Challenging Question # 6
A checkerboard is missing two of its squares. The lower left square and the upper right square are gone. That leaves 62 squares on the board. You are given 31 dominoes. Each domino is a rectangle that can cover exactly two squares on the checkerboard. Can you place all 31 dominoes on the checkerboard, so that all 62 squares are covered?
The Answer is:
Each domino covers one black square and one white square. All 31 dominoes must cover 31 black squares and 31 white squares. However, the modified checkerboard contains 32 black squares and 30 white squares, or vice versa. It cannot be covered with 31 dominoes.
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