If you want to cut a 3x3x3 cube in 1x1x1 pieces by using plane cuts, you would need six cuts, if no rearranging of pieces is allowed.

How many cuts would you need, if you were allowed to rearrange the pieces after each cut, and why?

All the adjacent cubes to the centre cube(CC)  need to be detached from CC as part of the said disection.

Consequently, the required number of cuts will always be six irrespective of whether one is reuired to rearrange the constituent pieces or otherwise.

Posted by K Sengupta on 2007-04-15 15:48:12