IMO Shortlist 1990 problem 19


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2. travnja 2012.
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Let P be a point inside a regular tetrahedron T of unit volume. The four planes passing through P and parallel to the faces of T partition T into 14 pieces. Let f(P) be the joint volume of those pieces that are neither a tetrahedron nor a parallelepiped (i.e., pieces adjacent to an edge but not to a vertex). Find the exact bounds for f(P) as P varies over T.
Izvor: Međunarodna matematička olimpijada, shortlist 1990