Problem
COM-B1-M07-P006 Opposite Corners
#6
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Two opposite corner cells are removed from an \(8\times8\) board. Prove that the remaining board cannot be tiled by dominoes.
Opposite corners have the same color.
In chessboard coloring, opposite corners of an \(8\times8\) board have the same color. After removing them, one color has two fewer cells than the other. Each domino covers one cell of each color, so the remaining region cannot be tiled.
Classical method standard, rewritten as a training task.