Friendly Beetles crawling on a Plane
Source: Sharygin Geometry Olympiad, Final Round 2016, Problem 4 grade 9
August 4, 2016
combinatoricsgeometry
Problem Statement
One hundred and one beetles are crawling in the plane. Some of the beetles are friends. Every one hundred beetles can position themselves so that two of them are friends if and only if they are at unit distance from each other. Is it always true that all one hundred and one beetles can do the same?