MathDB

Prove that for every integer

n\ge 3

there exists

N(n)

with the following property: whenever

P

is a set of at least

N(n)

points of the plane such that any three points of

P

determines a nondegenerate triangle containing at most one point of

P

in its interior, then

P

contains the vertices of a convex

n

-gon whose interior does not contain any point of

P

Problem Statement