Hosted by The Math ForumProblem of the Week 1146A Cute Game
There is a coin at each vertex of a regular 10gon. Alice and Bob take turns removing one coin, with Alice going first. A coin at vertex V can be removed only if there is an acuteangled triangle with vertices at V and at two other remaining coins. A player who cannot move loses. Who has a winning strategy? Note: A 90° angle is not acute. Extra credit: Solve this with 10 replaced by n. Source: Oct 2010 issue of Crux Mathematicorum, from a 2009 contest in Peru. © Copyright 2011 Stan Wagon. Reproduced with permission.

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