The mutilated chessboard problem is a tiling puzzle posed by Max Black in 1946. A standard 8x8 chessboard has two diagonally opposite corners removed, leaving 62 squares, and the puzzle asks whether 31 dominoes of size 2x1 can be placed to cover all of them. It cannot: each domino must cover one square of each color, and removing two same-colored opposite corners leaves an unequal number of black and white squares. More generally, if any two squares are removed from the chessboard, the rest can be tiled by dominoes if and only if the removed squares are of different colors. The problem is used in research on automated reasoning, creativity and mathematical philosophy.
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The mutilated chessboard problem is a tiling puzzle posed by Max Black in 1946
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