MathDB

Two players

A

and

B

play alternatively in a convex polygon with

n \geq 5

sides. In each turn, the corresponding player has to draw a diagonal that does not cut inside the polygon previously drawn diagonals. A player loses if after his turn, one quadrilateral is formed such that its two diagonals are not drawn.

A

starts the game. For each positive integer

n

, find a winning strategy for one of the players.

Problem Statement