Clue to Riddle #82: Cutting a 3-inch cube into 27 1-inch cubes

82. A carpenter, working with a buzz saw, wishes to cut a wooden cube, three inches on each side, into 27 one-inch cubes. He can do it 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?
3-inch cube The key to solving this, and proving it, is to consider the center cube. The one with no exposed faces.

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