A CARPENTER, working with a buzz saw, wishes to cut a wooden cube, three inches on a side, into 27 one-inch cubes. He can do this easily by making six cuts through the cube, keeping the pieces together in the cube shape. Can he reduce the number of necessary cuts by rearranging the pieces after each cut?
The answer:
There is no way to reduce the cuts to fewer than six. This is at once apparent
when you focus on the fact that a cube has six sides. The saw cuts straight—one
side at a time. To cut the one-inch cube at the center (the one which has no
exposed surfaces to start with) must take six passes of the saw.
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