LPELL

LPELL Information Proposer(s): Kenneth Gustavsson Proposed: 2011 Alt Names: Variants: ZBLS, VHLS Subgroup: unknown No. Algs: 96 Avg Moves: 7.4 HTM Purpose(s): FMC, Speedsolving

Last pair and edges of the last layer is a way to solve the last F2L pair and all edges of the last layer.

Intermediate

This is divided into two substeps:

• LPEOLL, orient all edges and pair up (any order). This is a intuitive step. Using algorithms is possible but you would need the same number as for ZBLS.
• LPEPLL, place the last pair and permute all edges. There are six cases and their mirrors.

LPELL is maybe not so useful for speedsolving, but for FMC. After this step is done you will have L4C left, 1:3 times it will be only L3C and 1:324 you will have a complete LL-skip. All L4C cases are easy to solve using one or two commutators. In FMC, to save moves the commutators are preferably inserted in the skeleton if such a point is found.

Optimal algs for the second step are found lower at this page.

Advanced

A second way to solve this step is to first pair up and then do the rest in one look. There are 48 + 48 mirror cases for the second half. An advanced method that, if you include L4C places the last pair and solve all of the last layer in two looks and 'only' 180 algs. Recognition for the edges is awful if you just look at it, but is not harder than COLL or something, if you use sticker colour recognition.

The cases are not listed on the internet, some day you may find them here...

Mad

• All in one?
• Forget it! There are thousands of cases. (six times ZBLS)

LPEPLL Cases

Note that all of these algorithms are written in the Western notation, where a lowercase letter means a double-layer turn and rotations are denoted by x, y, and z. (how to add algorithms) Click on an algorithm (not the camera icon) to watch an animation of it.

The names for the cases are where two of the edges will go, if it is a R side case, then these are first the edge sitting in UL and then the one in UB. For the L side cases these are UR and UB. The images assumes the UF edge is solved if the pair is above the slot, if it is some diffrent edge than UF, then just AUF it to solved position for recognition. Some algs may need a leading AUF if you are in the same position as the image, these are not explicity written here (the animations shows the correct position).

The average number of moves is 6 HTM not including any leading or ending AUF. All cases are having the same probability (1:2 R or L and 1:6 within these groups). The algs here are all optimal, if there are more than one for a case, then the other(s) does some diffrent LL-corner case than the first one.

R side pair

R LB Name: R LB Used in: LPEPLL Optimal moves: 9 HTM All solved here, but just placing the pair will swap two edges, that are optimally solved by sneaking in a backside Antisune. Alg R U' R2 U2 R U R' U R Alg D R' U R' U' R' U R2 D' Alg F2 L' U' L U F2 R U' R'	R RB Name: R RB Used in: LPEPLL Optimal moves: 3 HTM Z edges, just place from U2 position. Alg R U2 R'
R LR Name: R LR Used in: LPEPLL Optimal moves: 3 HTM The usual R U' R' pair. Alg R U' R'	R RL Name: R RL Used in: LPEPLL Optimal moves: 7 HTM Unexpected conjugate to solve. Alg R2 D L' B2 L D' R2 Alg R' U2 R U R' U R2 U2 R' U
R BL Name: R BL Used in: LPEPLL Optimal moves: 7 HTM Sune style solution. Alg R U R' U' R U' R' Alg R U' R' U R U2 R'	R BR Name: R BR Used in: LPEPLL Optimal moves: 7 HTM A 3-cycle commutator. Alg L' U2 R U R' U2 L Alg R' U2 R U R U' R2 U2 R U

L side pair

L RB Name: L RB Used in: LPEPLL Optimal moves: 9 HTM Mirror of R LB. Alg L' U L2 U2 L' U' L U' L' Alg D' L U' L U L U' L2 D Alg F2 R U R' U' F2 L' U L	L LB Name: L LB Used in: LPEPLL Optimal moves: 3 HTM Mirror of R RB. Alg L' U2 L
L RL Name: L RL Used in: LPEPLL Optimal moves: 3 HTM Mirror of R LR. Alg L' U L	L LR Name: L LR Used in: LPEPLL Optimal moves: 7 HTM Mirror of R RL. Alg L2 D' R B2 R' D L2
L BR Name: L BR Used in: LPEPLL Optimal moves: 7 HTM Mirror of R BL. Alg L' U' L U L' U L	L BL Name: L BL Used in: LPEPLL Optimal moves: 7 HTM Mirror of R BR. Alg R U2 L' U' L U2 R'