Combinatorics · Games · Winning strategy
Problem 2, 2024
← Prev · 14 / 14 · Next →Aca and Branko play the following game on a \(2023 \times 2024\) board. First Aca chooses a square of the board and places a queen on it. Then the players move the queen alternately, following the rules of chess, with Branko making the first move. Every move must end on a square on which the queen has not stood before; in particular, no move may end on the square where Aca initially placed the queen, since that square counts as visited from the start. The player who cannot make a move loses. Which player has a winning strategy?
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Serbian Municipal Competition 2024, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source