1997 IMO Problems/Problem 3

Problem

Let $x_{1}$ , $x_{2}$ ,..., $x_{n}$ be real numbers satisfying the conditions

$|x_{1}+x_{2}+...+x_{n}|=1$

and

$|x_{i}| \le \frac{n+1}{2}$ , for $i=1,2,...,n$

Show that there exists a permutation $y_{1}$ , $y_{2}$ ,..., $y_{n}$ of $x_{1}$ , $x_{2}$ ,..., $x_{n}$ such that

$|y_{1}+2y_{2}+...+ny_{n}|\le \frac{n+1}{2}$

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