DE-MO 1996 Problem 3

Let be given an arbitrary tetrahedron $ABCD$ with volume $V$ . Consider all lines which pass through the barycenter $S$ of the tetrahedron and intersect the edges $AD,BD,CD$ at points $A',B',C$ respectively. It is known that among the obtained tetrahedra there exists one with the minimal volume. Express this minimal volume in terms of $V$