Assume you are placing dominoes on an 8x8 chessboard, such that each domino will cover exactly two squares of the chessboard. Can you cover every square of the chessboard with dominoes, without having any dominoes hanging off the side of the board?

With a little thought, the answer to the above question should obviously be "Yes." Now suppose, the two OPPOSITE corners of the chessboard are removed.

Can the remaining 62 squares of the chessboard be covered by dominoes without having any dominoes hanging off the board?