MathDB
beautiful estimations with 2n integers [mod edit: reals ;) ]

Source: poland, I think 1999

May 1, 2005
inequalitiesintegrationfunctiontriangle inequalityinequalities proposed

Problem Statement

Prove that for any 2n 2n real numbers a1 a_{1}, a2 a_{2}, ..., an a_{n}, b1 b_{1}, b2 b_{2}, ..., bn b_{n}, we have \sum_{i < j}{\left|a_{i}\minus{}a_{j}\right|}\plus{}\sum_{i < j}{\left|b_{i}\minus{}b_{j}\right|}\leq\sum_{i,j\in\left[1,n\right]}{\left|a_{i}\minus{}b_{j}\right|}.
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