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.
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.
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