You know, I think Yuki does the OLL even with a parity, and then he recognises whether the permutation parity is present too, and does both or just the one in the one step.
SPeak later, Dan :) --- In [email protected], cmhardw <[EMAIL PROTECTED]> wrote: > > 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. Make Yahoo! your home page http://us.click.yahoo.com/dpRU5A/wUILAA/yQLSAA/MXMplB/TM --------------------------------------------------------------------~-> Yahoo! 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