Does anyone have any good ideas for a research paper on group theory (particularity the Rubik's Cube, but anything within the topic works)? It's for a IB math extended essay (for high school), and it seems many people here are cubers. So far i've considered investigating solvability of random configurations, but the only real way I've found is to solve it as much as possible until you either finish or get to an un-solvable state. I've also considered investigating the Devil's Algorithm (one that can solve any cube if repeated long enough) but I don't know if the rubik's cube group can be represented as a permutation group. Any ideas are very much appreciated!