Rubik’s Cube is one of the most popular puzzles in the world because of its apparent simplicity, but also because of the great complexity it hides. It is a small cube of colors with a clear objective: “a single color in each face”. It is so simple that anyone can try.

However, after a while with a Rubik’s cube in your hands, you realize that it is something much more complex. One of the ways that we can understand its complexity is by calculating the number of possible combinations of a Rubik’s cube. That is, the number of different ways you can place the pieces.

In total, a Rubik’s cube has 43,252,003,274,489,856,000 possible combinations. This is a huge number. Although we are so used to seeing large numbers that we are not aware of how big it is. To understand it better, I have created an infographic in which I compare the number of possible combinations of a Rubik’s cube with the number of seconds the universe has since the Big Bang:

Hope you like it and it has helped you to understand better the true magnitude of the number of combinations of a Rubik’s Cube.

By the way, we have to divide the number of combinations Rubik Cube into 12 because it is impossible to perform several operations:

- Change the orientation of an edge (2 possibilities) without altering the rest of the cube.
- Change the orientation of a corner (3 possibilities) without altering the rest of the cube.
- Swap the position of only two edges without also swapping two corners (and vice versa).

With all these combinations… are you still arguing that you once solved the Rubik’s Cube by chance? Better take a look at our Rubik’s Cube solutions and solve it by yourself.

For a properly assembled Rubiks cube that can be solved, the computation given is wrong, because there are combinations that are not possible to exist. As an example, if you dismantle the cube and put the pieces back randomly, there is a greater chance that it cannot be solved. In this case, any combinations derived from this improperly assembled cube is not counted as a valid combination.

Rubik’s cube 3*3*3. I don’t think this formula for counting is correct. Let’s consider one face. The central square color is fixed. The 8 others squares can take 6 values of color. So we get 6^8 combinations. ^ means power. As there are 6 faces, we have to multiply this by 6.

So, we get 6^9 = 10 077 696 “only”, which is a majorant, but a big number anyway.

But I think there are less combinations, because the 4 summits have only 3 colors and the 12 intermediary elements have only 2 colors. So there are redundant combinations to be eliminated.