How to solve the Last Layer
By S1neWav_ and crystalcuber
Introduction
Last Layer (LL) is the final step of the ZZ Method. After solving the First 2 Layers, we use algorithms (memorized move sequences) to solve the top layer.
CFOP users will already know to solve the Last Layer. The only difference with ZZ is that the edges are oriented, which reduces the total number of cases. For CFOP users, this means only the 7 cross-on-top OLL cases will occur.
The rest of this tutorial doesn't require knowledge of CFOP.
The ultimate goal of Last Layer in ZZ is to solve it in one step (ZBLL), but this requires learning 493 algorithms. To make it easier, we'll split it into 3 steps, or looks. In total, there are 13 algorithms.
This approach is called 3-Look Last Layer (3LLL). Here are the steps:
- OCLL: Orient the Corners of the Last Layer.
This step twists the top corners so the top side is a single color. - CP: Corner Permutation
This step swaps the corners around so they're solved relative to each other. - EPLL: Edge Permutation of the Last Layer.
This step swaps the edges around so the top layer is completely solved.
Step 1: OCLL
There are 7 OCLL cases. We recognize them by the shape formed by the top-colored stickers on the top layer. Everything else is ignored.
We call a corner "oriented" if its top-colored sticker is on the top.
An important pattern for OCLL recognition is called headlights: a pair of matching corner stickers on the same side.
| Name | Case | Algs |
|---|---|---|
| Sune | Sune | R U R' U R U2' R' |
| Antisune | Antisune | L' U' L U' L' U2 L |
| U | U | R2' D' R U2 R' D R U2 R |
| T | T | r U R' U' r' F R F' |
| L | L | F R' F' r U R U' r' |
| H | H | R U R' U R U' R' U R U2' R' |
| Pi | Pi | R U2' R2' U' R2 U' R2' U2' R |
Starting with the cases with no oriented corners:
- H has two pairs of headlights.
- Pi (π) has only one pair of headlights.
Next, the cases which have exactly one oriented corner:
- Sune has three misoriented corners that each need to twist clockwise.
- For antisune, they need to twist counterclockwise.
Finally, the cases with exactly two corners oriented:
- U has a pair of headlights.
- T has no headlights, but the two oriented corners are adjacent to each other.
- L has no headlights, and the two oriented corners are opposite each other.
Step 2: CP
There are only two CP cases. Like in OCLL, we look for headlights, but they look a bit different:
| Name | Case | Algs |
|---|---|---|
| Adjacent swap | Adjacent swap | R U R' U' R' F R2 U' R' U' R U R' F' |
| Diagonal swap | Diagonal swap | F R U' R' U' R U R' F' R U R' U' R' F R F' |
To recognize which case you have, look at the colors on the sides of the corners and ignore everything else. If you see only one pair of headlights, then it's an adjacent swap. If there are no headlights, then it's a diagonal swap.
Step 3: EPLL
There are 4 EPLL cases. Here they are:
| Name | Case | Algs |
|---|---|---|
| H Perm | H Perm | M2' U M2' U2 M2' U M2' |
| Ua Perm | Ua Perm | M2' U M U2 M' U M2' |
| Ub Perm | Ub Perm | M2' U' M U2 M' U' M2' |
| Z Perm | Z Perm | M2' U2 M U M2' U M2' U M |
First, learn these color relationships:
- Adjacent colors: colors belonging to sides next to each other on a solved cube (e.g. red/green).
- Opposite colors: colors belonging to sides across from each other on a solved cube (e.g. red/orange)
For EPLL, we recognize the case by looking at the color relationships on the sides of the cube.
- H has opposite colors on all four sides.
- Ua and Ub have one solved edge. With that solved edge in the back:
- Ua has opposite colors on the right side.
- Ub has opposite colors on the left side.
- Z has adjacent colors on all four sides.
Stepping up to 2LLL
After learning 3LLL and getting comfortable with it, we can unlock more speed. We can combine CP and EPLL into one step called PLL (Permutation of the Last Layer). There are 21 PLL algs, but the nice part is that you'll already know 6 PLLs from CP and EPLL. Now you will have a 2-look last layer (2LLL) every solve.
Check out 2LLL here.
What about 1LLL?
You can even solve the entire Last Layer in a single step, which is a significant speed advantage. In ZZ, you need to learn 493 algorithms in total (compared to 3916 for CFOP). Learn more here.