**Cutting
a cube**

How many cuts are necessary to divide a 4 x 4 x 4 cube into 64 identical smaller cubes? Rearranging pieces between cuts is allowed.

**Approaches**

9 cuts: 6 vertical and 3 horizontal cuts

need to "free" interior cubes, requiring at least 6 cuts; but is that minimum achievable?

6 cuts: two vertical and one horizontal cut to make eight 2 x 2 x 2 cubes; stack them; two vertical cuts to make 32 pieces 2 x 1; stack them; one vertical cut to make 64 pieces 1 x 2.

**Your
experience**

Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!

*Last updated 30 November, 2004*