Puzzle #13: Mutilated Chessboard and Dominoes

This is a famous puzzle that I have come across in many different puzzle books. I have taken this from one of Martin Gardner’s books – The Best Mathematical and Logic Puzzles (Puzzle #3).

The props for this puzzle are a chessboard and 32 dominoes. Each domino is of such size that it exactly covers two adjacent squares on the board. The 32 dominoes therefore can cover all 64 of the chessboard squares. But now suppose we cut off 2 squares at diagonally opposite corners of the chessboard (see graphic below) and discard one of the dominoes as well, i.e. we have 31 dominoes now. Is it possible to cover the 62 squares on the board with the 31 dominoes? If so, show how, and if not, prove that it is impossible?

Puzzle 13 graphic

Note for parents: Show a domino if your child has not seen one. Also, for kids younger than 10, try doing it with a 4×4 chessboard first.

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