Albus and Brian play on a square near lava
Source: Swiss MO 2023/2
March 12, 2023
combinatorics
Problem Statement
The wizard Albus and Brian are playing a game on a square of side length meters surrounded by lava. In the centre of the square there sits a toad. In a turn, a wizard chooses a direction parallel to a side of the square and enchants the toad. This will cause the toad to jump meters in the chosen direction, where is initially equal to and increases by after each jump. The wizard who sends the toad into the lava loses. Albus begins and they take turns. Depending on , determine which wizard has a winning strategy.