math

Math is correct reasoning. It is nothing more and nothing less.

A simple but difficult math problem: Place a knight on each square of a 7-by-7 chessboard. Is it possible for each knight to simultaneously make a legal move?

Solution: The board has 49 squares. Without loss of generality, suppose 24 of them are white and 25 are black. Consider the 25 knights resting on black squares. If they were each to make a legal move, they would have to move to 25 distinct white squares. Since there are only 24 white squares available, such a move can't be made.

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