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How about CFCE?

CCE just seems like it could be fast if it can even be done efficiently by a person. CFCE is more of just another 2LLL, while CCE vastly affects LL during all of F2L (as opposed to just LS), and an easy 1LLL with a tiny 29 algs for ELL. Looking to make a very unique variant on CFOP, although I didn't intend on it being insane lol
 
new method (BFL)
1) create a 1x2x3 cp block (no eo)
2) blockbuild the first two layers
3) solve ollep (preserving cp) (1/675 algs)
 
Roux FMC?

Solve F2B while influencing LSE, use an insertion in the blocks to solve LxC (Preferably you reduced to L3C during F2B) and then do LSE. Alex Lau reportedly used it in comps and got several sub-30's. I did a solve using it for the example solve thread and got a 27 without much effort. Probably not as good as Petrus/Free blockbuilding FMC but I think in the world of "stylized FMC" this could be a good approach if you're able to look into LSE really well.

SCRAMBLE: L2 D F2 U' B2 F2 D L2 D' F2 U L R2 F L R B U R F D

FINAL SOL: R2 B' U' B2 U' B' (R D' L' D R' D' L) F2 D2 F D' F D F B2 U F' B L F B'

R2 B' U' B2 U'//FB
B' * D' F2 D2 F D' F D//SB-1 move
F B2 U F' B L F B'//Edges (L3C redux)

*=R D' L' D R' D' L D

B' (R D' L' D R' D' L D) D'

I noticed several pairs premade, so I tried to influence an easy SB while solving FB. Solving SB was pretty straightforward and it ended with an extremely simple LSE (3 STM not including AFF/ABF) and I just got L3C which made for an easy insertion.
 
@Neuro this is actually really cool, great idea! I'm not too good with Roux though so I can't really give my critisism

Here's a random idea I thought of:
1) F2L-1 (blockbuild or cross/F2L)
2a) EO
2b) CO (completely 2-gen!)
3) L9P
 
Here's a beginner's method I thought of

1 - make a 2x2x3 block
1a - 3/4 cross
1b - expand into 1x2x3 block
1c - fill in last 2 edges
2 - fill in last two pairs and ignore last cross piece
2a - make one pair
2b - make second pair while preserving the first one
2c - put both pairs in their correct places
3 - solve corners
3a - permutation: use sexy-sledgehammer to switch front 2 corners
3b - orientation: either use sune or R' D' R D
4- solve edges
4a - orient edges using roux style stuff (basically M' U M orients an arrow in front)
4b - permute edges either by inserting last cross edge and forcing a U perm (by throwing in a M' U2 M if there is no solved line) and then doing a U perm Or flip cube over and use M' U2 M to insert whatever edge goes into the "bottom" layer until the whole thing is solved


I think the real elegance in this method is the skills learned with it transfer very well into any of the main methods including more obscure ones

Edit: it's also very customize-able, for example for step1 you can just do normal blockbuilding, you can do cfop stuff after 3/4 cross to fill in 2 slots, etc. For step 2 you can also do it so you solve f2l-1slot instead of f2l-1edge
 
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My Halloween contribution

Spooky method

1: Pumpkin - Build FB+Edge on bottom with the extra edge in DF
2: Graveyard - F2L represents the yard the Pumpkin sits on and the bodies rise
3: Skeleton - Skeletons are humans but they don't have innards; like how OLL has all the pieces oriented but not permuted
4: Zombie - Solve the layer; the proper flesh and skin of humans is present on the ominous zombie

For extra spook, always solve orange pumpkin.

Solve: R2 F2 L2 D L2 U' F2 U B2 D U L' U' R F2 D2 F U' L' R' U

D2 R2 L D' L2 D F' L D' z' y//Pumpkin (9/9)
F u y' R2 U2 R E' R u2 U y R' F' R//Graveyard (12/21)
R' U' F U R U' R' F' R//Skeleton (9/30)
M2 U M2 U2 M2 U M2//Zombie (7/37)

I recommend this wholeheartedly to no one except the undead and monsters as the method sucks for standard humans.
 
