In my paper Tiling Rectangles and Half Strips with Congruent Polyominoes, I asked if the L polyomino of size n , where n ≡ 2 mod 4 , can tile a rectangle using an odd number of tiles. Philippe Rosselet has shown that the answer is "yes".

L_{6} tiles a 14 × 21 rectangle:

L_{10} tiles a 22 × 55 rectangle:

L_{14} tiles a 30 × 105 rectangle:

In general, L_{4m+2} tiles an
(8m + 6) × (4m + 3)(2m + 1) rectangle.

Charles Jepsen has independently found a similar tiling, see [1, Figure 5].

**Reference:**

[1] Charles H. Jepsen, Lowell Vaughn and Daren Brantley,
Orders of *L*-shaped Polyominoes,
*Journal of Recreational Mathematics* **32** (2003-2004), no. 3,
pp. 226-231.

Updated May 15, 2005.