Question 107
A point $X$ is chosen inside a convex 100-gon ($X$ does not lie on sides or diagonals of the 100-gon). Initially, the vertices of the polygon are not marked. Pete and Bazil mark the vertices in turn. Pete starts and marks two vertices by his first move; after that, by any move a player marks one vertex. If after someone's move the point $X$ appears to lie inside a polygon whose vertices are all marked, the player who made this move loses the game. Prove that Pete has a winning strategy.