Combinatorics · Game theory · Winning strategy · Digits
The number \(2025\) is written on a board. Ana and Bojan play the following game, moving alternately. A move consists of erasing the number currently on the board and writing in its place the difference between that number and one of its nonzero digits; the player making the move chooses which digit to use. The player who writes \(0\) on the board wins.
Ana moves first. Determine which of the two players has a winning strategy.
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Serbian Regional Competition (Okruzno takmicenje) 2026, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source