IMO Shortlist 2012 problem C7
Dodao/la: arhiva3. studenoga 2013.
There are given
points on a circle labeled
in some order. Prove that one can choose
pairwise disjoint chords joining some of theses points so that the
sums of the pairs of numbers at the endpoints of the chosen chord are equal.
Izvor: Međunarodna matematička olimpijada, shortlist 2012