a cube is decomposed in a finite number of parallelepipeds
Source: German Olympiad (BWM) 2004, first stage, problem 4
June 15, 2004
geometry3D geometryspherecalculusinequalities solvedinequalities
Problem Statement
A cube is decomposed in a finite number of rectangular parallelepipeds such that the volume of the cube's circum sphere volume equals the sum of the volumes of all parallelepipeds' circum spheres. Prove that all these parallelepipeds are cubes.