| Given a chessboard (see below) and 32 dominoes, each the exact size of two of the squares on the chessboard, can you show how 31 of these dominoes can cover the chessboard, when a pair of diagonally opposite squares has been removed? |
Solution:
| Notice that a domino covers one white and one black square. Since we removed two white squares, there is no longer an equal amount of white and black squares. Thus, we cannot tile the checkerboard. |
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