100001-gon
Logic
Level
2
Dan and Sam play a game on a convex polygon of 100001 sides. Each one draws a diagonal on the polygon in his turn.
When someone draws a diagonal, it cannot have common points (except the vertices of the polygon) with other diagonals already drawn.
The game finishes when someone can't draw a diagonal on the polygon following the rules; that person is the loser. If Dan begins, who will win? This means, who has a winning strategy?
Clarification: The diagonals of a polygon are straight lines that join non-adjacent vertices.
This is the fourteenth problem of the set Winning Strategies.
by
Mateo Matijasevick