IMO Shortlist 1985 problem 8
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Avg: 0,0 Let be a set of points in space. From the family of all segments with endpoints in , segments have been selected and colored yellow. Suppose that all yellow segments are of different length. Prove that there exists a polygonal line composed of yellow segments, where , arranged in order of increasing length.
Izvor: Međunarodna matematička olimpijada, shortlist 1985