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2-look LL method:
1) solve EO while misorienting all LL corners - 57 algs I think
2) finish with one of 112 ZBLL algs
 
I got a solve under 40 moves with a more advanced version of that beginner's method I posted. I can't reconstruct because it was a hand scramble but that shows it really might have potential

steps I used: build 2 pairs where one side color and the end colors match, put them together into a 1x2x3 block with no respect to other centers, match up to other centers and expand into 2x2x3 block, build last 2 pairs of f2l, insert them, solve corners (cp then co), l5e.
 
1. CPLine
2. finish left block, place RF/RB edges oriented in RF/RB (swapped or not swapped) and place any two corners oriented on DRF/DRB
3. orient corners with 7 algs that can't destroy much of right block and thus are short (longest algs are 11 moves and include sexy move)
4. EO similar to Roux
5. using only R2, r2 and U turns to preserve CO, finish right block and place UL/UR (or UF/UB) in their correct position in the U layer
6. last 4 edges.

pros
  • doesn't temporarily break up solved parts of the cube except for one of the RF/RB edges during the algorithm, so only one piece.
  • only 7 algs, and the CPLine step is actually very easy and streamlined, so the method is about as difficult to learn as Roux with 2 look CMLL.
  • no rotations and the turns you use for each step are: (R,r,U,u,F,f) for CPLine, (R,r,U,u) for step 2, (R,U) for step 3, (R2, r2, M, U) for step 4, (R2, r2, U) for step 5, (M, U2) for step 6. So in total the move sets for the steps are rather nice, except the M turns during EO, those break the flow, because step 3 and 5 don't have M turns.

example solve: x' y //forward, forward relation --> there is no "swap corner"R' U R' U' r2 U //build pairf' R' f' //insert pair with mini-algorithm to finish CPLineu' M' u r R U' R' u2 //finish left block while placing any two corners oriented on DR and placing the RF/RB edges oriented in RF/RB (or RB/RF)U R U2 R' U' R U' R' //Anti-SuneU2 R2 M' U2 M' U' M'//EOR2 U r2 U' R2 U R2 U' R2 U2 M2 U//finish right block and solve UL/URM' U2 M2 U2 M//L4E

some details:
CPLine:
  1. rotate the cube s.t. DBL corner is oriented and in DBL position
  2. do an F,F',F2,f,f',f2 or no turn in your head that bring the cube in a position where the DFL corner is not in DFL position and where the DL edge is oriented in DL position or not in DL position at all.
  3. try to find a key swap involving the DFL corner exactly like in the 2GR method (see teoidus website)
  4. Start your solve with the F or f turn from step 2 of CPLine. If there is no key swap (the "no swap" case), you build a pair containing the DL edge and DFL corner and place the pair s.t. the DFL corner is oriented in the UFR position. Then do f' R' f' to solve the line and to bring the cube in a state where the corners can be solved with R,U turns. If there is a key swap, bring the pair in a position where it can be solved with an f,f' or f2 turn and bring the "swap corner" to UBR position, then do the f,f' or f2 turn to solve the line etc.
  5. in step 4 of CPLine, only use R,r,U,u turns to build the DL-DFL pair and to position it. But you can also use sequences like R' U' F' or U R F that don't destroy the CP.
  6. if your DL edge was solved during step 2 of CPLine or was solved to begin with, you obviously don't need to build any pair in step 4 of CPLine and just insert the DLF corner like described.
step 2:
placing oriented corners is super easy. You can for example form a pair on the U layer containing the oriented RF edge and a corner clockwise from the edge, whose U/D sticker is facing away from the RF edge, then insert it like an F2L pair. The fist pair you insert can be inserted with R or R' because there is no RD edge you have to care about.

