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239 Open MO, 2018, Senior League, Problem 1

Source: 239 Open MO, 2018, Senior League, Problem 1

April 4, 2023
combinatorial geometrygeometry

Problem Statement

Prove that in any convex polygon where all pairwise distances between vertices are distinct, there exists a vertex such that the closest vertex of the polygon is adjacent to it.
Proposed by D. Shiryayev, S. Berlov
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