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2017 points on the plane, n segments

Source: 2017 Saudi Arabia IMO Training Test p8

September 4, 2020
combinatoricscombinatorial geometrypoints

Problem Statement

There are 20172017 points on the plane, no three of them are collinear. Some pairs of the points are connected by nn segments. Find the smallest value of nn so that there always exists two disjoint segments in any case.