Problem A. 537. (May 2011)
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 June 10, 2011.
4 students sent a solution. 5 points: Ágoston Tamás, Backhausz Tibor, Frankl Nóra, Nagy 235 János.