Problem

Source: 2016 Argentina OMA Finals L3 p3

Tags: combinatorics, game, game strategy, winning strategy



Agustín and Lucas, by turns, each time mark a box that has not yet been marked on a $101\times 101$ 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.