MathDB

2

Part of 2023 Switzerland - Final Round

Problems(1)

Albus and Brian play on a square near lava

Source: Swiss MO 2023/2

3/12/2023
The wizard Albus and Brian are playing a game on a square of side length 2n+12n+1 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 dd meters in the chosen direction, where dd is initially equal to 11 and increases by 11 after each jump. The wizard who sends the toad into the lava loses. Albus begins and they take turns. Depending on nn, determine which wizard has a winning strategy.
combinatorics