Hey Ron, You don't need to count the 24 cycles, I had forgotten about the 12 cycle counting method that Frederick mentioned. That can absolutely detect parity every time. I personally still found it very difficult, it is a puzzle all by itself. Using it would be like solving two puzzles at once on stage. You have 15 seconds to frantically (and yes to get to even 25 seconds I had to frantically twist my cube around) discover parity, which I believe couldn't be done 100% of the time (who can solve the 3x3x3 in under 15 seconds 100% of the time?). But on the times you do discover it, with training, I think tracking the parity during the solve would not slow you down much at all. Any double turn does not change parity, and I had learned how specific sequences I use affected parity so I didn't have to count every move.
I personally think that noticing parity early, say whether or not the zbf2l case is parity or not would work. You don't have to know ZBF2L, but you could learn to recognize it, and all the patterns are the same so it wouldn't take much work. Also, something I found interesting while doing some 4x4 math before the tournament. Sometimes the regular parity alg is very fast for me, but sometimes the double is fast for me. So I would like to use both but still want 50-50 odds of double parity and not more. Well call the frequency that you use the regular parity x (0<=x<=1) and call the frequency that you use the double parity alg (1-x) the number of moves on average that it takes you to correct parities this way is (1/2)*(15x+23(1-x)) + (1/2)*(23x+15(1-x)) (1/2)*[-8x+23 + 8x +15] 19 So no matter the frequency you switch between the algs, you average 19 moves to solve parities. That is the same as always using the same alg. This works since they are the same number of moves in length. Also about the centers, when I was practicing solves when I knew the parity, I would forget about the parity after the 4th center (but I solve the 3rd and 4th simultaneously always). They way I put them together I would correct parity if I needed to just before putting those 2 centers together. THe 5th and 6th solve using only conjugates which don't change parity. If you do solve 3 centers, and correct parity to even while doing so, then you can only solve in conjugates to finish the last 3, but yes parity wouldn't change after that. I personaly am very skeptical of the usefulness of coutning cycles, even with the 12 cycle method, since for me it was so terribly difficult to try to even get sub-30 seconds. I think noticing during the solve might work better personalyl, but I am open to learning newer or better ways to detect during inspection. Also what about doing what I saw someone mention in an earlier post, why not do the OLL when you have OLL parity such that you end with one flipped edge only. At this point it would be very easy to discover if you also had PLL parity. I'm sure if we had faster algs to flip just that one edge to either solve OLL or OLL and PLL parity then this method would save time. I average about 6 seconds to do OLL parity with inner slices and maybe 6-7 right now with OLL + PLL aprity alg using just inner slices. If we can make this fast, then why not try that route also? We would need better algs for inner slice only though in my opinion. Can we get somthing with lots of r and l' moves? You could perform those like Bob and I do M' for the H permutation? Just some thoughts, Chris --- In [email protected], "Ron van Bruchem" <[EMAIL PROTECTED]> wrote: > > Hi friends, > > Could Chris/Per/Stefan please explain why they think there cannot be a method other than counting cycles? > I would love to see a proof! Or better, I would love to see a proof of a better method. :-) > > Yesterday I found a counter example of my factor 4 hypothesis: just swap the edge cubies UrF and URb. You have 0 flipped edge pieces, but you do have parity. > When I started this solve the total number of flipped edge pieces was 14 (=parity, which was the indeed the case), so somewhere in the solve it changed to a factor of 4. > > CLL=>ELL is indeed an interesting approach. :-) > > Orientation parity during F2L was an idea I already had, and I asked Jaap to find an algorithm for it, using his program. At the moment he is still on tour in Florida. :-) > > Stefan, I don't understand what you mean with your idea about dedges. > > Doing both parities in one is interesting. At the moment I use two algorithms (the normal one by Chris, and the double parity one by Frédérick), but both twist corners because I use multislice moves. It would be great to have a fast algorithm that does not twist corners... It would be great to have a fast algorithm for the orientation parity anyhow. Yuki can do the parity algorithm amazingly fast. I need to train for that. :-) > > Is it true that once you solved 3 centers, you cannot change parity anymore when you keep these centers intact? Because then the center positions are fixed? > In that case you only have to count the parity during the first three centers. Which is not a big task. > > Thanks and have fun, > > Ron > > ----- Original Message ----- > From: Stefan Pochmann > To: [email protected] > Sent: Sunday, November 13, 2005 4:08 AM > Subject: [Speed cubing group] Re: 4x4x4 parity without counting cycles > > > --- In [email protected], "Ron" <[EMAIL PROTECTED]> > wrote: > > > > One of the subjects was avoiding the orientation parity, as already > > investigated by Chris Hardwick. > > I really think there must be an easier way to check this parity, > > than to count the cycles. Counting cycles takes quite a lot of time, > > because you have to follow all pieces around the cube. > > I don't think there's an easy way out and like Per I don't think it > would be worth it anyway unless maybe you can really see it in 5-10 > seconds. > > Some in my opinion more realistic time-savers dealing with the > parities in a centers>edges>3x3 method: > > - Do CLL->ELL, solving both parities as part of ELL. It's an easy > 2-look LL. > > - Recognize and fix orientation parity before solving the last F2L > pair. Chris should already be able to recognize it since he's doing > ZBF2L and it's not hard to learn anyway. Now we just need a fast alg > that exploits the unsolved slot. Should be shorter/faster than what we > have so far. > > - While pairing up dedges, don't flip built dedges anymore (optimally > don't change them at all) and count flipped dedges. Then you could fix > the parity before starting the 3x3 step. An even shorter/faster alg > should exist. > > Cheers! > Stefan > > > > > > > > ------------------------------------------------------------------------------ > YAHOO! GROUPS LINKS > > a.. Visit your group "speedsolvingrubikscube" on the web. > > b.. To unsubscribe from this group, send an email to: > [EMAIL PROTECTED] > > c.. Your use of Yahoo! Groups is subject to the Yahoo! 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