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Problem of the Week 1146

A Cute Game

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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.

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18 October 2011