MathDB
Parallelogram Hater

Source: Rioplatense L2 2023 #4

December 6, 2023
geometrycombinatorics

Problem Statement

A set of points on the plane is antiparallelogram if any four points of the set are not vertices of a parallelogram. Prove that for any set of 20232023 points on the plane, no three of them are collinears, there exists a subset of 1717 points, such that this subset is antiparallelogram.