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Blue and red points lie on a line [Iran Second Round 1996]

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November 25, 2010
inequalitiescombinatorics proposedcombinatorics

Problem Statement

Let nn blue points AiA_i and nn red points Bi (i=1,2,…,n)B_i \ (i = 1, 2, \ldots , n) be situated on a line. Prove that ∑i,jAiBj≥∑i<jAiAj+∑i<jBiBj.\sum_{i,j} A_i B_j \geq \sum_{i<j} A_iA_j + \sum_{i<j} B_iB_j.
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