Question 14
(FIN 2′) Let $E$ be a finite set of points such that $E$ is not contained in a plane and no three points of $E$ are collinear. Show that at least one of the following alternatives holds:
(i) $E$ contains five points that are vertices of a convex pyramid having no other points in common with $E$;
(ii) some plane contains exactly three points from $E$.
(i) $E$ contains five points that are vertices of a convex pyramid having no other points in common with $E$;
(ii) some plane contains exactly three points from $E$.