Chessboard and Dominoes - Solution

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Solution

It is not possible to cover the chessboard with the 31 dominoes.

Explanation

Each domino covers one white and one black square. Therefore the dominoes would cover the same number of white and black squares.

However, the missing squares at the opposite corners are the same colour (in the picture above they are both white). So the chessboard must have two less squares of one colour than of the other.

Therefore, since the dominoes cover the same number of each colour squares, they can't cover the chessboard.

Notes

This puzzle was described by Simon Singh in his book "Fermat's Last Theorem" (page xxx in the paperback version).

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