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0331 combo geo 3rd edition Round 3 p1

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May 9, 2021
geometrycombinatorics3rd edition

Problem Statement

Let SS be a nonempty set of points of the plane. We say that SS determines the distance d>0d > 0 if there are two points A,BA, B in SS such that AB=dAB = d. Assuming that SS does not contain 88 collinear points and that it determines not more than 9191 distances, prove that SS has less than 20042004 elements.
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