A system for recognizing C*LL cases by Robert Smith

Introduction

Around spring of 2007, I decided I would finally learn CMLL for Roux’s method. However, recognizing the cases for CMLL was tedious. One way to recognize cases is to recognize only the L- and R-colors. This, if I remember correctly, requires one to remember two cases per algorithm. For anyone that has memorized more than 20 algorithms for a step in the solution he or she uses, then he or she knows that remembering recognition is sometimes more difficult than remembering the algorithms with which they go. Therefore, remembering two cases for a single algorithm was not my cup of tea. So I decided to make a new system of recognition.

The System of Hyperorientation

Instructions

This system, which I call hyperorientation, is mostly color neutral, meaning you can do CMLL (actually C*LL) and NMCMLL. This hits two birds with one stone, and makes finding easier cases simpler to find. It follows these simple instructions:

1.      Determine the orientation of the corners with respect to the U-color (which I will call the first orientation; rows A-H in the second table that follows).

2.      Look at the FUL-sticker’s color. This is purple in the diagrams, and the opposite of this color is pink.

a.       For case B, look at the UFL-sticker instead.

3.      Match your configuration, or second orientation, with the configuration in the appropriate row.

4.      Do the algorithm provided, or use your favorite one.

And that’s all there is to it!

Tables

CMLL Algorithms

Here is a table of CMLL algorithms for the Roux method. These algorithms were not created by me, so credit should be given where credit is due. Thom Barlow, also known as Kirjava, made these algorithms, not me. However, I did add the brackets for ease of memorization. Also, this table does not reflect hyperorientation recognition.

Noting on notation, the I means the solved state, (letter,number) means refer to that algorithm in the table, and the bold letters have no significance other than for distinction. Lastly, the bolded boxes are what I originally memorized first.

CMLL Algorithms Robert Smith	1	2	3	4	5	6
A	I	R’UL’ U²[RU’R’]U² LR	U’(A,2)	U²(A,2)	U(A,2)	[R’UL’]U² (RU’)x’  UL’U² [RU’R’] L²x
B	U [RU²R’] U’[RU’R’]	R² [U’L’U] (R’U²)B’ (UL)(UR’)	U²(F’L)(FL’) U²[L’U²L]	U²[RU²R’] U²(R’F)(RF’)	(R’U)(LU’) [RUR’]x	U² (R’U’)(RU’)y (FR’)(F’R)y’ [R’U²R]
C	[RUR’]U [RU²R’]	(L’U²)(LU²) (LF’)(L’F)	(FR’)(F’R) (U²R)(U²R’)	(RU’)(L’U’) (BU²) (RU’)(LU)  R²	(RU’)(L’U) (R’U’)L	U² [RUR’](UR’) (FR)(F’R)  U²R’
D	U[RU R’] U[RU’R’] U[RU’R’] U[RU²R’]	(R’F)(RF’)  U²F’ (UL’)(UL)F	y F’(R’F)U² F’(RF) U² [FRF’] y’	y (FR’)(F’R)  U[RU’R’] y’	U(R'F) [RUR'U']  F'(UR)	U L’U²[RU’R’] U²L [RU’R’]
E	R²y’ (R’U)(RU’) (R’U’) R²y [RF’R]	U (RU’)(L’U)R’  U²[B’UB]L	U²R²D R’U² x[RF’R’]x’ U²R’	(RB’)(UR’)B’ [RU’R’]B	U²R²U’ RF²[R’UR]F²R	U’ F[RUR’U’]F’
F	U’[RUR’] U   [RU²R’]U’   [RU²R’]U’   [RU’R’]	U² B’[RUR’]B   (RU’)BR’	U[L’U’L] U(LF’)(L'F)	U² B’[RUR’] B (RU’) BR’	U’ [RUR’U’] (R’F)(RF’)	(R’U)  R²D [r’U²r]  D’R² (U’R)
G	F [RUR’U’] [RUR’U’] F’	U’  LU² [L’U’L] [U’L²U] (lF’)[LFl’]	U F[R²U’R²]  [UR²U]F’ y[RU²R’]y’	U’  R’U² [RUR’]           [UR²U’] (r’F)R’F’r	(RU’)(L’U) (R’U)(LU) [L’UL]	U² (R’U’)(RU’) (R’U) [F’UF]R
H	[RUR’] U [RU’R’]U [RU²R’]	F [RUR’U’] F’[RUR’U’] (R’F)(RF’)	[RUR’] (UR)(UL’) (UR’)(U’L)	U²(H,2)	U²(H,3)	UF [RUR’U’] [RUR’U’] [RUR’U’]  F’

 

Hyperorientations

Here are the hyperorientation cases made completely by me. Instructions on how to decipher the diagrams are above.

There are extra “goodies” in this table. You will notice under each diagram, there is a letter pair of the form P^xQ. The P represents which orientation the second orientation is relative to the lettering scheme for the first orientation. The superscript x (either -1, +1, ±1, 0, or 2) represents how P is rotated (+1 means clockwise 90°, 2 means 180°, ±1 means either 90° clockwise or counterclockwise, etc.). So, for example, (A,3) has a P^x of G­^-1. This means that the second orientation matches that of orientation G in the first column, but is rotated counterclockwise. It’s really not all that difficult.

The letter Q can be Z, N, or X, and are described with an example in the following table. Note that these are not permutation diagrams.

So, actually, the hyperorientation diagrams aren’t necessary if you have the letter pairs, and the letter pairs aren’t necessary if you have the diagrams. But I included both for completeness. Also, you might notice that in the first column, where the first orientations are divided, there is a set of brackets next to each type. The brackets have six letters in them, and each letter represents the columns in order: [123456]. These letters just tell you what Q that column is. For example, we have A [zz xx nn]. This tells us that 1 and 2 are Z, 3 and 4 are X, and 5 and 6 are N. Notice that for each row, there are usually 2 of each type of Q.

