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IMO Shortlist 1977 problem 14

1977 geo komb shortlist
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.

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