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.