M2670

Part of Kvant 2021

Problems(1)

Must the 100-gon be convex?

Source: Kvant Magazine No. 10 2021 M2670

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

geometrycombinatorial geometryKvant