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Last Four Corners method

Information about the method
Proposer(s):	unknown
Proposed:	unknown
Alt Names:	L4C
Variants:	none
No. Steps:	1
No. Algs:	84
Avg Moves:	11.73 (Optimal HTM)
Purpose(s):	Speedsolving, FMC

Last four corners, abbrevaited L4C (or 4LC), is a method that solves the last layer corners preserving all the rest, a sub group of ZBLL and ZZLL. For a 2-look last layer this is preceeded with LLEF (ELL first).

See also:

Last Three Corners

2-look L4C

It is possible to solve most L4C in two looks using 3-cycle commutators (see L3C). The method is to use the first 3-cycle to solve one piece and at the same time move any placed but twisted corner out from position (to avoid the pure twists that uses long algs) and then follow it up with a second 3-cycle. This will solve all cases but the pure twists with 4 corners wrong, that you can solve in two looks using only the U-twist and puzzle orientations, the other pure cases, T and U use the U-twist, L and S; cycle the twisted corners using any 3-cycle and then the appropiate cycle to move them back.

Another way is to use COs that preserves edges but not corner permutation and then end the solve using CPLL. This will use lesser algs but more turns than the first approach.

L4C Cases

Because edges are solved at this point you cannot AUF as in CxLL so the number of cases is quadrupled, but because you cannot have parity that is reduced again by factor 2. The orientations are the usual seven COs plus the solved case (CPLL). The permutations (with fix position orientations) that occure are permutation solved, A-PLL a and b from all four angles, the two possible ways of E-PLL and finally X-PLL (that is H-PLL + U2) giving a total of twelve possible permutations. This gives a total of 8 * 12 = 96 cases, but it is possible to reduce that a bit because of duplicates. The whole group is larger, corner orientations are for real 27 so you will have 27 * 12 = 324, so the chance of a skip is 1:324.

Sub groups:

Pure CO; see Corner Orientation for the seven cases of pure orientation and algorithms to solve them.
All corners oriented; use the CPLLs for this, cases are A-PLL (a and b), E-PLL and H-PLL (X-PLL).
One corner solved; Last Three Corners, 16 cases that have both orientation and permutation, these you can find at the L3C page.

Algorithms

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.

Click on an algorithm (not the camera icon) to watch an animation of it.