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2player game, marking a box on 101x101 grid

Source: 2016 Argentina OMA Finals L3 p3

January 16, 2023
combinatoricsgamegame strategywinning strategy

Problem Statement

Agustín and Lucas, by turns, each time mark a box that has not yet been marked on a 101×101101\times 101 grid board. Augustine starts the game. You cannot check a box that already has two checked boxes in its row or column. The one who can't make his move loses. Decide which of the two players has a winning strategy.