step 3 (CO):

the algs are Sune, Anti-Sune, Bruno,
U case: Triple Sexy move
H case: U R' U' R2 U' R U2 R2 U' R
T case: U R U R' U' R U2 R' U R U' R'
L case: R U R' U' R U2 R' U2 R U2 R'

note that T and L contain a sexy move and that the algs are shorter than they would be if the right block would be solved already and had to be preserved.

step 5:

Using only R2 and U turns, build the DR line on the U layer starting with a pair consisting of the DR edge and one of the DR corners. To build this pair, use an R2 turn to place a DR corner in one of the DR positions, with the R color sticker either facing to the front or facing to the back, and place the DR corner in the U layer such that an R2 turn connects the corner and with the edge. Now do the same with the second DR corner piece to complete the line and align the line with the FR and BR edges s.t. an R2 turn solves the DR line as well as the line consisting of the FR and BR edges and the R center.
 
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new L6E method (M2r method)

1) O+1p (orient+1 pair)
solve all edge orientation as well as getting two edges that belong across from each other, across from each other (this is an edge-edge pair)
2) M2r (M2 reduction)
place the pair in UL UR (with the other pair pieces diagonal from each other)and preform either M' U2 M' or M U2 M to solve M2 reduction (solvable using only M2 and U) (if its not in M2r, but all pairs are solved you can E2 M' E2 M')
3) pl3p (permute last 3 pairs)
using M2 and U moves, solve the cube

examples
Scramble U M U2 M2 U2 M U' M' U M U' M' U2 M2 U M U2 M2 U2 M2 U' M' U2 M2 U'
1) U M' U M U' 2) M' U M U2 M 3) U2 M2 U' M2

U2 M' U M U' M U' M' U M U' M' U M U' M2 U M2 U M U M2 U M' U'

1) M U M' U M 2) M U2 M' 3) U M2 U' M2

U' M' U M' U' M U' M U2 M U2 M' U2 M' U M' U' M2 U' M' U M' U' M' U

1) U M' U M U' 2) M' U' M' U2 M' 3) U M2 U2 M2 U' M2

U' M U' M2 U' M2 U M2 U' M U M2 U2 M' U2 M U2 M' U2 M U' M U2 M2 U2

1) M' U2 M' U M' 2) U M U2 M 3) U M2 U' M2 U

M' U2 M' U M U2 M' U2 M' U' M' U M U' M' U' M' U2 M2 U' M U2 M2 U M

1) U' M' U M U M' 2) M U2 M' 3) U' M2 U' M2 U2

new method bloble (pronounced Bl O Bl E)

1) cp block
create a 1x2x3 block and solve cp at the same time.
2) oc
orient all corners while placing the remaining equator pieces oriented correctly
3) 2nd block
using <R2,M,U> solve the second 1x2x3 block
4) edges
solve last 6 edges using <M,U>
 
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2-look LL method:
1) solve EO while misorienting all LL corners - 57 algs I think
2) finish with one of 112 ZBLL algs
That would probably end up being a higher move count than oll/pll, harder recognition, and less ergonomic. I don't really like shooting down ideas but a better way to do that would be force a pi/H case zbll while inserting last pair and already have all edges oriented.
 
new method bloble (pronounced Bl O Bl E)

1) cp block
create a 1x2x3 block and solve cp at the same time.
2) oc
orient all corners while placing the remaining equator pieces oriented correctly
3) 2nd block
using <R2,M,U> solve the second 1x2x3 block
4) edges
solve last 6 edges using <M,U>
Interesting. How do you do step 2?
new L6E method (M2r method)

1) O+1p (orient+1 pair)
solve all edge orientation as well as getting two edges that belong across from each other, across from each other (this is an edge-edge pair)
2) M2r (M2 reduction)
place the pair in UL UR (with the other pair pieces diagonal from each other)and preform either M' U2 M' or M U2 M to solve M2 reduction (solvable using only M2 and U) (if its not in M2r, but all pairs are solved you can E2 M' E2 M')
3) pl3p (permute last 3 pairs)
using M2 and U moves, solve the cube

examples
Scramble U M U2 M2 U2 M U' M' U M U' M' U2 M2 U M U2 M2 U2 M2 U' M' U2 M2 U'
1) U M' U M U' 2) M' U M U2 M 3) U2 M2 U' M2

