Question 132
Two players play a game on a regular $n$-gon, where $n \ge 4$. Three counters start on consecutive vertices. In turn, each player slides one counter along any number of edges to another vertex of the polygon, without jumping over another counter, to strictly increase the area of the triangle formed by the counters. The loser is the first player who cannot make a legal move. For what $n$ does the first player have a winning strategy?