IMO Shortlist 2012 problem C2


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3. studenoga 2013.
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Let n \geq 1 be an integer. What is the maximum number of disjoint pairs of elements of the set \{ 1,2,\ldots , n \} such that the sums of the different pairs are different integers not exceeding n?
Izvor: Međunarodna matematička olimpijada, shortlist 2012