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Placing knights so that none attack

gamessymmetrychessboardstrategy

Two players alternately place a knight on an empty square of an 8 by 8 chessboard. Every knight on the board must be placed so that it does not attack any knight already there, and (since knights attack symmetrically) is not attacked by any. The player who cannot make a legal placement loses.

Who wins with best play, and what is the strategy?

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Look for a symmetry of the board that pairs every square with another square, and check whether a knight can ever attack its own partner square.

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Ants on a Pole and Collision ArgumentsBurnside's Lemma and Polya CountingChoosing Coordinates That Kill the ProblemSymmetry Shortcuts for Draws Without ReplacementGame Theory Basics

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