Mathematical and Physical Journal
for High Schools
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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