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Placing plates

Source: Problem Solving 101 by Stephen Muirhead (Chalkdust Magazine)
Two players take turns placing identical plates on a square table. The player who is first to be unable to place a plate loses. Which player wins?

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Tags: games, geometry, symmetry
If you enjoyed this puzzle, check out Sunday Afternoon Maths LVIII,
puzzles about games, or a random puzzle.

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