Problem

Source: 2019 ELMO Shortlist C1

Tags: combinatorics, Game Theory, Elmo, combinatorics solved



Elmo and Elmo's clone are playing a game. Initially, $n\geq 3$ points are given on a circle. On a player's turn, that player must draw a triangle using three unused points as vertices, without creating any crossing edges. The first player who cannot move loses. If Elmo's clone goes first and players alternate turns, who wins? (Your answer may be in terms of $n$.) Proposed by Milan Haiman