while p_node[1].remain_depth for n>1 except at the very beginning of the search). In this case, if we > for example had applied the move R, we need not to check R2 and R' any > more but we can continue with another axis. interesting idea. when i get a chance i'll see if i can also get a performance boost using this idea. for quarter turns, there is something similar i can do, but this is only because of the method i used for quarter turns. namely, i don't ever do R R , instead, i do R2 and count it as two moves. if applying the move R results in a branch of the tree that gets pruned, then we do not have to try R2. however, if i used a different method for quarter turns, where i only make one move at a time, then the R2 branch would be a sub-branch of the R branch. thus it would be pruned automatically. this suggests that it might be better to use this latter method for searching the tree. (the only reason i didn't do this is that i wanted to use one function for both quarter turns and face turns.) another idea, suggested to me by rich korf, is to use the line if ((node.remain_depth < ELEVEN) && (node.remain_depth < DIST)) continue; /* prune this branch */ where ELEVEN is just the constant 11, and DIST is the macro to look into the big table for the distance of the current coset. if the first part of the expression is TRUE , then we evaluate the second part. in this case we did a tiny bit of extra work to evaluate the first part. but if the first part is FALSE , then we save some work by not looking into the table. we lose a little bit of pruning (there are some cosets at distance 12) but this is very small. rich explained (if i understood correctly) that every look into the big table is expensive, because it will pull a small piece of the table into cache. but this piece is unlikely to be used again soon, so it probably displaced some more useful stuff from cache. the DIST macro is also a complicated expression, so it is also expensive in that way. when i tried this, i didn't measure any significant performance boost (< 1%). but the cache benefit would be more noticeable for longer searches, so perhaps my test was just too short. it also depends upon your DIST macro (or corresponding code); i think rich had more processing to do besides looking into the table. and it may also depend on the size of your secondary cache. i do have this in my huge optimal solver, so it must have given some improvement there, but i don't remember how much. i had to do lots of tweaking for performance issues on this program. herbert, if you have a program that uses the exact same coordinates as mine, you will find it amusing to try the positions * position created by R2 F' R2 F2 D2 F' R2 F2 R2 D2 F' D2 F' * inverse of the above position. and noticing the huge difference. because of this, i thought about maybe solving either the input position or its inverse, depending upon which should be faster. my experiments showed that it wasn't easy to predict which would be easier by looking only at the distances of the 3 initial cosets. but perhaps doing a mini-search on each, and looking at how many nodes they spawn would give a better guess. of course, we can't expect to get the kind of performance boost suggested by the extreme example above, but we might get something. then i had a more ambitious idea: maybe we could prune the search tree by having the program realize "the inverse of this position is too far from start". the conclusion i eventually arrived at was that it wouldn't be possible to keep track of the coset of the inverses by using transformation tables. so this idea probably won't work. mike From cube-lovers-errors@mc.lcs.mit.edu Wed Jan 13 18:08:03 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA27220 for ; Wed, 13 Jan 1999 18:08:03 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 12 Jan 1999 23:18:11 +0000 From: David Singmaster To: cube-lovers@ai.mit.edu Message-Id: <009D220A.48E392F4.2@ice.sbu.ac.uk> Subject: Clinton and Rubik? Date: Sun, 10 Jan 1999 09:28:19 -1000 From: drogers@math.hawaii.edu (Douglas Rogers) Message-ID: <199901101928.JAA01661@knuth.hawaii.edu> To: wpr3@tutor.open.ac.uk Subject: From Monica Lewinsky to the Roubik Cube Bill, Here is a quotation that might be appropriate for The Mathematical Gazette. Senator Trent Lott (R-Missouri), Senate Majority Leader, speaking on 6th January, 1999, to reporters about arrangements for the impeachment of the President, declared, ``All sides of this Rubik's cube have been talked about. We hope to have this all resolved tomorrow''. [As quoted in The New York Times for 7th January, p. A1.] The natural inference here is that Senators have a version of the Rubik cube on which the US President and friends are depicted, the object of the exercise being to twist things so as to get the US President into or out of compromising positions - it was thoughtful of the Senate Majority Leader to spare us the details, and to leave this to our imagination. DGR. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Thu Jan 14 13:12:53 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA02647 for ; Thu, 14 Jan 1999 13:12:53 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Clinton and Rubik? Date: 14 Jan 1999 14:43:30 GMT Organization: California Institute of Technology, Pasadena Message-Id: <77kvqi$o6k@gap.cco.caltech.edu> References: David Singmaster writes: > Senator Trent Lott (R-Missouri), Senate Majority Leader, >speaking on 6th January, 1999, to reporters about arrangements >for the impeachment of the President, declared, ``All sides >of this Rubik's cube have been talked about. We hope to have >this all resolved tomorrow''. [As quoted in The New York Times >for 7th January, p. A1.] Of course, claiming that they can REsolve it implies that it was already SOLVED at some point in the past ... :-) -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- "... I guess that explains why you're automatically dogmatic!" From cube-lovers-errors@mc.lcs.mit.edu Mon Jan 25 14:16:47 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA15939 for ; Mon, 25 Jan 1999 14:16:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Sun Jan 24 00:08:55 1999 Date: Sun, 24 Jan 1999 00:07:11 -0400 (EDT) From: Jerry Bryan Subject: Re: Corners Only, Ignoring Twist In-Reply-To: To: Cube-Lovers Reply-To: Jerry Bryan Message-Id: On Sun, 27 Sep 1998, Jerry Bryan wrote: > In developing a no-twist, no-flip version of the program, I decided to try > it out on the corners only case. Here are the results. Here is one more tidbit on this subject. The program which performed the God's Algorithm search for the no-twist corners only case produced a summary by symmetry class. I was surprised to note that there were two positions for which Symm(x)=M. Normally, there is only one position for the corners where Symm(x)=M, namely the position which fixes all the corners (i.e., Start). However, if twists are ignored, then the central inversion of the corners has the property that Symm(x)=M. This is analogous to the Pons Asinorum position where the edges are centrally inverted. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Mon Feb 1 15:08:06 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA14298 for ; Mon, 1 Feb 1999 15:08:05 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Sun Jan 24 13:57:32 1999 Message-Id: <19990124185842.5788.rocketmail@send103.yahoomail.com> Date: Sun, 24 Jan 1999 10:58:42 -0800 (PST) From: Han Wen Subject: Query on Octagon Cube Edge Parity Problem To: Cube Lovers Hi, I ran into an unusual scenario with the Octagon cube recently where only ONE edge piece was flipped and all the other pieces were positioned and oriented properly. This is bizarre of course, because with a Rubik's cube, this is an impossible scenario; there must be a minimum of TWO edge pieces flipped. Does anyone understand the redundancy that allows this strange edge parity problem? And I guess, how to solve it. I lamely mixed the cube up again, resolved until the problem "went away". For those who may not be familiar, the Octagon cube is a variant of the Rubik's Cube. The cube is organized by color into 8 columns of three cublets: corner, edge, corner. If you look at the top face you see that the half of the corner cublets have been cut away so the the face forms an octagon instead of a square. This octagon shape is extended down through the middle and bottom layer, so that the puzzle looks like an octagon "tube". There are a total of 10 colors, two for the top and bottom faces, and 8 for the eight columns of (top-middle-bottom) cublets. == _________________________________________________________ Han Wen Applied Materials 3050 Bowers Ave, MS 1145 Santa Clara, CA 95054 e-mail: Han_Wen@amat.com / hansker@yahoo.com From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 2 17:09:46 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA18816 for ; Tue, 2 Feb 1999 17:09:46 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Tue Jan 26 09:45:56 1999 Date: Tue, 26 Jan 1999 14:45:54 +0000 From: "Collins, Lindon" Subject: Middle layer last? To: "'Cube Lovers'" Message-Id: Sorry if I'm retreading old ground but I'm new to this. 1. I remember reading somewhere an article that advocated solving the middle layer of the cube last. I have got some fairly short moves to place cubes from the middle layer onto the bottom layer, but when it comes to solving the middle layer, I seem to be trusting to luck that I have reached a favourable position. I cannot see how I am going to reduce my average number of moves to solve the cube using this method. I think there are two possibilities:- 1. There are some cool moves for solving the middle layer last that I have missed. 2. I should forget about solving the middle layer last, and stick to my usual method (ie. top,middle,bottom) 2. A more general question is: What is the shortest (practical) method for solving the cube that anyone knows of? (keyword: "practical" - don't say 22 moves) Thanks, Lindon Collins Swindon, UK From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 2 17:56:32 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA19088 for ; Tue, 2 Feb 1999 17:56:32 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 1 Feb 1999 17:16:54 -0500 From: michael reid Message-Id: <199902012216.RAA07304@chern.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Query on Octagon Cube Edge Parity Problem Cc: hansker@yahoo.com > I ran into an unusual scenario with the Octagon cube recently where > only ONE edge piece was flipped and all the other pieces were > positioned and oriented properly. This is bizarre of course, because > with a Rubik's cube, this is an impossible scenario; there must be a > minimum of TWO edge pieces flipped. the "octagon" puzzle has some "edges" with only one visible face. namely, these are the U-D layer edges on a cube, which were shaved when the cube was modified in shape. these edges have no visible orientation, so flip one of these along with the edge that's definitely in the wrong orientation. in a similar way, it's possible to get positions that appear to have the wrong permutation parity. there are four vertical columns of two corners and an edge each. these do not have any fixed "home" location, so that any permutation of these also constitutes a "solved" state. (well, at least most people would consider it to be solved.) but swapping two of these columns creates an odd permutation parity. thus you can swap two columns, and also swap a pair of edges or corners, which gives the impression of incorrect parity. for a simple example, do R2 F2 R2 from the solved position. the edges UF and DF have been swapped, and it looks like nothing else has happened. in fact, the FL column has been swapped with the BR column as well. mike [Moderator's note: I hadn't noticed that this had such an obvious answer. Thanks also to Jon Ferro, Steve LoBasso, der Mouse, Guy N. Hurst, Michael Ehrt, and Christ van Willegen for also providing the answer. I've selected Mike Reid's, since he points out the other notable ambiguity of the Octagon. What wasn't noted is that the Spratt wrench can be used to flip the noted edge along with three of the ambiguous edges. --Dan] From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 2 19:27:15 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA19586 for ; Tue, 2 Feb 1999 19:27:15 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36B77B8B.2A223AA5@sgi.com> Date: Tue, 02 Feb 1999 14:26:19 -0800 From: Derek Bosch To: "Collins, Lindon" Cc: "'Cube Lovers'" Subject: Re: Middle layer last? References: well, if you want "simple", the only two moves you really need are: the edge 3-cycle... U2^U2v (UB->DF->UF) and the 2-edge flip... ^U^U^U2vUvUvU2 (flips UF and UB) assuming you are holding the cube so that the left and right faces are solved (where ^ is moving the middle slice up, and v is moving the middle slice down) note, once you get used to those moves, you can create variations that move and flip, like: U'^U'^U2vU'vU these are also REALLY ergonomic - very easy to do rapidly... -- Derek Bosch "A little nonsense now and then (650) 933-2115 is relished by the wisest men"... W.Wonka bosch@sgi.com From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 2 21:16:59 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA20404 for ; Tue, 2 Feb 1999 21:16:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 2 Feb 1999 20:27:26 -0500 Message-Id: <00131725.C22092@scudder.com> From: Jacob_Davenport@scudder.com (Jacob Davenport) Subject: Re: Middle layer last? To: "'Cube Lovers'" 1. I learned the solution of top, middle, and then bottom many years ago. I forgot most of it, so when I asked Kristin Looney to remind me how to do the cube, she showed me her solution, which is top corners, bottom cFrom cube-lovers-errors@mc.lcs.mit.edu Sat Feb 6 01:46:02 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA20404 for ; Tue, 2 Feb 1999 21:16:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 2 Feb 1999 20:27:26 -0500 Message-Id: <00131725.C22092@scudder.com> From: Jacob_Davenport@scudder.com (Jacob Davenport) Subject: Re: Middle layer last? To: "'Cube Lovers'" 1. I learned the solution of top, middle, and then bottom many years ago. I forgot most of it, so when I asked Kristin Looney to remind me how to do the cube, she showed me her solution, which is top corners, bottom corners, top and bottom edges at the same time, then middle edges. It is a much easier solution to do and to teach. A variant of it can be found at http://www.unc.edu/~monroem/rubik.html, although in this variant he is more rigid about how to solve the top and bottom edges. So, I'd forget your original method of top/middle/bottom, because it does not revel in the corner/edge dichotomy of the cube. I only use top/middle/bottom when solving cubes with complicated patterns, such as those at http://www.wunderland.com/WTS/Kristin/CustomCubes.html. 2. The shortest, pratical, method for solving the cube, in my opinion, is the one discussed above. Kristin, who does not have incredibly fast hands, did very well in speed cube competitions when pitted against people who had hot hands but the top/middle/bottom solution. Also, I can teach someone this solution in an hour. -Jacob From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 9 15:30:14 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA04382 for ; Tue, 9 Feb 1999 15:30:14 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 7 Feb 1999 21:18:58 +0000 From: David Singmaster To: reid@math.brown.edu Cc: CUBE-LOVERS@ai.mit.edu Message-Id: <009D3667.F01254DB.8@ice.sbu.ac.uk> Subject: Re: Query on Octagon Cube Edge Parity Problem Similar parity problems can be produced by recolouring a cube. I once sold a cube to someone who came back a few minutes later with two centers exchanged. I accused him of taking it apart, but then I fiddled with it and got it back right, which amazed me even more. Then I discovered that two opposite faces of the cube were colored red! Some time later, I had an example with two adjacent sides having the same color. In 1980, Tamas Varga showed me some cubes with just two colors and I then made up numerous such color variants. E.g. using just two colors, have the three faces of one color meet at an corner, or not meet at a corner (these are the only two ways of coloring the faces with two colors, three faces of each color). Also fun is a three color cube - two opposite sides red, two opposite sides white and two opposite sides blue. Then every corner is red, white, blue - except half of them are red, blue, white. All these are difficult to solve for people who have only done ordinary cubes. In the mid 1980s, Edward Hordern showed me a cube which I recall he said Nob Yoshigahara had invented, but my example was made by Marcel Gillen. This appear to be a 4^3, but when turned, it moves eccentrically. Examination shows that it is a 3^3 with three layers of pieces glued to three adjacent faces. Edward's original example had no colors, so it took some time to solve as one didn't know where pieces went. Further, the eccentric movement causes parts to protrude, making it hard to hold and to move. All in all, a most enjoyable variant. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 9 20:27:47 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA06044 for ; Tue, 9 Feb 1999 20:27:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990208030401.14755.rocketmail@send1e.yahoomail.com> Date: Sun, 7 Feb 1999 19:04:01 -0800 (PST) From: Han Wen Subject: Moves for Solving the Pyramorphix puzzle To: Cube Lovers Hi For those cube masters out there getting bored, you may want to play with Meffert's latest puzzle, the Pyramorphix. It only takes about 1-2 hours to solve, but it provides some Square-1-like entertainment. For those who may not be familiar, the Pyramorphix looks like the Pyraminx's little brother with 4 pieces instead of 9 pieces for each face. However, unlike its big brother, the Pyramorphix turns a lot differently (90 deg rotations), morphing into different shapes as you twist and turn. As you know, with the Pyraminx, you're always rotating little pyramids about one of the 4 tips. However, with the Pyramorphix, when starting out with the pyramid shape, you rotate an edge and its two adjacent corners (i.e. the whole edge of a given face). The rotation axes lie along the intersection of the 4 center triangle pieces. There appears to be 6 general shapes you can "morph" the Pyramorphix into I'll affectionately call: the Pyramid, the Butterfly, the Crown, the Rocket, the Airplane and the truncated Star of David. (There are actually two truncated Star of Davids, mirror images of one another). You'll know what I mean if you actually have the little creature in your hands. The hardest part of this puzzle is figuring out how to morph between all these different shapes. I solve the Pyramorphix by first solving the 4 corner pieces and then orienting the 4 center pieces. First, a few notation definitions. Hold the Pyramorphix so that you have one of the faces facing you. I'll call that face Front (F). The face on the bottom will be called Down (D), and the faces left and right of the F face will be called Left (L) and Right (R) respectively. An edge will refer to a center piece and its two adjacent corner pieces. I'll specify which edge by indicating the two faces the edge intersects (e.g. R-D edge is the edge formed by the interesection of the Right and Down faces). Now, unfortunately, I can't just refer to rotations of edges, because as you'll see, sometimes you need to rotate strange shapes that look nothing like an edge. Instead, it's better to refer to slices. Namely the plane about which one of the edges rotates on. So, if you look at the F face, you'll see three slices: the R-D slice (60 deg), the L-D slice (120 deg) and the horizontal F-slice (0 deg). When the Pyramorphix is in its pyramid shape, you can rotate the two edges on the R-D and L-D slices, but you cannot rotate the corner piece sitting on the F-slice. Don't worry, when we morph the pyramid into the Rocket, you'll see that you'll be able to rotate the tip of the rocket about the F-slice. Now, that I've thoroughly confused you, here are my notations for actual moves: R - 90 deg clockwise rotation about the R-D slice L - 90 deg clockwise rotation about the L-D slice F - 90 deg clockwise rotation about the F-slice R2 - 180 degree rotation about the R-D slice R' - 90 degree counterclockwise rotation about the R-D slice Finally, hold the Pyramorphix in your hands, so the the F-face is facing towards you with the tip of the triangle pointing up. If you now rotate the puzzle so the the D-face is facing towards you, you should see an upside-down triangle with the tip pointing down. I will refer to the three corner pieces that you see as: DL - left corner piece DR - right corner piece DM - middle corner piece _______________________________________________________ To solve the four corner pieces, first get them in their proper positions by performing 180 rotations of the edges. Now, you need to orient the corners by making appropriate clockwise or counterclockwise twists. Here are some moves to do this: Name: Single corner twister Move: (R L' R' L) ^2 Shapes: Butterfly - Star of David - Airplane - Airplane - Star of David - Star of David - Butterfly - Pyramid Action: Clockwise (CW) twist of DM corner Name: