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.
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
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