Question 172
Let $n \geqslant 2$ be a natural number. We are given $2 n$ balls. On each of these balls a number is written. Suppose that, whenever the balls are grouped into $n$ pairs, two of these pairs have the same sum.
a. Show that four of these balls carry the same number.
b. Show that the number of distinct values written on the balls is $\leqslant n-1$.
a. Show that four of these balls carry the same number.
b. Show that the number of distinct values written on the balls is $\leqslant n-1$.