Question 7
A carpenter wishes to cut a wooden $3\times3\times3$ cube into twenty-seven $1\times1\times1$ cubes. He can do this easily by making $6$ cuts through the cube, keeping the pieces together in the cube shape as shown.
What is the minimum number of cuts needed if he is allowed to rearrange the pieces after each cut?
What is the minimum number of cuts needed if he is allowed to rearrange the pieces after each cut?