It has long been known that only four pentominoes can tile rectangles:
For other rectangles that these pentominoes tile, see Mike Reid's Rectifiable Polyomino Page.
Rodolfo Kurchan's online magazine Puzzle Fun studied the problem of tiling some rectangle with two different pentominoes, in Issue 19, and revisited the problem in Issue 21. The August 2010 issue of Erich Friedman's Math Magic broadened this problem to use two polyominoes of any size, not necessarily the same.
Here I study the related problem of tiling some rectangle with two pentominoes, using the same number of copies of each.
For other sizes of polyominoes, see issue 26 of Puzzle Fun.
F | I | L | N | P | T | U | V | W | X | Y | Z | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
F | * | 28 | 4 | × | 8 | × | 12 | 4 | × | × | 8 | × |
I | 28 | * | 4 | 24 | 4 | 56 | ? | 12 | 56 | ? | 8 | 60 |
L | 4 | 4 | * | 4 | 4 | 24 | 4 | 4 | 4 | ? | 8 | 32 |
N | × | 24 | 4 | * | 4 | 24 | 4 | 4 | × | × | 8 | × |
P | 8 | 4 | 4 | 4 | * | 12 | 4 | 6 | 8 | 40 | 4 | 12 |
T | × | 56 | 24 | 24 | 12 | * | 96 | × | 64 | × | 4 | × |
U | 12 | ? | 4 | 4 | 4 | 96 | * | 136 | × | × | 12 | × |
V | 4 | 12 | 4 | 4 | 6 | × | 136 | * | 72 | × | 12 | 4 |
W | × | 56 | 4 | × | 8 | 64 | × | 72 | * | × | 14 | × |
X | × | ? | ? | × | 40 | × | × | × | × | * | 20 | × |
Y | 8 | 8 | 8 | 8 | 4 | 4 | 12 | 12 | 14 | 20 | * | 8 |
Z | × | 60 | 32 | × | 12 | × | × | 4 | × | × | 8 | * |
Last revised 2023-07-24.