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MathNet 2026 — Part 02 Question 181

Math Olympiad Vault · MathNet 2026 — Part 02

Question 181

Diogo and Helen play the tira game, which consists of the following. Given a checkerboard of squares $1 \times 1$, each player in turn has the right to choose a square and then remove all the squares below it from the checkerboard, all the squares to the left of it, and all the others that are below and to the left of it. For example, given the checkered below, Question illustration the player who has the turn can select the square below marked in gray, leaving the squares shown to his opponent. Question illustration loses whoever takes the last square.
a) Given the checkered below, Helen starts playing. Show a strategy for her to win the match, regardless of Diogo's strategy. Question illustration
b) Given the checkered below, Helen starts playing. Show a strategy for her to win the match, regardless of Diogo's strategy. Question illustration