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The Chessboard and the Dominoes

The props for this problem are a chessboard and 32 dominoes. Each dominoe 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.

Carl Lee
Wed Apr 21 08:26:07 EDT 1999