porkynator
Member
It is almost a year since I published this post; that approach isn't bad, but I wasn't fully satisfied. So I recently started working again on ZZ-d, and tonight I finished. Now I am satisfied with this method, I think it can be suitable for speedsolving (although probably useful only for OH) and I think it deserves a new thread (unlike the old approach).
What's new?
With my old method, you permuted corners by doing an average of 9 moves after building the first 3x2x1 block. With this new method you will achieve the same result by adding fewer moves (I haven't calculated anything this time, but the average movecount should be around 5 and the worst case 7) while completing the first 3x2x1 block. It may be only 1 move better than the old method, but some of the new permuting algs are super-fast (like U R' or R U R') and I think they are way better for OH. Moreover, with this new method you solve CP before finishing the first block, which is how zz-d was originally meant.
There are 24 different patterns to recognize and 18 algorithms (1 to 3 moves long) to learn. This isn't a big problem, but it more difficult than my old approach.
Before we begin...
...I want to "expand" my old method.
If you have built a 2x2x1 block on LBD and the LFD corner is already placed (not caring about orientation) you may want to use my old approach to solve corners' permutation now. But there's a problem: your LF edge may be stuck on RF, RD or RB after you are done with the permutation. This is a problem. But I've "generated" more algorithms, so that you can choose which one to use to avoid the edge getting stuck. Here we go:
For the "nothing to do" case you can do any R* move to free your edge.
For the L' U R U' L case you can also use U L' U R' or R2 L' U R2.
For the L' U R2 U' L case you can also use R2 L' U R or L' U' R.
The method
First of all, place the DR corners on DR, as in the old method. Then, if the DLF corner is in place you use the "expanded" old method, otherwise you put it in ULB. Now you are ready to recognize the corners' pattern (you can do it by looking only at 3 corners, URB, URF and ULF).
In the spoiler the table with the cases.
Instead of numbers or letters I gave the 6 different cases the name of 6 random pokemons.
In the next spoiler I listed 3 algs for each case. Note that 3 algs are enough to cover all possible "last edge saving" cases.
Once you performed the permuting algorithm, you can solve the remaining pair of the left block using only L and U moves (you can obviously use also L2, L', U2 and U'). After completing the first block this way, you can solve the whole cube 2-gen (using only R and U moves).
UPDATE
When one of the DR corners is in DLF setup moves can be long. So I decided to find algorithm even for this case(s). I only did it for when the two DR corners are in DLF and DBR, thinking that when one of them is in DFR recognition can be so bad that you may just want to R' to see the hidden corner.
Considering that when DRF is in DLF the DR corners are OK, and that when DRF is in DBR they are swapped, you can use the same recognition system (thinking of the corner in DRF as if it was in DFL) and apply these transformations:
Pikachu becomes Machamp and Machamp becomes Pikachu.
Squirtle becomes Dragonite and Dragonite becomes Squirtle.
Bulbasaur becomes Pidgey and Pidgey becomes Bulbasaur.
Minor Update
The mysterious "Charmander Case" did not actually exist: it was a Bulbasaur case. I don't know how it happened, maybe I was setupping the case in a wrong way, but it seemed to me that the Bulbasaur algs did not work for that one. But they did. So, no more Charmander and all makes way more sense now.
Thanks to collins for finding this out.
______________________________________________
I haven't tried this method yet, but I hope I can find enough time to learn it.
What do you think about this approach to ZZ-d? Was it a waste of time for me to think of it or will it be called the "not-missing-anymore"-link?
______________________________________________
EDIT (2021-03-10): all of the pictures broke because I let my old website die, so I re-uploaded them. Since the forum now has a 20 image per post limit I replaced them with links. It's probably better if you refer to the pdf attached below.
______________________________________________
EDIT 2 (2021-03-16): N's-cvt proposed a better recognition system that relies on looking at just 3 last layer corners, see this file and his post.
What's new?
With my old method, you permuted corners by doing an average of 9 moves after building the first 3x2x1 block. With this new method you will achieve the same result by adding fewer moves (I haven't calculated anything this time, but the average movecount should be around 5 and the worst case 7) while completing the first 3x2x1 block. It may be only 1 move better than the old method, but some of the new permuting algs are super-fast (like U R' or R U R') and I think they are way better for OH. Moreover, with this new method you solve CP before finishing the first block, which is how zz-d was originally meant.
There are 24 different patterns to recognize and 18 algorithms (1 to 3 moves long) to learn. This isn't a big problem, but it more difficult than my old approach.
Before we begin...
...I want to "expand" my old method.
