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Do the maths. Each corner can be in one of 7 places. So it's 7!=5040. Then you do more maths and do it properly but that's effort. So it's got an upper bound of 5040.

Do the maths. Each corner can be in one of 7 places. So it's 7!=5040. Then you do more maths and do it properly but that's effort. So it's got an upper bound of 5040.

That's kinda the idea behind the HD method. It reduces to opposite V's, which is only marginally harder. Full case count doesn't actually seem very bad at all:

(Sorted by color pattern on U/D face)
PBL: 5 cases
V's: 21 cases
Adj/adj: at most 36 cases
Adj/opp: at most 36 cases
Opp/opp: at most 36 cases

That's lower than I expected, and definitely a very feasible alg count. Recognition does not seem good, but I don't know if that would be a big deal with the ability to one-look. I think this is really cool: this is one of the most commonly proposed methods, but it's always shot down because no one ever check to see how high the alg count actually was.

I don't intend on reducing down to the state I described, but rather the user of the method I'm looking into could choose to learn the algs in case it comes up.
I'm sure this method has been proposed before, but I really like it and think it could be interesting for those who want to get decent at 2x2 but don't care enough about it to learn EG.

1: OPS - Opposite Pseudo-Sides. Orient the corners so that the U and D faces consist only of two opposite colors. Can very easily be planned in inspection, at least if you do the sides one at a time.
2: Solve the rest. (Messy PBL?). I currently do this by orienting the corners and then Ortega PBL, but there must be better ways. Much of the time you just have NLL, so it would be advisable to know that.

With this method, I currently average sub-5, about a second faster than I do with Ortega. If you do OPS one side at a time, the POLL algorithms (Pseudo-OLL) should be better than regular OLL. For example, H would be just R2 U2 R('), and U can either be the regular alg or R U2 R U2 R('). I haven't found better algs for any other case yet, though.

1: OPS - Opposite Pseudo-Sides. Orient the corners so that the U and D faces consist only of two opposite colors. Can very easily be planned in inspection, at least if you do the sides one at a time.
2: Solve the rest. (Messy PBL?). I currently do this by orienting the corners and then Ortega PBL, but there must be better ways. Much of the time you just have NLL, so it would be advisable to know that.

I don't intend on reducing down to the state I described, but rather the user of the method I'm looking into could choose to learn the algs in case it comes up.
I'm sure this method has been proposed before, but I really like it and think it could be interesting for those who want to get decent at 2x2 but don't care enough about it to learn EG.

1: OPS - Opposite Pseudo-Sides. Orient the corners so that the U and D faces consist only of two opposite colors. Can very easily be planned in inspection, at least if you do the sides one at a time.
2: Solve the rest. (Messy PBL?). I currently do this by orienting the corners and then Ortega PBL, but there must be better ways. Much of the time you just have NLL, so it would be advisable to know that.

With this method, I currently average sub-5, about a second faster than I do with Ortega. If you do OPS one side at a time, the POLL algorithms (Pseudo-OLL) should be better than regular OLL. For example, H would be just R2 U2 R('), and U can either be the regular alg or R U2 R U2 R('). I haven't found better algs for any other case yet, though.

I just wanted to point out that the first step takes only 3.7 moves on average optimally, so doing it one side at a time is likkee a lot of extra moves. Also your OPS is commonly known as Corner Orientation, or CO.

Here's some examples of doing OPS aka CO in under 4 moves on average:
Scr: F2 U F' U' F R2 F' R U' -- (y') U R'
Scr: F R' U' R F U' F U F' -- (z x') R
Scr: F' U2 F' R F2 R' F2 R' F' -- (y') R' U2 R
Scr: U R' F2 U2 F' U2 F' U F' -- (y') F R
Scr: U2 F2 R U' R2 F R F2 U2 -- U' R2 U R'
Avg of 5 is just 2.4 moves, but I do admit these were really easy scrambles, and I know it usually takes around 4 moves.
If you want more information on how to do this or just CO and Guimond in general, then perhaps this is a good place to start.

And then for finishing the cube once you have CO, I'd have to say NLL is the way to go, but if you don't want to learn 36 algs then PBL is an alright choice.

And then for finishing the cube once you have CO, I'd have to say NLL is the way to go, but if you don't want to learn 36 algs then PBL is an alright choice.

Random 2x2x2 Ortega thought.
Instead of just using the normal OLLs, why not use OLLs that will solve the adjacent swap case on the bottom? You get this case 2/3 of the time, and it's pretty easy to force it. Then your OLL can solve the bottom layer. Now you only have PLL on the top layer, so you have a much higher chance of a PLL skip, plus the recognition is much faster and easier.
Or I guess you could learn 21 OLLs, so you have one for each of the 3 bottom layer cases. It gets kinda stupid at that point though...

Have you ever heard of EG? It is where you solve a face, then you solve everything. It's 128 algs, which is exactly what you're describing, just worse. EG isn't super hard to learn, so just go with that.

Yesterday, I wrote a custom solver in JavaScript to find some algs for the CMLL with a missing edge set:

It let me make more state definitions than Cube Explorer, and that helped with finding shorter algs.

I set it to find all <RUF> algs up to about 10 moves, and it found over 60 working algs! Some of the algs are a bit hard to execute.

I also threw together a website showing the algs I found and the corresponding CMLL case (the position of the FR edge might not be visible in all cases).

Have you ever heard of EG? It is where you solve a face, then you solve everything. It's 128 algs, which is exactly what you're describing, just worse. EG isn't super hard to learn, so just go with that.

Yes, but what I am describing is just what seems like a better way of learning ortega/LBL, I'm not trying to replace EG, I'm just trying to make a beginner method better.

Yes, but what I am describing is just what seems like a better way of learning ortega/LBL, I'm not trying to replace EG, I'm just trying to make a beginner method better.

This may be a bad idea, but maybe you could use Ortega on a 3x3? As long as you have a white corner piece to go with the correct middle layer edge piece, then you can just do PLLs to fix the top and bottom layers.

This may be a bad idea, but maybe you could use Ortega on a 3x3? As long as you have a white corner piece to go with the correct middle layer edge piece, then you can just do PLLs to fix the top and bottom layers.

This may be a bad idea, but maybe you could use Ortega on a 3x3? As long as you have a white corner piece to go with the correct middle layer edge piece, then you can just do PLLs to fix the top and bottom layers.

I have actually tried this method. I average between 20 and 25 seconds normally, but with this method I got over 1 minute. That is interesting that Varasano was invented before Ortega.