red and green sections by points in space
Source: Polish MO Recond Round 1982 p6
September 9, 2024
geometrycombinatoricscombinatorial geometry3D geometry
Problem Statement
Given a finite set of points in space, any two distances between the points of this set are different. Each point of the set is connected by a line segment to the closest point of the set . This way we will get a set of sections, one of which (any chosen one) we paint red, all the remaining sections we paint green. Prove that there are two points of the set that cannot be connected by a line composed of green segments.