RO-NMO 2005 Problem 81
We consider a cube with sides of length 1. Prove that a tetrahedron with vertices in the set of the vertices of the cube has the volume if and only if 3 of the vertices of the tetrahedron are vertices on the same face of the cube.
Dinu Serbanescu
Dataset text AI-MO AoPS. Quoted with source.
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