Problem of the Week 1146
A Cute Game
There is a coin at each vertex of a regular 10-gon. 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 acute-angled 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.