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Kind of a weird idea, but what if you just did ZZ but also did CP while building EO cross thus reducing the last layer to 84 cases so you can PLL skip every time with 84 algorithms
Doing cp during eocross isn't feasible in a speedsolve. The only time I think it's viable is during last slot, which is what zz-d is.
 
ZZ-D is what you'd want to look at. CPLS is the most feasible way in a speedsolve, but overall ZZ-A is better. If you want something a bit more abstract, look at 2GR, but that's not very good for speedsolving.
 
More 42 variants:

VHLC Variant (Intermediate)​

51-52 moves​

  • Mehta-style FB on D (lD) - 7 moves
  • "2.5 QB" - 7 moves
Basically, solve 2 E-layer Ledges and any Redge, positioning this Redge in DR.

  • Insert FR or BR F2L pair to form square. - 7 moves
  • "VHLC" - 8 or 9 moves / 16-32 cases
Insert correctly-oriented U layer corner into unsolved slot, while solving EO. Correctly-oriented means that the corner would be oriented correctly after un-transforming (i.e., R or R').

  • Conjugated NMCLL - 11 moves
This could be done in 2 looks for 7 additional moves. This is where most of the work would lie in creating this variant. Does anyone know how many cases this would entail?

  • un-transform - 2 moves
  • L5EP-FR - 9 moves

WVLC Variant (Beginner)​

58-59 moves​

  • Mehta-style FB on D (lD) - 7 moves
  • "2.5 QB" - 7 moves
Basically, solve 2 E-layer Ledges and any Redge, positioning this Redge in DR.

  • Insert FR or BR F2L pair to form square. - 7 moves
  • "WVLC" - 9 or 10 moves / 27 cases
Insert correctly-oriented U layer corner into unsolved slot, while solving CO. Correctly-oriented means that the corner would be oriented correctly after un-transforming (i.e., R or R').

  • Conjugated NMCLL (Oriented) - 10 moves / 6 cases
This would be the equivalent of the 2nd look of 2-look Conjugated NMCLL. For this step, you could use CLL algs which destroy EO on the LL (e.g., FRUR'U'F').

  • un-transform - 2 moves
  • L5E-FR - 16? moves
EO and EP. My gut tells me that L5EOP-FR followed by EPLL would be the most effective approach here.
 
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More 42 variants:

VHLC Variant (Intermediate)​

51-52 moves​

  • Mehta-style FB on D (lD) - 7 moves
  • "2.5 QB" - 7 moves
Basically, solve 2 E-layer Ledges and any Redge, positioning this Redge in DR.

  • Insert FR or BR F2L pair to form square. - 7 moves
  • "VHLC" - 8 or 9 moves / 16-32 cases
Insert correctly-oriented U layer corner into unsolved slot, while solving EO. Correctly-oriented means that the corner would be oriented correctly after un-transforming (i.e., R or R').

  • Conjugated NMCLL - 11 moves
This could be done in 2 looks for 7 additional moves. This is where most of the work would lie in creating this variant. Does anyone know how many cases this would entail?

  • un-transform - 2 moves
  • L5EP-FR - 9 moves

WVLC Variant (Beginner)​

58-59 moves​

  • Mehta-style FB on D (lD) - 7 moves
  • "2.5 QB" - 7 moves
Basically, solve 2 E-layer Ledges and any Redge, positioning this Redge in DR.

  • Insert FR or BR F2L pair to form square. - 7 moves
  • "WVLC" - 9 or 10 moves / 27 cases
Insert correctly-oriented U layer corner into unsolved slot, while solving CO. Correctly-oriented means that the corner would be oriented correctly after un-transforming (i.e., R or R').

  • Conjugated NMCLL (Oriented) - 10 moves / 6 cases
This would be the equivalent of the 2nd look of 2-look Conjugated NMCLL. For this step, you could use CLL algs which destroy EO on the LL (e.g., FRUR'U'F').

  • un-transform - 2 moves
  • L5E-FR - 16? moves
EO and EP. My gut tells me that L5EOP-FR followed by EPLL would be the most effective approach here.
I like it. There are likely some refinements relating to EO and possibly the pairs used to finish the square on the right. I haven't seen the application of transformation used with FR L5EP. Just FR L5E.

I wouldn't call everything that uses transformation a variant of 42.
 
Here is 1:
1. Solve cross
2. Solve F2L rotationless by
a. Solve back left
b. Solve back right and front left
c. solve front right
3. solve OLL
4. solve PLL
If you get bad edges for 2a and 2b, Use another slot to pair them up. For 2c, if you get a bad edge, move edge to M slice withh U/ U', do M/M', solve pair, then insert edge back.
Basically ZZ-EO
 
Here is 1:
1. Solve cross
2. Solve F2L rotationless by
a. Solve back left
b. Solve back right and front left
c. solve front right
3. solve OLL
4. solve PLL
If you get bad edges for 2a and 2b, Use another slot to pair them up. For 2c, if you get a bad edge, move edge to M slice withh U/ U', do M/M', solve pair, then insert edge back.
Basically ZZ-EO
Interesting take on improving CFOP, but unfortunately methods like this tend to simply be slower. Although rotationless solves are nice, having one or two rotations during F2L doesn't lose as much time as jumping through hoops to avoid it.
 
Opp: M2 U2 M2
Adj: Either R U R' U' M2 U2 M2 U' R U' R' or M2 U' M U2 M U2 M2 U' M2
W: M2 U M U2 M' U' M2
Cw O (I think this is Ob): M' U' M2 U' M2' M
Ccw O (Oa?): M' U M2 U M2 U M
All of these algs presume lefty M moves apart from Cw O, which is probably fastest with righty, but doing ring-ring is fine and probably preferable if you use lefty normally. For righty, just mirror the algs.
 
Opp: M2 U2 M2
Adj: Either R U R' U' M2 U2 M2 U' R U' R' or M2 U' M U2 M U2 M2 U' M2
W: M2 U M U2 M' U' M2
Cw O (I think this is Ob): M' U' M2 U' M2' M
Ccw O (Oa?): M' U M2 U M2 U M
All of these algs presume lefty M moves apart from Cw O, which is probably fastest with righty, but doing ring-ring is fine and probably preferable if you use lefty normally. For righty, just mirror the algs.
ty all of you guys
EDIT: I optimised these for me (righty M moves, lefty U moves)

Opp: M2 U2 M2
Adj: M2 U' M2 U2 M' U2 M' U' M2
W: M2 U M U2 M' U' M2
Cw O: M' U' M2 U' M2' U' M
Ccw O: M' U M2 U M2 U M
 
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Back with another probably bad method idea:
Step 1. Solve a face plus 2 f2l pairs on the left
Step 2. Do coll to solve the top corners
Step 3. Do an algorithm to solve the UL edge (or more; I just came up with this and don't know how to gen algs)
Step 4. Do another algorithm to solve the rest of the cube (still don't know how to gen algs so this also might not be possible)
 
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