Last Three Corners


Information

Proposer(s):

Anthony Snyder, Ryan Heise

Proposed:

unknown

Alt Names:

L3C

Variants:

L4C, CxLL

Subgroup:


No. Algs:

24

Avg Moves:

~10 HTM, 9.56 optimal HTM

Purpose(s):

^{}


Last three corners, abbrevaited L3C (or 3LC), is a method that solves three of the last layer corners preserving all the rest, a sub group of L4C, ZBLL and ZZLL.
Usage: besides L4C, CxLL, ZBLL and ZZLL it is useful for FMC and the 3cycles are nice for Freestyle BLD. L3C is the final stage in the Snyder Method.
See also:
External links
 [1] Ryan Heise explains an intuitive approach to solve the last three corners.
L3C Cases
The group have 27 cases including solved, 3*3 orientations and 3 permutations. Most of the cases (18) are pure 3cycles, the rest are pure twists U, T, L, S and S. Some of the twist occures 2 times (U, T and L) and the Ttwist is the same as the Utwist if the puzzle is reoriented. Subtracting the duplicates and solved it will be 22 cases left. 16 of them are pure L3C cases and listed at this page, the rest are in one of two sub groups.
Sub groups
The naming system used here is adapted to BLD, the ULB corner is always the solved one and URF is the 'buffer' with U as the buffer sticker. The piece in the buffer will go to two places, either URB or UFL and the sticker in U will go to any of the three stickers on each goal position and that sticker is in uppercase, the other two letters will be in lowercase. The second half of the name is the same but from the goal position of the first. The last piece will always go to the first buffer position so that will not be in the name.
Example: CW APLL is UflUrb and CCW APLL is UrbUfl.
Algorithms
Note that all of these algorithms are written in the Western notation, where a lowercase letter means a doublelayer 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 following four cases are mirror + inverses of the first so you only need '1 alg' for all.

Mirror to the side and inverse in diagonal.

uFlUrb

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM


uRbUfl

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM


UfluRb

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM


UrbuFl

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM


The following four cases are mirror + inverses of the first so you only need '1 alg' for all.

Mirror to the side and inverse in diagonal.

ufLuRb

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM


urBuFl

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM


uFlurB

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM


uRbufL

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 9 HTM


The following four cases are mirror + inverses of the first so you only need '1 alg' for all.

Mirror to the side and inverse in diagonal.

ufLUrb

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM


urBUfl

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM


UflurB

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM


UrbufL

Name: 3cycle commutator
Used in: L3C, L4C, BLD
Optimal moves: 8 HTM


ufLurB

urBufL

uFluRb

Name: Anti Niklas a
Used in: L3C, L4C, BLD
Optimal moves: 10 HTM


uRbuFl

Name: Anti Niklas b
Used in: L3C, L4C, BLD
Optimal moves: 10 HTM

