A. 537. The edges of the complete graph on n vertices are labeled by the numbers in such a way that each number is used exactly once. Prove that if n is sufficiently large then there exists a (possible cyclic) path of three edges such that the sum of the numbers assigned to these edges is at most 3n-1000.
(Kolmogorov Cup, 2009; a problem by I. Bogdanov, G. Chelnokov and K. Knop)
Deadline expired on 10 June 2011.