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MathNet 2022-part-01 — 197 problems (EN–VI) Question 77

Math Olympiad Vault · MathNet 2022-part-01 — 197 problems (EN–VI)

Question 77

Two players play the game on the $3 \times 2021$ board all cell of which are initially white. The players make their moves in turn, in one move a player paints black two not necessarily adjacent white cells located either in the same row or in the same column. The player who cannot make a move loses.
Which of the players can win regardless of the opponent's game?