Given a mutilated chessboard where two diagonally opposite squares are missing (the unmutilated version of it has $64$ squares), and given $31$ domino pieces, is it possible to cover the entire chessboard with the dominoes?
This is a classic problem and has a very popular solution: http://en.wikipedia.org/wiki/Mutilated_chessboard_problem#Solution.
Is there any other solution to this problem?