cube puzzler

You have a 3" cube. You can cut it into 27 1" cubes by making 6 cuts (ala Rubix).

Can you cut it into 27 1" cubes with fewer than 6 cuts, by restacking the pieces between cuts? If so, how? If not, why not?

No, you cannot.

Consider the center smaller cube created when the cutting process is complete. It has six faces (obviously, being a cube) each of which was created by a cut and each orthangonal to the other. So no single cut could make two of those faces.

Therefore, six cuts are the minimum required.

  • Rick

Good call, Bricker.

Good job. And speedy too.

You have a standard 8x8 checkerboard with 1" squares. You have 32 1"x2" dominoes. There are plenty of ways to arrange them to cover the board. Now remove the upper left corner and the lower right corner from the board. Can you now cover it with 31 dominoes? If so, how? If not, why not?

No, you cannot do it with opposite corners missing, though you can do with adjacent ones missing. Opposite corners are the same color (black or white) and each dominoe has to cover a black and a white square.

The two squares you remove are both black (or both white). Each domino covers one black and one white square. However, you’re then using the dominos to cover 32 white squares and 30 black squares, which is impossible, since they’re unequal.

Wait a minute. This wasn’t an actual inquiry but rather brain-teaser time? Off to MSPIMS with ye.


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