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Hazel Method - A True 1LLSLL (Official Thread)

Aerma

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I've created a method that allows you to solve last slot + last layer in just 513 algorithms (providing EO is solved), despite there being tens of thousands of possible cases (hundreds of thousands when EO isn't solved!). This is possible by using 2 algorithms at a time, while only needing a single look.

The magic of this method is what I call MLS (Magic Last Slot, Miranda Last Slot, take your pick).

Let's look at this setup: L' F2 D' F2 U F2 D' L2 D2 F2 R U' L R' U2 R U R' U'

MLS solves the F2L pair without messing anything up on the last layer. It essentially swaps the pieces in the F2L slot with the proper F2L pieces. It has 20 algorithms.
Now, back to the setup. What would happen if we swap UFR with DFR, and FR with UB? Well, we would be left with a Sune ZBLL case. I know this because of looking at UBR, UBL, and UFL. We don't need to figure out the orientation of the UFR corner to know that it's Sune. Now we just need to know exactly which Sune case it is. Judging by those same three corners, it's a diagonal swap COLL, and judging by the last layer edges it's the 54th Sune case.
So, all we have to do is apply the MLS algorithm and then go right into the ZBLL algorithm with no pause.
The MLS algorithm for this F2L case is currently this: U2 R U R B2 L2 D L D' L B2 R2 U2
(Please keep in mind that this is the algorithm that needs the most work, other F2L cases have much better ones.)
The algorithm for Sune 54 is this: L' U2 R U' L U' R' U L' U L U2 R U2 R' U'
The AUF does need a second look (hence the U' at the end), but if you know how to predict AUF in ZBLL then it isn't a problem at all.
There is a slight problem that is raised with MLS, unfortunately: when one or both of the F2L pieces are in the slot, it isn't possible to solve it without messing up something on the U-layer. To address this issue, I simply made these rules for the MLS algorithms:
- When the F2L corner is correctly permuted, UFR and UBR will swap places.
- If that F2L corner is incorrectly oriented, whichever corner is in the UFR position will have its orientation changed to counter it (for example if DFR is twisted clockwise, UFR will be shifted counterclockwise).
- If the F2L edge is correctly permuted and the F2L corner is not, the UF and UR edges will be swapped.

Here are all of the current MLS algorithms: https://docs.google.com/spreadsheets/d/1DRDsazUslZ810MMIHVJE3SoZxyRrbQdnMWEaj7_EQok/edit?usp=sharing
 
Last edited:

_zoux

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Pretty obvious method, with a horrible recognition.
LS -> ZBLL will be faster + more efficient :p
 

Thom S.

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Case 18: R U' R' F' R U' F U' F' U2 R' F F' R U2 F U F' U R' F R U R'
the inverse is almost good enough to be bad but better than the existing case. I'll maybe try later

Case 19: D2 R2 B2 L U' L' B2 R2 D' R' D R D2
If you can do fingertrick left D2s I believe it's better
U2 R2 U R2 D R' U' R D' R D R' U R U D' Regripless

Didn't try for long but they may be worth it
 

Aerma

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Case 18: R U' R' F' R U' F U' F' U2 R' F F' R U2 F U F' U R' F R U R'
the inverse is almost good enough to be bad but better than the existing case. I'll maybe try later

Case 19: D2 R2 B2 L U' L' B2 R2 D' R' D R D2
If you can do fingertrick left D2s I believe it's better
U2 R2 U R2 D R' U' R D' R D R' U R U D' Regripless

Didn't try for long but they may be worth it
Very interesting! For case 19 I think I like the regripless one more, and I definitely prefer it over the current alg. Thanks!

@GenTheThief it's a similar concept in that it's a 2-alg 1LLSLL, I'd say there are pros and cons of both. M-CELL has far fewer algorithms required, but Hazel lets you use a more standard approach to the solve (as in F2L-1).
 

Thom S.

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CFOP will always the best method for solving 3x3 .
No, it's actually pretty bad :p
You two hit a nerve there.

CFOP is neither a bad method, nor the best method.
How would we define best method? Would you also say that CFOP is the best for FMC? No, nobody says that. That would be a stupid thing to say, right. Let's look into the future. 7 years, 20 years, 300 years, infinite years. Would you think that the best method was created within the first 10 years of the Rubik's cubes existence? Imagine someone finds sucsess with a different method(Lau, Mansour, asmallkitten Tao Yu, Hessler, whoever you wish to name there) or finds sucsess with CFOP, should they switch to CFOP because it's the best or go away from CFOP because it's actually pretty bad? Some methods are better than others, that is true but I wouldn't argue about which of the big four is better because it doesn't go anywhere
 

_zoux

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You two hit a nerve there.

CFOP is neither a bad method, nor the best method.
How would we define best method? Would you also say that CFOP is the best for FMC? No, nobody says that. That would be a stupid thing to say, right. Let's look into the future. 7 years, 20 years, 300 years, infinite years. Would you think that the best method was created within the first 10 years of the Rubik's cubes existence? Imagine someone finds sucsess with a different method(Lau, Mansour, asmallkitten Tao Yu, Hessler, whoever you wish to name there) or finds sucsess with CFOP, should they switch to CFOP because it's the best or go away from CFOP because it's actually pretty bad? Some methods are better than others, that is true but I wouldn't argue about which of the big four is better because it doesn't go anywhere
Good points, but i wrote that only to annoy him tbf :p
 
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