MathDB
Cube

Source: RMO 2003, District Round

May 29, 2006
geometry3D geometryanalytic geometryleast common multiplealgebra proposedalgebra

Problem Statement

In the interior of a cube we consider 2003\displaystyle 2003 points. Prove that one can divide the cube in more than 20033\displaystyle 2003^3 cubes such that any point lies in the interior of one of the small cubes and not on the faces.
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