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, 2019

Combinatorics Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

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 $\frac32(n-3)$ nice diagonals.

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