IMO LongList 1967, Hungary 2
Source: IMO LongList 1967, Hungary 2
December 16, 2004
geometry3D geometryeuclidean distanceCyclicpoint setIMO ShortlistIMO Longlist
Problem Statement
In the space points are given. Every pair of points determines some distance. Suppose all distances are different. Connect every point with the nearest point. Prove that it is impossible to obtain (closed) polygonal line in such a way.