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Silly little 4x4x4 method:
- Solve white and yellow centers, place on left and right
- Build a 1x3x4 block on left
- Extend to 2x3x4 block OBLBL style
- Pair up and build a 1x3x4 block on right (flip an edge with rU2r' or r'U2r)
- CLL
- Solve UL and UR edges, not sure best way to do this
- Solve last 6 edges with <r, U2>
- Solve last 10 center pieces with commutators
 
Silly little 4x4x4 method:
- Solve white and yellow centers, place on left and right
- Build a 1x3x4 block on left
- Extend to 2x3x4 block OBLBL style
- Pair up and build a 1x3x4 block on right (flip an edge with rU2r' or r'U2r)
- CLL
- Solve UL and UR edges, not sure best way to do this
- Solve last 6 edges with <r, U2>
- Solve last 10 center pieces with commutators

Step 4 uses too many slices. Slow. Commutators eww.
 
Silly little 4x4x4 method:
- Solve white and yellow centers, place on left and right
- Build a 1x3x4 block on left
- Extend to 2x3x4 block OBLBL style
- Pair up and build a 1x3x4 block on right (flip an edge with rU2r' or r'U2r)
- CLL
- Solve UL and UR edges, not sure best way to do this
- Solve last 6 edges with <r, U2>
- Solve last 10 center pieces with commutators

What benefit is there in postponing centers until after edge placement? Is it really that much harder to do edges with centers already made?
 
A method I thought of... I don't know if it's original or not. It's not very fast in any case.
1.)Fix all bad edges
2.)Move all E layer pieces to their layer (creates belt around cube)
3.)Orient corners on top and bottom layer using ocll without messing up edge orientation (use RUR'U'x3 to fix parity)
4.)Solve the top and bottom layers like you would on a 3x3x2
5.)Do z' rotation and finish the E layer pieces using a 3 cycle/Roux 4c technique
6.)Fix any opposite swap parity on top and middle layers using R2 U2 R2 U2 R2 U2
 
Same with Roux ;)

K4 is one of the fastest 4x4 methods, and that finishes with commutators.

But yeah, it's slow.

but roux 3x3 slicing is easy because 3x3s turn perfect. Those gosh darn aosus take hundreds of solves until the construction error of the two piece design in the edges smooths out and the inner slices become fast.
 
I don't know alot about other methods, but that sounds a lot like an inefficient version of the belt method.

Lol yeah. I've been experimenting with the belt method a lot lately, the main problems I've been running into with it are that 1.) double (corner and edge) parity is really annoying 2.) fast times require full oll 3.) its really difficult to group both edges and corners into their layers 4.) its really hard to preserve a fully solved belt. With my method I was basically trying to fix the edge parity and oll problem by fixing bad edges at the beginning and fix the problem of preserving the belt by only requiring the pieces to be in the right layer but lol yeah its still pretty inefficient.
 
i was randomly thinking about LL, and started thinking about the viability of random 2-look LL sets.

for example, i thought about this:
1. solve a 1x1x3 block. (which forces one other edge to be permuted, if that matters)
2. orient and permute the rest.

that might be easier with EO already done.
for step 1, in other words, solve one colour/side. this leaves you with 6 pieces all crammed together that aren't solved.
idk what the algs will look like, and i didnt have a piece of paper with me but in my head it seems like a lot of algs.
recognition would be easy for step 2, but i have no clue for step 1.
step 1 can be colour neutral, which will reduce algs i guess but recognition gets even harder lol.

this doesn't seem too viable because of step 1 recognition (i might be mistaken about how difficult it is) but the point is i was getting creative with LL. maybe there are other good ideas.
 
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For 3x3:
Solve a line from LD to RD +All f2l edges.
Solve all edges using M,U
Use commutators to solve the corners. could be used as blind maybe? Idk i dont do blind but..

Okay here is another one. Similar to CFCE, but not quite
Cross
F2l (LS=VHLS to fix EO)
OLLEP (same as OLLCP but permutes edges instead of corners)
CPLL (corner PLL)
 
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Okay here is another one. Similar to CFCE, but not quite
Cross
F2l (LS=VHLS to fix EO)
OLLEP (same as OLLCP but permutes edges instead of corners)
CPLL (corner PLL)

this has been suggested before but here are some flaws:
if you want a COLL twin (OCLLEP?) then that'd be more viable to learn, since nobody wants to learn OLLCP anyway. plus ZZ solves would benefit every solve.
if you have EO done already, the EP has bad recognition because you have to look at 3 edges (therefore 3 sides). it's like trying to recognize CP in CPEOLL. it's just not good because you're forced to look at 3 sides. this isn't a problem for non-OCLL cases (if you just had OLLEP), but again there's a problem of alg count that nobody wants to learn.

but the bigger problem is CPLL.
if you wanna argue that A perm = U perm in speed, fine. at least for 2 hands.
H perm = H perm.
Z perm > E perm, there's a rotation and it's longer and it's just a bad alg in general. nobody wants to force E perms.

plus, EPLL comes with the advantage that the entire set can be done <M,U> so the case doesn't affect your hand positioning. also, <R,U> for one hand and big cubes.

overall, it's just very difficult to argue that CPLL can be compared to EPLL.

as for OLLEP, i would have to look at the algs but the OLLCP algs aren't that bad anyway. especially for COLL, since there are so many commutators.

HOWEVER there is a bright side to OCLLEP. if my brain is working properly, i think it can be done 2-gen.
 
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No its like edges first then comms. Edges first could work for bld, but you lose any efficiency because the corner memo will have to be done while considering for edge moves, which completely jumble all the corners unless you are careful.

I thought that said all F2L pairs, which would have meant Roux finishing with L4C.
 
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