SHARYGIN 2020 Problem 23
A non-self-intersecting polygon is nearly convex if precisely one of its interior angles is greater than .
One million distinct points lie in the plane in such a way that no three of them are collinear. We would like to construct a nearly convex one-million-gon whose vertices are precisely the one million given points. Is it possible that there exist precisely ten such polygons?
Dataset text AI-MO AoPS. Quoted with source.
Solutions
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