Here’s a classic from Martin Gardner:
Suppose that you have a 3″ on a side wooden cube and a buzz saw. You wish to cut the cube into 27 smaller cubes, each 1 cubic inch. It is easy to see that you can do this with six cuts. You simply hold the cube in its original position while making two cuts that trisect each face.
Can it be done if fewer cuts? If so, tell us how. If not, prove that it can’t be done.