**Welcome to The Rubik Zone**, a site for all things related to the famous Cube of Erno Rube.

I got my first rubik’s cube as a gift from my uncle. It looked cute and innocent – a bunch of brightly colored squares. A few twists later, and it was messed beyong repair, and stayed that way for months.

Now, more than 20 years on, **The Rubik Zone** is here. Check out the menus to see what we have.

On the original packaging of the first Rubik’s cubes sold, the distributor boasted

*More than 3 billion combinations!*

This has been compared with McDonalds boasting

*Over a hundred and twenty hamburgers sold!*

In actual fact, there are over ** 43 billion billion** combinations. This is a number just a bit too big for most people to grasp. But it’s actually not as big as you might think.

For example, it’s the cost of only 70,000 Iraq Wars, measured in Iraqi Dinars. Now 70000 is a number I can wrap my head around.

Alternatively, imagine

- you start buying Rubik’s cubes, messing them up, and posting them off to other people.
- Suppose you kept doing this until you had posted a cube to every single man woman and child on earth.
- Suppose also you persuaded
*everybody else*to start doing the same.

*just over*43 billion billion cubes lying around. And guess what? There’d be about a 2 in 5 chance that

*one*of those cubes was actually solved, by pure chance.

*Alpha Centauri*.

**a new, Rubik moon!**It would have its own gravity – not strong, admittedly, but strong enough that a visitor couldn’t just jump off. The only problem would be that if it fell back to earth, the shock wave would flatten 90% of the trees and buildings on the entire planet.

I think the math is off on this. The puzzle is not a 3x3x3 puzzle. It’s 8 corner pieces that can change positions and be oriented 3 ways combined with an independent 10 side piece puzzle that can be oriented in 2 ways. I don’t understand why, but part of the geometry of the puzzle dictates that no piece can rotate independently – any piece that does must rotate another piece. I think this effectively cuts the number of possibilities in half.

To simplify this down to the 2×2 puzzle, you have 8 pieces to make up the puzzle. Each puzzle piece can have 3 orientations. So the answer is the number of different places to put the puzzle pieces times the number of different combinations of orientations that the pieces can have (divided by 2 because of the rotation dependency).

I’m still struggling with the right math, but I think this it. There are 8! different ways to arrange the 8 corner pieces. Each piece can have 3 orientations, which is 3^8 different ways to combine them. So, I get a much larger number at 40320 * 6561 / 2 = 132,269,760 different positions that the 2×2 puzzle can have.

Expanding this to the 3×3 is actually the 2×2 puzzle times a 10 side piece / 2 orientation puzzle calculated the same and still with the same rotation dependency. So that is the 2×2 answer * (3,628,800 * 1024 / 2) which is 245,750,018,605,056,000 (245.75 quadrillion), significantly less than a 3x3x3 grid answer. But still really big.

Not 100% sure on this, but my best guess – I know the 3x3x3 is out because that isn’t how the cube is made up.

Well, for the 2x2x2, the eight corner pieces can’t be all independently rotated – you can choose an arbitrary rotation for seven of them, and then the 8th is determined. So that’s 8! x 3^7.

And for the 3x3x3, why do you say there are ten edge pieces? Surely you mean twelve?