Hey! Like commented before, will this really save any time for a complete solve? Even if one determines the parity from the give scramble one must keep track of it from the outset if one wants to utilise the information. This means while doing the centers and also while pairing up the edges. Those clever tricks to track/eliminate the parity will slow down the solve, i guess more than simply solving normally and deal with it at the 3x3x3 stage. Well, that is my firm belief anyway. Those who want to prove me wrong, please do so :-) I know Chris Hardwick, Ron and yo Frederick at least are interested in it.
My idea to deal w parity is to change my own cage method so that i would solve complete first layer then opposite layer. Then middle layers edges (with trivial inner layer quarter-turn parity fix) and no equivalent to the permutation parity of the pairing-up method. Then finally do the rest of the centers. One could also use empty "dedge"s on those first 2 layers while solving the middle layers edges. Im sure it can be fast, but a bit unusual :-) As for doing the last 4 centers im sure it can be fast. Once u reach the state where all unsolved centers are on opposite faces u need maximum 2 algs and u are done :-) And those algs are short. For the 5x5x5 cube im not really that convinced that this new approach will be more efficient than my current approach (or the pairing-up). Cheers! -Per > --- In [email protected], Frédérick BADIE <[EMAIL PROTECTED]> wrote: > > > I can't prove it, but I am almost 100% convinced that counting the > > full cycles is the only way. > > Hi, I think it is not necessary counting the full cycles with the 24 > cubies, but we can calculate a combination between the cycle for the > 12 pairs and the orientation for each 12 pairs separatly. > > Here's the method: > > Definition : > Current Pair : Any combinations of two edges cubies. > FirstEdge and SecondEdge are two edges cubies whith the two same > colors. > MyCounter values 0. > > I take one pair. > It's my Current Pair. > I add 1 to MyCounter. > > The left part of my Current Pair is my First Edge. > The pair where my Second Edge is becomes the Current Pair. > > If the Second Edge is good oriented (according blindfold), I add 1 > to my counter, else I add nothing. > > The left part of my Current Pair is my First Edge. > The pair where my Second Edge is becomes the current pair. > > If the Second Edge is good oriented (according blindfold), I add 1 > to my counter, else I add nothing. > > I do this until my Second Edge is on the first pair I choose at the > beginning. > > The first pair must be twice the current pair. > > When I finish one cycle, I choose for current pair one pair i have > not seen yet.ETC..... > > Until the 12 pairs have been seen. > > One example: > > On a boy color sheme up/yellow face/blue. > I do an "f" and a b2 move and I flip the UL and UR edges( as we do > when we have 2 edges flipped in a blindfold resolution) . The > parity/signature will be odd. > > I take the UR pair. the left part is yellow/orange. > I add one to my counter , it values 1. > > The other yellow/orange is on the UL pair and good oriented . I add > 1 to my counter = 2. > The other UL edge is White/red. > > The other white/red is on the DL pair and not good oriented . I add > nothing and my counter = 2. > The other DL edge is Yellow/red. > > The other yellow/red is on the DR pair and not good oriented . I add > nothing and my counter = 2. > The other DR edge is Yellow/orange. > > The other yellow/orange is on the UR pair and good oriented . I add > 1 and my counter = 3. > > My counter = 3 , so the parity is odd. > > Do this with all cycles if they are more cycle. > Don't forget the pair already "good paired" and add 1 if it is not > good oriented. > > Let's suppose the cube solved with only the UL pair flipped. > > I take this pair UL and add 1. > The left part is yellow/red. the other yellow/red is on UL pair and > not good oriented. I add nothing. The cycle is finish. the parity is > odd. > > Have fun, > Frédérick. > ------------------------ 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/speedsolvingrubikscube/ <*> 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/