If you have built a 2x2x1 block on LBD and the LFD corner is already placed (not caring about orientation) you may want to use my old approach to solve corners' permutation now. But there's a problem: your LF edge may be stuck on RF, RD or RB after you are done with the permutation. This is a problem. But I've "generated" more algorithms, so that you can choose which one to use to avoid the edge getting stuck. Here we go:
For the "nothing to do" case you can do any R* move to free your edge.
For the L' U R U' L case you can also use U L' U R' or R2 L' U R2.
For the L' U R2 U' L case you can also use R2 L' U R or L' U' R.
The method
First of all, place the DR corners on DR, as in the old method. Then, if the DLF corner is in place you use the "expanded" old method, otherwise you put it in ULB. Now you are ready to recognize the corners' pattern (you can do it by looking only at 3 corners, URB, URF and ULF).
In the spoiler the table with the cases.
Instead of numbers or letters I gave the 6 different cases the name of 6 random pokemons.
| Pattern | DR corners OK | DR corners SWAPPED |
| Picture 1 | Pikachu Case | Squirtle Case |
| Picture 2 | Bulbasaur Case | Machamp Case |
| Picture 3 | Pidgey Case | Dragonite Case |
| Picture 4 | Machamp Case | Bulbasaur Case |
| Picture 5 | Pikachu Case | Squirtle Case |
| Picture 6 | Dragonite Case | Pidgey Case |
| Picture 7 | Pidgey Case | Dragonite Case |
| Picture 8 | Bulbasaur Case | Machamp Case |
| Picture 9 | Machamp Case | Bulbasaur Case |
| Picture 10 | Dragonite Case | Pidgey Case |
| Picture 11 | Machamp Case | Bulbasaur Case |
| Picture 12 | Pidgey Case | Dragonite Case |
| Picture 13 | Machamp Case | Bulbasaur Case |
| Picture 14 | Pidgey Case | Dragonite Case |
| Picture 15 | Squirlte Case | Pikachu Case |
| Picture 16 | Dragonite Case | Pidgey Case |
| Picture 17 | Squirtle Case | Pikachu Case |
| Picture 18 | Bulbasaur Case | Machamp Case |
| Picture 19 | Pikachu Case | Squirtle Case |
| Picture 20 | Dragonite Case | Pidgey Case |
| Picture 21 | Bulbasaur Case | Machamp Case |
| Picture 22 | Squirtle Case | Pikachu Case |
| Picture 23 | Pikachu Case | Squirtle Case |
| Picture 24 | Squirtle Case | Pikachu Case |
Pikachu Case L' U2 R2 or L' U R' or L' U' R
Squirtle Case R2 or R' U R' or L' U R
Bulbasaur Case R or R' U' R or R2 U' R'
Machamp Case R' or U R' or R U' R
Dragonite Case U' R2 or U2 R or R U' R2
Pidgey Case R U R' or R U' R' or R2 U' R or Do nothing (yay!)
Squirtle Case R2 or R' U R' or L' U R
Bulbasaur Case R or R' U' R or R2 U' R'
Machamp Case R' or U R' or R U' R
Dragonite Case U' R2 or U2 R or R U' R2
Pidgey Case R U R' or R U' R' or R2 U' R or Do nothing (yay!)
UPDATE
When one of the DR corners is in DLF setup moves can be long. So I decided to find algorithm even for this case(s). I only did it for when the two DR corners are in DLF and DBR, thinking that when one of them is in DFR recognition can be so bad that you may just want to R' to see the hidden corner.
Considering that when DRF is in DLF the DR corners are OK, and that when DRF is in DBR they are swapped, you can use the same recognition system (thinking of the corner in DRF as if it was in DFL) and apply these transformations:
Pikachu becomes Machamp and Machamp becomes Pikachu.
Squirtle becomes Dragonite and Dragonite becomes Squirtle.
Bulbasaur becomes Pidgey and Pidgey becomes Bulbasaur.
Minor Update
The mysterious "Charmander Case" did not actually exist: it was a Bulbasaur case. I don't know how it happened, maybe I was setupping the case in a wrong way, but it seemed to me that the Bulbasaur algs did not work for that one. But they did. So, no more Charmander and all makes way more sense now.
Thanks to collins for finding this out.
______________________________________________
I haven't tried this method yet, but I hope I can find enough time to learn it.
What do you think about this approach to ZZ-d? Was it a waste of time for me to think of it or will it be called the "not-missing-anymore"-link?
______________________________________________
EDIT (2021-03-10): all of the pictures broke because I let my old website die, so I re-uploaded them. Since the forum now has a 20 image per post limit I replaced them with links. It's probably better if you refer to the pdf attached below.
______________________________________________
EDIT 2 (2021-03-16): N's-cvt proposed a better recognition system that relies on looking at just 3 last layer corners, see this file and his post.
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