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Parity is manifested within the game of chess in multiple ways. Considering a chess board, the parity can be indicated by the color of the square. Thus, say dark squares are odd and light squares are even. According to the rules of chess, the bishop, for example, can only move diagonally. In a sense, it is moving one over, one up/down (and vice versa). Therefore, it is moving two spaces, or an even amount of spaces. Parity principles tell us, then, that if the bishop started on an even (light) square, it can only ever move onto other even squares. The same is true for an odd (dark) square.  This same idea was is  critical in solving the mutilated chess board problem which states: "Suppose a standard 8x8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2x1 so as to cover all of these squares?"