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Noob's Approach to Missing Link for ZZ-d (it sucks, but it still works! :D)

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Disclaimer: Whatever I'm gonna post down here is very noobish and even trivial, and it's not the same as the original Missing Link concept proposed by ZZ himself.

The Missing Link is supposed to permute corners. But doing it at the end of the 2x2x3 block is ridiculously difficult imo because one has to keep track of 6 unsolved corners.

So, like all my other "methods" (I prefer the term "approaches") proposed in the last few days, I've found a way to fix the Missing Link problem just before LL. So far I've already got the algs for the R U' R' insertion case. There are only 6 algs, because there are only 6 ways the LL corners can be permuted.

It'd take me less than 5 minutes to generate algs for the R U R' case so it's not that big a deal. The main problem now is recognition. Extremely time-consuming. I'll start working on the R U R' case once I solve the recognition problem for the R U' R' case. In the meantime, if you get an R U R' case, you can just do R U2 R' to set it up into an R U' R' case :D

Here are the algs:
(ULF = 1, URF = 2, URB = 3, ULB = 4)
To swap nothing: R U' R' (3)
To swap 1 and 2: U' L' U R U' R' L or B' R U' R' U B (7 or 6)
To swap 2 and 3: U R U L' U R' U' L (8) (7 without initial AUF)
To swap 3 and 4: y L' U' L F R U' R' F' (7)
To swap 4 and 1: R U2 L' U R' U' L (7)
To swap diagonal corners: L' U2 R U R' U2 L (7)

Probability of getting every case is 1/6. So to force a 2-gen 1LLL, you'd be doing (3 + 5*7)/6 - 3 = 3.33 more moves on average for your F2L. Pretty worthwhile for a 2G1LLL imo.

Main problem now is recognition. I've been working on a system that works for me and maybe some others, but might not work for everyone in general. This is due to the fact that I always start with white on U and red on F for ZZ, and I never do cube rotations. Also, my BLD cube orientation is white on U and red on F as well. With these two complementing factors, I know my LL corners very well, e.g. I know instantly that white-blue-red is named "2" and it belongs to UFR.

So here's the system: Just before the R U' R' insertion, look at the UFR, URB and UBL corners, in that order (or in any other order you like). And memorize that number sequence. E.g. If I have white-red-green, white-orange-green and white-red-blue on UFR, URB and UBL respectively, then my number sequence would be 142. Then, figure out which alg to apply.

Here's my list:
R U' R': 142, 213, 324, 431
U' L' U R U' R' L: 143, 214, 321, 432
y L' U' L F R U' R' F': 123, 234, 341, 412 (most obvious number patterns for the hardest alg :))
U R U L' U R' U' L: 132, 243, 314, 421
R U2 L' U R' U' L: 134, 241, 312, 423
L' U2 R U R' U2 L: 124, 231, 342, 413

If you look at the URF, URB and UBL corners in the same order as I do, and use the same numbering scheme as I do, then you should have the same list. If not, you'd have to generate your own list :p

Here's the problem: The numbers don't appear to follow any pattern. In fact, I'm pretty sure they don't. So if you were to use this system, you'd have to brute force memorize all these by heart, and instantly know what alg to apply when you get a random number sequence like 324. That doesn't sound too nice.

So I've come up with something else that's still in the works. I've reassigned every corner to a specific letter, instead of a number. However, this is a real pain in the butt because it's hard to find 4 letters that give you pronounceable, meaningful words no matter how you arrange any 3 of them. I've come up with YAMO and SAKI and a few of their variations so far. Few rules to note if you wanna use this system, make sure your two consonants are pronounceable when put together either way. Something like G and B wouldn't work because AGB isn't pronounceable and neither is BGA. Also, Y is a nice consonant to use because it can double as a vowel sound. E.g. if I reassign 1, 2, 3 and 4 to Y, A, M and O respectively, 341 would become MOY and 231 would become AMY. That's about how it works.

Another alternative could simply be the Major System. Go Google/Wikipedia that if you don't know what that is. I think the Major System can be really useful for this. I might just learn it if my current reassign-to-letters approach doesn't work well.

Okay, that's all. It doesn't solve the original Missing Link problem, but it does give 2G1LLL :D
 
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#3
Sounds interesting.. How many 1LLL algorithms does that give you?
I have though about something like this a couple of weeks ago, but i was focusing on the 3rd F2L slot instead, and then use the 4th slot for edge phasing.

I use the same cube orientation for ZZ and BLD as you do :)
 
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Missing Link not as in the puzzle?
Nope :D

Sounds interesting.. How many 1LLL algorithms does that give you?
I have though about something like this a couple of weeks ago, but i was focusing on the 3rd F2L slot instead, and then use the 4th slot for edge phasing.

I use the same cube orientation for ZZ and BLD as you do :)
I don't like this method at all actually :p 27*12 = 324 algs if I'm not mistaken. Edit: I was mistaken after all, it's 84, not 324 :)

2G1LLL is probably gonna be longer than RUL 3-gen LL. If you really hate L moves that much, every RUL 3-gen alg can be customized to consist of at most 1 L move and 1 L' move while the rest of the moves are R and U turns (this can be proven very easily).

