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Turan consequence

Source: Moldova 2007 IMO-BMO TST III problem 4

March 24, 2007
geometryrhombusPutnamcombinatorics proposedcombinatorics

Problem Statement

We are given nn distinct points in the plane. Consider the number τ(n)\tau(n) of segments of length 1 joining pairs of these points. Show that τ(n)≤n23\tau(n)\leq \frac{n^{2}}3.
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