Competition problem — Combinatorics

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Combinatorics Difficulty 5.1 AIME, harder Prove it Belarus

Thirty rays with the origin at the same point are constructed on a plane. Consider all angles between any two of these rays. Let $N$ be the number of acute angles among these angles.
Find the smallest possible value of $N$ .

Solution

Answer: 135.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.