| On an 8 by 8 chessboard you have one single
knight. It is in the bottom left square of the board. Can the knight touch
down once, and only once, on all 64 squares to end up in the opposite corner? |
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No! The knight already occupies one white square, leaving
63 squares left. That is an uneven number. When the knight moves, he always
moves from a black square to a white or from a white square to a black.
As the two opposing squares are white, it would require an even number of
moves for the knight to land there. |