Slicing the cube
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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1 solution
Consider the small cube in the very center of the original 3 by 3 by 3 cube. Each of its faces must be formed by a cut. So no matter how you rearrange the pieces, you need 6 straight cuts to form that cube.