IMO 1977 SL 14

(FIN 2‘) Let E be a finite set of points such that E is not contained in

imoshortlistmathematicsolympiad

IMO 1977 SL 14

Problem

(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.