The last goodie in the table are the backgrounds of the individual cells. Even though it looks like it was shaded by column, they are actually shaded relative to the cells’ rows. The actual colors mean nothing, but corresponding colors in each row have the same P. For example, in B, the redish background represents D⁰. Seeing that the columns match mostly with color, it is apparent that there is some nice symmetry and stuff.

Remember that those goodies are simply goodies, and are not needed for hyperorientation.

Hyperorientation Recognition Robert Smith	1	2	3	4	5	6
A [zz xx nn]	H±1Z	G0Z	G-1X	G­0X	G-1N	H±1N
B [nxn zxz]	D0N	C0X	F0N	C0Z	F0X	D0Z
C [zz xx nn]	B+1Z	B0Z	B2X	B0X	B2N	B+1N
D [zz xz nn]	B0Z	G2Z	D-1X	D-1Z	D-1N	B0N
E [zz xx nn]	G-1Z	E2Z	B+1X	E2X	B+1N	G-1N
F [zx xx nn]	E2Z	H±1X	B0X	H±1X	B0N	E2N
G [nxn zxz]	F-1N	D-1X	G2N	D-1Z	G2X	F-1Z
H [nxn zxz]	H±1N	E2X	F-1N	E2Z	F-1X	H±1Z

 

Hyperorientations with Corresponding CMLL Algorithms

This last table is a sort of combination of the first and second tables. There are a few differences, though.

·         There are no permutation diagrams, obviously. They aren’t necessary.

·         The cell’s background colors do not mean the same thing as in the second table. Now they are shaded by Q, not by P.

o   Red = Z

o   Blue = N

o   Green = X

·         In some cells, there isn’t an algorithm, but rather something of the form U*{Qn}. This simply means to turn U as instructed, and then do the algorithm the letters in the curly braces refer to (Q is Z/N/X, and n is the index. So, “{Z2}” means “do the second Z algorithm in this row.”)

Again, these algorithms were made by Thom Barlow, also known as Kircoffee.

Hyperorientation Recognition with Algorithms Robert Smith
I	R’UL’ U²[RU’R’]U² LR	U{Z2}	[R’UL’]U² (RU’)x’  UL’U² [RU’R’]  L²x	U’{Z2}	U²{Z2}
U²[RU²R’] U²(R’F)(RF’)	U² (R’U’)(RU’)y (FR’)(F’R)y’ [R’U²R]	U [RU²R’] U’[RU’R’]	U²(F’L)(FL’) U²[L’U²L]	R² [U’L’U] (R’U²)B’ (UL)(UR’)	(R’U)(LU’) [RUR’]x
[RUR’]U [RU²R’]	(L’U²)(LU²) (LF’)(L’F)	(RU’)(L’U) (R’U’)L	U² [RUR’](UR’) (FR)(F’R)  U²R’	(FR’)(F’R) (U²R)(U²R’)	(RU’)(L’U’) (BU²) (RU’)(LU)  R²
U[RU R’] U[RU’R’]×2 U[RU²R’]	(R’F)(RF’)  U²F’ (UL’)(UL)F	y  (FR’)(F’R) U[RU’R’] y’	U(R'F) [RUR'U']  F'(UR)	U L’U²[RU’R’] U²L [RU’R’]	y F’(R’F)U² F’(RF) U² [FRF’] y’
R²y’ (R’U)(RU’) (R’U’)  R²y [RF’R]	U (RU’)(L’U)R’  U²[B’UB]L	U²R²U’ RF²[R’UR]F²R	U’ F[RUR’U’]F’	U²R²D R’U² x[RF’R’]x’ U²R’	(RB’)(UR’)B’ [RU’R’]B
U’ [RUR’]U [RU²R’]U’×2 [RU’R’]	U’ [RUR’U’] (R’F)(RF’)	(R’U)  R²D [r’U²r]  D’R² (U’R)	U² B’[RUR’]B   (RU’)BR’	U[L’U’L] U(LF’)(L'F)	U² B’[RUR’] B (RU’) BR’
U’  R’U² [RUR’] [UR²U’] (r’F)R’F’r	U² (R’U’)(RU’) (R’U) [F’UF]R	F [RUR’U’] [RUR’U’] F’	U F[R²U’R²]  [UR²U]F’ y[RU²R’]y’	U’  LU² [L’U’L] [U’L²U] (lF’)[LFl’]	(RU’)(L’U) (R’U)(LU) [L’UL]
U²{X1}	UF [RUR’U’]×3 F’	[RUR’] U [RU’R’]U [RU²R’]	[RUR’] (UR)(UL’) (UR’)(U’L)	F [RUR’U’] F’[RUR’U’] (R’F)(RF’)	U²{N2}

Other Stuff

Important note: This system was designed for the advanced learner. Asking questions is fine, but asking questions without thinking for yourself first is not.

Give this recognition system a try. It should always work, unless I made some terrible error. And say thanks to Kirjava for prompting me to publish it, but still not leaking it.

You can download a printable version of the three tables as a PDF here (161 KB). It does not include directions, and there be minor semantic differences.

You can probably find me as Quadrescence on ircstorm at #rubik, or you can email me at quadricode@gmail.com. Feel free to ask questions. Just don’t ask me to explain it all to you; I did that here.

All of the images and text (except the algorithms) are copyright ©2008 Robert Smith. I don’t care if you use anything on this page, just give credit where it’s due, and maybe link here.