Sets on plane with (3,2)-property
Source: Sharygin contest. The final raund. 2008. Grade 10. Second day. Problem 8
August 31, 2008
geometry unsolvedgeometry
Problem Statement
(A.Akopyan, V.Dolnikov) Given a set of points inn the plane. It is known that among any three of its points there are two such that the distance between them doesn't exceed 1. Prove that this set can be divided into three parts such that the diameter of each part does not exceed 1.