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RedstoneTim

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Conjugated COLL should work. Then, you would just have L5EP. Although this would probably be better with ZZ than Petrus.

1. EOCross (probably better than EOLine)
2. Left pairs/block
3. BR slot
4. Conjugated COLL (42 algs)
5. L5EP (16 algs, 12 without EPLLs)

Seems pretty good, especially for it's alg count.
This is the basic idea of ZZ-Zipper. Conjugated COLL should probably be added as an alternative to L5CO though.

conjugated coll seams like an interesting Idea it also probably would not take to many moves
After some thought, I've noticed that this won't work. COLL doesn't preserve edge permutation, so L4C would have to be used. The disadvantages are that L4C is 84 algs, recognition will be a lot harder and that it's also considered one of the worst ZBLL subsets. So this seems to be a pretty bad approach.

Edit: For everyone wondering how Conjugated COLL works, I've made a wiki article for it.
 
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zimlit

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After some thought, I've noticed that this won't work. COLL doesn't preserve edge permutation, so L4C would have to be used. The disadvantages are that L4C is 84 algs, recognition will be a lot harder and that it's also considered one of the worst ZBLL subsets. So this seems to be a pretty bad approach.

Edit: For everyone wondering how Conjugated COLL works, I've made a wiki article for it.
True but saving over a hundred algs is still worth it
 

Skewbed

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This is the basic idea of ZZ-Zipper. Conjugated COLL should probably be added as an alternative to L5CO though.


After some thought, I've noticed that this won't work. COLL doesn't preserve edge permutation, so L4C would have to be used. The disadvantages are that L4C is 84 algs, recognition will be a lot harder and that it's also considered one of the worst ZBLL subsets. So this seems to be a pretty bad approach.

Edit: For everyone wondering how Conjugated COLL works, I've made a wiki article for it.
Conjugated COLL would preserve EO, which allows for L5EP.
Preserving edge permutation would allow for one look for both algs, but L4C has worse algs than COLL.
Both work, but I think that conjugated COLL would be better.
 

Athefre

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I've been thinking for a few years that a new term should be added to the cubing language. In cubing, we use the word conjugation. This is where one performs a setup move, then a sequence, then the setup move is undone. This is a very broad term and there have been more specific developments where conjugation has been applied. For example:

+ CLL
+ ELL, OLLCP, and CLL+1
+ It has been applied to PLL
+ I used it to reduce ZBLL to 160 cases
+ NMCLL/EG
+ NMLL

So, what I propose is that we use the term Transformation when it is used in this way. It is the application of a conjugation with the intent to change one case into another. I've thought about making a Transformation page on the Wiki, but I'm a busier person now than I was years ago and haven't kept up with other developments that could potentially be added to this Transformation wiki page. I explored this concept pretty heavily from 2010 to 2012 with positioning an oriented corner and conjugating CxLL to transform the cases, transforming ZBLL and others to reduce cases or make cases easier, 2x2 methods, and in NMLL. Really transformation can be applied to almost anything, but if anyone knows of other significant developments within this concept, let me know.
 

ProStar

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@ProStar finishes his algs?
I haven't started yet, I can't get cube explorer to work on my computer for some reason

COLL, but only to avoid diagonal plls, so it would be fewer algs and not as bad for the sune and antisune cases
SpeedCubeReview has a vid on that, it's called how to learn COLL without algs or something
 

ProStar

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Ok, idea for a different way of teaching beginners method:

Cross - Normal
Corners - Solve corners on bottom, use sexy move to insert
Middle edges - Line the edge up so it makes a bar with the center, then move it away from where it needs to go. Then do the alg(sexy move), then you can just do these three moves(do F' U' F) to insert it. You can make that part use only sexy and a little intuitive part. Use lefty sexy(L' U' L U) for the left side.
Orient Yellow Edges - Use F (sexy) F' and you're able to cycle through the 3 cases.
Permute Yellow Edges - take the pair out (R U R'), then the alg (sexy), then put the pair back in(R U' R'). You can repeat this until edges are permuted.
Orient Yellow Corners - Flip yellow on bottom, then use the alg(sexy) to orient the corners(normal beginners)
Permute Yellow Corners - With yellow on bottom, take a corner out (R U R'), do D moves so that the correct corner is above the two correct edges, then put the edge back in(R U' R'). Then repeat for all the corners. Then the cube is solved :)

So with this, you only need sexy move(R U R' U') and lefty sexy(L' U' L U) to solve the cube(with maybe a couple moves added/subtracted, like for yellow cross/corners or something).