Left-side double corner twister Move: (R L R' L' ) ^2 Shapes: Butterfly - Star of David - Crown - Star of David - Crown - Star of David - Butterfly - Pyramid Action: CCW twist of DL corner, CW twist of the DM corner Name: Right-side double corner twister Move: (R' L' R L) ^2 Shapes: Butterfly - Star of David - Crown - Star of David - Crown - Star of David - Butterfly - Pyramid Action: CCW twist of DR corner, CW twist of the DM corner Name: Triple corner twister Move: (R' L R L') ^2 Shapes: Butterfly - Star of David - Star of David - Airplane - Airplane - Star of David - Butterfly - Pyramid Action: CW twist of DL corner, CW twist of DR corner, CCW twist of DM corner _______________________________________________________ Now, to orient the center pieces in place, here are some moves to do this: Name: Double edge swapper Move: R' L2 F2 L2 R Shapes: Butterfly - Rocket - Rocket - Butterfly - Pyramid Action: Swap F <--> L and R<-->D center pieces Name: Tricycle swap Move: (L R2 F' R2 L') (R' L2 F L2 R) Shapes: (Butterfly - Rocket - Rocket - Butterfly - Pyramid ) ^2 Action: Permute F --> R --> L --> F center pieces Name: Edge swapper Move: (R' L2 F L2 R) (L R2 F R2 L') (R' L2 F L2 R) Shapes: (Butterfly - Rocket - Rocket - Butterfly - Pyramid ) ^3 Action: Swap F <--> D center pieces With these short collection of moves, you should be able to readily solve the Pyramorphix... _______________________________________________________ Epilogue: So, you've solved the Pyramorphix, bored silly and you want to know what's next?! Check out Meffert's Puzzle Ball. It's actually a bit more challenging. Happy puzzling.... :) == _________________________________________________________ Han Wen Applied Materials 3050 Bowers Ave, MS 1145 Santa Clara, CA 95054 e-mail: Han_Wen@amat.com / hansker@yahoo.com From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 9 22:42:43 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id WAA06436 for ; Tue, 9 Feb 1999 22:42:43 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <714F77ADF9C1D111B8B60000F863155102DD6CBA@tbjexc2.tbj.dec.com> From: Norman Diamond To: Subject: Re: Moves for Solving the Pyramorphix puzzle Date: Wed, 10 Feb 1999 11:34:47 +0900 Hey! Everyone on this list _already_ knows moves to solve Pyramorphix, although it often requires careful staring at the thing in order to recognize the exact configuration each time. You see, everyone on this list knows how to solve 3x3x3 Rubik's cube. And everyone knows how to solve 2x2x2 Rubik's cube because it's a subset of the 3x3x3, without edges or centers. And everyone knows how to solve Pyramorphix because it's a subset of the 2x2x2, where some of the corners don't need orienting. -- Norman.Diamond@dec-j.co.jp [Not speaking for Compaq] From cube-lovers-errors@mc.lcs.mit.edu Thu Feb 11 21:17:42 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA23979 for ; Thu, 11 Feb 1999 21:17:41 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.3.32.19990210083221.0092a700@cscan02.caddscan.com> Date: Wed, 10 Feb 1999 08:32:21 -0500 To: Cube-Lovers@ai.mit.edu Reply-To: From: Bryan Main Subject: Puzzle Stores in London area I'll be going to the london/cambrige area in a few days and was wondering if anyone knew where there are any puzzle stores that have cube puzzles. I'm not really looking for 3x3x3 cubes since I have enough, mainly I'm looking for the other ones like pyrimix, megamix etc. thanx in advance. bryan [Please respond directly to Bryan; if there are particularly worthwhile and non-repettive suggestions he can send them to cube-lovers --Moderator ] From cube-lovers-errors@mc.lcs.mit.edu Fri Feb 19 12:26:12 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA19007 for ; Fri, 19 Feb 1999 12:26:11 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 18 Feb 1999 23:45:18 -0400 (EDT) From: Jerry Bryan Subject: Edges only, Ignoring Flips, Face Turn Metric To: Cube-Lovers Message-Id: I have completed a God's Algorithm run in the face turn metric for the group consisting of edges only ignoring flips. The size of the group is therefore 12! The results are as follows: Distance Patterns Positions Branching From Factor Start 0f 1 1 1f 2 18 18.000 2f 9 243 13.500 3f 75 3240 13.333 4f 920 42535 13.128 5f 11406 542234 12.748 6f 136423 6529891 12.043 7f 1386164 66478628 10.181 8f 6481303 310957078 4.678 9f 1969536 94443600 0.304 10f 129 4132 0.000 Total 9985968 479001600 I should mention that Herbert Kociemba was the first to calculate the "patterns" column. He did it as a part of an investigation into developing an IDA* optimal solver, with the patterns column being part of a patterns data base used by the IDA* algorithm. I used my usual program where (for example) I calculate the set of all positions which are 10f from Start by forming the products of all positions which are 5f from Start in lexicographic order, and throwing away the duplicates and the ones that are shorter than 10f. This technique is reasonably efficient when the branching factor is fairly constant, as it is at this distance from Start for larger problems such as the whole cube. However, it is very inefficient for this particular problem. I have to calculate about (542234^2)/48 products just to get the 129 products I keep at 10f from Start. (The "divide by 48" takes symmetry into account.) In a "one level at a time" search by contrast, the tail of the distribution usually goes very quickly because there are so few positions in the tail. I have come to believe that any corners only (with or without twist) or edges only (with or without flip) group, or the group which keeps both corners and edges but without twists and flips, will be a fairly poor pattern data base for IDA*. The problem is that any such search space will have a diameter which is too small, and more importantly will have an average distance from Start which is too small. Here is why I think the diameter and average distance from Start will be too small for these groups. Consider the quarter turn metric. We know immediately that the maximum branching factor is 12 because there are 12 quarter turns. We know almost as immediately that the maximum branching factor beyond one move from Start is 11 because there is always at least one quarter turn that goes closer to Start. Finally, readers of Cube-lovers know that the maximum branching factor is asymptotic to about 9.3 because of Dan Hoey's syllable analysis. Syllable analysis takes into account moves which commute because they are on opposite faces such as RL=LR. (Similar analysis for the face turn metric yields an asymptotic maximum branching factor of about 13.3) I have come to think of syllable analysis not just as an upper limit for the branching factor but as a predictor for the branching factor. Indeed, the actual branching factor differs from the branching factor "predicted" by syllable analysis only because of duplicate positions which arise from processes which are not accounted for by syllable analysis. Such duplicate positions must exist by the finiteness of the problem, else a God's algorithm search would be infinite. But such duplicate positions are non-trivial and are generally not very close to Start. With the full cube, they are quite rare as close to Start as has been searched so far (10f and 12q, respectively). What happens with a typical search is that the branching factor stays relatively constant until within a couple of levels of the mode of the frequency distribution of the distances from Start. The branching factor then declines rapidly due to duplicate positions, and there is a short tail in the frequency distribution just past the mode. The key point is that syllable analysis is identical for all groups involving corners only, edges only, corners and edges, and/or with or without twists and flips. Hence, the basic branching factor is the same for all such groups. Therefore, the mode of the distribution is reached much sooner when the group is smaller and the average distance from Start is much smaller. What would be desirable for a pattern data base for IDA* would be a subgroup of G whose branching factor was smaller so that the mode, the diameter, and the average distance from Start would be larger. That is, what would be desirable would be a subgroup which was not constrained by standard syllable analysis. Failing that, it seems to me that the only way to improve the pattern data base is to make it larger. In this light, I interpret what Mike Reid (and more recently) Herbert Kociemba have done with their IDA* programs is to find clever ways to make their pattern data bases as large as possible, but they do it in such a way (using symmetry and other equivalence classes) that their large data bases are small enough to store in memory' As I think has been mentioned before, a group such as has a small branching factor but is not suitable as a pattern data base for IDA* because the distance from Start for a particular position in may be larger than the distance from Start for the same position in G. Jerry Bryan From cube-lovers-errors@mc.lcs.mit.edu Fri Feb 19 17:17:38 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA20548 for ; Fri, 19 Feb 1999 17:17:37 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Douglas Zander Message-Id: <199902192002.OAA04117@solaria.sol.net> Subject: 2by alternative mechanism To: cube-lovers@ai.mit.edu Date: Fri, 19 Feb 99 14:02:03 CST Hello, I remember someone asked if there were two different mechanisms to the 2x2x2 cube but I can't remember if it was answered. Last night while doing a patent search I came across a mechanism totally different than what my own cube looks like. It is U.S. Patent # 5826871 Oct '98 Basically, it is a standard Rubik's Cube with the central layers hidden underneath and one quadrant is fixed in place. I am wondering if there exists a web site with all the diagrams of all different puzzles from their patent pages. As you may know, patents and patent diagrams are *not* covered by copyright issues, you may photocopy them for personal viewing and even display them on a web page. I think such a web page would be nice to have; a web page of all the diagrams of the working mechanisms of all the puzzles discussed on this list. (The thing is though that soon the U.S. Patent office will be adding the diagrams to their web pages. www.uspto.gov) Anyone wish to start such a page? I have access to a patent depository. :-) -- Douglas Zander | dzander@solaria.sol.net | Shorewood, Wisconsin, USA | From cube-lovers-errors@mc.lcs.mit.edu Mon Feb 22 13:23:12 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA29004 for ; Mon, 22 Feb 1999 13:23:12 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 22 Feb 1999 17:23:57 +0000 From: David Singmaster To: cube-lovers@ai.mit.edu Message-Id: <009D4210.9784799A.12@ice.sbu.ac.uk> Subject: Fwd: Request for spectacular cube-solving - Can anyone help? From: mytv-film@t-online.de To: MX%"david.singmaster@sbu.ac.uk" Subj: rubik's cube Date: Wed, 17 Feb 1999 17:49:19 +0100 To: david.singmaster@sbu.ac.uk Subject: Rubik's cube Hello Mr. Singmaster, my name is Gvksen and I'm working for the new German TV show "Guinness -Show of Records" on behalf of the German Broadcast Station ARD. In one of our next shows we would like to present a person who is able to solve a classical Rubik's Cube in a spectacular way. For example by studying the cube first for a couple of minutes and then solving it without looking at it. On an internet homepage with different links to Rubik's cube fans we've read that there is a young man in U.K. called John White who is able to do that: Studying the cube for 10 minutes and than solving it behind his back in 136 seconds. Now, we're looking for this young man, who is or was a mathematics student at the University of Warwick. Our investigation up to now brought us to you, so you are considered to be one of the leading "Rubik's cube experts" in the world. In addition you were a judge during the "Rubik's Cube World Championship". So you may know a lot of persons and beyond that a lot of different variations of solving a Rubik's cube in an impressive way. We would be very happy if you could give us a hint or some advice concerning our idea of presenting this category of record in our show. One characteristic feature of our show is the fact that we present a record as a competition. That means: We would invite the record holder and a challenger who believes himself capable of being able to solve a cube in a similar way. In the best case this challenger should be a person who speaks German. Do you know anyone who could be suitable? I hope that these are not too much questions and I would like to thank you even now for your help and kind co-operation. Our e-mail address: mytv-film@t-online.de kind Regards Gvksen MyTV Film and Tv Production DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Tue Feb 23 11:10:32 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA03941 for ; Tue, 23 Feb 1999 11:10:32 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990222194015.5998.rocketmail@send105.yahoomail.com> Date: Mon, 22 Feb 1999 11:40:15 -0800 (PST) From: pete beck Subject: Cubes in the news (was: Request for spectacular cube-solving...) To: David Singmaster , cube-lovers@ai.mit.edu It must be the age of the CUBE. Pete Beck ---------------- from Yahoo! News Technology Headlines Monday February 22 1:19 PM ET Corrected: Rubik Cube Whiz Offers Millennium Bug Solution LONDON (Reuters) - A man who solved the riddle of Rubik's cube has invented a test kit to detect where the millennium computer bug will strike. At the age of 12, Patrick Bossert shot to fame when he worked out his own solution to the mystifying cube and wrote a bestseller about it that sold 1.5 million copies. Now 30, he and a team of software experts at London-based WSP Business Technology have developed Delta-T Probe, a program that can work out whether microchips embedded in electronic equipment are likely to fail on January 1, 2000. Delta-T works by electronically detecting equipment to identify chips that process date and time, making it likely to malfunction when 1999 becomes 2000. ``Only a small percentage of systems will fail to recognize the next millennium, but finding out which ones might go wrong is a huge and costly process,'' said Bossert, technical director at WSP Business Technology, a unit of consulting engineering group WSP Group Plc. Bossert estimates hundreds of millions of chips are buried deep inside equipment in Britain. The chips control devices such as security systems, fire alarms, production lines, medical equipment and telecommunications. Bossert expects one in 500 embedded systems will take equipment back in time to Jan. 1, 1900, causing equipment to fail. British supermarket chain Sainsbury's Plc is among major companies that have tested Delta-T. Sainsbury's said a trial run at one of its stores in Devon, southwestern England, had been a success. Hi, this is Pete Beck's personal e-mail site, a.k.a. Just Puzzles is a hobby mail order seller of "Mechanical puzzles" specializing in Rubik's Cube type puzzles. HOME is at - post POB 267, Wharton NJ 07885, answering machine is 973-625-4191. Current as of 10 Nov 1998. From cube-lovers-errors@mc.lcs.mit.edu Wed Feb 24 12:52:23 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA07939 for ; Wed, 24 Feb 1999 12:52:23 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 22 Feb 1999 12:13:16 -0800 (PST) From: Tim Smith To: cube-lovers@ai.mit.edu Subject: Re: Fwd: Request for spectacular cube-solving - Can anyone help? In-Reply-To: <009D4210.9784799A.12@ice.sbu.ac.uk> Message-Id: > In one of our next shows we would like to present a person who is able to > solve a classical Rubik's Cube in a spectacular way. A spectacular way I'd like to see someone do the cube is while juggling. Instead of that old routine where the juggler juggles some fruit and eats the fruit while juggling it, juggle three (or more!) cubes, and solve them at the same time. --Tim Smith From cube-lovers-errors@mc.lcs.mit.edu Wed Feb 24 13:57:12 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA08541 for ; Wed, 24 Feb 1999 13:57:12 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990223234105.19048.rocketmail@web4.rocketmail.com> Date: Tue, 23 Feb 1999 15:41:05 -0800 (PST) From: "Jorge E. Jaramillo" Subject: Number of moves To: cube A lot has been said about world records solving the cube when it comes to time but I don't recall seeing anywhere how many moves the person who holds the record did. Does anyone know? === Jorge E Jaramillo From cube-lovers-errors@mc.lcs.mit.edu Wed Feb 24 15:56:12 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA08933 for ; Wed, 24 Feb 1999 15:56:11 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36D3B818.E20EFCD6@ibm.net> Date: Wed, 24 Feb 1999 00:28:08 -0800 From: "Jin 'Time Traveler' Kim" Reply-To: chrono@ibm.net To: cube-lovers@ai.mit.edu Subject: Acquiring rare puzzles References: <199902192002.OAA04117@solaria.sol.net> This may be common knowledge to many of you on this list, but I thought I'd mention these and give everyone a fair shot (as well as maybe angering some who used it as a resource to locate some harder to find pieces). 1) If you are looking for some rare pieces like the Revenge, Megaminx, Alexander's Star, these items often come up for auction at http://www.ebay.com In the three weeks or so that I've been actively participating in auctions, I've seen several of each of the following: Rubik's Revenge, Alexander's Star, Missing Link, Megaminx, and Whippit. I've also seen Skewb, 5x5x5, Rubik's Magic, Pyraminx, Mickey's Challenge, and any number of others come up for bidding. Haven't seen a Rubik's Domino (2x3x3), though. For a general idea of what's there, try doing a search for the key word "rubik" at the site. That's just for starters. I even saw a Cuboctahedron (yes, just a shaved down 3x3x3 cube) go for over 60 dollars. Incredible. Using eBay I have personally added two more Revenges to my collection. 2) There is also someone on the net who seems to be contacting people directly and trying to sell a stock of puzzles he ran across. His email is jo_schumacher@[see moderator's note]. Try emailing him for availability and pricing. For example, he was last selling mint Revenges for $109 and Alexander's Stars for $70. I haven't bought anything from him yet so consider it an "at your own risk" venture. -- Jin "Time Traveler" Kim chrono@ibm.net http://www.slamsite.com/chrono '95 PGT - SCPOC [ Moderator's note: At least one person on the list has complained about getting spam from schumacher, and it sure looked like spam to me. I certainly can't countenance sending e-mail to offer goods for sale to list members who haven't indicated a willingness to receive such an offer. When it comes to spammers, "at your own risk" includes "at the risk of helping to make this medium unusable. I usually steer the numerous requests from people seeking Rubik's Revenge to ebay (and to yard sales, and to simulations). But note that the FTC says that internet auctions are the growth zone for Internet fraud. This can be somewhat mitigated by sending your money through an escrow agent--see ebay for information on that. ] From cube-lovers-errors@mc.lcs.mit.edu Wed Feb 24 17:03:02 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA09093 for ; Wed, 24 Feb 1999 17:03:01 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: From: "Schmidt, Greg" To: "'Tim Smith'" , cube-lovers@ai.mit.edu Subject: RE: Fwd: Request for spectacular cube-solving - Can anyone help ? Date: Wed, 24 Feb 1999 13:53:02 -0500 While we're at it, I might as well add that I think the juggler should be blindfolded! -- Greg [ And holding her breath underwater! And counting to one hundred backwards with her toes! Greg also notes that you can't trust ebay's auction ending dates. Caveat browsor. -- Moderator ] From cube-lovers-errors@mc.lcs.mit.edu Thu Feb 25 11:25:26 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA12413 for ; Thu, 25 Feb 1999 11:25:25 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <4.1.19990224195654.0092e1c0@mail.vt.edu> Date: Wed, 24 Feb 1999 20:38:44 -0500 To: cube-lovers@ai.mit.edu From: Kevin Young Subject: Oddzon version of the cube In-Reply-To: <36D3B818.E20EFCD6@ibm.net> References: <199902192002.OAA04117@solaria.sol.net> I am curious if anyone has had the same problems with the current official Rubik's cube that is in production. I bought a Rubik's cube last year in a toy store. This was the newest version made by Oddzon. I noticed that there was a clear sticker overtop of each of the colored stickers. In less than a month this clear sticker peeled up. I just don't remember the original cubes by Ideal wearing down that fast. In fact I still have a couple cubes from Ideal with stickers still intact. I contacted Oddzon by email and have received several responses from them, forwarding my email to the appropriate department. Currently my concern is with under review by the Quality Control and Marketing department. They have claimed that this concern about the stickers is not common. Maybe I just got a bad cube, I don't know. But, in order for them to make a better product, I'm sure it's going to take a strong voice from the people actually buying the products. I just encourage everyone if they have experienced the same thing with the stickers with the Oddzon