--- In [email protected], "Doug Lee" <[EMAIL PROTECTED]> wrote: > > Ignoring the solved case and counting mirrors together but inverses > distinct... > > First off, I looked at the number of totally distinct cases, that'd be > 6!/2 = 360. Exploiting two planes of symmetry that gives 90 cases > while exploiting 4 planes of symmetry gives 15 cases. > > But that was just to get a rough estimate so that I know that my > answer is going to be between 14 and 79. Some cases are self-mirrors > that shouldn't be counted twice and some cases have more or less > symmetry than others... a bit of a mess trying to apply Burnside's > Lemma on. > > So then I broke it up into categories: > There are 8 cases involving a 5-edge cycle. > There are 7 cases involving a 4-edge cycle and a 2-edge cycle. > There are 6 cases involving two disjoint 3-edge cycles. > There are 4 cases involving a single 3-edge cycle. > There are 6 cases involving two disjoint 2-edge cycles. > There is the solved case. > > Thus I conclude that there are 31 cases not counting the solved case. > Also 3 of the algs needed are from PLL, so it's really only 28 algs to > memorize, some of which maybe inverse of each other. > > That is a quick count, nothing rigorous... see if you can find any > flaws in my reasoning. > > > -Doug
That's a lot better than my quick guesstimate. Thanks. Now, any ideas on how to find the algs for the exact cases, or the average move count for them? If it's really only 31 cases+inverses and mirrors, I would be very interested in learning them. Especially considering how many of those I know already, like the 3 PLL's and the 3 cases permuting M slice pieces only. Thanks for your help. -Mike team [zb] ------------------------ Yahoo! Groups Sponsor --------------------~--> Get fast access to your favorite Yahoo! Groups. Make Yahoo! your home page http://us.click.yahoo.com/dpRU5A/wUILAA/yQLSAA/MXMplB/TM --------------------------------------------------------------------~-> Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/zbmethod/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
