MathDB
2011 ToT Fall Senior A p1 points with different distances

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March 22, 2020
combinatorial geometrycombinatoricspointsdistance

Problem Statement

Pete has marked several (three or more) points in the plane such that all distances between them are different. A pair of marked points A,BA,B will be called unusual if AA is the furthest marked point from BB, and BB is the nearest marked point to AA (apart from AA itself). What is the largest possible number of unusual pairs that Pete can obtain?