Olympiad problems

2013 Germany Team Selection Test, 3

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 $n$?

2013 Moldova Team Selection Test, 4

Tags: IMO Shortlist , combinatorics , Extremal combinatorics , Doublecounting , Hi

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 $n$?

2013 Taiwan TST Round 1, 4

Tags: IMO Shortlist , combinatorics , Extremal combinatorics , Doublecounting , Hi

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 $n$?

2013 Germany Team Selection Test, 3

Tags: IMO Shortlist , combinatorics , Extremal combinatorics , Doublecounting , Hi

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 $n$?

2012 IMO Shortlist, C2

Tags: IMO Shortlist , combinatorics , Extremal combinatorics , Doublecounting , Hi

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 $n$?

2013 Brazil Team Selection Test, 2

Tags: IMO Shortlist , combinatorics , Extremal combinatorics , Doublecounting , Hi

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 $n$?