IMO Shortlist 1985 problem 8
Avg:
Avg:
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