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Special partition of set.

Source: Sharygin 2017 Day 2 Problem 10.8 Grade 10

August 2, 2017
geometry

Problem Statement

10.8 Suppose SS is a set of points in the plane, S|S| is even; no three points of SS are collinear. Prove that SS can be partitioned into two sets S1S_1 and S2S_2 so that their convex hulls have equal number of vertices.