Question 12
(IRE 2) Let $n,k$ be positive integers with $k\le n$ and let $S$ be a set containing $n$ distinct real numbers. Let $T$ be the set of all real numbers of the form $x_1+x_2+\cdots+x_k$, where $x_1,x_2,\ldots,x_k$ are distinct elements of $S$. Prove that $T$ contains at least $k(n-k)+1$ distinct elements.