(I learned from the Rubik's tutorial and basically did brute force 4lll for LL, so maybe this is the normal method lol)

Here's an example solve that gives comments on how you'd explain it. Be warned, it's over 180 HTM, has more lines then the reconstruction of Feliks' entire Ao5 WR, and has a stupid amount of U U' lol
Okay, I posted this a while ago(~1.25 months) as a way to simplify the beginner's method. After some toying with it(don't worry, I haven't devoted my entire life to this for the past month :p), I came up with a way to remove the intuitive part from the E layer edges

Middle edges - Line the edge up so it makes a bar with the center, then move it away from where it needs to go. Then do the alg(sexy move), then you can just do these three moves(do F' U' F) to insert it. You can make that part use only sexy and a little intuitive part. Use lefty sexy(L' U' L U) for the left side.
Here's what I got:

Middle edges - Line the edge up so it makes a bar with the center, then move it away from where it needs to go. Then do the the sexy move that affects the side where the piece needs to go(i.e: The piece needed to go to the left, so you did a U'(moving it to the right), then did the alg the affected the left side(lefty sexy) (because that's where the piece needs to go). Then rotate the cube towards where the piece needs to go(so if it needed to go to the left, do a y') and do the alg you didn't just use(so if you just did lefty sexy, then do normal sexy this time)

Everything else is the same way as before
 

Athefre

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I'm pretty sure this 42, 22, and Conugated CxLL that people are talking a lot about now is the same thing that I already developed eight years ago. I don't think someone else's name should be credited on something that someone did first, even if they "re-developed". I could "re-develop" Roux, CFOP, or PLL then have my name as a proposer on the Wiki pages. I also think that the name Conjugated CxLL isn't a good fit for what is actually happening. The step of building a 1x2x2 block and adding an oriented corner could be a page of its own with a proposer I guess and an L5C page could reference this option of intentionally orienting a corner then using conjugated CLL. But Conjugated CxLL is the concept that I proposed and developed and the page should be updated to describe what it really means.

In 2012 I created this CLL Transformation Table and presented it as a mostly new concept within cubing methods. The idea of conjugating to transform CLL cases into another. Others have used conjugation for steps before, but, as far as I know, not to this extent and hadn't developed anything. A few months later I combined it with my work on NMCLL to use it in corner solving methods, like 2x2. In this Non-Matching CLL/EG post I detailed how this transformation could be used with CLL and EG in combination with the addition of non-matching corners. The first step and even the sequences make use of aligning oriented corners on U, then doing an R turn to transform the case. Using this, a face or layer is almost always already available after a scramble or just one or two moves away.

Even the 42 wiki page has this quote:

"it is possible that the "V" does not need to "correctly" solved. In a similar way to how EG solves only a face, only the one colour of the "V" may need to be solved. It is possible to use other more advanced Briggs3 techniques such as NMLL. With the techniques listed previously it is possible that the first step may frequently become a "skipped" step or have only a 1 or 2 move solution when combined with colour neutrality thereby giving much easier 1-looking." --- After this "V", it is turned into a face or layer, so it is the same concept.
 
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RedstoneTim

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I guess and the L5CO page could reference this option of intentionally orienting a corner then using conjugated CLL
"To reduce the amount of algorithms to only 42, Conjugated CxLL with COLL can be used. However, this leads to slightly higher movecount and also requires orienting one corner. " (Source: https://www.speedsolving.com/wiki/index.php/L5CO)

I also think that the name Conjugated CxLL isn't a good fit for what is actually happening.
I basically invented that name based on Joseph Briggs' Conjugated CMLL because I thought that this would make most sense to someone who already knows about 42.

