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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 n3n \geq 3 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.