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Problem 1

Part of 2024 Argentina Cono Sur TST

Problems(1)

Two players alternately colour two cells from the same row or column

Source: Argentina Cono Sur TST 2024 P1

8/9/2024
Two players take turns playing on a 3×10013\times1001 board whose squares are initially all white. Each player, in his turn, paints two squares located in the same row or column black, not necessarily adjacent. The player who cannot make his move loses the game. Determine which of the two players has a strategy that allows them to win, no matter how well his opponent plays.
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