IMO Shortlist 1985 problem 8


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 0,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
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.
Izvor: Međunarodna matematička olimpijada, shortlist 1985