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PQ <PP_i => n<15 in 3D

Source: 1966-67 Germany R4 12.6 https://artofproblemsolving.com/community/c3208025_

October 13, 2024
geometrycombinatoricscombinatorial geometry3D geometry

Problem Statement

Prove the following theorem: If there are nn pairs of different points PiP_i, i=1,2,...,ni = 1, 2, ..., n, n>2n > 2 in three dimensions space, such that each of them is at a smaller distance from one and the same point QQ than any other PiP_i, then n<15n < 15.
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