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2-player game on a horizontal 3 x 2015 white board

Source: 2015 Saudi Arabia IMO TST II p2

July 24, 2020
combinatoricsgamegame strategy

Problem Statement

Hamza and Majid play a game on a horizontal 3×20153 \times 2015 white board. They alternate turns, with Hamza going first. A legal move for Hamza consists of painting three unit squares forming a horizontal 1×31 \times 3 rectangle. A legal move for Majid consists of painting three unit squares forming a vertical 3×13\times 1 rectangle. No one of the two players is allowed to repaint already painted squares. The last player to make a legal move wins. Which of the two players, Hamza or Majid, can guarantee a win no matter what strategy his opponent chooses and what is his strategy to guarantee a win?
Lê Anh Vinh
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