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Consider the problem of tiling an n-by-n chessboard by polyomino
pieces that are k-by-1 in size (copies of the straight-line polyomino of
size k). Every one of the k pieces of each polyomino tile must
align exactly with one of the chessboard squares.
Clearly, it is not always possible to tile the entire board. For example, n2 may not even be a multiple of k. However, there is always some arrangement such that the least number of chessboard squares are left un-tiled. Let m=m(n,k) be this number. This month's question: prove that for any choice of n and k, the value of m is always a perfect square. |
List of solvers:Radu-Alexandru Todor (2 March 00:15)Lorenz Reichel (2 March 01:09) Lian Wang (2 March 16:11) Jan Fricke (4 March 00:02) Dan Dima (4 March 03:45) Joseph DeVincentis (6 March 02:11) Dharmadeep Muppalla (16 March 03:49) Guangda Huzhang (19 March 00:54) Thomas Mack (21 March 02:19) Daniel Bitin (22 March 00:35) Itsik Horovitz (31 March 00:25) |
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