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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

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

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

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

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

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

Last edited: Jan 24, 2009

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