product, to contact them. Most of the time, I still play with my cube I got from Ideal from 1982. It was called "Rubik's Cube Deluxe". It was the official Rubik's cube that had colored tiles instead of stickers. That cube is holding up like new. I also made a motion to Oddzon to put the "Rubik's Cube Deluxe" back into production. That motion is now with the Senior Marketing Manager at Oddzon. It's his voice to decides which products go into production. I also encourage anyone that wants to see that version back into production, to contact Oddzon. Oddzon has been incredibly helpful and incredibly nice. They have informed me that two new Rubik's products will be coming out this year from Oddzon. They should be out by the middle of the summer. They werent at liberty to say what products they were. I can think of some that I'd like to see back into production. I'll have to wait and see. On another note. I do not endorse ebay, however, I have had a bit of success with ebay. I won two different auctions on ebay. They were both for Cubes by Ideal, never opened or played with, cellophane still intake. I was lucky enough to get them for under 20 bucks apiece. But, use caution. I wouldn't recommend ever auctioning on an item from a seller with negative or low feedback. Definantly be careful. I've been really lucky with the products I've won. Cheers, Kevin From cube-lovers-errors@mc.lcs.mit.edu Thu Feb 25 17:28:33 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA13231 for ; Thu, 25 Feb 1999 17:28:33 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19990225085830.00963b40@mail.spc.nl> Date: Thu, 25 Feb 1999 08:58:31 +0100 To: cube-lovers@ai.mit.edu From: Christ van Willegen Subject: RE: Fwd: Request for spectacular cube-solving - Can anyone help ? At 13:53 24-2-1999 -0500, you wrote: >While we're at it, I might as well add that I think the juggler should >be blindfolded! Hey! _I'm_ already teaching my blind friend how to solve a cube! We marked the colors of the cube with braille letters spelling 1 - 6 dots. We're having a terribly hard time to teach him to solve it. It's fun, though... Would a team of 3-4 blind people competing to solve the cube be considered 'spectacular'? I think juggling is too hard. I'll ask my gf, though (she knows how to juggle a bit, _and_ how to solve the cube). Christ van Willegen From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 8 21:24:30 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA27010 for ; Mon, 8 Mar 1999 21:24:29 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19990225090214.009654a0@mail.spc.nl> Date: Thu, 25 Feb 1999 09:02:15 +0100 To: cube-lovers@ai.mit.edu From: Christ van Willegen Subject: Megaminx solving times? Hi, I've been practising the Megaminx, and I can now solve it without resorting to formulas written down on paper. I can do it in about 10 minutes. How does this compare to other people's times? And, what method do you use? The method I developed relies heavily upon the standard cube moves, and I solve the Mega- minx going down from one flat top in rings. I needed to adapt 1 (one!) standard cube formula to get it to work on the Megaminx. Christ van Willegen From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 8 22:00:14 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id WAA27135 for ; Mon, 8 Mar 1999 22:00:13 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 25 Feb 1999 10:56:09 -0700 (MST) From: Paul Hart To: cube-lovers@ai.mit.edu Subject: Re: Oddzon version of the cube In-Reply-To: <4.1.19990224195654.0092e1c0@mail.vt.edu> Message-Id: On Wed, 24 Feb 1999, Kevin Young wrote: > I noticed that there was a clear sticker overtop of each of the colored > stickers. In less than a month this clear sticker peeled up. I just > don't remember the original cubes by Ideal wearing down that fast. In > fact I still have a couple cubes from Ideal with stickers still intact. [...] > They have claimed that this concern about the stickers is not common. > Maybe I just got a bad cube, I don't know. No, it's not just you. I had this exact problem with an Oddzon cube. Eventually all Oddzon cubes will develop this problem after any extended use, I believe. The "stickers" appear to be actually nothing more than some sort of colored paper glued to the cube surface, with a thin transparent plastic film covering the paper. Like Kevin mentions, this plastic film begins to peel up at the corners and edges of the stickers after extended usage of the cube, perhaps due to fingerprint oils. Eventually the film will fall off (or it gets to the point where it must be deliberately removed), and the underlying colored paper is completely ruined not long after. I noticed this very same phenomenon with one of the "C4" cubes, those cubes with Rubik's profile in the center of the one of the sides. It seems that these newly manufactured cubes are not up the level of quality of cubes from "back in the day". All of the original Ideal cubes that I have seen have stickers that appear to be made of straight colored plastic. Even the clone knock-offs from that era used these stickers. These solid plastic stickers seem to hold up much better than the paper-based ones used on the Oddzon products. After my disappointing results with my Oddzon cube, I pledged to never again buy one of their products until they change or improve their sticker design. Paul Hart -- Paul Robert Hart ><8> ><8> ><8> Verio Web Hosting, Inc. hart@iserver.com ><8> ><8> ><8> http://www.iserver.com/ From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 9 12:30:38 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA29026 for ; Tue, 9 Mar 1999 12:30:37 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: In-Reply-To: <4.1.19990224195654.0092e1c0@mail.vt.edu> References: <36D3B818.E20EFCD6@ibm.net> <199902192002.OAA04117@solaria.sol.net> Date: Thu, 25 Feb 1999 10:06:33 -0800 To: Kevin Young From: Patrick Weidhaas Subject: Re: Oddzon version of the cube Cc: RUBIK cube group Kevin Young wrote: >... I bought a Rubik's cube last year in a >toy store. This was the newest version made by Oddzon. I noticed that >there was a clear sticker overtop of each of the colored stickers. In less >than a month this clear sticker peeled up.... Kevin, I do not have an answer for you, but your email made me wonder why stickers are being used at all? As far as I know, nobody has produced a cube (or variation) where the plastic "cubies" are colored appropriately without relying on stickers. Is that process so much more expensive, or do the toy-makers want to give their customers a chance to cheat by switching the stickers in case they can't get the puzzle solved? Patrick ------------------------------------------------------------------ Patrick P. Weidhaas e-mail: weidhaas1@llnl.gov Parallel I/O Project voice: 925-422-7704 Lawrence Livermore National Laboratory fax: 925-422-6287 P.O. Box 808, L-560 Livermore, CA 94551-0808 From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 9 13:06:35 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA29238 for ; Tue, 9 Mar 1999 13:06:35 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36D5AE30.23D2@zeta.org.au> Date: Fri, 26 Feb 1999 07:10:24 +1100 From: Wayne Johnson Reply-To: sausage@zeta.org.au To: Kevin Young Cc: cube-lovers@ai.mit.edu Subject: Re: Oddzon version of the cube References: <199902192002.OAA04117@solaria.sol.net> <4.1.19990224195654.0092e1c0@mail.vt.edu> Kevin Young wrote: > I am curious if anyone has had the same problems with the current official > Rubik's cube that is in production... However, it must be said that they are not suddenly aware of this. This has been a problem for some time. Frankly, I have a Rubik's original from 5 years ago with the same propblem. Oddzon don't seem to built the items or make them in colours that Rubik himself even approves of (take the new colours of the magic for instance - terrible). I am currently on the lookout for an asian fake cube because they have always been (dare I say it) better quality in the sticker dept. My Fake is 15 years old with all stickers nicely attached. Come on Oddzon... a cube that wears out in a month?.... I think this is very clever and deliberate marketing. Regards, Wayne From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 9 13:31:19 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA29345 for ; Tue, 9 Mar 1999 13:31:18 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <4.1.19990225180850.0094e010@mail.vt.edu> Date: Thu, 25 Feb 1999 18:12:51 -0500 To: cube-lovers@ai.mit.edu From: Kevin Young Subject: Re: Request for spectacular cube-solving - Can anyone help ? In-Reply-To: <3.0.32.19990225085830.00963b40@mail.spc.nl> I am currently trying to learn how to do it without looking. Have a long ways to go. I use to be able to do it, watching the cube of course, in less than a minute. After 17 years and not being a school age boy anymore, and forgetting some of my tricks, I can still do it everytime in approx. 90 seconds. Long ways away from being a world champion. But, currently I'm working on the no looking thing. Right now, I can put two pieces at a time in their appropriate position, behind my back, however, after those pieces are set, I have to look. Good luck to all that are trying to learn how to do it blindfolded. Regards, Kevin Young From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 9 14:01:38 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA29506 for ; Tue, 9 Mar 1999 14:01:37 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <714F77ADF9C1D111B8B60000F863155102DD6D3A@tbjexc2.tbj.dec.com> From: Norman Diamond To: cube-lovers@ai.mit.edu Subject: RE: Fwd: Request for spectacular cube-solving - Can anyone help ? Date: Fri, 26 Feb 1999 09:24:41 +0900 Christ van Willegen [c.v.willegen@spcgroup.nl] wrote: >We marked the colors of the cube with braille letters spelling >1 - 6 dots. I have a magic domino which was actually manufactured that way. Bought it from Christoph Bandelow about 13 years ago. Dr. Bandelow, you're on this list, right? Were there ordinary Rubik's cubes with the same feature? (Question to self: How can the words "ordinary" and "Rubik's" be placed next to each other in a sentence?) -- Norman.Diamond@dec-j.co.jp [Not speaking for Compaq] From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 14:54:38 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA04110 for ; Wed, 10 Mar 1999 14:54:37 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199902261047.CAA19201@f15.hotmail.com> From: "Philip Knudsen" To: cube-lovers@ai.mit.edu Subject: RE: Request for spectacular cube-solving Date: Fri, 26 Feb 1999 02:47:40 PST What about solving the cube while performing a full-length rap? I even know someone who can do that: MYSELF ;-) Actually I am a singer, but I _do_ rap from time to time _and_ I also happen to speak german. But I can't joggle :-( ____________________________________ Philip K Vendersgade 15, 3th DK - 1363 Copenhagen K Denmark Phone: +45 33932787 Mobile: +45 21706731 E-mail: philipk@bassandtrouble.com E-mail: philipknudsen@hotmail.com [Moderator's note: Philip also mentions his good experiences with ebay. The cube-lovers list isn't running a poll on them, so no one else needs to send reports of their performance. Pay your money, take your chances, seek advice from appropriate sources. ] From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 15:49:18 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA04363 for ; Wed, 10 Mar 1999 15:49:18 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 26 Feb 1999 09:06:55 -0500 (Eastern Standard Time) From: Dale Newfield Reply-To: DNewfield@cs.virginia.edu To: cube-lovers@ai.mit.edu Subject: RE: Fwd: Request for spectacular cube-solving - Can anyone help ? In-Reply-To: <3.0.32.19990225085830.00963b40@mail.spc.nl> Message-Id: On Thu, 25 Feb 1999, Christ van Willegen wrote: > Hey! _I'm_ already teaching my blind friend how to solve a cube! > We marked the colors of the cube with braille letters spelling > 1 - 6 dots. We're having a terribly hard time to teach him to solve > it. It's fun, though... How difficult is it to read braille when the characters are in arbitrary orientations? Have you thought of using some other coding technique that might prove more easy to distinguish in any orientation? (Any idea what that might be?) -Dale [Moderator's note: I'm inordinately proud of my own invention, which I thought I mentioned years ago but can't find in the archives: Wire symbols glued to a destickered cube, polished to a high gloss. The symbols are blank opposite dot, square opposite circle, and plus opposite X. The supergroup is marked by a cutout at a corner of each face center and the adjacent cubies. I can solve it behind my back, but when I lent it to a blind computer scientist, he gave up. --Dan] From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 19:40:41 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA05581 for ; Wed, 10 Mar 1999 19:40:41 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Fwd: Request for spectacular cube-solving - Can anyone help ? Date: 26 Feb 1999 20:52:13 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7b71ht$3pp@gap.cco.caltech.edu> References: Christ van Willegen writes: >Would a team of 3-4 blind people competing to solve the cube be >considered 'spectacular'? I think juggling is too hard. I'll ask >my gf, though (she knows how to juggle a bit, _and_ how to solve >the cube). How about team solving? n people, n cubes, everyone makes one move and passes the cube to the left. Repeat. :-) -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- "Pop", "Soda", or "Coke"? http://www.ugcs.caltech.edu/~almccon/pop_soda/ From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 20:15:40 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA10243 for ; Wed, 10 Mar 1999 20:15:39 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sat, 27 Feb 1999 05:00:50 +0100 (MET) From: Martin Moller Pedersen Message-Id: <199902270400.FAA482087@bonestell.daimi.au.dk> To: cube-lovers@ai.mit.edu Subject: help on 5x5x5 wings I am trying to solve my new cube the 5x5x5 cube. I have managed to solve all of it except the wings. The wings are the y's in the following diagram: ZyZyZ yZZZy ZZZZZ yZZZy ZyZyZ I have many moves for the 3x3x3 but I can't figure out how to apply these moves to the wings. Thanks for all help. /Martin From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 20:47:02 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA10386 for ; Wed, 10 Mar 1999 20:47:01 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 4 Mar 1999 23:09:00 -0500 From: michael reid Message-Id: <199903050409.XAA24597@cauchy.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Edges only, Ignoring Flips, Face Turn Metric jerry writes > I have completed a God's Algorithm run in the face turn metric for the > group consisting of edges only ignoring flips. The size of the group is > therefore 12! The results are as follows: [ ... ] very interesting. i hope that you'll also do the quarter turn metric. > I have come to believe that any corners only (with or without twist) or > edges only (with or without flip) group, or the group which keeps both > corners and edges but without twists and flips, will be a fairly poor > pattern data base for IDA*. The problem is that any such search space > will have a diameter which is too small, and more importantly will have an > average distance from Start which is too small. another shortcoming of this coset space for ida* is that transformations aren't easy to compute. for the cosets spaces i've used, they always split up as a product of smaller coset spaces. then i use transformation tables for everything. ida* spend a lot of time moving from a position to its neighbors. instead of keeping the cube position, i just keep track of which coset i'm in. then i need to find out what coset i'll be in if i apply the turn F (for example). i always do this by using transformation tables. to simplify things, suppose that my coset space had 1000000 cosets. i could use a table with 18 * 1000000 entries that tells me which coset i go to by applying a given turn. if my coset space is a product of two spaces, each with 1000 cosets, then i only need a tranformation table with 18 * 1000 entries for the first coordinate and one of the same size for the second coordinate. this is really addressing implementation issues of ida*, not so much the effectiveness of it. mike From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 21:22:07 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA10444 for ; Wed, 10 Mar 1999 21:22:06 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36E4A993.5AB5@zeta.org.au> Date: Tue, 09 Mar 1999 15:54:43 +1100 From: Wayne Johnson Reply-To: sausage@zeta.org.au To: cube-lovers@ai.mit.edu Subject: Speed cube times Hello All, There doesn't seem to be any records these days kept of people's current solving times for the cube. Perhaps they should be shared here? My current time for solving the 3x3x3 Rubik's cube is 47 seconds using the Petrus method and involved: Building the 2x2x2, finishing the bottom and mid layer, 1 edge alignment, 1 corner swap, 2 sunes, and 1 clockwise edge rotation. How are other people's speeds fairing? Wayne Johnson http://www.zeta.org.au/~sausage/rubikscube.html [Moderator's note: Since this may result in a large number of very small messages, please send your answers to Wayne, who I hope will summarize the results for the list. ] From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 22:03:13 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id WAA10588 for ; Wed, 10 Mar 1999 22:03:12 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Megaminx solving times? Date: 9 Mar 1999 15:46:55 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7c3fpf$mte@gap.cco.caltech.edu> References: Christ van Willegen writes: >I've been practising the Megaminx, and I can now solve it >without resorting to formulas written down on paper. I can >do it in about 10 minutes. How does this compare to other >people's times? I've never solved mine for speed, because I'm afraid of more stickers falling off (already 3 are missing and I have to "deduce" what they are). 10 minutes sounds reasonable -- I'm not sure I've ever resorted to formulas written on paper. (For one thing, I'm not sure I know of any notation!) >And, what method do you use? The method I developed relies >heavily upon the standard cube moves, and I solve the Mega- >minx going down from one flat top in rings. I needed to >adapt 1 (one!) standard cube formula to get it to work on >the Megaminx. This brings up, actually, a rather embarrasing point for me as a puzzle solver. At first I had no idea how to generalize the standard cube moves I used to the Megaminx. So, eventually I figured out a new method, which was: 1. Solve a large chunk of it by normal moves, perhaps leaving only three faces unsolved; 2. Solve the edges of the remaining faces (if you can solve an Alexander's Star, you can do this); 3. Solve the corners. I found this quite effective. About a year later, when my Megaminx was in storage and I was playing with the Cube, I suddenly realized that my method for the Megaminx would work perfectly well for the Cube! (O, for that matter, anything with a similar structure of "corners" with three faces and "edges" with two faces.) I chastized myself heavily for not realizing this "obvious generalization", and with it was able to work out more moves for the Cube. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- "Pop", "Soda", or "Coke"? http://www.ugcs.caltech.edu/~almccon/pop_soda/ From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 22:50:04 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id WAA10715 for ; Wed, 10 Mar 1999 22:50:04 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 9 Mar 1999 19:08:55 +0000 From: David Singmaster To: weidhaas1@llnl.gov Cc: cube-lovers@ai.mit.edu Message-Id: <009D4DE8.BDBAD646.12@ice.sbu.ac.uk> Subject: Re: Oddzon version of the cube Re: coloured cubies. I only ever saw one version of the cube where the black plastic ccubies had painted faces. The colours were rather paler than on the ordinary cubes and one colour was violet. I can't find it immediately, but I should find it if I stop an look. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 10 23:23:35 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id XAA10879 for ; Wed, 10 Mar 1999 23:23:34 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 9 Mar 1999 19:24:29 +0000 From: David Singmaster To: sausage@zeta.org.au Cc: cube-lovers@ai.mit.edu Message-Id: <009D4DEA.EA4E5AAE.11@ice.sbu.ac.uk> Subject: Re: Oddzon version of the cube It's depressing that manufacturers can't provide a decent cube. When the C4 cube was introduced about 10(?) years, I found the mechanism very poor and poeple told me that their examples broke within an hour of buying it. As you say, the Asian pirates had become very good in 1982 or so and I believe Ideal was actually buying production from some of the same companies. Regarding cubes with printed colours, I have located mine. It has violet replacing orange, but is otherwise the usual colours and arrangement. The colours are pretty good, but because the plastic surface is not perfectly smooth, it gives the effect of a matte finish, rather than a glossy finish, which is why I remember the colours as a bit paler. My records indicate this was bought in a regular Rubik Cube packaging, but I don't recall when and I've never seen the technique used again. I suppose one has to place squares of coloured material against the cube and then fuse the colour into the surface of the plastic and this seems likely to be more expensive than the use of stickers. The elimination of orange may be due to the fact that many orange colours are based on cadmium which is toxic and not permitted on objects for children. