KöMaL 2011 A537

The edges of the complete graph on $n$ vertices are labeled by the numbers $1,2,\dots,\binom{n}{2}$ 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 3$n$-1000. ( Kolmogorov Cup, 2009; a problem by I. Bogdanov, G. Chelnokov and K. Knop )