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Bundeswettbewerb Mathematik 1976 Problem 2.3

Source: Bundeswettbewerb Mathematik 1976 Second round

September 11, 2022
circlecombinatoricsparallel

Problem Statement

A circle is divided by 2n2n points into 2n2n equal arcs. Let P1,P2,…,P2nP_1, P_2, \ldots, P_{2n} be an arbitrary permutation of the 2n2n division points. Prove that the polygonal line P1P2⋯P2nP1P_1 P_2 \cdots P_{2n} P_1 contains at least two parallel segments.
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