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N points, total number of pairwise distances of these N points is at most n

Source: Indian Postal Coaching 2007 set 3 p5

May 25, 2020
combinatoricscombinatorial geometrydistance

Problem Statement

There are NN points in the plane such that the total number of pairwise distances of these NN points is at most nn. Prove that N≤(n+1)2N \le (n + 1)^2.
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