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 11 18:02:02 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA14965 for ; Thu, 11 Mar 1999 18:02:02 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <714F77ADF9C1D111B8B60000F863155102DD6D8E@tbjexc2.tbj.dec.com> From: Norman Diamond To: cube-lovers@ai.mit.edu Subject: Re: Oddzon version of the cube Date: Wed, 10 Mar 1999 09:36:17 +0900 Patrick Weidhaas [weidhaas1@llnl.gov] wrote: >As far as I know, nobody has produced a cube (or variation) where the >plastic "cubies" are colored appropriately without relying on stickers. I think I have mentioned on this list before that I bought one in India in 1996. >Is that process so much more expensive, I think it is not. I am not an expert on manufacturing so can't really say if it's more expensive to make a multicolored plastic piece than it is to make (or buy) adhesive tapes and punch stickers out of them for attachment to unicolored pieces. But I do think, when the version with multicolored plastic pieces could be retailed for 35 rupees, the cost of manufacture must be less than 35 rupees, the difference between this method of manufacture and the more common method must be less than 35 rupees, and I'd lay odds on a distributor not even noticing the difference in costs if they went that way. (35 rupees was about 120 yen then. 35 rupees would be about 100 yen now, though the product's price in rupees might have risen.) >or do the toy-makers want to give their customers a chance to cheat >by switching the stickers in case they can't get the puzzle solved? Interesting. Is this the reason why the stickers come off by themselves :-) Maybe they don't know that some people used to disassemble cubes and rearrange the cubies :-) Of course early Rubik's Revenges used to disassemble themselves that way. -- Norman.Diamond@dec-j.co.jp [Not speaking for Compaq] From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 11 18:27:53 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA15052 for ; Thu, 11 Mar 1999 18:27:53 -0500 (EST) Message-Id: <199903112327.SAA15052@mc.lcs.mit.edu> Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 9 Mar 1999 22:40:45 -0500 (EST) From: Nicholas Bodley To: Patrick Weidhaas Cc: Kevin Young , RUBIK cube group Subject: Re: Oddzon version of the cube In-Reply-To: On Thu, 25 Feb 1999, Patrick Weidhaas wrote: {snips} }Kevin, } }I do not have an answer for you, but your email made me wonder why stickers }are being used at all? As far as I know, nobody has produced a cube (or }variation) where the plastic "cubies" are colored appropriately without }relying on stickers. Ideal once made a deluxe Cube that had individual colored plastic tiles attached to the cubies. It also had a mechanism (same general principle, just different details) that would self-align as you began a maneuver with a slight misalignment, instead of jamming. In other words, it was a good bit more tolerant of misalignment. It would be delightful if they'd reissue it! }Is that process so much more expensive, or do the }toy-makers want to give their customers a chance to cheat by switching the }stickers in case they can't get the puzzle solved? It was maybe almost twice the price of the standard Cube, iirc. Swapping stickers is silly! Learn how to disassemble (but reassemble as a solved Cube; iirc, there are 11 wrong ways to do it, essentially). Most of the movable-piece puzzles can be disassembled, but not all. }Patrick |* Nicholas Bodley *|* Autodidact & Polymath * Electronic Tech. (ret.) |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* Frequent crashes are unacceptable in a mature |* Amateur musician *|* computer industry. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 11 19:29:29 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA15277 for ; Thu, 11 Mar 1999 19:29:29 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19990310090119.00960d80@mail.spc.nl> Date: Wed, 10 Mar 1999 09:01:20 +0100 To: cube-lovers@ai.mit.edu From: Christ van Willegen Subject: Stickers Re: Oddzon version of the cube >I do not have an answer for you, but your email made me wonder why stickers >are being used at all? As far as I know, nobody has produced a cube (or >variation) where the plastic "cubies" are colored appropriately without >relying on stickers. Is that process so much more expensive, or do the >toy-makers want to give their customers a chance to cheat by switching the >stickers in case they can't get the puzzle solved? Switching stickers is a no-no. You can so this a couple of times, after that they'll just fall off... I've seen cubes that have real plastic colors! They are 3by's in black, with colored square bricks on the faces that form the colors. They are about $5 (I think). I haven't bought one to check quality (yet?). Perhaps if the mechanism is alright, these might be better suited for the cube-addict. But I'm afraid that the mechanism won't be able to stand lots of use. Perhaps I'll just go ahead and try the experiment. After all, it's only $5... Christ van Willegen [ Moderator's note: I take it you mean they are available in the Netherlands? Anywhere else? ] From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 11 20:18:19 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA15460 for ; Thu, 11 Mar 1999 20:18:19 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990310085110.13787.qmail@hotmail.com> From: "Philip Knudsen" To: cube-lovers@ai.mit.edu Subject: Re: Oddzon version of the cube Date: Wed, 10 Mar 1999 00:51:10 PST Patrick Weidhaas wrote: >As far as I know, nobody has produced a cube >(or variation)where the plastic "cubies" are >colored appropriately without relying on stickers.... Cubes like that are probably more expensive to manufacture. However, a "Deluxe" version, using plastic tiles, was produced by Ideal in the early 80's. Pretty hard to get now, i'm afraid. I also have one that seems newer, this also has plastic tiles. It came on a card, that had the name "Old Brand Magic Cube" on it. The back of the card has a (poor) solution printed, and there is also a picture of an Octagon, supposedly by same manufacturer. Apart from the plastic tiles, there is nothing deluxe about this last one - the turning is o.k. but not VERY smooth. ____________________________________ Philip K Vendersgade 15, 3th DK - 1363 Copenhagen K Denmark Phone: +45 33932787 Mobile: +45 21706731 E-mail: philipk@bassandtrouble.com E-mail: philipknudsen@hotmail.com From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 11 21:43:05 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA15667 for ; Thu, 11 Mar 1999 21:43:04 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990310090218.28861.qmail@hotmail.com> From: "Philip Knudsen" To: cube-lovers@ai.mit.edu Subject: Re: Oddzon version of the cube Date: Wed, 10 Mar 1999 01:02:17 PST Paul Hart wrote: >After my disappointing results with my Oddzon cube, >I pledged to never again buy one of their products >until they change or improve their sticker design. You're right about their Cube, but the other Rubik products by OddzOn are fine, or at least acceptable. For instance, I think the Eclipse is MUCH better in design than the Magic Strategy Game by Matchbox, 10 years earlier. Same game, but much more attractive and somehow also better gameplay. Another example is Rubik's Bricks, which is Rubik's version of the Soma Cube. There is a short mention of it in "Cubic Compendium", but OddzOn were the first to market it - and their version is excellent! BTW has anyone seen/tried any of the other new stuff by OddzOn, like "Rubik's Infinity" or Rubik's Double Tangram" ??? __________________________________ Philip K Vendersgade 15, 3th DK - 1363 Copenhagen K Denmark Phone: +45 33932787 Mobile: +45 21706731 E-mail: philipk@bassandtrouble.com E-mail: philipknudsen@hotmail.com From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 11 22:12:57 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id WAA15733 for ; Thu, 11 Mar 1999 22:12:56 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 10 Mar 1999 10:43:27 -0500 (EST) From: der Mouse Message-Id: <199903101543.KAA28632@Twig.Rodents.Montreal.QC.CA> To: cube-lovers@ai.mit.edu Subject: Re: Oddzon version of the cube > [...] made me wonder why stickers are being used at all? As far as I > know, nobody has produced a cube (or variation) where the plastic > "cubies" are colored appropriately without relying on stickers. A while ago, I took the smoothest-acting Cube I have, peeled off all the stickers, took the thing apart, and painted all the facicles. Et voila! no more sticker problems! Now, I just need to do that with one of the 5-Cubes I have, the one that's suffering from the Dread Orange Sticker Disease; it's already lost one orange sticker completely, and about four more are so loose that only a piece of masking tape is keeping them with the Cube. (Assuming I can figure out how to get it apart non-destructively.) I agree, it would be much more pleasant if the plastic itself were coloured. But that would require at least six different plastics, instead of one, which is probably why it's not done commercially. Low volume already makes the things expensive.... On the other hand, I wonder how much more it really would cost to do coloured plastics. Anyone with enough experience in the industry to say? der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 11 23:48:09 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id XAA16027 for ; Thu, 11 Mar 1999 23:48:08 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 10 Mar 1999 22:04:21 +0000 From: David Singmaster Computing To: Norman.Diamond@dec-j.co.jp Cc: CUBE-LOVERS@ai.mit.edu Message-Id: <009D4ECA.6A22DEF3.10@ice.sbu.ac.uk> Subject: RE: Fwd: Request for spectacular cube-solving - Can anyone help ? Yes there were ordinary cubes made with markings fo the blind. Rainier Seitz, product manager fro Arxon, the German distributor, made the first examples by heating a needle and making dice-like marking of one to six spots. Several versions were made commercially or by specialist firms. I have examples with zero to five spots in this style, alos with brass studs of five sizes and then Ideal (perhaps only Arxon) produced a version with moulded plastic facelets having symbols on them: +, -, hollow circle, square, triangle and solid circle. Meffert made pyramids with four different textures of surface I asked a blind friend if they were easyily distinguished and he said yes. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 12 00:15:29 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id AAA16151 for ; Fri, 12 Mar 1999 00:15:29 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 10 Mar 1999 22:19:21 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Re : Re: Edges only, Ignoring Flips, Face Turn Metric In-Reply-To: <199903050409.XAA24597@cauchy.math.brown.edu> To: michael reid Cc: Cube Lovers Message-Id: On Thu, 04 Mar 1999 23:09:00 -0500 michael reid wrote: > jerry writes > > > I have completed a God's Algorithm run in the face turn metric for the > > group consisting of edges only ignoring flips. The size of the group is > > therefore 12! The results are as follows: > [ ... ] > > very interesting. i hope that you'll also do the quarter turn metric. > I have completed a run out to 11q (took a long time). Regrettably, the diameter proved to be greater than 11q. I now have a run in progress out to 12q. It's going *very* slowly. The problem I described where my method is inefficient calculating the tail of the distribution is even worse for the quarter turn metric than for the face turn metric for this particular problem. Also, to calculate to 11q or 12q I have to store all the positions out to 6q, which I can do. I don't think I can store out to 7q on the computer I have. Even if I could, a run to 13q or 14q would be too slow, I think. I know from parity considerations that the diameter is greater than 12q, so in some ways my run to 12q is a fool's errand. That is, there are less than 12!/2 odd positions through 11q, so there must be at least a few at 13q. My only hope is that all the even positions will show up by the time I get to 12q. If so, I would know that the rest of the odd ones must be at 13q. Otherwise, I am doomed for now. I have an idea of how to approach the inefficiency in the tail. Since I am calculating ends-with for each position I calculate, I know for sure for each position I calculate which quarter-turns go further from Start and which go closer. The idea is that once I get to the tail of the distribution, I once again begin storing calculated positions in memory (those which are at the maximal distance which I am able to calculate). From there, I continue further from Start in a more traditional fashion, leaping one level at a time rather than many levels at a time. This works because I have knowledge of which quarter turns go closer to Start, and hence I don't have to worry about comparing against those positions closer to Start which I am not able to store. If I had time to put this plan into action, the run time for the tail of the distribution should be only a few minutes or a few seconds. ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 12 14:16:07 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA18031 for ; Fri, 12 Mar 1999 14:16:06 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 10 Mar 1999 23:47:56 -0500 Message-Id: <001B5B91.C22092@scudder.com> From: Jacob_Davenport@scudder.com (Jacob Davenport) Subject: Re: Request for spectacular cube-solving To: cube-lovers@ai.mit.edu Wei-Hwa Huang suggested: >How about team solving? n people, n cubes, everyone makes one move >and passes the cube to the left. Repeat. :-) Well, I'm left handed and Kristin Looney is right handed, and her solution is the one I use as well. So we have solved it together, each contributing one hand. Of course it helps a little that both of us can solve it one handed, but hey.... -Jacob Davenport From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 12 14:57:16 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA18330 for ; Fri, 12 Mar 1999 14:57:15 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36E7D039.265049BA@marlboro.edu> Date: Thu, 11 Mar 1999 09:16:25 -0500 From: Jim Mahoney Organization: Marlboro College To: Martin Moller Pedersen Cc: cube-lovers@ai.mit.edu Subject: Re: help on 5x5x5 wings References: <199902270400.FAA482087@bonestell.daimi.au.dk> Martin Moller Pedersen wrote: > > I am trying to solve my new cube the 5x5x5 cube. > I have managed to solve all of it except the wings. > The wings are the y's in the following diagram: > > ZyZyZ > yZZZy > ZZZZZ > yZZZy > ZyZyZ > > I have many moves for the 3x3x3 but I can't figure out how to apply these moves > to the wings. Hi Martin. Here's an excerpt from a longer disucussion of the NxNxN cube which I posted to cube-lovers some time ago. Other folks have done similar work, and published consistent results. In what follows a "cubie" is one of the small, colored cubes that make up the NxNxN, a "slice" is an NxN plane of the cube (even if the inside cubies don't exist), and an "orbit" is a set of cubies which can be moved into each other's places, like the corners or edges. The method below can be made to work for any kind of orbit, including the "wings" you ask about. Good luck, Jim Mahoney -- excerpt from http://www.marlboro.edu/~mahoney/cube/NxN.txt -- ===================================================================== (VI) How to Cycle Three Cubies ===================================== ===================================================================== The basic idea is to find a move sequence that will (1) take a chosen cubie off from its "hot seat" on a chosen slice *without* (here's the trick) disturbing any other cubie on that slice. The rest of the cube can be completely scrambled by this operation. Then (2) rotate the chosen slice, (3) undo step (1), putting the original cubie back into its original slice and undo whatever changes were made to the other cubies, and (4) undo step 2. The sequence always of the form A R A' R' where "A" is step 1, "R" is a rotation of a single slice, and the ' mark means, as usual, the inverse operation. Here's a detailed example, using the Corner orbit of a 3x3x3 cube, with the top layer as the "chosen slice" and the cubie marked "1" in the unfolded sketch of a cube below as the focus of attention. In eight moves the cubies in locations 1, 2, and 3 will trade places. The starting position: U a - 1 - 2 - d - (a,1,2,d,e,3,g,h) are a Corner orbit. | L | F | R | B e - 3 - g - h - (U, D, L, R, F, B) are the possible D clockwise rotations. (1) Get "b" off the chosen slice, without disturbing any other cubie on that slice. Replace it with the cubie that you want to put in its place. e - a - 2 - d - -> L -> | | | | 3 - 1 - g - h - e - a - 2 - d - -> D -> | | | | h - 3 - 1 - g - a - 3 - 2 - d - -> L' -> | | | | After L D L' e - h - 1 - g - The top layer was (a,b,c,d); now it is (a,f,c,d). "b" has been taken off the top slice, and "f" is in its place. (2) Rotate the chosen slice to place a new cubie in the hot seat. 3 - 2 - d - a - -> U -> | | | | After (L D L') U e - h - 1 - g - (3) Undo step 1, which pops the chosen cubie "b" back to its original slice, *and* (here's the key part), restore (nearly) all other cubies to their original locations, since none of the disturbed ones were on the slice that rotated in step (2). 3 - 1 - d - a - -> L D' L' -> | | | | After (L D L') U (L D' L') e - 2 - g - h - (4) Undo step 2, restoring the chosen slice back to its original position. a - 3 - 1 - d - -> U' -> | | | | After (L D L') U (L D' L') U' e - 2 - g - h - So the move sequence to cycle corners (1,2,3) is simply (L D L') U (L D' L') U' (reading left to right). With a few extra moves before this sequence (which should be undone afterwards) to arrange the cubies which should be moved into the places which are actually modified by this operation (or a similar one), this trick and its variations can be used to put back all 8 corners into their proper places. And with a bit of exploration, this same idea can be used to cycle three cubies of any type, in any orbit, on any layer, without disturbing anything else. For the Edge-Singles on the 3x3x3, for example, to bring an edge off the top slice without disturbing anything else on top, step (1) can be S D S', where "S" vertical is a rotation of a center slice. From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 12 15:58:21 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA18643 for ; Fri, 12 Mar 1999 15:58:20 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36E7D3A7.1796@ameritech.net> Date: Thu, 11 Mar 1999 08:31:03 -0600 From: Hana Bizek Reply-To: hbizek@ameritech.net To: cube-lovers@ai.mit.edu Subject: color Hello, cube-lovers, May I address an issue of cube colors, brought here by Dr. Singmaster? Color problem is crucial to those of us who engage in creating multi-cube designs, particularly if those designs are 3-dimensional. In such designs it is possible to suppress colors and create designs of, e.g., three colors only on its faces. No, I have not gone insane, I know what I am talking about. It is most unpleasant for a designer to have stickers falling off his or her cubes! The cubes should be well-made and their colors distinct. I find the orange and red colors to be nearly identical in hue. The red is light and the orange is dark, which is bad. I try to solve the problemn by suppressing orange in my 3-, 4- and 5-color designs, but it is irritating. Why can't the cube makers replace red-orange colors by pink-dark red for better contrast? Another issue is parity pairs. In solution algoirithms you don't kave to know them, but they are crucial in 3-dimensional-design algorithms. They make the above-mentioned color suppression possible. Now why can't the manufacturers sell such pairs? If they don't know what parity pairs are, I will tell them. Hana Bizek physicist, and 3-d Rubik's cube designer [Moderator's note: By parity pairs, I rather suspect he means mirror-image pairs.] From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 12 16:53:45 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA18789 for ; Fri, 12 Mar 1999 16:53:45 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 10 Mar 1999 23:53:19 -0500 Message-Id: <001B5BAE.C22092@scudder.com> From: Jacob_Davenport@scudder.com (Jacob Davenport) Subject: Re: help on 5x5x5 wings To: cube-lovers@ai.mit.edu, Martin Moller Pedersen I have a decent solution to the 5x5x5 on my web page at www.wunderland.com/WTS/Jake. I call those cubies "wings" also, and I foolishly assumed that I invented the term. Either that, or you have looked at my solution and are still having trouble. Please let me know if this page is helpful or not. If not, I would be happy to explain further how I solve the wings. Indeed, 3x3x3 