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MathNet 2018-part-01 — 181 problems (EN–VI) Question 171

Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)

Question 171

Maria and Pedro play on a $9 \times 9$ board. Maria starts by painting 46 unit squares of the board red. Then Pedro must choose a $2 \times 2$ square. If the square chosen by Pedro has 3 or more cells painted red, he wins the game. Otherwise, Maria wins. Which of the two can always guarantee victory regardless of the opponent's play?