A carpenter, working with a buzz saw, wishes to cut a wooden cube, three inches on a side, into 27 one-inch cubes. This can be easily done by making six cuts through the cube, keeping the pieces together in the cube shape. Can the carpenter reduce the number of necessary cuts by rearranging the pieces after each cut?
Amanda Montañez
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 that has no exposed surfaces to start with) must take six passes of the saw.
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A version of this puzzle originally appeared in the February 1957 issue of Scientific American.