Hey Ron, I can't prove it, but I am almost 100% convinced that counting the full cycles is the only way.
I also tried something like looking at each piece in terms of BLD cubing orientation. That reason this doesn't work is that you can switch two pieces that are oriented the same way using the parity alg + center rotater (so quite literally only those two pieces switch) and they both appear to be oriented. For every orientation case you invesitate, switching exactly two edges and still having it look the same way in terms of orientation is possible. So this method cannot identify parity in all cases. I think counting cycles, with a year or two of practice, could be done in the 15 second inspection maybe as much as 75% of the time. The problem is you would not have a good plan for starting your solve. The solve itself would start very nearly like a no-inspection solve. Plus, 25% of the time you would be very near completing the cycles counting right as the judge says "put your cube down". This can't be good for a concentration zone or solving rhythm. My next goal, and Ron I've already mentioned this to you, is to use a "one parity method". After using ZBLL for a while I came to realize that 5/6 of the COLL cases can be viewed as having switched only two corners (which is odd parity if you consider the F2L solved and the LL face turned correctly). So what I want to do is to memorize for each COLL case exactly which two corners are swapped (I already know this for the COLL cases I know for ZBLL, I just need to learn it for the rest). So 5/6 of the time I will have "odd parity", maybe not really but from my viewpoint of considering the corners I will. Then I look at the edge permtutation in relation to the two "solved" corners and see if it is also odd. I like this because 5/6 of the time I check for odd permutation of edges. The 1/6 is even becase that is the only case where the corners are fully solved (permutation) in relation to eachother. So I just memorize the 1/6 cases that are even and in those cases check for even edge permutation. I can do it now already but it is very slow. However, I believe it will speed up the method a small amount when fully practiced and here is why: Let's consider just the scenario where you have OLL parity, the no OLL parity situation is exactly the same for the "one parity" method or whatever you want to call it. Regular solving: (1/2)*(15) + (1/2)*(15 + 8) = 19 So it takes 19 moves on average to solve the OLL parity case with the regular method. This includes 1/2 the time just the OLL parity and 1/2 the time also the PLL parity using Stefan Pochmann's 8 move fixer. One-parity solving: (1/2)*(15) + (1/2)*(15) = 15 so you save 4 moves on average. Here is my idea on how it affects the time too: Regular solving: (1/2)*(5.25+2.75) + (1/2)*(5.25) = 6.63 seconds to solve parities on average One-parity solving: (1/2)*(5.25) + (1/2)*(4.75) = 5.00 seconds So you have up to 1.63 seconds to identify double parity without it affecting your average at all. If you spend 1.63 seconds every OLL parity solve just staring at your cube and not doing any turns, as long as you can always correctly guess double parity or not, then you will break even with one parity over executing 2 parity algs 1/4 your solves. This time difference only gets better the faster you can execute the double parity alg. So it won't save much time, but it saves time. And at top level solving for any puzzle any amount of time saved is good. Also, on the rare easy cases where you can identify double parity in .5 seconds you will save up to 3 seconds off that solve. That's a full second in a competition mean that comes off your times. So it's a lot of work, for very little gain. But it's gain nonetheless so I think it will be worth it to learn. Plus it's something that ZBLL would teach you anyway, so I might as well learn it now and be comfortable knowing the structure of my ZBLL algs even more, having already memorized the corner structure of each one. In short I want to learn it, but I realize that it is a lot of work for very little gain. I feel the cycles counting method is worse though in terms of lots of work for a disproportional amount of gain. But then again it would be a gain, so maybe it is worth it, who knows? Chris --- In [email protected], "Ron" <[EMAIL PROTECTED]> wrote: > > Hi friends, > > I had a nice talk with Frédérick Badie during WC 2005 about > improvements on 4x4x4. > > 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 am pretty convinced there must be an easier way. Something like > this: > Take the orientation of all edges according to blindfolded cubing. > For each edge pair, count whether the single cubies are oriented > according to that standard. The total number of flipped edge cubies > must have the factor 4. > > I took some randomly scrambled cubes and it was correct, but I am > sure that in fact this hypothesis is not correct. > Factor 2 does not work (1 flipped edge pair has that...) > > Anyway, please find a counter example of the factor 4. > > Or better, please find an easy way to check the 4x4x4 orientation > parity. Maybe you can do this with diagonal cubies or whatever? > > Or proof that the only way is to follow the cycles. > > Thanks and have fun, > > Ron > ------------------------ Yahoo! Groups Sponsor --------------------~--> Get fast access to your favorite Yahoo! Groups. 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