moves will not help you with the wings. -Jacob From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 12 17:23:13 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA18928 for ; Fri, 12 Mar 1999 17:23:13 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19990311084938.00953240@mail.spc.nl> Date: Thu, 11 Mar 1999 08:49:39 +0100 To: DNewfield@cs.virginia.edu, cube-lovers@ai.mit.edu From: Christ van Willegen Subject: RE: Fwd: Request for spectacular cube-solving - Can anyone help ? At 09:06 26-2-1999 -0500, Dale Newfield wrote: >On Thu, 25 Feb 1999, Christ van Willegen wrote: >> Hey! _I'm_ already teaching my blind friend how to solve a cube! >> We marked the colors of the cube with braille letters spelling >> 1 - 6 dots. We're having a terribly hard time to teach him to solve >> it. It's fun, though... > >How difficult is it to read braille when the characters are in arbitrary >orientations? Have you thought of using some other coding technique that >might prove more easy to distinguish in any orientation? (Any idea what >that might be?) It's not the characters that count, just the numbers of dots. And it seems to be reasonably easy to read the number of dots in any position. Besides, it was the easiest and quickest thing we could think of. The problem with (most) blind people is lack of 3D concepts (I'd almost put a Duh! here). I know I solve the first layer of the cube with insight in the movement of cubelets. I've had lots of trouble describing what I do to my friend! Diagrams are impossible to draw, so you'd have to describe in words _exactly_ where cubelets are to be placed w.r.t. the rest of the cube before a formula can be applied. Too bad we didn't have any time to practise, yet. But we will! > >-Dale > >[Moderator's note: I'm inordinately proud of my own invention, which I >thought I mentioned years ago but can't find in the archives: Wire >symbols glued to a destickered cube, polished to a high gloss. The >symbols are blank opposite dot, square opposite circle, and plus >opposite X. The supergroup is marked by a cutout at a corner of each >face center and the adjacent cubies. I can solve it behind my back, >but when I lent it to a blind computer scientist, he gave up. --Dan] That's also a nice idea. I might try that if the braille dots thing doesn't work. Do you have pictures of this thing on-line? [Moderator's reply: No pics, but the above description should get you pretty close. The only symbols you might want help with are Dot: Made with a short tight spiral of wire, Plus and X: Double-outlined so that they can be made with a continuous strand of wire, end to end. After gluing them down, I put an extra cover of cement to protect the wire and blunt the sharp ends. Silicone protectant ("Armor All" TM in the US) gives it a good feel. I used steel wire about .2mm thick, like a paperclip, but perhaps I should stay vague so you will invent your own variation. ] Dr. Bandelow! Please adjust your machines to make cubes like this :-) [But building it is half the fun! --Dan] Christ van Willegen From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 12 18:03:02 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA19154 for ; Fri, 12 Mar 1999 18:03:02 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: In-Reply-To: <009D4DE8.BDBAD646.12@ice.sbu.ac.uk> Date: Thu, 11 Mar 1999 10:14:14 -0800 To: David Singmaster From: Patrick Weidhaas Subject: Re: Oddzon version of the cube Cc: cube-lovers@ai.mit.edu Thanks for your info re coloured cubies. I also got some info from Kevin Young, see below. Patrick Date: Thu, 25 Feb 1999 15:58:16 -0500 To: Patrick Weidhaas From: Kevin Young Subject: Re: Oddzon version of the cube Patrick, As a long time cubist, I can assure you that at one time Ideal did make a cube called "Rubik's Cube Deluxe". They used tiles instead of stickers. They were colored appropriately. In fact, that is still the cube that I use almost all of the time. The tiles are colored with blue on one side opposite of white, red opposite of orange, and yellow opposite of green. On the center red tile, was written in Gold Lettering "Rubik's Cube Deluxe". This placement of the Rubik's Cube logo differs from the Ideal sticker version, where that version has the logo on a sticker on top of the white center cube. The gold lettering has faded over the past 17 years, but the cube is like new other than that. If I remember correctly this was a limited release by Ideal. If you can find another one out there that someone is willing to sell to you, I recommend getting it. Sincerely, Kevin Young From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 12 18:39:11 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA19304 for ; Fri, 12 Mar 1999 18:39:10 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Thu, 11 Mar 1999 10:34:35 -0800 (PST) To: Cube-Lovers@ai.mit.edu Subject: Re: Speed cube times Message-Id: <21178-36E80CBB-632@mailtod-121.bryant.webtv.net> My records: LAYER BY LAYER - 33 sec. I can get it under a minute almost every time. My average is about 55 sec. I use a very eclectic approach in order to get as few moves as possible. I'll start off w/ Jiri's or Lars Petrus' method for the top, depending on which might get fewer moves. For the bottom, I use a whole bunch of different methods that I have learned on the web to finish it w/ as few series as possible. Usually it takes 3 series of moves to finish off the last layer. Often only 2 series, at the most 4. I average about 65 turns. My hands aren't super fast, so I try to make up for it by looking ahead and limiting the number of moves. If I take the time to practice the hand movements and fingering, I think I can increase my time dramatically. My goal is to get it down to average under 30 seconds (yeah right). =) CORNERS FIRST - 47 sec. My average is about 1 min. I basically use Matthew Monroe's method w/ a few tricks of my own. I just wish there is more info on this method on the web. The fingering is much easier and faster to do than the layer method, but it takes me longer because I have to use so many more turns. I'm guessing there is lots of info I don't know about in the books that have been written on this method, but I don't know how to get my hands on 'em. Could somebody point me to a web page or a book store that could help? I'm looking for more series of moves on this method. ONE HANDED! - 1 min 12 sec. I have been so addicted to cubing recently that I would spend hours at a time. So much so that my arms and hands would get tierd, and I would sometimes get pains in my wrists & forearms. (But as an addict I still keep on going) One day my right hand gave up, so I thought...what the hell, why not try w/ my left by itself! At first it took me about 5 min, then I got it down to 3 min. After a little bit more practice, I now average about 1 min, 45 sec! Again, I'm not super fast, I just look ahead and use as few moves as possible. On the web I saw that the record for one hand is 53 seconds. I'm hoping to beat that someday. Does anybody else on this list specialize one handed? Got any good one handed records? MY FEET!!! - 7 min 19 sec. I didn't think I could do it, but after my success w/ one hand, I had to try it. I also remember seeing somebody do it on that's incredible. At first it took me about 20-30 minutes...I didn't bother timing myself, because I didn't think I could do it. The hardest part is doing long sequences of moves in the last layer. I've messed up a lot at that point. Sometime later I tried it again, and did it in 10 min, then finally my record. I would practice this a lot more, but my legs get tierd lifting and manipulating the cube after just a couple of tries. With some practice, I could probably get it down to 5 minutes. ----- This brings me to a couple of ideas for a spectacular feat. (No pun intended) How about solving two cubes at once...one in eace hand...solving w/ feet and hands at the same time? ----- I have to say I'm pretty proud of these accomplishments. I'm new to this. 4 months ago I couldn't even solve a cube. I just barely learned how in November. Now I'm addicted. I wore out the stickers on two brand new cubes in my first 3 weeks. (A problem which is currently being addressed on this mailing list) It has gotten so bad that It's interfered w/ my school work. (As I'm writing this, I should be studying for my Trig exam) -Alex Montilla- From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 15 13:18:24 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA28320 for ; Mon, 15 Mar 1999 13:18:23 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Reply-To: WaVeReBeL@webtv.net Date: Thu, 11 Mar 1999 13:47:33 -0800 (PST) To: Cube-Lovers@ai.mit.edu Subject: Local Cubists Message-Id: <10765-36E839F5-696@mailtod-122.bryant.webtv.net> I feel like I was born in the wrong era. I'm 20 years old and in college right now. If I had been born 10-15 years earlier, I might be training to be in competitions. I was a little too young when it was in its prime in the 80's. I got my hands on a cube this past November & now am hooked for life. I went from 30 mins to 3 mins in the 1st month, & in 2 more months got it down to under a minute. I bring a cube everywhere I go. Tons of people come up to to talk to me about it. 99% of the time they would say: "You know what I used to do?" and then either: 1) peel off the stickers or 2) take it apart. I used to laugh along at this amusing anecdote, for I myself admit to both. But, after the 100th person...Its just annoying. There is no one I can share my hobby with. Of all these people, in the 4 months I've been into this, I have only met one person who actually knew how, but it was years ago, and has since lost interest. I got one of my friends into it, but he isn't at a level where he can compete w/ me yet. Plus, he's too busy to put some serious time into it. With the exception of my one friend, I feel all alone when it comes to cubes. Right now I am looking for any cube enthusiasts, beginner through advanced, in my area who want to get together to compete, buy/sell/trade books & cube related stuff, share secrets/techniques that can only be taught in person (there are limits as to what text & 2D images on a web page & in books can convey about manipulating a 3D cube), etc. All of my knowledge on cubes is from people's web pages, but practically all of them are made to teach the beginner. My current goal is a 30 second average. At a 55 sec average w/ a 33 sec record, I'm not too far from my goal. I achieved this using moves I've gotten from the web. I would like to talk to people personally, and see some of the books no longer in print. I read somewhere that there are over a hundred written. Please contact me if you have books I can look at, or know where I can get a hold of them. I would like also to join any local clubs if any still exist or, If there are enough people interested, start a new one. A lot of people who have seen me playing with mine in public have asked me if the Rubik's Cube has "come back" like a new craze. Although there isn't, I would sure like to see one. And how about a new championship? That would be cool. Not a world wide thing, but it wouldn't be hard to set up a small local one with a small prize like a Megaminx. Any thoughts on this? Has this been attempted lately? I live in Carson, California. So, if anyone in the LA/South Bay area is interested, please contact me. -Alex Montilla- waverebel@webtv.net ipiiika@aol.com From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 15 14:13:32 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA28563 for ; Mon, 15 Mar 1999 14:13:31 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "Noel Dillabough" To: "'Christ van Willegen'" Cc: Subject: RE: Stickers Re: Oddzon version of the cube Date: Thu, 11 Mar 1999 20:47:24 -0500 Message-Id: <000801be6c2a$49a18160$030a0a0a@noel> In-Reply-To: <3.0.32.19990310090119.00960d80@mail.spc.nl> I too found a "tiled" cube that was about $5 USD with plastic tiles rather than stickers. At first this seemed ideal since there can be no wear and tear on the stickers. However quite soon afterwards the tiles start to come off. Perhaps if they were glued better... > with colored square bricks on the faces that form the colors. They > are about $5 (I think). I haven't bought one to check quality (yet?). > Perhaps if the mechanism is alright, these might be better suited for > the cube-addict. But I'm afraid that the mechanism won't be > able to stand > lots of use. > I would be willing to pay more for puzzles of better quality. On a similar note, old versions of the Rubik's Revenge puzzle are fetching prices over $75 USD. The puzzles are basically unusable, as they are so stiff and brittle from age that they fall apart. The best buy is to buy a used Rubik's Revenge, one that was actually used during the 80s and was worn in. These puzzles are not so stiff and are actually usable. Anyway back to my point, I was wondering how many people on this list would be interested in getting a manufacturer to do a good quality run of 4x4x4 cubes? A place in the U.S. called "Puzzlets" was supposed to have a sign up list to create a production run of these cubes, but I have heard that they are no longer in business. Perhaps there is enough interest in the cube lovers' list? [Moderator's note: Has anyone else found aged, unused 4^3s more brittle than the originals? Even the early ones were usually stiff; I needed to take them apart and apply wax or other lubricant. And still they broke much too easily, due to the tiny necks on the face centers. Perhaps the only advantage aged, used cubes have is that the stiff ones whose owners didn't lubricate them are long broken. --Dan] From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 15 15:58:49 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA28969 for ; Mon, 15 Mar 1999 15:58:49 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 12 Mar 1999 01:01:52 -0500 From: michael reid Message-Id: <199903120601.BAA15248@euclid.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re : Re: Edges only, Ignoring Flips, Face Turn Metric i guess i'm not sure what you're doing, jerry. but i don't think it should be *that* difficult. the number of configurations is 12! = about 480 million. if you divide out by symmetry, you get about 10 million configurations. this should be small enough to store in memory and do a complete breadth-first search of the space. mike From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 15 16:49:33 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA29195 for ; Mon, 15 Mar 1999 16:49:32 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36E8B44F.3A68D055@erco.com> Date: Fri, 12 Mar 1999 07:29:35 +0100 From: "michael ehrt" Reply-To: m.ehrt@erco.org To: cube-lovers@ai.mit.edu Cc: der Mouse Subject: Re: Oddzon version of the cube References: <199903101543.KAA28632@Twig.Rodents.Montreal.QC.CA> > Now, I just need to do that with one of the 5-Cubes I have, the one > that's suffering from the Dread Orange Sticker Disease; it's already > lost one orange sticker completely, and about four more are so loose > that only a piece of masking tape is keeping them with the Cube. > (Assuming I can figure out how to get it apart non-destructively.) That's not a big problem. Underneath each center piece there's a screw (just like in some (or all?) 3x3s, although we don't need to open it to take it apart). Just open one of them and the whole thing comes apart. And if you've never taken it apart, enjoy the beautiful mechanism. Putting it together again is a pretty nice puzzle itself :-) Michael From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 15 17:46:20 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA29418 for ; Mon, 15 Mar 1999 17:46:19 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <006c01be6c55$1fdab740$ca685dcb@uwe> From: "UMroaming" To: "Cube-Lovers" Subject: MULTI COLORED PLASTIC SURFACES Date: Fri, 12 Mar 1999 14:27:24 +0800 der Mouse wrote: >> [...] made me wonder why stickers are being used at all? As far as I >> know, nobody has produced a cube (or variation) where the plastic >> "cubies" are colored appropriately without relying on stickers. > >A while ago, I took the smoothest-acting Cube I have, peeled off all >the stickers, took the thing apart, and painted all the facicles. >Et voila! no more sticker problems! It is not to difficult to make cubes or other puzzles without stickers and to spray paint the surfaces, the price is about the same. I once made a Pyraminx test run using this method. As David Singmaster mentioned the plastic surface under the sticker has some flow lines which are unavoidable and the sticker serves in part to hide these imperfections. >>The one which I bought in India did not have spray-painted >>surfaces, it was made out of multicolored plastic. So I think that >>manufacturers can afford it. The problem with molding the cubes out of colored plastic is the corner pieces. as they have to be molded in 3 different colored plastic, such tooling and molding procedure is extremely expensive and I can not imagine that India has the technology to produce such an item. What would make more sense is to make the stickers out of small clip on plastic tiles such as is used in my Impossiball this would not increase production cost, but totally new tooling would need to be made costing around US$50,000.00. I made a survey for my Pyraminx many years ago. Using either colored plastic tiles or the none slip fluorescent stickers and the stickers won. >Now, I just need to do that with one of the 5-Cubes I have, the one >that's suffering from the Dread Orange Sticker Disease; it's already >lost one orange sticker completely, and about four more are so loose >that only a piece of masking tape is keeping them with the Cube. >(Assuming I can figure out how to get it apart non-destructively.) > >I agree, it would be much more pleasant if the plastic itself were >colored. But that would require at least six different plastics, >instead of one, which is probably why it's not done commercially. >Low volume already makes the things expensive.... No problem to use different colored plastics only the corner pieces pose a problem. >On the other hand, I wonder how much more it really would cost to do >colored plastics. Anyone with enough experience in the industry to >say? As mentioned above there would be no cost increase apart from new tooling having to be made for the corner pieces and the flow marks on some of the surfaces will be noticeable. The best solution would be spray painting, as is being done with my Orbix and the 4 colored rings on my 3D-Puzzle Balls. I hope that this clears up your discussion on why Manufacturers use stickers. Regards Uwe HAPPY PUZZLING Uwe Meffert P.O. Box 24455, Aberdeen, Hong Kong. Tel. 852-2518-3080, Fax. 852-2518-3282 Email:- uwe@ue.net www.ue.edu www.ue.net www.mefferts-puzzles.com From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 15 18:31:44 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA29588 for ; Mon, 15 Mar 1999 18:31:44 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19990312090954.009582d0@mail.spc.nl> Date: Fri, 12 Mar 1999 09:09:55 +0100 To: cube-lovers@ai.mit.edu From: Christ van Willegen Subject: Re: Plastic colors Re: Stickers Re: Oddzon version of the cube Reply-To: Christ van Willegen At 09:01 10-3-1999 +0100, I wrote: >I've seen cubes that have real plastic colors! They are 3by's in black, >with colored square bricks on the faces that form the colors. They >are about $5 (I think). I haven't bought one to check quality (yet?). >Perhaps if the mechanism is alright, these might be better suited for >the cube-addict. But I'm afraid that the mechanism won't be able to stand >lots of use. > >Perhaps I'll just go ahead and try the experiment. After all, it's only >$5... I was wrong... They are not $5, but $2.50 :-) They're using some quite agressive glue to put the plastic colors on the faces. The color sceme is weird (White <-> Red, Green <-> Yellow, Blue <-> Orange, White, Green and Yellow are clockwise). When I bought it, two cubelets were glued together! Also, there are traces of the glue everywhere. The machanism is not too well, but it doesn't fall apart easily. The spring loaded mechanism is quite strong! When I took it apart, the springs pulled the centre pieces together quite a bit. I think that after some time, it may turn quite well. It will never be a professional cube, however... On a side note, my gf claims she saw these cubes at Intertoys or Toys-R-Us for about $1.50... > >[ Moderator's note: I take it you mean they are available in the > Netherlands? Anywhere else? ] As far as I could tell, these are manufactured somewhere in Europe. I could buy lots and send them to someone willing to re-ship them locally (as in: In the States). I know the moderator usually doesn't approve of scemes like this, but if people _really_ want one, it's the only way... Shipping is _way_ over $1.50 apiece. If people really want one, let me know, and also if you'd be willing to re-ship from the USA (to someone else there). Christ van Willegen From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 15 19:01:32 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA29641 for ; Mon, 15 Mar 1999 19:01:32 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 12 Mar 1999 11:10:18 +0000 From: David Singmaster To: whuang@ugcs.caltech.edu Cc: cube-lovers@ai.mit.edu Message-Id: <009D5001.60154AD6.25@ice.sbu.ac.uk> Subject: Re: Fwd: Request for spectacular cube-solving - Can anyone help ? Very hard to have a person do just one move and pass it on. Perhaps allow five seconds? A bit of spectacular solving would be to have someone make five or six moves and let the solver work out how to unscramble it in the same number of moves. Kate Fried in Budapest could do four moves, perhaps five, regularly. