MathDB
Problem 2

Source: 21-st Iberoamerican Mathematical Olympiad

May 6, 2007
inequalitiesinequalities unsolved

Problem Statement

For n real numbers a1, a2, … ,an,a_{1},\, a_{2},\, \ldots\, , a_{n}, let dd denote the difference between the greatest and smallest of them and S=∑i<j∣ai−aj∣.S = \sum_{i<j}\left |a_i-a_j \right|. Prove that (n−1)d≤S≤n24d(n-1)d\le S\le\frac{n^{2}}{4}d and find when each equality holds.
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