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Source: Romania NMO 2008, 9 form, Problem 3

April 30, 2008
inequalities proposedinequalities

Problem Statement

Let n n be a positive integer and let ai a_i be real numbers, i \equal{} 1,2,\ldots,n such that ∣ai∣≤1 |a_i|\leq 1 and \sum_{i\equal{}1}^n a_i \equal{} 0. Show that \sum_{i\equal{}1}^n |x \minus{} a_i|\leq n, for every x∈R x\in \mathbb{R} with ∣x∣≤1 |x|\le 1.
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