IMO Shortlist 1977 problem 14
Kvaliteta:
Avg: 0,0Težina:
Avg: 0,0 Let
be a finite set of points such that
is not contained in a plane and no three points of
are collinear. Show that at least one of the following alternatives holds:
(i)
contains five points that are vertices of a convex pyramid having no other points in common with 
(ii) some plane contains exactly three points from



(i)


(ii) some plane contains exactly three points from

Izvor: Međunarodna matematička olimpijada, shortlist 1977