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Isosceles Triangle In Colored 35-Gon

Source: Bundeswettbewerb Mathematik 2017, Round 2 - #2

September 3, 2017
combinatoricscombinatorics unsolvedColoringPolygonsisosceles

Problem Statement

In a convex regular 3535-gon 1515 vertices are colored in red. Are there always three red vertices that make an isosceles triangle?