1997 IMO Problems/Problem 3

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



$|x_{i}| \le \frac{n+1}{2}$, 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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See Also

1997 IMO (Problems) • Resources
Preceded by
Problem 2
1 2 3 4 5 6 Followed by
Problem 4
All IMO Problems and Solutions