In the final step, solve the last layer. The major advantage of ending in a last layer is that recognition is easy. Most of the stickers are on the sides of the last layer, with two out of three sides in view.
Solve the last six triangles. In the basic version, this step is accomplished in 2 sub steps. First, one side is completed using an algorithm then the other two sides are solved using the same set of algorithms.
First, check for a triangle and edge pair. This is called a diamond. Move the other triangle to the diamond to complete a side.
*Note: The algorithms are executed from a corner in front hold unless otherwise noted. The images depict an overhead view of the last layer with the front corner at the bottom of the images.
U' F' r U R' U' r' F R
L U' r' F R F' r U R' L'
U' R' F' r U R U' r' F
U r' F' r U R' r U' r' F R
If there are no diamonds, use one of the algorithms to move a triangle to an edge and form a diamond. Then follow the process of completing a side.
Once one side is completed, use the same algorithms to solve the remaining two sides. It only takes one application of an algorithm to solve both sides at once.
There are additional algorithms that can further speed up the process. If there are no diamonds when starting the step, a separate algorithm can be used to form a complete side instead of just a diamond. There will be three possibilities when there are no diamonds - two matching triangles on a side, called headlights, two matching stickers around a corner, called cat ears, or there are two matching stickers on opposite sides, called a chameleon. Use the associated algorithm to complete a full side. Learning these algorithms will make for a two step process for solving all triangles.
(U') R' F' r U r R2' F R U r' F' r2 R'
Headlights (swap two sides)
R' F' r U R r' U' r' U' F U r
Cat ears
(U') BR' U' R U' BR U BR' R' U BR
Chameleon
Once accustomed to the two look version of solving the triangles, algorithms can be learned to solve all cases in a single step. There are just 35 algorithms and the recognition works similar to PLL. Each case can be identified based on its pattern. These patterns consist of the diamonds, headlights, cat ears, and chameleons that were practiced in the two look version. Visit the document below for the algorithm list.
Finally, the last three corners will be solved. In the basic version, the corners are oriented then permuted. There is just one algorithm for orientation and two for permutation. In the one look version, there are only five algorithms.
First, orient the corners using the following algorithm. Turn the upper layer to have the two misoriented corners on the back.
r U R' U' R F R' U R F' U' r'
Orient two corners
To permute the corners, use the following algorithm. The algorithm cycles the corners clockwise. Use the algorithm once or twice to cycle the corners and complete the permutation. {F, BR} means to rotate the puzzle to move the front layer to the upper layer and the BR layer to the front.
{F, BR} R' U R' D' R U' R' D R2
One look L3C is only five algorithms. You will already know two of the algorithms. So only three additional algorithms are needed.
(U) r' U' R' F' U r' F r U' F U' R U r
Pure two flip
r U R' U' R F R' U R F' U' r'
Two flip clockwise permutation
(U) r U F R' U' R F' R' U R U' r'
Two flip counterclockwise permutation
{F, BR} R' U R' D' R U' R' D R2
Clockwise permutation
{F, BR} R2' D' R U R' D R U' R
Counterclockwise permutation
The ultimate goal for the last layer may be to learn 1LLL. Sets can be learned while using the two look last layer method. One of the great things about 1LLL is that it can be recognized by only checking the sides. There is no need to check the U face or any other positions. In this way, it is similar to PLL recognition. The U face stickers and underside stickers of the corners will never be on the sides, so they will never be involved on the sides within the recognition. The overall recognition will be similar to the two look last layer, but extended to have larger blocks and other patterns.
PLL can also be used. There is only one algorithm for orienting the corners, so it will likely be best to combine the corner orientation with solving the last triple of the first two layers. This will then lead directly into PLL. The corners can be easily and intuitively oriented while placing the bottom triple. It may also be viable to combine it with solving the final center of the triple or in a much larger set of one look last triple and corner orientation. Combining corner orientation with the last triple leads to a reduced one look last layer similar to reducing to ZBLL.