# 1LOLL even parity

#### bobthegiraffemonkey

##### Member
I've been taking a look at this recently: recognising the OLL case when you have parity on 4x4x4 or 6x6x6, and solving in 1 look. I couldn't find a thread on it already, which was surprising, but since I have all the cases generated I thought I should gauge what people think of it.

There are 54 cases for 1 or 3 flipped edges (27 each), or 36 without mirrors. For some cases, the best thing to do is standard OLL parity alg + OLL alg, though it is helpful to try and avoid bad OLL cases when doing this. For some cases I have found a cool trick (my inspiration was conjugating the parity alg with B' R'). So far I know about 25 cases.

My favourite trick: R' F R F' [OP] R U' R'

Does anyone use this already? Maybe just for a few cases? Let me know what you think, and feel free to point out any typos I made in the algs and/or better algs for any cases.

Matt

#### Cyrus C.

##### Member
Yea, about a year ago I was looking at this... I think I even posted a thread. Someone said Chris Hardwick had something about it on his website, I can't find it though.

I think, in the long run, you're going to save only one or two moves. A lot of the times Parity, OLL will be faster I think. However, there's nothing wrong with trying it, if you already know 25 cases, keep going, it may actually be quicker. Also, if you don't do this already, you can control the OLL case to avoid bad OLLs by AUFing before you execute the parity algorithm.

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#### Joker

##### Member
This is old. But yeah, it does save time.

#### LNZ

If you have only one of the four edges on the top layer in the "solved" state on an even ordered cube,
this is a useful method of getting to a completed cross.

Put the solved edge in the front-right position so the others form a "C" pattern.

Then do B' R' + OLL Parity alg + R B.

Then you suddenly have the cross and the parity solved.

#### bobthegiraffemonkey

##### Member
Updated some cases with the use of this alg, and improved a few old ones. There is now a maximum movecount of 9 (you can get smaller ones sometimes with a rotation instead of an AUF, but AUF is faster), not including the parity alg (of course), and there doesn't seem to be any bad cases. I've used shorthand notation, mostly for laziness, but it should be easy enough to understand and I've given a small guide to it (eg. SFR = sune, Front Right = R U R' U R U2 R'). OLL parity doesn't suck quite so badly any more. Now I just need to get used to recog before Guildford Summer Open at the weekend (I know most of it already).

Hope someone find this useful, it should give fairly speed-optimal algs (you can change it a little for your own preferences, algs as given are what I use) for all OLL cases with parity, with not much to learn. Please point out any mistakes or improvements.

View attachment 1LOLLp.zip

#### bobthegiraffemonkey

##### Member
Parity CP

Me again. I've fixed a couple of mistakes and tweaked some stuff. Main addition is OLL parity + CP. Not sure how worthwhile this is, but whatever, it's fairly easy to learn and EPLL is good, so I'm uploading it and probably going to use it. Basically, you usually solve all but one edge, then solve parity and CP together. For some cases, it's better to setup to a line unsolved rather than one edge, and for a couple of cases I do parity alg + COLL. I posted provisionally about this recently in random cubing discussion recently, but I've worked on it since then. Any mistakes, just let me know and I'll try and try and fix them. Out of curiousity, does anyone else actually use the stuff I posted here before, or anything similar?

Matt

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