Rich asks: << Has the diameter of the Rubik's cube puzzle been established yet? We now have enough computing power to find & prove the distance- to-start for any particular position, using the obvious square-root meet-in-the-middle algorithm and a big disk. We can search for edge positions by generating random positions and using the exact distance algorithm to guide a hill-climb away from the start position. But this is only heuristic.
This is asking, given the usual 6 generators of the group G of all Rubik cube positions (say, holding the armature fixed), what is the maximum over all g in G of [the smallest size of a word in those generators that represents g]. A question stemming from ignorance: Are there results in this area which can specialize to answer Rich's question about G (or at least shed light on it) ? --Dan