Must the 100-gon be convex?
Source: Kvant Magazine No. 10 2021 M2670
March 9, 2023
geometrycombinatorial geometryKvant
Problem Statement
There are 100 points on the plane so that any 10 of them are vertices of a convex polygon. Does it follow from this that all these points are the vertices of a convex 100-gon?From the folklore