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Filling a 2x2 square two-player game

Source: Baltic Way 1996 Q16

March 19, 2011
combinatorics proposedcombinatorics

Problem Statement

On an infinite checkerboard two players alternately mark one unmarked cell. One of them uses ×\times, the other ∘\circ. The first who fills a 2×22\times 2 square with his symbols wins. Can the player who starts always win?
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