CPLS

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CPLS method
Information about the method
Proposer(s): Baian Liu, ?, ?
Proposed: 2009?
Alt Names: none
Variants: none
No. Steps: 1
No. Algs: 26
Avg Moves: ~10
Purpose(s):


CPLS (short for Corner Permutation and Last Slot) is a substep used to solve the final F2L corner (usually DFR) and permute the last-layer corners while preserving the corresponding edge and EOLL. If used when only the last F2L corner, EPLL, CPLL, and COLL remain, CPLS leaves just EPLL and COLL, which may be solved using 2-generator. Although seemingly hard to recognize, CPLS can be very beneficial, especially for one-handed solvers if fast 2-generator algorithms are used.

A two-step solution to EPLL and COLL requires only 11 algorithms: 7 for OCLL, which leaves 4 EPLL cases. One-step solution, known as 2GLL, has 84 cases. Note that this is also referred to as ZZ-d.

History

CPLS was proposed by Baian Liu in 2009. (who else?)

Learning Approach

CPLS is naturally divided into the subsets - +, O, I, Im, and C, the same classification used for CLS. The first three sets have 6 algorithms each, the next two have 3 each, and the final set has only 2. One recommended order, for ease of learning and recognition, is C, O, I, Im, -, +.

Recognition

One possible disadvantage of CPLS is its seemingly difficult recognition. The following system, however, works well. First, position the last slot to URF.

Scramble: x R' U R U' R' U R U' R' U R U' x' (yellow on top, red on front).

This is an O case. Look at the remaining three U-layer pieces. Let's keep a system to *always* start with UFL.

Once reaching any of the three corners, in this order, the first goal is to locate the U-layer (yellow) sticker: on top in this case.

Next, look at the sticker *clockwise* from this sticker. In other words, the sticker on the F face, or the FLU sticker. This should be red. I note this, and that my red FACE is currently on B. I now pretend that the entire F face is orange, because when rotated, that sticker lies on that face.

Repeat for LUB and BRU. For the L face, you should come out with green, since the sticker at LUB is green. For the B face, you should come out with orange, since the sticker at BRU is orange.

This case may be written [O BLF], meaning B is on F, L on L, and F on B. This notation, however, depends on the initial AUF.

From the above, we can visualize that F = red, L = green, and B = orange. Knowing that yellow is our U-layer sticker, we know that the above can't be right - those colors aren't allowed to be like that! So what we must do is switch those "face." To do this, we must switch the corners that these pieces are represented by. For example, the UFL piece represents the Front face. In this case, we must switch the UFL and UBR corners. To understand what to do now, we go over to https://sites.google.com/site/devastatingspeed/3x3x3/cpls and try to find the right case. Knowing that we have a diagonal switch (switching UFL and UBR has essentially the same effect as switching UFR and UBL), we look for the O case with the diagonal swap, which is in the 3rd row, second column, yielding us the algorithm x (U R' U' R)*3 x'

Example Solves

This recognition method is best illustrated with example solves. Standard color scheme is assumed throughout. Scramble with white on top (U) and green in front (F).

Scramble 1: D' B' D2 F2 R F' L' R B L' F' U' R' B F2 U R2 D L2 D2 U' B R' F2 D'

A Petrus approach

2x2x2: x2 D B' R' D2 L2 (5/5)
2x2x3: x' y D R D' U' L' U L (7/12) -note that this sets up for an Im case later on.
EO: y U M' U M (4/16)
F2L: x y U2 R' U' R U R' U' R2 U2 R' (10/26) [ewww]
CPLS (Im FBL): y2 U R' F2 R D' L' U2 L' U' L2 D (11/37)
2GLL (Pi Ua1): y (y) R U2 R2 U2 R U R2 U R2 U' R2 U2 R' U2 R(16/53)
AUF: U2 (1/54)


Scramble 2: L2 F' L2 F L' D B D2 U2 L2 D L' R B' L2 U B2 R2 D2 R B2 D U2 B' F'

A RH OH ZZ approach

EOCross: L B' R' U D F R D R' D R' (11/11)
BL slot: U2 R U R' L U L' (7/18)
FL slot: L2 U2 L U L' U L2 (7/25)
BR slot: U R' U' R U' R' U R (8/33)
FR edge: R U R' (3/36) [gah, it kills me not to do CLS for this case :(]
CPLS setup: U2 (1/37)
CPLS (O): y U2 z' U L' D2 L U' L' D2 z (8/45)
2GLL (T Ub2): z' U L2 U' L' U L' U' L U L U' L U L2 U' (15/60)
AUF: L2 (1/61, or 57 with cancellations)


Scramble 3: L' R' B F U B2 D2 F2 L F2 D U' B' U D2 F2 B L2 R2 B U2 B' D2 U2 R

A CFOP approach

Cross: x2 F D L2 U2 L F' (6/6)
BL slot: F' U2 F L U' L' (6/12)
FR slot: U R U2 R' U R' F R F' (9/21)
BR slot: U' R' U2 R2 B R B' (7/28)
ELS setup: y U (1/29)
ELS: R U' R' F' U2 F (6/35)
CPLS (+): U' U' y R' U L' U' R U L (9/44) 	
2GLL (Pi Ub3): y' (y) R U2 R2 U' R' U R U' R' U' R' U' R' U2 R U2 (15/59, or 56 with cancellations)

See Also

External Links