A carpenter wants to saw a wooden cube that measures three inches on each side into 27 one-inch cubes. This can be done by making six cuts through the cube, keeping the pieces in their original position. Is there a way to reduce the number of cuts by rearranging the pieces after each cut?
Think of the one-inch cube at the very center. How many cuts are needed to get the cube in the center?
It is impossible to reduce the number of cuts to less than six.
A cube has six sides, and to cut the one-inch cube at the center requires six passes of the saw.