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All distances between points are >1 or \leq 2

Source: Romanian TST 2022, Test 1, P5

May 14, 2022
combinatoricsgeometry

Problem Statement

Given is an integer k≥2k\geq 2. Determine the smallest positive integer nn, such that, among any nn points in the plane, there exist kk points among them, such that all distances between them are less than or equal to 22, or all distances are strictly greater than 11.
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