# Proof: All PLLs can be recognized by looking at any 2 faces (and why it's bad)



## blah (Aug 9, 2009)

*Background*
A couple of days ago, Lucas challenged me to come up with a recognition system to distinguish between all the G and R perms by looking at only two faces. To make this clearer, given any G or R perm from any of the four starting positions (that's 6*4 = 24 positions), by looking at only two faces, one must be able to tell exactly which perm it is, and what AUF to perform, without doing any U moves or cube tilts.

I remember reading from Macky's website, back when I was still a noob and he was still actively competing, that all PLLs can be recognized by looking at only two faces, ANY two faces. I didn't give it much thought back then. Like all beginners, I didn't think I'd ever be advanced enough to need that kind of recognition, and like all beginners, I was wrong 

*Proof*
It's a very simple proof, really, what I mainly want to share is my opinion on why it isn't a very good idea to learn this after all.

Proof: If all nine stickers on the U face are of the same color, then there would be no ambiguity regarding the permutation of pieces on the U layer if the colors of the following six stickers are known: FUL, FU, FRU, RUF, RU and RBU. If it isn't already clear, here's the explanation:

Since the colors of all U stickers are known, the identities of the ULF, UFR and URB corners can be confirmed, because any corner can be defined if any two stickers on it and their positions relative to each other are known. Consequently, the identity of the UBL corner can also be confirmed, this is trivial.

Obviously, the identites of the UF and UR edges can be confirmed because all 4 stickers on them are known. Since the permutation of all corners and two edges are known, the permutation of the remaining two edges, UB and UL, can be confirmed too due to permutation parity (I won't go into too much detail on this).

There you have it. I apologize for not being able to word the entire proof succinctly enough, but it's really simple to understand, I'd be glad if someone is able to reproduce this proof in a more concise manner 

*Warning*
Anyway, I hope I don't get some silly responses like this: _This is stupid. It takes too long to derive the identities of the "un-see-able" pieces, and to determine their relative positions with respect to each other, yadda yadda yadda..._ Obviously this is just a proof, not a method for PLL recognition.

*Why this isn't a good recognition technique in my opinion*
Perform the following algorithms on two different (solved) cubes with the same starting position, i.e. same U and F colors:
1. R' U R' Dw' R' F' R2 U' R' U R' F R F (V perm)
2. [r] U R' U' L U R U' Rw2' U' R U L U' R' U [r u2] (E perm, make sure you do the rotations)

Now compare both cubes side by side with the position that you ended up with. They both have NO blocks on F and R, and they differ by only ONE color (the RU sticker). I think it'd take a LOT of practice for one to tell these two cases apart almost instantly  On the contrary, a slight cube tilt to look at the B and L faces enables one to tell them apart instantly, literally.

This is just one example. I'm sure there are others.

Also, I don't have scientific substantiation for this, but I'd like to point out that recognizing blocks is probably much easier for most people.

Besides, there are 21*4 - 16 = 68 distinct cases one must learn to tell apart from each other (16 cases lost due to symmetry). I don't know if I'm willing to invest that much time and effort in something that can be made easier simply by tilting the cube.

I'd like to hear other opinions on this


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## bwatkins (Aug 9, 2009)

i just worked through your examples, and i think your right, it would be nice, its just not worth the effort. Well explained though, i never thought of anything like this before


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## darthyody (Aug 9, 2009)

About two months ago I fiigured this out while trying to improve my recognition times. I wrote every different sticker combination for each permutation. I think it would be worth learning for some of the harder-to-recognize permutations but like the E and V. It also makes it faster/easier to diistinguish between Ns and Js. Really, after writing all of the different sticker patterns, it didn't seem too bad since it's not like you're learning algs. Personally, I think learning them would be helpful/worth it once you feel like a fraction of a second of your solving time is worth spending hours of practice for.


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## Inf3rn0 (Aug 9, 2009)

It would be cool if you could do it quickly. Still that's really interesting. So far ive only learnd 12/21 PLLs lol. I dread learing the G's.


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## blah (Aug 9, 2009)

Inf3rn0 said:


> It would be cool if you could do it quickly. Still that's really interesting. So far ive only learnd 12/21 PLLs lol. I dread learing the G's.


If I remember correctly, I believe brunson's Drill Sergeant has such a PLL recognition trainer.


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## Swordsman Kirby (Aug 9, 2009)

Inf3rn0 said:


> It would be cool if you could do it quickly. Still that's really interesting. So far ive only learnd 12/21 PLLs lol. I dread learing the G's.



http://fn.dy.fi/old/misc/ll/index.pl


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