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I just realized Petrus—W is basically Petrus but switching to a Roux variant halfway through.

I have a CFOP to Petrus/ZZ idea:
1. F2L-2/XXCross
2. EO
3. Petrus/ZZ
 
Like I said, it's Petrus/Petrus-W with an extra cross edge inserted, which is worse
Not really inserted, because cross already does that. The problem with just doing Petrus-W is it loses being CFOP.

I'll try one last time to give this method some viability:
1. F2L-1
2. EO
3. Insert LP + OCLL
4. PLL
 
Allrighty, I got this idea for a petrus variant :

1. 2x2 in back
2. 223 in back
3. EO from front, (front determines the orientation of the E edges, like in ZZ)
4. Left and right F2L pairs
5. COLL
6. L5EP
This could be good since you don't have to rotate, you have more ergonomic 22 and 223s, you get to orient 4 edges at a time instead of 2, and you have less pieces to solve after EO.

I was not sure if I should chime in on Petrus-W, but here goes. There was a similar method I used last year called WaterZZ/WaterPetrus. Instead of solving the right F2L pair in step 4, you can just do L5C and then L6EP (You can also mirror it if you want). It's also more flexible since steps 1-3 are solved within a single step, so you can use ZZ, Petrus, or other methods/techniques to reach EO223. You can do Shadowslice's way of solving L5C, but I still think learning all 614 algs alongside one-looking EO223 will make it an "end-game" method in the far future since you can solve EO223 in about a second if you do it in 10tps, do EO223+pair in one look, which is about 13 moves on average, and it can be combined with ZBLL. Petrus-W is probably much more viable as of now and less alg-heavy compared to WaterZZ though.
 
I have an interesting idea. What if you solved the S and M slices first? It would go something like this:
1. Solve M and S slices
2. Orient remaining pieces
3. Pair up edge+2 corner pairs
4. Place the pairs with F2/R2/L2/B2

Here’s a few ideas based off of this:
1. Solve S and M slices + EO
2. Orient Corners (1L: 49 algs, 2L: 7 algs)
3. Permute to pair up all edge and 2 corner pair
4. Place the pairs with F2/R2/L2/B2


1. Solve S and M slices
2. Orient all pieces (1L: 98 algs, Orient F2L, then OCLL: 21 algs)
3. Permute to pair up all edge and 2 corner pair
4. Place the pairs with F2/R2/L2/B2


1. Solve S and M slices + EO/OCLL
2. Orient remaining pieces
3. Permute to pair up all edge and 2 corner pairs
4. Place the pairs with F2/R2/L2/B2

1. Solve Cross
2. Solve Top edges, kind of like doing F2L. You can also use insertion algs to orient/Permute remaining pieces
3. Can't really make more steps because of how undeveloped it is
 
totally intuitive commutators last layer solve for begginers

put last layer on bottom, then:

(not necessarily in this order)

CO: sexy move <D, D', D2>
EO: [M' U' M U M' U2 M, <D, D', D2>]
CP: R <U, U'> R' <D, D', D2> (remove, reinsert corners)
EP: M' <U, U'> M <D, D', D2> (remove, reinsert edges)

Examples:



 
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CLP for Roux sounds good, but if there are more algs than CMLL or COLL then it's not really suitable. This would be like doing Last Pair in Roux and then Winter Variation, something like WVLP + Roux. Less Algs than CMLL maybe in some situations and can be influenced in the solve, but not really practical if you want to be sub 10 maybe (?)
 
CLP for Roux sounds good, but if there are more algs than CMLL or COLL then it's not really suitable. This would be like doing Last Pair in Roux and then Winter Variation, something like WVLP + Roux. Less Algs than CMLL maybe in some situations and can be influenced in the solve, but not really practical if you want to be sub 10 maybe (?)

Just because something has more algs doesn't mean its bad. 2lll has less algs that 4-look, but almost everyone knows 2-look. People use EOLR even though it has more algs than EO then L/R. Also it's WVCP(Winter Variation Corners Permute) not WVLP
 
2x2x3 + pair( can be done in many ways, i.e. 3/4 cross and pairs, 1x2x3 + 2x2x2)
Last pair with corner orientation(like ZBLS with corner)(could be WV or SV)
L5EO
L5EP + CP/PLL + DF edge(96 or fewer algs - 21 PLL = <75 algs(also some will just be setup moves to PLL))(If this subset hasn’t been named yet tell me (I want to name a subset))
Wait. L5EO? What about the DF edge?
 
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