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eleven points

Source: Netherlands 1993

June 28, 2009
geometry proposedgeometry

Problem Statement

Eleven distinct points P1,P2,...,P11 P_1,P_2,...,P_{11} are given on a line so that PiPj≤1 P_i P_j \le 1 for every i,j i,j. Prove that the sum of all distances PiPj,1≤i<j≤11 P_i P_j, 1 \le i <j \le 11, is smaller than 30 30.
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