Question 96
Let $n \geq 2$ be a positive integer. We have $2 n$ balls, on each of which an integer is written. It holds that, whenever we form $n$ pairs with the balls, two of these pairs have the same sum.
(1) Prove that there are four balls with the same number.
(2) Prove that the number of distinct values on the balls is at most $n-1$.
(1) Prove that there are four balls with the same number.
(2) Prove that the number of distinct values on the balls is at most $n-1$.