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MathNet 2018-part-02 — 181 problems (EN–VI) Question 113

Math Olympiad Vault · MathNet 2018-part-02 — 181 problems (EN–VI)

Question 113

On a plane a finite number of points are marked of which no three are collinear. Assume that there exists a non-convex polygon with all of its vertices located at some of those points. Prove that there exists a non-convex quadrilateral such that all its vertices lie at the marked points.