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Determine the existence of an n-gon with given points

Source: 2018 Latvia BW TST P7

June 5, 2022
combinatoricscombinatorial geometrycombinatorics unsolved

Problem Statement

Let n≥3n \ge 3 points be given in the plane, no three of which lie on the same line. Determine whether it is always possible to draw an nn-gon whose vertices are the given points and whose sides do not intersect. Remark. The nn-gon can be concave.
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