HMMT November 2022 H6
- Theme
A regular octagon is inscribed in a circle of radius 2. Alice and Bob play a game in which they take turns claiming vertices of the octagon, with Alice going first. A player wins as soon as they have selected three points that form a right angle. If all points are selected without either player winning, the game ends in a draw. Given that both players play optimally, find all possible areas of the convex polygon formed by Alice's points at the end of the game.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
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