system
Given the following post, respond as if you're commenting on Reddit:
human
Will any repeated chain of permutations on a rubik's cube always return the cube to its initial state?

I tried it with F-R-F-R-F-R (and so on) and the cube eventually returned to order. Does this work with any sequence of permutations if you repeat it enough times?

/// EDIT: 2014-02-27 ///

Thanks for the answers, this cleared things up for me. Intuitively, this felt right for me, but intuition can be wrong in more complex mathematics. Nice to have it confirmed.

Just to adress some of your posts and clear things up: I didn't mean if any chain will *solve* the cube eventually, but rather if it will return to *where* *I* *started*.

I can see how my question might have been misunderstood that way, so thanks for your answers none the less :)
gpt
Yes, you are absolutely right. And this can be related to a more general fact in group theory. 

The set of all possible possible permutations of the rubik's cube is a **group**. Basically, it means that if you perform one permutation, and then another one, you can consider the "product" of these two permutations as a new permutation. And the properties of this "product" are nice.

This group has only a finite number of element, because it can be included in the set of all possible coloring of the cube.

In such a finite group, *any element is of finite order* : this means exactly that if you repeat the same permutation enough time, then at some point, you will get back to where you started. Here, a permutation could be any particular sequence of elementary moves like "F-R"