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IMO Shortlist 2012, Combinatorics 7

Source: IMO Shortlist 2012, Combinatorics 7

July 29, 2013

combinatoricsIMO Shortlist

Problem Statement

There are given

2^{500}

points on a circle labeled

1,2,\ldots ,2^{500}

in some order. Prove that one can choose

100

pairwise disjoint chords joining some of theses points so that the

100

sums of the pairs of numbers at the endpoints of the chosen chord are equal.