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Lots of different differences

Source: Brazilian Math Olympiad 2007, Problem 6

November 2, 2007
floor functionLaTeXinductioncombinatorics unsolvedcombinatorics

Problem Statement

Given real numbers x1<x2<…<xn x_1 < x_2 < \ldots < x_n such that every real number occurs at most two times among the differences x_j \minus{} x_i, 1≤i<j≤n 1\leq i < j \leq n, prove that there exists at least ⌊n/2⌋ \lfloor n/2\rfloor real numbers that occurs exactly one time among such differences.
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