Date: 6 Dec 1980 16:42 PST From: McKeeman.PA at PARC-MAXC Subject: Re: That 28 move Plummer Cross In-reply-to: DCP's message of 6 DEC 1980 1745-EST To: DCP at MIT-MC (David C. Plummer) cc: McKeeman, CUBE-LOVERS at MIT-MC David, Suppose one could prove local maxima had configurations that were invariant under the rotation group of the whole cube. (I am not at all sure it is even true.) There are a small number of such symmetric configurations, and they could probably be easily tabulated. One of them would have to be maximally distant from home. Thus if we had a QTW solution for each of them, the maximum over that set would bound God's Algorithm. I see no reason to believe that a QTW cannot take you between two solutions that are at the same distance. As DPC pointed out, there are a lot of even identity paths. E.g., (RUR'U')^6. The two furthest points on the path are (by symmetry) necessarily equally distant, yet connected by a QTW. Bill