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 15 19:37:47 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA29754 for ; Mon, 15 Mar 1999 19:37:46 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Fri Mar 12 07:39:01 1999 Date: Fri, 12 Mar 1999 12:34:43 +0000 From: David Singmaster To: c.v.willegen@spcgroup.nl Cc: cube-lovers@ai.mit.edu Message-Id: <009D500D.2B3620CA.27@ice.sbu.ac.uk> Subject: RE: Stickers Re: Oddzon version of the cube Cubes with tiles instead of stickers came out very early on. I recall one called Gyro Cube, which I think was Korean, about 1981?. Then Ideal took on the idea as the Deluxe Cube. I've got an example made in China (real PRC, not Taiwan, and for the Chinese market). Recently, I've bought an example at a newsagent's in London for somewhere in the #1 to #2 range and it worked moderately well (the previous two which I bought recently were virtually immovable!). A large version of this (about 90mm or 3 1/2 in on an edge) was on sale from a street vendor in December, but I don't know if he has any left and I haven't seen it elsewhere. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 13:06:51 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA01896 for ; Tue, 16 Mar 1999 13:06:51 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Reply-To: WaVeReBeL@webtv.net Date: Fri, 12 Mar 1999 10:31:40 -0800 (PST) To: Cube-Lovers@ai.mit.edu Subject: Re: Oddzon version of the cube Message-Id: <1095-36E95D8C-2128@mailtod-121.bryant.webtv.net> In-Reply-To: "Philip Knudsen" 's message of Wed, 10 Mar 1999 00:51:10 PST I too have seen many of these cubes w/ plastic tiles. I have many different brands including the "Old Brand Magic Cube". I find them at swap meets. Most sell for $2, but I recently found a vendor who sells 'em for ONLY $1! I immediately bought 5 on the spot. The next time I go down there, I think I'll buy out the shop's stock of cubes. Either that, or ask how to get them myself. The quality is pretty bad. The turning is pretty sticky, but w/ some lube and a little wear and tear, it's alright. Plus, they break apart pretty easily. When they're really worn out, cubies start popping out all the time. If you use WD-40, it'll eat away at the plastic resulting in really smooth turning. It'll be great for about 3-4 weeks of daily cubing, but the WD-40 will take its toll, and the cube will start falling apart. But for a few bucks every 3-4 weeks is worth it to me. The good thing about these is that you can make your own "deluxe" cube. First, with a little bit of effort, and a good razor blade, you can pry off the plastic tiles. Next, strip off all the stickers (If they haven't already fallen off by themselves) and wipe off the sticky residue on your smoothest, sturdiest cube. Then, super glue the tiles in any color arrangement you want! (the tiles come in the standard colors) The tiles may have a slightly rough surface after you pry them off, so you might have to strip off any scarring/hardened glue w/ a razor to make sure it's nice and flat when glued down. This process isn't easy. It took me hours. But in the end, it's all worth it. I've only done one so far, but it works so well, I don't need to do another one yet. I've been cubing daily, hours at a time for about two months with the same cube. -Alex Montilla- P.S. I live in Carson, CA. E-mail me if you want to know where I get em. From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 13:34:31 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA01985 for ; Tue, 16 Mar 1999 13:34:30 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: In-Reply-To: <001B5B91.C22092@scudder.com> Date: Fri, 12 Mar 1999 15:17:53 -0400 To: cube-lovers@ai.mit.edu From: Kristin Looney Subject: Re: Request for spectacular cube-solving Cc: alison@wunderland.com Jake wrote: >Well, I'm left handed and Kristin Looney is right handed, and her solution >is the one I use as well. So we have solved it together, each contributing >one hand. Of course it helps a little that both of us can solve it one >handed, but hey.... wow! that explains it! I had forgotten that you are left handed! I started teaching Alison to solve the cube last night, and we did a few trials at the solving-it-together-with-on-hand-each thing, and had a really hard time at it. -Kristin Looney kristin@wunderland.com http://wunderland.com/Home/Rubik.html To all the fishies in the deap blue sea, Joy. From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 14:07:10 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA02065 for ; Tue, 16 Mar 1999 14:07:09 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <00e001be6cdf$a0cabaa0$75c4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: Cc: "Martin Moller Pedersen" Subject: Re: help on 5x5x5 wings Date: Fri, 12 Mar 1999 23:25:23 -0000 Martin Moller Pedersen wrote >I am trying to solve my new cube the 5x5x5 cube. >I have managed to solve all of it except the wings. >The wings are the y's in the following diagram: >ZyZyZ >yZZZy >ZZZZZ >yZZZy >ZyZyZ Here's a set of explicit processes: a lower-case letter means a turn of the layer containing the wing piece next to the outer layer denoted by the corresponding capital letter, and in the same sense. The brackets show the movement of the pieces in the upper layer. l F' L F l' F' L' F (Bl, lF, Lf) F2 r2 D R2 D' r2 D R2 D' F2 (Br, Fl, Rf) r' U b U' F2 U b' U' F2 r (Bl, lF, Fr) R2 U2 l D' l' U2 l D l' R2 (Br, Fl, bR) b L2 D l D' L2 D l' D' b' (Lb, Fl, fL) l2 U2 r' l U2 l' U2 l U2 r l U2 r' U2 l U2 r l2 U2 (Fl, rF) The final sequence swaps a pair of pieces in the front face. There's been a lot of discussion of this move in Cube-lovers over the years. The process I've quoted changes pieces in the central nine on the back face, but nothing will show if all the cube except the top layer is solved. The other processes change no other pieces. Roger Broadie From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 14:43:02 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA02189 for ; Tue, 16 Mar 1999 14:43:02 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36EAE6E9.6B1F0608@okanagan.net> Date: Sat, 13 Mar 1999 14:30:04 -0800 From: Karen Loewen Reply-To: Karen Loewen To: cube-lovers@ai.mit.edu Subject: Speed Cubing I have I question for any one willing to answer. I was wondering if the people who can get the rubik's cube under 45 seconds did you actually figure it all out by yourself. Or did you find out how through books, email, websites etc? My best time is 90 seconds but I can't seem to beat it the way I do it. I don't want any one telling me ways to do it faster because I want to find out for myself. But I am wondering are there certain ways to achieve faster times. Please just answer yes or no. Also I have just ordered the 5x5x5 and I was wondering how much harder is it than the 4x4x4. Thanks. [Moderator's note: Send responses to Karen; I hope she will send cube-lovers a summary of the results of her survey. ] From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 15:39:51 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA02419 for ; Tue, 16 Mar 1999 15:39:50 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36EB0B28.1169@ameritech.net> Date: Sat, 13 Mar 1999 19:04:40 -0600 From: Hana Bizek Reply-To: hbizek@ameritech.net To: cube-lovers@ai.mit.edu Subject: parity pairs References: <36E7D3A7.1796@ameritech.net> > [Moderator's note: By parity pairs, I rather suspect he means mirror-image > pairs.] Let me tell you what I mean by parity pairs, why very few have probably heard about this concept and why they are crucial in 3-dimensional (3-d) cube art. Suppose one has two cubes of identical color scheme such that the color on both cubes' up, down, front and back faces are exactly the same. If the color of the left face of one cube is identical to the color of the right face of the other cube, such a pair of cubes is said to form a parity pair. The color scheme is still identical, but the ORIENTATION of the faces is reversed for one of the members of the pair. One cannot obtain parity pairs by conventional cube manipulations, but must obtain them either from the manufacturer, or switch the faces themselves manually. I would prefer to buy such pairs from the toymaker, for it pains me to tamper illegally with those stickers. I have devised a simple algorithm to do it as painlessly as possible, but it still is a pain. But will a manufacturer sell me parity pairs? The reason so few people know about parity pairs is that such pairs are moot in solution algorithms. You do not need to concern yourself at all with parity pairs, you just have one cube and painlessly solve it. Ditto for 2-dimensional (2-d) designs (unless you treat them as lxmx1) designs. However, they are essential in 3-d cube art. They are responsible for reflection-equivalent designs, designs of fewer than six colors and ultimately fractal design prototypes. They also determine special symmetries in a 3-d design. They are the cornerstone of 3-d design theory. Without their presence all of the 3-d designs I have constructed would not be possible. Why all this self-serving fuss about parity pairs and 3-d designs? The point is this: given four parity pairs, one can construct a 2x2x2 larger clean design, that has three colors only on its six faces. The internal faces that touch are colored the same. Those colors are hidden inside the design or suppressed. Such an array of cubes, when used as corners, produce, e.g., reflection-equivalence in a design. Go to your cube collection, extract four parity pairs and see for yourselves. So I think you got the idea, Mr. Moderator. Just one slight correction; I am a "she," not a "he." You will find this almost incredible, but women too, love the cube. Hana Bizek (female) physicist and 3-d Rubik's cube designer [Moderator's note: On the contrary, there are several women on cube-lovers, and Dame Kathleen Ollerenshaw is well-known as one of the earliest writers about Rubik's cube and one of the first victims of Cubist's Thumb. I just didn't know that "Hana" was a woman's name, and I had forgotten that this information was presumed by a mention of you in the archives. I apologize for the oversight. As for nomenclature, the reason no one knows about "parity pairs" is that the term is ambiguous--"parity" could refer to representatives of any even division of a set into two parts. If you wish to enable people to know what you mean without going through your somewhat confusing description, then you should use the term "enantiomorphic pairs", "chiral pairs", or "mirror-image pairs". I believe these are the standard terms used by chemists, physicists, and everyone else, respectively. There is an interesting question, though, which your hobby may give you a particular ability to answer. According to _Rubik's Cubic Compendium_, the most common color scheme has red opposite orange, blue opposite green, and white opposite yellow. This permits two mirror-image color schemes, distinguished by whether red, white, and blue go clockwise or anticlockwise around a corner. The question is whether there is a tendency for one of these schemes to predominate, and if so, which and by how much? For instance, one enantiomorph predominates extremely strongly in the manufacture of dice, though I don't know why. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 16:11:07 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA02530 for ; Tue, 16 Mar 1999 16:11:07 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990314063522.18949.rocketmail@send103.yahoomail.com> Date: Sat, 13 Mar 1999 22:35:22 -0800 (PST) From: Han Wen Subject: Temporary Fix for OddzOn Sticker Peel To: Cube Lovers Hi, For those folks out there, like myself, frustrated with OddzOn sticker peel problem, there is an effective method to prolonging the life of these pitiful stickers. I got this technique from one of the posts on the Rubik's website. Currently, the plastic laminate that makes up the surface of the stickers for OddzOn Rubik's Cubes starts to peel at the edges after only a few weeks of intensive playing. Well, get yourself some long-lasting acrylic nail polish and paint over all the stickers. (Make sure you do this when the cube is brand new.) I know, it's a pain in the ass, but it's worth it. The first coat lasts for about 2-3 weeks before the edges start peeling again. What I do then is take a razor blade and cut off the peeled away sections and then nail polish over the stickers again. You'll probably get another 2-3 weeks of intensive play again before the cut laminate starts peeling again. However, after I repeated this process once more (razor blade cut/nail polish over), the stickers have now lasted over several months without additional peel. Hope this helps... == _________________________________________________________ Han Wen Applied Materials 3050 Bowers Ave, MS 1145 Santa Clara, CA 95054 e-mail: Han_Wen@amat.com / hansker@yahoo.com From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 16:52:10 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA02705 for ; Tue, 16 Mar 1999 16:52:10 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 15 Mar 1999 13:27:05 -0700 (MST) From: Paul Hart To: Noel Dillabough Cc: cube-lovers@ai.mit.edu Subject: RE: Stickers Re: Oddzon version of the cube In-Reply-To: <000801be6c2a$49a18160$030a0a0a@noel> Message-Id: On Thu, 11 Mar 1999, Noel Dillabough wrote: > On a similar note, old versions of the Rubik's Revenge puzzle are > fetching prices over $75 USD. The puzzles are basically unusable, as > they are so stiff and brittle from age that they fall apart. Really? I haven't noticed this in my own collection as far as I can see. > Anyway back to my point, I was wondering how many people on this list would > be interested in getting a manufacturer to do a good quality run of 4x4x4 > cubes? I think this would be an excellent idea. > A place in the U.S. called "Puzzlets" was supposed to have a sign up > list to create a production run of these cubes, but I have heard that > they are no longer in business. Is Puzzletts out of business? Their web site is still up at least. Check it out at: http://www.puzzletts.com/ [Moderator's note: If you get a response from puzzletts, please contact cube-lovers-request@ai.mit.edu. I've had several people say they don't answer.] > Has anyone else found aged, unused 4^3s more brittle than the originals? > Even the early ones were usually stiff; I needed to take them apart and > apply wax or other lubricant. And still they broke much too easily, due > to the tiny necks on the face centers. A year or two ago I had the very good fortune of stumbling across a number of 4x4x4 cubes that were brand new in their unopened original boxes from 1982. Of the two cubes that I personally opened and used extensively, I did not notice any unusual stiffness. The 4x4x4 does suffer from the known weak neck in the center pieces that is prone to snapping, but aside from that the cubes were in excellent condition and have held up very well. I'm not sure if lubricating the cube will remedy the tendency for the neck to break, but perhaps it would since it seems to happen when the cube jams slightly. The first of the two cubes to suffer a broken center piece became my spare parts cube that I use to keep the other in good running condition. Paul Hart -- Paul Robert Hart ><8> ><8> ><8> Verio Web Hosting, Inc. hart@iserver.com ><8> ><8> ><8> http://www.iserver.com/ From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 17:24:14 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA03425 for ; Tue, 16 Mar 1999 17:24:14 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <01BE6F31.56407CA0.Jean.LEBLANC@wanadoo.fr> From: Jean Leblanc To: "Cube-Lovers (Adresse de messagerie)" Subject: Re:speed cube times Date: Mon, 15 Mar 1999 22:14:43 +0100 Bonjour les fous du cube Honestly, I think I am an unrecognized champion. I CAN solve the cube within 5 minutes or more, especially when I throw it through the window into the garden (my dog loves cubes, too). If somebody can do worse, please tell me ! I didn't make up a method to solve 3*3*3, nor 4*4*4. My cube (my only 3*3*3) is a poor clone of the 80's ; it creaks and get jammed but it still works ! I'm a poor lonesome cubist... My wife and my children are not interested in cubes; shall I sacrifice my family to a plastic coloured God ? "Il faut savoir raison garder !" After all, I should be very interested in a new fabrication of 4*4*4, because mine is broken. Jean Leblanc Muret France. From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 17:55:07 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA04015 for ; Tue, 16 Mar 1999 17:55:07 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <714F77ADF9C1D111B8B60000F863155102DD6DAD@tbjexc2.tbj.dec.com> From: Norman Diamond To: cube-lovers@ai.mit.edu Subject: Old 4^3s Date: Tue, 16 Mar 1999 09:45:38 +0900 Noel Dillabough [noel@mud.ca] didn't write, but his message contained: >[Moderator's note: Has anyone else found aged, unused 4^3s more brittle than > the originals? Even the early ones were usually stiff; I needed to take > them apart and apply wax or other lubricant. And still they broke much > too easily, due to the tiny necks on the face centers. Perhaps the only > advantage aged, used cubes have is that the stiff ones whose owners didn't > lubricate them are long broken. --Dan] Nob Yoshigahara told me that he had designed a correction for the original design of the 4^3 cubes so that they would not fall apart. In my experience, early 4^3s easily fell apart, and then when a cubie hit the floor it easily broke. In my experience, later 4^3s don't easily fall apart. I would guess that the manufacturer accepted Nob-sensei's advice. -- Norman.Diamond@dec-j.co.jp [Speaking for Norman Diamond not for Compaq] From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 18:24:27 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA04139 for ; Tue, 16 Mar 1999 18:24:26 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <001301be6f56$1a197860$4a121fc8@default> From: "Jorge E. Jaramillo" To: "cube" Subject: Easy to find tile cubes Date: Mon, 15 Mar 1999 21:38:27 -0500 I live in Colombia South America and here it is very easy to find cubes with tiles instead of colored stickers. They are also very cheap (less than U$ 2). They are (I guess) those Asian cubes that are not that durable. They have this mechanism of one screw under the center tile. If you twist them many times they unscrew and come apart but since they are so cheap when I break one I just buy another one Jorge E. Jaramillo kingeorge@hotmail.com Cut the chain and chase the dream Savatage 1984 From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 19:02:58 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA04595 for ; Tue, 16 Mar 1999 19:02:58 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 16 Mar 1999 08:59:41 +0000 (GMT) From: the terminal sloth To: Cube-Lovers Subject: Re: MULTI COLORED PLASTIC SURFACES In-Reply-To: <006c01be6c55$1fdab740$ca685dcb@uwe> Message-Id: On Fri, 12 Mar 1999, Uwe Meffert wrote: > ... > It is not to difficult to make cubes or other puzzles without stickers and to > spray paint the surfaces, the price is about the same. I once made a > Pyraminx test run using this method. As David Singmaster mentioned the > plastic surface under the sticker has some flow lines which are unavoidable > and the sticker serves in part to hide these imperfections. Why can't you take a modelling knife or a file and remove these lines? And use a bit more paint where necessary (easier with acrylic than with spray paints). Obviously this isn't practical for large-scale manufacture. > I hope that this clears up your discussion on why Manufacturers use > stickers. Alex -- Alexander Lewis Jones - the terminal sloth sometimes I sits and thinks, sometimes I just sits From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 19:32:55 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA04688 for ; Tue, 16 Mar 1999 19:32:54 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199903160937.KAA24418@bednorz.get2net.dk> From: "Klodshans" To: cube-lovers@ai.mit.edu Date: Tue, 16 Mar 1999 10:36:42 +0000 Subject: Re: OddzOn version of the cube Reply-To: klodshans@get2net.dk Wayne Johnson wrote: > I've got the new magic. > Works exactly the same except that the colours are pretty ugly. > Matchbox did a nice one that was rainbow on black. > The new ones are yellow on red. I agree. I have all the different Magics and the OddzOn version is not an improvement. The weird thing is that their website www.rubiks.com shows a picture of the Magic thats looks like one of the Matchbox ones (BTW on the same site I read the other day that OddzOn is planning to make their own deluxe cube). Anyway, in the message that Wayne responded to, I was not talking about Magic, but the "Magic Strategy Game" by Matchbox which is a completely different thing. As I wrote, this has been re- launched by OddzOn under the new name "Eclipse", and in this case the OddzOn guys have actually improved the original design, in my opinion. ______________________________________ Philip K E-mail: philipk@bassandtrouble.com E-mail: klodshans@get2net.dk web: http://hjem.get2net.dk/philip-k From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 20:02:41 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA04847 for ; Tue, 16 Mar 1999 20:02:40 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <13546.9903160941@sun2.mcs.le.ac.uk> Date: Tue, 16 Mar 1999 09:41:52 +0000 (GMT) From: "M. P. Baker" Reply-To: "M. P. Baker" Subject: Re: Stickers vs. tiles To: cube-lovers@ai.mit.edu David Singmaster wrote: > Recently, I've bought an example [of a tiled cube] at a > newsagent's in London for somewhere in the #1 to #2 range and it worked > moderately well (the previous two which I bought recently were virtually > immovable!). A large version of this (about 90mm or 3 1/2 in on an edge) was > on sale from a street vendor in December, but I don't know if he has any left > and I haven't seen it elsewhere. These cubes appear to be available from street vendors all over the UK. I've recently bought some in Leicester and Plymouth. They also sell them in a "gadget" shop at the end of my street, the sort of place that also sells blow-up aliens etc. The large ones are really nice for displaying patterns on, and came with a solution entertainingly translated from some Chinese type script :-) -------------------------------------------- Matthew Baker Dept. of Mathematics and Computer Science University of Leicester mpb2@mcs.le.