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11 pairs from 22 points in plane

Source: 1971 Hungary - Kürschák Competition p2

October 15, 2022
combinatoricscombinatorial geometry

Problem Statement

Given any 2222 points in the plane, no three collinear. Show that the points can be divided into 1111 pairs, so that the 1111 line segments defined by the pairs have at least five different intersections