BG-MO 1977 Problem 2

In the space are given $n$ points and no four of them belongs to a common plane. Some of the points are connected with segments. It is known that four of the given points are vertices of tetrahedron which edges belong to the segments given. It is also known that common number of the segments, passing through vertices of tetrahedron is $2n$ . Prove that there exists at least two tetrahedrons every one of which have a common face with the first (initial) tetrahedron.

N. Nenov, N. Hadzhiivanov