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The mutilated chessboard

You are given a chessboard where two diagonally opposite corners have been removed and a large bag of dominoes of such size that they exactly cover two adjacent squares on the chessboard.
Is it possible to place 31 dominoes on the chessboard so that all the squares are covered? If yes, how? If no, why not?

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Tags: chess
If you enjoyed this puzzle, check out Sunday Afternoon Maths XV,
puzzles about chess, or a random puzzle.

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