Can a proof-of-work estimate the mixing time of a Rubik's cube? Forgive the flight-of-fancy; if this is too far-fetched I will delete. To start off, as of now (1d6e05de09721d4d56107ffbcf54dc557b881e7c83ae36) the number of hashes performed every ten minutes, about 2^71 or so, is not that far off from the order of the Rubik's cube group, about 2^68 or so. That is, presently Bitcoin miners perform slightly more hashes every 10 minutes than the number of positions on a 3x3x3 Rubik's cube. Elements of the Rubik's cube group are usually written as a combination of moves on the 6 faces (front, back, down, etc.) A move is often called an "algorithm" in cube terminology, or a "word" in discussions about group theory. Thus, each algorithm can be written as a string of moves, e.g. FUDF^2B^-1, etc. The "mixing time" tau of the Rubik's cube group is the estimated number of scrambles that are needed to go from the solved position to a "random
