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At least a few cubes are required to form a big cube

If nis of the form a3d for some positive integer a then we rst divide the unit cube into a2d small cubes of side length 1a2 In the second step we subdivide each small cube into ad even smaller subcubes of side length 1a3 and we are done We call these subcubes tiny If nis not of this special form we have a3d n a3d1 for some a In this case after the rst step the number of

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