L5C
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L5C (Last Five Corners) is a step used in various methods which solves five corners that remain unsolved. Much like CxLL, L5C comprises multiple variants with each one differing depending on the pieces that are to be preserved on the rest of the puzzle.
Contents
Variants
L7E method
One method which uses L5C contains the steps of 1x2x3 on the left, 1x2x2 on the right, L5C, then L7E. The algorithms for this version of L5C were first developed by James Straughan.
Zipper
The Zipper method makes use of L5C after solving the first two layers and leaving out a corner edge pair. First, the last five corners are solved, then the last five edges are solved.
Nautilus
One variant for the Nautilus Method uses L5C. After the first block and 2x2x2 are completed, the last five corners are solved and finally the solve is finished by solving the remaining six edges.
2x2x2
L5C can also be used as a method for the 2x2x2 puzzle. Three corners of a layer are solved, then the remaining five corners are solved. This is also called 1LLS.
Advancements
Conjugated CxLL
L5C contains a lot of algorithms to be memorized if the user's intent is to complete it in a single step. One idea to reduce the number of algorithms is to make use of transformation to solve the corners using Conjugated CxLL. Assuming that the three solved corners are on the D layer with the empty slot at DFR, a corner from the U layer can be positioned at UBR, and an R turn performed to create a pseudo layer on the D layer. The four corners currently on the U layer are then solved relative to the U layer corner that was placed on the D layer, then the pseudo is undone. This results in all five corners being correctly solved. Conjugated CxLL reduces the number of required algorithms to the same 42 that are in CxLL.
SL5C
In SL5C, the algorithms are truncated to leave out the last few moves. Or algorithms are generated which solve the corners to a state which is a few turns away from solved. The result of SL5C is that the corners are left in a pseudo state. This reduces the movecount of L5C and improves the ergonomics. When paired with a compatible method, such as the L7E method described in the Variants section, SL5C can be a natural fit that improves the method.
