Olympiad Maths Prep

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Combinatorics Difficulty 5.1 AIME, harder Prove it Belarus

The vertices of the regular 2n+12n+1-gon are marked on a circle. Two players play the following game. They, in turn, delete exactly one of the vertices. The player wins if after his move all triangles with the vertices in the remained points are obtuse.
Who of the player wins if both of them play to win?

Solution

4. See the 38th All-Russian Mathematical Olympiad, Final Round, Problem 11.7.

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