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N <= (n + 1)^2 points - All-Russian MO 2004 Regional (R4) 10.4

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September 27, 2024
geometrycombinatoricscombinatorial geometry

Problem Statement

N≥3N \ge 3 different points are marked on the plane. It is known that among pairwise distances between marked points there are not more than nn different distances. Prove that N≤(n+1)2N \le (n + 1)^2.
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