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MathNet 2020 — Math Olympiad Vault — Part 02 Question 46

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 02

Question 46

Martin writes an integer on a board. Théo may repeatedly replace it by that integer plus $2$ or minus $3$, as often as he wishes. Théo wins if he reaches $2020$ in finitely many steps; otherwise Martin wins. Which player has a winning strategy?