We call a diagonal of a polygon nice, if it is entirely inside the polygon or entirely outside the polygon. Let P be an n–gon with no three of its vertices being on the same line. Prove that P has at least 3(n−3)/2 nice diagonals.Proposed by Bálint Hujter, Budapest and Gábor Szűcs, Szikszó combinatoricspolygonkomal