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 16 20:35:46 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA04946 for ; Tue, 16 Mar 1999 20:35:46 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 16 Mar 1999 05:14:55 -0500 (EST) From: Nicholas Bodley To: Cube Mailing List Subject: Taking apart the 5^3 Message-Id: As nearly as I can remember, you can begin dismantling one of these by rotating the top slice by maybe 30 degrees or so, then prying upward on one of the "wing" cubies (between the center and the corner cubies). Use your thumb, nail side down, and lift. Experiment with different amounts of rotation; you'll find a position where the "wing" cubie's "foot" will push aside many others. Once it's disengaged, life becomes easier. This method, if you choose the proper cubie to pry, and align it properly with the "loosest" neighbor below it, is harmless. Just possible that I'm suggesting the wrong cubie to pry, but iirc, the center cubies are more directly held than the "wings". Believe me, the insides of a 5^3 are utterly amazing. The scheme used for the 3^3 can't hold a 5^3 together unaided; the mechanism is an extension of that in the 5^3, but has an additional set of retaining surfaces, generally spherical in their geometry. The shape of a "foot" on a corner cubie is something to behold; it could be a bit of a challenge to define it in a CAD program. As I've said before, don't even think of allowing your cat to watch the process! Sorting the pieces for reassembly is part of the fun. |* Nicholas Bodley *|* Autodidact & Polymath * Electronic Tech. (ret.) |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* |* Amateur musician *|* -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 13:35:41 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA07047 for ; Wed, 17 Mar 1999 13:35:40 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199903170235.VAA11730@garnet.sover.net> Date: Tue, 16 Mar 1999 21:37:49 -0500 To: Nicholas Bodley From: Nichael Lynn Cramer Subject: Re: Taking apart the 5^3 Cc: Cube Mailing List In-Reply-To: Nicholas Bodley wrote: >As nearly as I can remember, you can begin dismantling one of these by >rotating the top slice by maybe 30 degrees or so, then prying upward on >one of the "wing" cubies (between the center and the corner cubies). Use >your thumb, nail side down, and lift. Oh course, if you want to wimp out, the center face cubie is held on by a screw (at least his is true on my 5Xs). Just take off the sticker (this is probably easier on the orange side...) and the rest becomes pretty easy. --- Nichael Cramer loose shoes, nichael@sover.net a tight schedule, http://www.sover.net/~nichael/ and a warm place to write Lisp... From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 14:07:04 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA07131 for ; Wed, 17 Mar 1999 14:07:03 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <015c01be7033$e646df80$8ccfaf8b@uwe> From: "UMroaming" To: "Christ van Willegen" Cc: "Cube-Lovers" , "Jing Meffert" Subject: Re: MULTI COLORED PLASTIC SURFACES Date: Wed, 17 Mar 1999 13:05:23 +0800 Dear Christ Thanks for your email, I will answer / comment in text > From: Christ van Willegen > Date: Wednesday, March 17, 1999 12:29 AM > Subject: Re: MULTI COLORED PLASTIC SURFACES > Uwe Meffert > I saw one of your newer cubes in Eindhoven, The Netherlands > last week. They are black, and have plastic tiles as the colors. > By the way, 'newer' as in: I've never seen them before. > Prices vary from $1.50 to $2.50 (about 3 to 5 DM, your name > makes me assume you're German, but I may be wrong, of course). > I saw them at 'Jolie/Promida' in Eindhoven, my gf saw them at > Intertoys (she's not sure...) in Veldhoven. YES I AM GERMAN LIVING IN HONG KONG > I've modified one of those cubes (with glue and electricity wire) > to bear symbols that can easily be discerned by hand (as you may > be aware from previous discussions on this list, one of my friends > is blind, and I wanted to learn him how to solve the cube). > I assume (from glue residues found on the cube (even glueing together > two cubelets!)) that the tiles are glued on. How 'hard'/'expensive' > would it be to make these tiles not square, but pre-formed? It > would make the cubes nicer, and even more useful for blind people > (and seeing people who would like to learn to solve the cube > behind their backs). The forms would be: THE CUBES THAT YOU REFER TO ARE NOT MINE BUT A CHEAP COPY OUT OF CHINA. Different textured labels including tile labels should be easily purchasable from a good stationary store and you can easily up a few samples by hand. About 12 years ago I made 50k pieces of my Pyraminx with 4 different texture material for the Blind which I donated to several Blind Intitutes around the world and I understand that some of the players where able to solve the pyraminx by themselves without any help. > - Filled square > - Open square > - Filled circle > - Open circle > - Plus sign > - Star (6-points) > Do you like the idea? Is it marketable? Is it produceable? It's Produceable yes marketable NO. > probably a bit harder to produce. I don't know if the tiles are > glued on by hand, or if they are glued on by machines. It would > make a big difference... All the self adhesive labels are glued on by hand one side at a time using a sort of special scotch tape with its adhesive properties being lower then the adhesive on the labels. > The cubes I have (2 of them) suggest hand production. A few tiles > are glued on a bit skew, and the colors are not in the same order. > I'd assume a machine would glue them on in perfect alignment and > always in the same order. Thats because the cubes are from a small copy company that does not care about quality > By the way: I can solve the ImpossiBall! I'm using about the same > sequences of rotations as I do on the cube. CONGRATULATIONS With warm regards Uwe HAPPY PUZZLING Uwe Meffert P.O. Box 24455, Aberdeen, Hong Kong. Tel. 852-2518-3080, Fax. 852-2518-3282 Email:- uwe@ue.net www.ue.edu www.ue.net www.mefferts-puzzles.com From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 14:36:56 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA07208 for ; Wed, 17 Mar 1999 14:36:55 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Jerry Bryan To: Cube Lovers Subject: Re : Re: Edges only, Ignoring Flips, Face Turn Metric In-Reply-To: <199903120601.BAA15248@euclid.math.brown.edu> Message-Id: Date: Wed, 17 Mar 1999 00:34:12 -0500 (Eastern Standard Time) On Fri, 12 Mar 1999 01:01:52 -0500 michael reid wrote: > i guess i'm not sure what you're doing, jerry. but i don't think > it should be *that* difficult. the number of configurations is > 12! = about 480 million. if you divide out by symmetry, you get > about 10 million configurations. this should be small enough to > store in memory and do a complete breadth-first search of the space. > The way you describe the search is how Herbert Kociemba did it, but it is not how my program does it. I think his program only took an hour or two. I am applying my program to a problem to which it is not well suited because I do not have time to write one more like Herbert's. I tend to think that the most fundamental design decision in a program which does a Start rooted breadth first search for a cube space is to decide whether the search space can fit in memory. If it can, and if there is an easy way to index the search space, then the permutations themselves do not have to be stored. All that has to be stored is the distance from Start for each permutations. These distances are usually stored one per byte, or sometimes one per half-byte. There is even some discussion the Cube-lovers archives about how the storage can be reduced to two bits per permutation. If the search space cannot fit in memory, then it seems to me to be the case that some representation of the permutations themselves must be stored in addition to the distance from Start for each permutation. My program is designed to search as much as possible of the 4.3*10^19 search space for the entire cube group, so it stores permutations. To make it into a program to search edges only without flips, I simply fixed the corners and the flips, plus I made the lexicographic ordering consider edges before corners. But it still stores the permutations. It's sort of a quick and dirty solution which runs very slowly for the problem at hand. When a search space consists of the elements of a cube group, it is easy to index the search space. But when a cube group is reduced by symmetry the result is generally not a group and the resultant search space is (in my experience) not very easy to index. The thing about Herbert's program that I have trouble comprehending is that he is able to reduce the search space by symmetry and still have the indexing be well behaved. He has posted a clear exposition of his method, so the problem is in my understanding rather than in his explanation. The reason reduction by symmetry results in poorly behaved indexing for the search space is because not all positions are equally symmetric. There is much discussion of this phenomenon in the archives under the general heading of "the real size of cube space". Herbert seems to have overcome this problem for the edges problem. But if I understand correctly, he does not believe the same solution can be applied to the corners. If Q[n] is the set of permutations which are n moves from Start, then my program is calculating the product Q[6]Q[6] (all products of the form st for s and t in Q[6]) as a way to determine Q[12]. For the whole cube, most such products are in fact 12q from Start and most such products are distinct. There is very little wasted time or energy. But for edges only without flips, Q[12] is in the tail of the distribution so most such products are either duplicate or are less than 12q from Start. Nearly all the products are a waste of time. My program does reduce by symmetry to certain extent. If R[n] is the set of representatives (patterns) which are n moves from Start, then I only store R[n]. (R[n] is about 48 times smaller than Q[n].) Q[n] is inferred via pointers to R[n], and is represented as Q[n]=R[n]^M, where M is the set of 48 rotations and reflections of the cube. Secondly, I only produce elements of R[2n] rather than elements of Q[2n], which in theory speeds up the program by about 48 times but which in practice only seems to speed it up by about 20 times. But for the edges without flips search, this kind of a speedup is utterly dwarfed by all those wasted products from Q[6]Q[6]. My program always runs into this problem when it gets into the tail of a distribution. ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us Pellissippi State Technical Community College From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 15:30:12 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA07461 for ; Wed, 17 Mar 1999 15:30:12 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199903171610.RAA18270@bednorz.get2net.dk> From: "Klodshans" To: cube-lovers@ai.mit.edu Date: Wed, 17 Mar 1999 17:09:42 +0000 Subject: Re: OddzOn version of the cube Reply-To: klodshans@get2net.dk In-Reply-To: <4.1.19990316202534.0092a160@mail.vt.edu> Kevin Young wrote: > Where at on www.rubiks.com does it say that Oddzon > is planning on making a deluxe version? At www.rubiks.com, go into the "news" section. The announcement for an OddzOn deluxe Cube was added on March 11th. ______________________________________ Philip K E-mail: philipk@bassandtrouble.com E-mail: klodshans@get2net.dk web: http://hjem.get2net.dk/philip-k [Moderator's note: http://www.rubiks.com/deluxe.html says in one place that they are planning to have "super high quality durable stickers" and in another that "there won't be stickers" so it's anyone's guess what they have in mind. They're also considering "holographic center labels" vs. "the classic look" and say they will be conducting a poll. Rumors that the Tartan design is being promoted by one of its inventors are unverified, and those were gifts, not bribes. --Dan] From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 16:04:42 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA07630 for ; Wed, 17 Mar 1999 16:04:42 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36EFE0A5.3B50AF48@switchview.com> Date: Wed, 17 Mar 1999 12:04:37 -0500 From: Michael Swart Organization: Switchview To: Roger Broadie , cube-lovers@ai.mit.edu Cc: Martin Moller Pedersen Subject: Re: help on 5x5x5 wings References: <00e001be6cdf$a0cabaa0$75c4b0c2@home> Regarding 5x5x5 wings Roger Broadie said: > l F' L F l' F' L' F (Bl, lF, Lf) > F2 r2 D R2 D' r2 D R2 D' F2 (Br, Fl, Rf) > r' U b U' F2 U b' U' F2 r (Bl, lF, Fr) > R2 U2 l D' l' U2 l D l' R2 (Br, Fl, bR) > b L2 D l D' L2 D l' D' b' (Lb, Fl, fL) > l2 U2 r' l U2 l' U2 l U2 r l U2 r' U2 l U2 r l2 U2 (Fl, rF) Wow, that's a big help. I discovered the following long-winded maneuvers a while ago. Changing 'wings' on D. RT = (r' D' r D' r' D2 r) (right thingy) LT = (l D l' D l D2 l') (left thingy) 1. RT D2 RT D2 LT D2 LT D2 (Fl, Bl)(fL, Fr) 2. RT D LT D' RT LT D' RT D LT (fL, bL)(Fl, Br) (Side note, RT and LT are used by me to get the last squares of the fourth layer) Michael Swart Michael.Swart@switchview.com From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 16:30:30 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA07704 for ; Wed, 17 Mar 1999 16:30:29 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36EEEF3F.2645@zeta.org.au> Date: Wed, 17 Mar 1999 10:54:39 +1100 From: Wayne Johnson Reply-To: sausage@zeta.org.au To: cube-lovers@ai.mit.edu Subject: Speed cubing results - March 99 Hello all, This is the list so far. There are others to go on, but I need CURRENT best times, and CURRENT averages: Name Method Best Time Average Time Lindon Collins Layer by Layer 38 sec 47.5 sec Jiri Fridrich Fridrich 14 sec 20 sec Ryan Heise Fridrich 34 sec 43 sec Ryan Heise Petrus 40 sec 56 sec Wayne Johnson Petrus 47 sec 65 sec Wayne Johnson Layer by Layer 58 sec 75 sec Karen Loewen Karen Loewen 90 sec *** Clive McCaig Layer by Layer 38 sec 60-75 se Alex Montilla Layer by Layer 33 sec 55 sec Alex Montilla Corners first 47 sec 60 sec Alex Montilla One hand only 73 sec 01:45 Alex Montilla Feet only 07:19 N/A Han Wen Fridrich 25 sec 40 sec Wayne From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 17:02:28 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA07808 for ; Wed, 17 Mar 1999 17:02:28 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Douglas Zander Message-Id: <199903120225.UAA13599@solaria.sol.net> Subject: cube with colors attached To: cube-lovers@ai.mit.edu (cube) Date: Thu, 11 Mar 99 20:25:33 CST I received as a present many years ago the Game of Rubik's Cube. (I forget the exact name) but just in case anyone wonders about it, it is a hard mechanism to turn. The cubies each had plastic colored blocks fitted into the cube surface with holes for pegs. What you were supposed to do was place a peg into a hole then play some game with an opponent. Does anyone else have this cube game? How rare is this? Also, I wish to start a new topic about the cube. Has anyone ever thought of making a large cube out of wood so that there is a lot of wood (or clay) on the outside of the cube and then carve something like a human head out of the material? (a bust) Then the object is to scramble and reconstruct the head. (Has this been talked about before?) I think a white bust of an ancient Greek (like white marble statues) would be cool. -- Douglas Zander | dzander@solaria.sol.net | Shorewood, Wisconsin, USA | From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 17:40:24 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA07928 for ; Wed, 17 Mar 1999 17:40:23 -0500 (EST) Message-Id: <199903172240.RAA07928@mc.lcs.mit.edu> Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 9 Mar 1999 22:46:57 -0500 (EST) From: Nicholas Bodley Reply-To: Nicholas Bodley To: Norman Diamond Cc: cube-lovers@ai.mit.edu Subject: Magic Domino: WTB; also, What's its mechanism like? In-Reply-To: <714F77ADF9C1D111B8B60000F863155102DD6D3A@tbjexc2.tbj.dec.com> Highly unlikely that anyone has one that they'd like to part with, but I'd like to buy a Magic Domino. [...] I'd love to know what the mechanism of a Magic Domino is like, inside. |* Nicholas Bodley *|* Autodidact & Polymath * Electronic Tech. (ret.) |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* Frequent crashes are unacceptable in a mature |* Amateur musician *|* computer industry. [Moderator's note: Anyone who has one for sale, please contact nbodley by e-mail. --Dan] From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 18:39:41 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA09036 for ; Wed, 17 Mar 1999 18:39:41 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: TSWatts@aol.com Message-Id: <2d4d92d3.36eef932@aol.com> Date: Tue, 16 Mar 1999 19:37:06 EST To: cube-lovers@ai.mit.edu Subject: Puzzlets On 3/16/99 hart@iserver.com (Paul Hart) asked if Puzzlets is still in business. I can verify that they are in fact still in business in the Supermall in Auburn, Washington (near Seattle). They recently moved from a location in downtown Seattle which may be the source of the confusion. I can't say anything one way or the other about their tendency to not answer Emails, but I have spoken to the owner recently about various cube-like puzzles and he was very knowledgeable and willing to talk to me at length (unfortunatley I don't remember his name). I'm surprised he isn't a part of this Email group! I can also tell you that he DOES still maintain a list of people who would be interested in paying to get somebody to do another run of 4x4x4 cubes (aka "Rubik's Revenge"). Apparently no manufacturer will do it unless they can do a run of 30,000 of them! Also, I know he has a list of people who would be willing to pay a premium for a used version of the 4x4x4, if anyone's interested. I traded my 4x4x4 with him for some other merchandise since I find the 5x5x5, which I only just learned existed about two months ago, to be basically the same degree of difficulty as the 4x4x4, just bigger. They do have some 5x5x5's in stock. -Tom Watts Puyallup, WA, USA From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 17 19:17:00 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA09149 for ; Wed, 17 Mar 1999 19:16:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Wed, 17 Mar 1999 15:41:21 -0800 (PST) To: Cube-Lovers@ai.mit.edu Subject: Re: Speed cubing results - March 99 Message-Id: <18576-36F03DA1-15@mailtod-122.bryant.webtv.net> In-Reply-To: Wayne Johnson 's message of Wed, 17 Mar 1999 10:54:39 +1100 As far as timing is concerened, do you include a preview before the timer is started, or is it done "cold" (No looking at all before the timer starts)? If a preview is allowed, how long do you get? Is there a standard for this that everyone is going by? For longer times this shouldn't matter too much, but for record keeping and fast times such as Jiri's 14 seconds, I can see how a few seconds in the begining can really make a difference. Is there a FAQ about this? Also, are you people timing yourselves or do you have someone to do it? I do it myself. It doesn't affect my time too much, but I can shave off a second or two if someone else does it. -Alex- From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 18 12:34:38 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA12194 for ; Thu, 18 Mar 1999 12:34:38 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <01BE7093.03AB1640@slip129-37-51-185.ca.us.ibm.net> From: Derrick Schneider To: "cube-lovers@ai.mit.edu" Subject: RE: Puzzlets Date: Wed, 17 Mar 1999 