Question 105
The vertices of a regular $n$-gon are marked. Two players play the following game: they, in turn, select a vertex and connect it by a segment to either an adjacent vertex or the center of the $n$-gon. A player wins if after his move it is possible to get from any vertex to any other vertex moving along segments.
For each integer $n \ge 3$ determine who has a winning strategy.
For each integer $n \ge 3$ determine who has a winning strategy.