Problem
COM-B1-M07-P002 Two Cells of One Color
#2
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Two cells of the same color are removed from a \(6\times6\) board in chessboard coloring. Prove that the remaining board cannot be tiled by dominoes.
Each domino covers one cell of each color.
The full \(6\times6\) board has equal numbers of black and white cells. Removing two cells of the same color destroys this equality. But every domino covers one black and one white cell, so any domino tiling would cover equal numbers of the two colors. Contradiction.
A general form of the classical corner problem.