You have a cubical piece of wood, 3 by 3 by 3. Clearly, if you are not allowed to rearrange the cut pieces between slices, it will take six slices to cut it into 27 1 by 1 by 1 cubes. (2 slices in each of the 3 spatial directions, 1/3 and 2/3 of the distance along the edges.)

Now suppose you are allowed to rearrange the pieces after each cut.

Can you cut it into 27 1 by 1 by 1 cubes in fewer than 6 straight cuts?

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