I'm pretty sure this 42, 22, and Conugated CxLL that people are talking a lot about now is the same thing that I already developed eight years ago. I don't think someone else's name should be credited on something that someone did first, even if they "re-developed".
I did not know that you have already thought of this idea, neither do I think that Briggs did. I just created this article based on what I knew about 42, but will ensure to add you as a proposer. I do believe though that Joseph Briggs should be kept as a co-proposer though because I'm almost certain he came up with the idea independently and has also developed it further. (For example, he's created this case list.)
This would be in similar fashion to how his SSC method was proposed by him but both Briggs and Adam are shown as the proposers because Adam independently came up with ECE and brought new ideas like EZD to the method.

I could "re-develop" Roux, CFOP, or PLL then have my name as a proposer on the Wiki pages.
Obviously, you aren't a co-proposer just by thinking of a concept someone else has already thought of. There would firstly need to be evidence that you also came up with the idea and you secondly would need to develop it further and think in ways the original proposer did not (compare how you initially invented this concept for 2x2, but Briggs thought of this for Roux and only later applied it to 2x2).

In conclusion, I would say that Conjugated CxLL (or whatever you want to call it) was created independently by both of you at different times, and that therefore, you and @shadowslice e deserve credit for it.
 

Athefre

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I do believe though that Joseph Briggs should be kept as a co-proposer though because I'm almost certain he came up with the idea independently and has also developed it further. (For example, he's created this case list.)


Obviously, you aren't a co-proposer just by thinking of a concept someone else has already thought of. There would firstly need to be evidence that you also came up with the idea and you secondly would need to develop it further and think in ways the original proposer did not (compare how you initially invented this concept for 2x2, but Briggs thought of this for Roux and only later applied it to 2x2).

In conclusion, I would say that Conjugated CxLL (or whatever you want to call it) was created independently by both of you at different times, and that therefore, you and @shadowslice e deserve credit for it.
I don't feel like he created anything new or added anything to the concept. He only applied the concept that already exists to the Roux method. That doesn't mean that the concept of CLL Transformation/Conjugated CxLL was developed further. He applied it to Roux and made a list of specific cases. He didn't propose the entire concept. I have done a lot of work developing the Roux method, such as NMCLL, Non-Matching Centers, and others, but I'm never going to say that I co-proposed the whole Roux method or even CMLL or LSE. That is Gilles Roux only. I only developed a part of it. My name is on the NMCLL page proposers only because I didn't see a Developer option. I am not a co-proposer. If there is a way to add a Developer option to wiki pages, then maybe this is ok:

Proposer: James Straughan
Developer: James Straughan, Joseph Briggs

I basically invented that name based on Joseph Briggs' Conjugated CMLL because I thought that this would make most sense to someone who already knows about 42.
I have a post a little above where I talk about transformation/conjugation. I'm planning to make a wiki page about Transformation. I think for this, CLL Transformation is a better name. But I guess Conjugated CxLL is ok for now.

I'm passionate about this because this transformation concept that I spent many hours on is something I'm a little proud of. I'm proud to have been the one to really propose it and explore it in various ways.
 

RedstoneTim

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I don't feel like he created anything new or added anything to the concept. He only applied the concept that already exists to the Roux method. That doesn't mean that the concept of CLL Transformation/Conjugated CxLL was developed further. He applied it to Roux and made a list of specific cases. He didn't propose the entire concept.
I've asked him on discord whether he had known of your ideas before and his reply was "I had no clue about any of his posts when I proposed stuff".
He did also develop it further just by applying it to Roux because, as far as I can tell, your idea was specifically for 2x2, so I would argue that 42 is fully his creation.

I have done a lot of work developing the Roux method, such as NMCLL, Non-Matching Centers, and others, but I'm never going to say that I co-proposed the whole Roux method or even CMLL or LSE. That is Gilles Roux only. I only developed a part of it. My name is on the NMCLL page proposers only because I didn't see a Developer option. I am not a co-proposer.
What I've been trying to say is that Briggs independently came up with the same approach and developed it further, for example also by popularizing it (e.g. most people here, me included, would've never heard of that hadn't it been for him).
It's not like he took what was just there, he created this all without any prior knowledge like you, just some years later.

If there is a way to add a Developer option to wiki pages, then maybe this is ok:

Proposer: James Straughan
Developer: James Straughan, Joseph Briggs
There seems to be no option to do that. It would be possible to add that to the template, but that would add this for all methods and is not really worth it just for that.

Would it be okay for you if we just said that you invented and developed Transformation for 2x2 while Briggs later independently did something similar for Roux?
 
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