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Intersection of collinear segments

Source: Czech and Slovak Olympiad 1981, National Round, Problem 2

October 11, 2024
combinatorial geometrygeometryclosedSegment

Problem Statement

Let nn be a positive integer. Consider n2+1n^2+1 (closed, i.e. including endpoints) segments on a single line. Show that at least one of the following statements holds: a) there are n+1n+1 segments with non-empty intersection, b) there are n+1n+1 segments among which two of them are disjoint.
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