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Existence of a line intersecting many segments

Source: Caucasus MO 2024, Juniors P4

March 15, 2024
combinatorics

Problem Statement

Given a set PP of n>100n>100 points on the plane such that no three of them are collinear, and a set SS of 20n20n distinct segments, each joining a pair of points from PP. Prove that there exists a line not passing through a point from PP and intersecting at least 200200 segments from SS.
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