Dominoes on a chessboard puzzle
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This is a famous puzzle first seen in a Scientific American under Mathematical Games entitled "The Mutilated Chessboard" by Martin Gardner. The puzzle was stated as follows:
The props for this problem 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 two squares at diagonally opposite corners of the board and discard one of the dominoes. Is it possible to place the 31 dominoes on the board so that all the remaining 62 squares are covered? If so, show how it can be done. If not, prove it impossible.
[edit] Solution
The puzzle is impossible. Any way you would place a domino would cover one white square and one black square. A group of 31 dominoes would cover 31 white and 31 black squares of a chessboard, leaving one white and one black square uncovered. The directions had you remove opposite corner squares, and such squares are always either both black or both white.