U2 M' U M U' M U' M' U M U' M' U M U' M2 U M2 U M U M2 U M' U'

1) M U M' U M 2) M U2 M' 3) U M2 U' M2

U' M' U M' U' M U' M U2 M U2 M' U2 M' U M' U' M2 U' M' U M' U' M' U

1) U M' U M U' 2) M' U' M' U2 M' 3) U M2 U2 M2 U' M2

U' M U' M2 U' M2 U M2 U' M U M2 U2 M' U2 M U2 M' U2 M U' M U2 M2 U2

1) M' U2 M' U M' 2) U M U2 M 3) U M2 U' M2 U

M' U2 M' U M U2 M' U2 M' U' M' U M U' M' U' M' U2 M2 U' M U2 M2 U M

1) U' M' U M U M' 2) M U2 M' 3) U' M2 U' M2 U2
How is this different from what most advanced rouxers do already?
 
new method bloble (pronounced Bl O Bl E)

1) cp block
create a 1x2x3 block and solve cp at the same time.
2) oc
orient all corners while placing the remaining equator pieces oriented correctly
3) 2nd block
using <R2,M,U> solve the second 1x2x3 block
4) edges
solve last 6 edges using <M,U>

According to your post, (if I understood you correctly), you do step 2 by building 2 pseudo-pairs (an oriented equator edge together with any corner, but the corner is twisted in such a way that inserting the pseudo-pair with R,U into an F2L slot would orient the corner), inserting one pseudo-pair into an F2L slot and keeping one pseudo-pair on the U layer. Then you apply one of 27 short R,U algorithms to insert the second pseudo-pair into an F2L slot while orienting all corners(most of them are 7 moves I think).

If you orient the right block edges at the start of step 2, and bring them to the U and R layers, you can do step 3 with only R2 and U turns and without M turns (if the DR edge is in DF/DB you do one r2 turn in step 3). This way, steps 2 and 3 can be done with only R,r and U turns, and step 4 is pure M,U. So you don't have to switch between R,U and M,U turns, meaning that the ergonomics of the method should be pretty great imo. This would also mean that edge orientation will not change during step 3, so you can influence the edge orientation case that you solve in step 4 already with the algorithm from step 2, and avoid bad EO cases.

The turns each step can be done with are then:
CPLine: R,r,U,u,F,f
finish LB: R,r,U,u
put RB edges oriented on R and U layers: R,r,U
step 2: R,U
step 3: R2, U
L6E a+b: M,U
L6E c: M,U2

Moreover, this method is very easy. I posted an easy way to do CPLine here (simplified CPLine from 2GR method), and already started generating the 27 algorithms for step 2 two days ago (had the same idea of doing step 2 (I called it COLine) with pseudo-pairs), and will definitely finish generating them and post them in a few days.
 
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On "blobl" (...really? blobl? that's what we're going with?)

I stopped doing this a little while back because there got to many too many ridiculous questionable proposals, but:

Approximate movecount:
10 CPFB (note: FB is ~7)
3 pseudo-pair insert + 3 second pseudo-pair + 8 CO (note: SB is ~14 and 3 moves for each pseudopair is a pretty conservative estimate)
8 SB (note: CMLL is 10)
13 LSE
= 45

So we've saved some moves in CMLL? for more moves in FB, and we're left with a method that doesn't flow as well, is more complicated, and is at best as efficient as roux.
 
I too think that blobl is not the best name and that Roux is better than this, because it has fewer steps. The appeal of the method (for me) lies more in the fact that it does not destroy regions of the cube that were solved in a previous step, like CMLL, OLL, PLL do.
 
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