MathDB
How Many Nice Diagonals

Source: KöMaL A. 764

March 20, 2022
combinatoricspolygonkomal

Problem Statement

We call a diagonal of a polygon nice, if it is entirely inside the polygon or entirely outside the polygon. Let PP be an nn–gon with no three of its vertices being on the same line. Prove that PP has at least 3(n−3)/23(n-3)/2 nice diagonals.
Proposed by Bálint Hujter, Budapest and Gábor Szűcs, Szikszó
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