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P2- second combinatorics exam of 2017 Iran MO 3rd round

Source: 2017 Iran MO 3rd round, second combinatorics exam P2

September 12, 2017
Irancombinatorics

Problem Statement

Two persons are playing the following game on a n×mn\times m table, with drawn lines: Person #1\#1 starts the game. Each person in their move, folds the table on one of its lines. The one that could not fold the table on their turn loses the game. Who has a winning strategy?