IMO Shortlist 2012 problem C2
Dodao/la:
arhiva3. studenoga 2013. Let

be an integer. What is the maximum number of disjoint pairs of elements of the set

such that the sums of the different pairs are different integers not exceeding

?
%V0
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