AND recognition time for my Missing Link method sucks.

Disadvantages of this method so far (in my opinion):
1. Recognition for Missing Link sucks
2. Recognition for 2G1LLL sucks (relative to ZZLL and my 1LLL variation)
4. Lengths of algs suck
5. Not really a disadvantage, more like "not an advantage over other variations": You don't even get 1 step fewer. What's the point of having easy-to-perform 1LLL algs when you have to go through so much $#!% just to achieve that?

Are you still sure you wanna learn this? :p

Edited.
 
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#5
Nope, that was exactly why i abadonned my versoin with 3rd/4th slot ;-)
Also, I like your corner-control method a lot better.
 
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#8
There are 84 2GLL situations, unless I've messed up the calculation. (12 cases for each cross-OLL case).

As far as my experience goes, 2GLL cases are as easy to recognize as ordinary ZBLL.

What's more: they're fast like nobody's business (extremely finger shortcut-friendly). Way faster on average than full ZBLL.
 
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There are 84 2GLL situations, unless I've messed up the calculation. (12 cases for each cross-OLL case).
There are 27 cross-OLLs :D 3^3 = 27. Edit: I was stupid. MHordecki's right :D

As far as my experience goes, 2GLL cases are as easy to recognize as ordinary ZBLL.
You mean as hard :p
 
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There are 27 cross-OLLs :D 3^3 = 27.
Can you prove that? How many cross-OLLs are there in COLL?
I thought 3^3 was pretty obvious already :eek:

AUF to permute all corners. ULF can have 3 different orientations, so can UFR, and so can URB. UBL's orientation is determined by the other 3, so it's irrelevant. 3*3*3 = 27. Is that clear enough? Edit: Again, I was being stupid :p

You mean as hard :p
Actually it's rather simple, provided you can recognize COLL on the fly.
Check out Jason Baum's excellent article: http://jmbaum.110mb.com/zbll.htm
Yup, read it some time ago.
 
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#12
Am I missing something?
27 cross OLL's? That would be like half of OLL has the cross solved... Last time I checked there was Sune, AntiSune, U, T, L H and Pi making 7...
Then I'm pretty sure there are 12 edge permutations yielding 84 algs for 2GLL.
 
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Am I missing something?
27 cross OLL's? That would be like half of OLL has the cross solved... Last time I checked there was Sune, AntiSune, U, T, L H and Pi making 7...
Then I'm pretty sure there are 12 edge permutations yielding 84 algs for 2GLL.
Oh, you're right. So is Michal Hordecki then :) Sorry, my bad :eek:

I forgot that there was the magical technique of AUF a.k.a. the O perm ;)
 
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Tried some CCT scrambles, here's what I got:

F L2 R B2 F' D' U L F' U2 B D2 U R D2 U2 F' R U' L2 D2 U2 F2 L' D2
EOLine: R' B' D' F D F' D' L D (9)
Block 1: U' R' U' R L U L (7)
Block 2: U' L' U R U' L (5.5)
Slot 1: L U L' U2 L U' L' (6.5)
Slot 2 Setup: U R U R' U (4.5)
2GLL Setup: U R U L' U R' U' L (7.5)
2GLL: (U2) R' U2 R2 U R' U R U2 R' U' R' U R U (15)
Total Move Count: 55

L2 R2 B2 L' R B2 F L U' R2 D' F2 D' U B2 F2 L' B D2 F' D2 F2 L2 R2 B2
EOLine: B L U F D R' D' (7)
Block 1: U R' U2 R U L (6)
Block 2: U' R U R' U' R2 U R (8)
Slot 1: U2 R U2 R' U' R (6)
Slot 2 Setup: skip (0)
2GLL Setup: y2 B' R U' R' U B (6)
2GLL: (U') U' R' U' R2 U R2 U R2 U2 R2 U2 R U (13)
Total Move Count: 46

L R' B' F' D U2 R2 B D U L R' U' B2 R' B2 F2 R U' B' F2 D' L R2 U'
EOLine: L2 B' F R F L2 D (7)
Block 1: U R' U' R L2 U L (7)
Block 2 + Slot 1: R U' R2 U R (5)
Slot 2 Setup: U2 L' U2 L2 U L' (6)
2GLL Setup: L' U2 R U' L U R' (7)
2GLL: R' U R U2 R' U' R U2 R' U' R U' R' U R U' (16)
Total Move Count: 48

I guess some Petrus guy with good blockbuilding skills could easily sub-45 everytime (move count) :rolleyes: My EOLine and blockbuilding suck pretty badly.

But I can see it's got lots of potential for OH, lots. Other than the first stupid EOLine which I suck at and can be further improved on with some practice (hopefully), everything else is RUL 3-gen, and LL is 2-gen. Pretty amazing imo.
 
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