Fewest cuts to dice a cube into 27

Question

You have a solid 3 	imes 3 	imes 3 cube of cheese and want to cut it into 27 unit cubes. Between cuts, you are allowed to rearrange and stack the pieces however you like before making the next straight (planar) cut. What is the minimum number of straight cuts needed? Does stacking help?

Accepted Answer

You need 6 cuts, and, surprisingly, rearranging pieces does not help at all. A simple 6-cut method. Make 2 parallel cuts to slice the cube into 3 slabs in the x-direction, 2 more for the y-direction, and 2 more for the z-direction: 2 + 2 + 2 = 6 cuts. That clearly produces 3 	imes 3 	imes 3 = 27 unit cubes without any stacking. Why you can't do better, even with stacking. Focus on the center cube, the little cube buried in the very middle of the 3	imes3	imes3 block. In the finished result this center cube has 6 faces, and none of those faces was on the surface of the original cube. Every …

Fewest cuts to dice a cube into 27

Your answer

More Brainteasers questions