RU-ALLRUSSIAN 1977 Problem 1
P is a polygon. Its sides do not intersect except at its vertices, and no three vertices lie on a line. The pair of sides AB, PQ is called special if (1) AB and PQ do not share a vertex and (2) either the line AB intersects the segment PQ or the line PQ intersects the segment AB. Show that the number of special pairs is even.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
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