Problem A. 764. (December 2019)
A. 764. We call a diagonal of a polygon nice, if it is entirely inside the polygon or entirely outside the polygon. Let \(\displaystyle P\) be an \(\displaystyle n\)-gon with no three of its vertices being on the same line. Prove that \(\displaystyle P\) has at least \(\displaystyle \frac32(n-3)\) nice diagonals.
Proposed by Bálint Hujter, Budapest and Gábor Szűcs, Szikszó
(7 pont)
Deadline expired on January 10, 2020.
Statistics:
7 students sent a solution. 7 points: Tóth 827 Balázs, Weisz Máté. 3 points: 2 students. 2 points: 2 students. 0 point: 1 student.
Problems in Mathematics of KöMaL, December 2019