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## Question

If rearrangement of the pieces between cuts in not

permitted, a cube can be cut into 27 cubes by slicing

twice in each of three perpendicular planes.

By permitting rearrangement of the pieces, [slicing

and stacking], can this be done with fewer than 6 cuts?

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yes

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I worked on this for 1/2 hour...

I discovered that minimum 6 slices are required, because the most middle cube always needs a new cut to be separated from its each adjacent cube. Since it has 6 sides and 6 adjacent cubes, 6 cut is mandatory.

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I worked on this for 1/2 hour...
I discovered that minimum 6 slices are required, because the most middle cube always needs a new cut to be separated from its each adjacent cube. Since it has 6 sides and 6 adjacent cubes, 6 cut is mandatory.

Nice proof.

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Oops. Thanks LIS

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