373. Cutting a Cube. In a mathematical journal, the following question and answer appeared.

Question: "A carpenter wants to cut a wooden cube with a side of 3 inches into 27 cubes with a side of 1 inch. He can easily do this by making 6 cuts while keeping the pieces together so they don't fall apart. What is the minimum number of cuts if the carpenter is allowed to rearrange the pieces in any way during the cutting process $?$"

Answer: "The minimum number of cuts is 6, since it takes 6 cuts, one for each face, to separate the inner cube."

Now, suppose the inner cube is missing. What is the minimum number of cuts in this case if the pieces can be rearranged in any way during the cutting process $?$
373. After the first cut, the cube splits into 2 parts. The larger of these (consisting of 17 one-inch cubes) contains one central cube, for four faces of which another cut is required. After the last of these is made, there will remain at least two one-inch cubes undivided - regardless of any rearrangement of the pieces - for which another cut will be required. Thus, the minimum number of cuts is 6.

[C. Newman, M. M., 41, 102 (February 1968).]