IMO 1976 LL BUL2

Origin: BUL

Problem

Let P be a set of n points and S a set of l segments. It is known that: (i) No four points of P are coplanar. (ii) Any segment from S has its endpoints at P. (iii) There is a point, say g, in P that is the endpoint of a maximal number of segments from S and that is not a vertex of a tetrahedron having all its edges in S. Prove that l \leqn2 3 .