Mathematical and Physical Journal
for High Schools
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Problem A. 537. (May 2011)

A. 537. 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 3n-1000.

(Kolmogorov Cup, 2009; a problem by I. Bogdanov, G. Chelnokov and K. Knop)

(5 pont)

Deadline expired on June 10, 2011.

Statistics:

4 students sent a solution.
5 points:Ágoston Tamás, Backhausz Tibor, Frankl Nóra, Nagy 235 János.

Problems in Mathematics of KöMaL, May 2011