16:27:10 -0800 I also can't comment on their non-responding trend (though a recent move might be reason enough), but the owner's name is Mike Green, I believe, and he's the one you e-mail when going to www.puzzletts.com. Derrick From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 18 13:22:39 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA12312 for ; Thu, 18 Mar 1999 13:22:38 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 18 Mar 1999 00:53:22 -0500 (EST) From: der Mouse Message-Id: <199903180553.AAA24726@Twig.Rodents.Montreal.QC.CA> To: Cube-lovers@ai.mit.edu Subject: Re: Taking apart the 5^3 > As nearly as I can remember, you can begin dismantling one of these > by rotating the top slice by maybe 30 degrees or so, then prying > upward on one of the "wing" cubies (between the center and the corner > cubies). Use your thumb, nail side down, and lift. Well, I fiddled with it and finally managed to get one of my 5-Cubes apart (I used the one with the loose stickers). I found it more effective to turn a "thick slice" (ie, the outer two slices turned together) about 45 degrees, then pry with my thumb between the corner and wing of the turned slice. (This is perhaps ambiguous. Start with a solved 5-Cube, turn the U face 45 degrees clockwise, so the URF cubie and the RF wing cubie next to it are just above the middle of the F face. Then stick your thumb between those two cubies, nail towards the URF corner cubie, and lever the wing cubie down.) It's harder to get the last wing cubie back in than it is to take the first wing cubie out, but by reversing the move I described above I find it not too difficult. Now I just need to find paints that will stick well to the plastic these things are made of. (The paints I used for the 3-Cube I painted don't stick as well as I'd like.) > Believe me, the insides of a 5^3 are utterly amazing. [...] The > shape of a "foot" on a corner cubie is something to behold; True. Quite impressive to look at. Indeed, once you've taken out the off-center face cubies and the wing cubies, you're left with something that looks like a ricketey skeletal 3-Cube (and indeed can, if you're careful, be manipulated as such). Amusingly, I realized that as long as you get that "ricketey 3-Cube" put together in its solvable orbit, it's impossible to put the rest of the 5-Cube together unsolvably! (Unless you've marked the face cubies so they're distinguishable, of course.) der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 18 13:40:33 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA12366 for ; Thu, 18 Mar 1999 13:40:33 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36F09AFF.752D8854@ibm.net> Date: Wed, 17 Mar 1999 22:19:44 -0800 From: "Jin 'Time Traveler' Kim" Reply-To: chrono@ibm.net To: skouknudsen@get2net.dk Cc: cube-lovers@ai.mit.edu Subject: Some more Rubik's Revenge notes References: <199902251022.LAA13413@bednorz.get2net.dk> Check that, the Korea cube is definitely of poorer quality than either Macau or Hong Kong yet at the same time has its own merits. The reason that the cube felt more like it was going to break was because the middle "wing" cubelets and corner cubelets are "hollow." The material is also softer, but somehow it feels like the corner pieces are sturdier than the earlier ones made in Macau and Hong Kong. I am assuming it was made later because seldom are puzzles made of higher quality in later runs, especially when the tooling is probably more expensive and when the print run is so short. But all 3 versions wear the same "(c) I.T.C. 1982" (Ideal Toy Company?) with the different "Made in..." markings. Anyway, the puzzle was easily disassembled without the need to remove a screw (There IS no screw unlike the others). Just like popping open a standard cube. Looser tolerances went into making this piece so this was not a difficult task. Like I said, the corner cubelets actually feel sturdier than the others but the overall the plastic used is much softer and tolerances aren't tight. Of course, this makes for an easier turning puzzle but tends to "stick" a lot because of the hollow pieces. If these "hollows" were somehow smoothed in, this would be a pleasure to work on instead of the stiffer (and more break prone) Macau and Hong Kong cubes. As it is, the center windows tend to bind easily against each other and I think ultimately it will break just as easily (if not more easily) than the Macau or Hong Kong deals. Oh yeah, the Korea Revenge also feels slightly lighter than the Macau or Hong Kong cubes for obvious reasons. Hmmm... I think I'll cc the cube list with this. Might be interesting to some. I wonder how I could squeeze some of this into the Cube FAQ... -- Jin "Time Traveler" Kim chrono@ibm.net http://www.slamsite.com/chrono '95 PGT - SCPOC From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 18 14:09:55 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA12457 for ; Thu, 18 Mar 1999 14:09:55 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <0F8184664EA9D21192F70008C75D16925CAEFF@esealnt145> From: "Johan Myrberger (EBC)" Reply-To: johan.myrberger@bigfoot.com To: "'cube-lovers@ai.mit.edu'" Subject: RE: cube with colors attached Date: Thu, 18 Mar 1999 09:24:44 +0100 > ... Has anyone ever thought of making a large cube out of wood so > that there is a lot of wood (or clay) on the outside of the cube and > then carve something ... Something like this has been manufactured. I believe it was by Disney corp. They made cubes which loked like the head of Donald Duck and Mickey Mouse if my memory serves me. regards /Johan Myrberger mailto:Johan.Myrberger@bigfoot.com From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 18 14:41:45 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA12540 for ; Thu, 18 Mar 1999 14:41:45 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: C.McCaig@queens-belfast.ac.uk Date: Thu, 18 Mar 1999 09:56:55 GMT To: Cube-Lovers@ai.mit.edu Message-Id: <009D54AE.1E20C937.3@a1.qub.ac.uk> Subject: Re: Speed cubing results - March 99 > As far as timing is concerened, do you include a preview before the > timer is started, or is it done "cold" (No looking at all before the > timer starts)? If a preview is allowed, how long do you get? Is there > a standard for this that everyone is going by? i usually do it cold. i use the layer-by-layer method, so a preview isnt really all that advantageous. i've tried jiri's method, but i couldnt get used to it, and only once managed to break 60 secs with it. > Also, are you people timing yourselves or do you have someone to do it? > I do it myself. It doesn't affect my time too much, but I can shave off > a second or two if someone else does it. i just use my watch, with the alarm set to go off, and the display reading the seconds (so the alarm goes off at :00) and then look when i've completed the cube. > -Alex- Clive -- Clive McCaig Dept. Applied Mathematics Queens University Belfast Northern Ireland From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 18 19:04:31 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA14621 for ; Thu, 18 Mar 1999 19:04:31 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 18 Mar 1999 07:35:57 -0500 (EST) From: Jiri Fridrich To: WaVeReBeL@webtv.net Cc: Cube-Lovers@ai.mit.edu Subject: Re: Speed cubing results - March 99 In-Reply-To: <18576-36F03DA1-15@mailtod-122.bryant.webtv.net> Message-Id: I recommend that we accept the same rules as during the 1st (and the last) world championship. We had a chance to pick up the cube and look at it for 15 seconds. It was then returned to the table and the actual solving followed. Most competitors actually needed only 5-10 sec. to figure out the first couple of moves. Timing? I think most of us when we practice do the timing ourselves. I have one more point regarding the average. We should standardize this as well. For example, one can solve the cube 12 times, remove the worst and the best time and average the remaining 10. Or, do you want to list all the times during a practice and average them together? Jiri ********************************************* Jiri FRIDRICH, Research Scientist Center for Intelligent Systems SUNY Binghamton Binghamton, NY 13902-6000 Ph/Fax: (607) 777-2577 E-mail: fridrich@binghamton.edu http://ssie.binghamton.edu/~jirif/jiri.html ********************************************* From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 18 19:37:40 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA14746 for ; Thu, 18 Mar 1999 19:37:39 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36F18BF0.5950@hrz1.hrz.tu-darmstadt.de> Date: Fri, 19 Mar 1999 00:27:44 +0100 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: Cube Lovers Subject: Re: Re : Re: Edges only, Ignoring Flips, Face Turn Metric References: Jerry Bryan wrote: > > On Fri, 12 Mar 1999 01:01:52 -0500 michael reid > wrote: > > > i guess i'm not sure what you're doing, jerry. but i don't think > > it should be *that* difficult. the number of configurations is > > 12! = about 480 million. if you divide out by symmetry, you get > > about 10 million configurations. this should be small enough to > > store in memory and do a complete breadth-first search of the space. > > > When a search space consists of the elements of a cube group, it is > easy to index the search space. But when a cube group is reduced by > symmetry the result is generally not a group and the resultant search > space is (in my experience) not very easy to index. The thing about > Herbert's program that I have trouble comprehending is that he is able > to reduce the search space by symmetry and still have the indexing be > well behaved. He has posted a clear exposition of his method, so the > problem is in my understanding rather than in his explanation. I think you are right to say that the indexing of a cube group reduced by symmetries does not behave very well. For this reason I must build a table which maps the index to a representative of the corresponding equivalence class. I have no method to directly compute the index. About 10 million entries would be possible but quite a lot, so I defined two edge permutations x and y as "equivalent" if x = MyN with two symmetries M and N. So I reduced by another factor of about 48 and got 208816 classes. If x is a representative of such a class with index i, Mx with an arbitrary symmetry M is a representative of a "real" symmetry class. The "well behaved" index of the latter is computed by 48*i + Index(M), where index(M) enumerates the symmetries from 0 to 47. The problem with that which I did not realize first is, that Mx and M'x could be equivalent, which led to wrong results when computing the God's Algorithm for positions more than 3 face turns from start (I compared my results with Jerry's, who made a quick run for positions up to 6 face turns). With some exta computation this problem could be fixed. Herbert Kociemba From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 19 10:32:05 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id KAA16650 for ; Fri, 19 Mar 1999 10:32:05 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Fri, 19 Mar 1999 02:07:36 -0800 (PST) To: Cube-Lovers@ai.mit.edu Cc: IBILUIE@aol.com, IPIIIKA@aol.com Subject: Re: Speed cubing results - March 99 Message-Id: <9085-36F221E8-14@mailtod-122.bryant.webtv.net> In-Reply-To: Jiri Fridrich 's message of Thu, 18 Mar 1999 07:35:57 -0500 (EST) I think that if we are to be keeping track records & averages, we should ALL stick to one standard. Using tournament rules sounds like a good idea. This makes comparing times more accurate. Almost everybody responded w/ a different preview time (anywhere from no preview to 15 seconds). People like me who started cold had a disadvantage to those who had a preview. A 15 second preview sounds good to me. This gives enough time to familiarize oneself w/ the cube, look for pieces, and plan out the first few moves. I've been timing myself cold which means much time is wasted at the beginning. Having a preview helps a lot. When it comes to averages, I guess there is no standard. I agree w/ disregarding the high & low extremes though. They can distort the average (arithmetic mean). This should give a more accurate representation. Also, the more entries calculated into the average the better. I hope I'm not going overboard. It's not like we're in a tournament. If all that is necessary is an informal rough estimate, then you can disregard this entire message. =) -Alex Montilla- From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 19 11:06:11 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA16721 for ; Fri, 19 Mar 1999 11:06:11 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199903191105.MAA28298@bednorz.get2net.dk> From: "Klodshans" To: cube-lovers@ai.mit.edu Date: Fri, 19 Mar 1999 12:04:43 +0000 Subject: RE: cube with colors attached Reply-To: klodshans@get2net.dk In-Reply-To: <0F8184664EA9D21192F70008C75D16925CAEFF@esealnt145> Johan Myrberger wrote: > > ... Has anyone ever thought of making a large cube out of wood so > > that there is a lot of wood (or clay) on the outside of the cube and > > then carve something ... > > Something like this has been manufactured. I believe it was by Disney corp. > They made cubes which looked like the head of Donald Duck and Mickey Mouse if > my memory serves me. These "cubes" were made by Disney in Spain. They work with a 2x2x2 mechanism. The mechanism seems to be different to the one used in the Rubik's Mini Cube - you can see a screw inside the "cube" when turning slightly on two axis simultaniously. A bit similar to the Pyramorphix - maybe these were also manufactured by Meffert ? I have seen them for sale at Puzzle-shop www.puzzle-shop.de and from Pete Beck/Just Puzzles www.freeyellow.com/members4/justpuzzles/ They are quite fun to operate - one can turn Mickey's ears so they point backwards instead of upwards, or turn his eyes so they look like i don't know what. Pretty perverse ;-) Philip ______________________________________ Philip K Vendersgade 15, 3th DK - 1363 Copenhagen K Denmark Phone: +4533932787 Mobile: +4521706731 E-mail: philipk@bassandtrouble.com E-mail: klodshans@get2net.dk web: http://hjem.get2net.dk/philip-k From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 19 12:02:52 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA16859 for ; Fri, 19 Mar 1999 12:02:51 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 19 Mar 1999 11:14:58 +0000 From: David Singmaster Computing To: c.v.willegen@spcgroup.nl Cc: cube-lovers@ai.mit.edu Message-Id: <009D5582.3042380C.305@ice.sbu.ac.uk> Subject: RE: Fwd: Request for spectacular cube-solving - Can anyone help ? It is true that some blind people have limited 3-D perception, but a colleague once told me he came into a graduate student room and heard the only blind student in his class explaining subdivisions in n-dimensions to the other students! DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 19 12:47:00 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA17302 for ; Fri, 19 Mar 1999 12:46:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 19 Mar 1999 12:16:04 +0000 From: David Singmaster To: hbizek@ameritech.net Cc: cube-lovers@ai.mit.edu Message-Id: <009D558A.B96AC759.280@ice.sbu.ac.uk> Subject: RE: parity pairs Conway noted the two mirror-image orientations of the standard colour pattern (W/Y, B/G, R/O). One of the corners has BOY at a corner and he called this a BOY, versus the mirror-image YOB. I think he read the colours clockwise? Certainly most of the production was BOY and one had to hunt a bit for YOBs. Some cubists were particularly keen to have one orientation rather than the other. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 19 13:23:41 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA17372 for ; Fri, 19 Mar 1999 13:23:40 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <001001be7220$d2f8e740$0237a8c0@uwe> From: uwe@ue.net (Uwe Meffert) To: "der Mouse" Cc: "Cube-Lovers" Subject: Re: Taking apart the 5^3 Date: Fri, 19 Mar 1999 23:53:58 +0800 >>From: der Mouse <> >>To: Cube-lovers@ai.mit.edu >>Date: Friday, March 19, 1999 11:03 AM >>>I found it more effective to turn a "thick slice" (ie, the outer two >>>slices turned together) about 45 degrees, then pry with my thumb >>>between the corner and wing of the turned slice.... That procedure is not recommended as it voids the implied warranty and has the danger of permanently stripping the thread inside the center of the cube. If you must take the cube apart do so by prying off one of the center small squares and then loosening one of the screws, which later after re-assembly should be re-tightened. Regards Uwe HAPPY PUZZLING Uwe Meffert P.O. Box 24455, Aberdeen, Hong Kong. Tel. 852-2518-3080, Fax. 852-2518-3282 Email:- uwe@ue.net www.ue.edu www.ue.net www.mefferts-puzzles.com From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 19 15:00:22 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA17650 for ; Fri, 19 Mar 1999 15:00:21 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <4.1.19990319114446.0095a7d0@mail.vt.edu> Date: Fri, 19 Mar 1999 11:48:07 -0500 To: Cube-Lovers@ai.mit.edu From: Kevin Young Subject: Mustering Interest in the Rubik's Cube Hi- I've been a cubist since elementary school in 1980. My interest increases and decreases in waves, however, it never dies. I'm now back in school at Virginia Tech as a computer science major. Does anyone have any suggestions on how to muster serious interest with some of my peers at the University? Thank you, Kevin Young From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 19 19:31:58 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA18275 for ; Fri, 19 Mar 1999 19:31:57 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 19 Mar 1999 16:21:33 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Re : RE: parity pairs In-Reply-To: <009D558A.B96AC759.280@ice.sbu.ac.uk> To: Cube Lovers Message-Id: On Fri, 19 Mar 1999 12:16:04 +0000 David Singmaster wrote: > Conway noted the two mirror-image orientations of the standard colour > pattern (W/Y, B/G, R/O). W/Y, B/G, R/O is the "differ by yellow" standard, which I prefer as "the" standard. However, there are also references in Cube-Lovers archives to W/B, R/O, and Y/G as a standard or as the tournament standard. I have no idea who gets to be the standards body to select "the" standard. But as one example of why I like the W/Y, B/G, R/O standard, many of the local maxima at 12q from Start are only "somewhat symmetric", but the eye's sense of symmetry in looking at them can be much stronger. The reason is that the eye (or my eye, at least) can easily identify W/Y as the "same" color, B/G as the "same" color, and R/O as the "same" color. And when such identifications are made, the symmetry of many of the 12q local maxima is much stronger than it would be otherwise. I really haven't looked at them with any other color scheme, but I can't imagine that the apparent symmetry would look as strong otherwise. Also, in all the various discussions about stickers, falling off and otherwise, there have been comments about cubes where it is hard to tell the colors apart, depending on the exact colors which are used, how faded the colors are with age, etc. I guess my experience has been pretty positive in that my stickers have not fallen off and with one notable exception, the colors seem easy to distinguish. The exception is that with my 2x2x2 Pocket Cube, it is very difficult to distinguish the orange from the red stickers unless I have very, very good lighting conditions. This particular cube has always been this way. I can think of no reason that a 2x2x2 should be this way as compared to a 3x3x3 or a 4x4x4, but it does seem to be the case. ---------------------------------------- Jerry Bryan From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 22 13:38:42 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA22950 for ; Mon, 22 Mar 1999 13:38:42 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sat, 20 Mar 1999 06:50:39 -0500 (EST) From: Nicholas Bodley To: Uwe Meffert Cc: der Mouse , Cube-Lovers Subject: Re: Taking apart the 5^3 In-Reply-To: <001001be7220$d2f8e740$0237a8c0@uwe> Message-Id: On Fri, 19 Mar 1999, Uwe Meffert wrote: }>I found it more effective to turn a "thick slice" (ie, the outer two }>slices turned together) about 45 degrees, then pry with my thumb }>between the corner and wing of the turned slice.... }That procedure is not recommended as it voids the implied warranty and has }the danger of permanently stripping the thread inside the center of the }cube. } }If you must take the cube apart do so by prying off one of the center small }squares and then loosening one of the screws, which later after re-assembly }should be re-tightened. Since I was the first to suggest this method, I'll retract the advice. Indeed, it would be really unfortunate to strip the threads in the plastic that hold a screw in place. Mr. Meffert is, and has been, a formidable inventor and manufacturer of cube-like puzzles for quite some time, for those who don't recognize his name. I'd follow his advice; definitely! Do note that he said "loosen", not "remove" the screw. I posted recently about special care in reinserting a removed screw. My regards to all... NB |* Nicholas Bodley *|* |* Waltham, Mass. *|* |* nbodley@tiac.net *|* |* Amateur musician *|*