MathDB

Suppose

n\geq 4

and let

S

be a finite set of points in the space (

\mathbb{R}^3

), no four of which lie in a plane. Assume that the points in

S

can be colored with red and blue such that any sphere which intersects

S

in at least 4 points has the property that exactly half of the points in the intersection of

S

and the sphere are blue. Prove that all the points of

S

lie on a sphere.

Problem Statement