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.
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Let $A$ be a set of $n$ points in space. From the family of all segments with endpoints in $A$, $q$ 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 $m$ yellow segments, where $m \geq \frac{2q}{n}$ , arranged in order of increasing length.