What is ZBLL? ZBLL is a set of algorithms that solves the whole last layer of a 3x3 Rubik's Cube in one look, as long as the top already shows a yellow cross. Instead of doing OLL and then PLL as in CFOP, you spot the case and do a single sequence of moves. The catch: the set has 493 cases.
Find your case fast
Look at your cube from above and tap the picture that matches it to see how to solve it. Grey cells are stickers you can ignore.
This post explains what ZBLL is, when you can use it, what the case groups look like, and who should really take it on. Every move sequence here was tested on the EasyRubic cube simulator.
What is ZBLL?
ZBLL stands for Zborowski-Bruchem Last Layer. It is named after Zbigniew Zborowski and Ron van Bruchem, who put forward the ZB method in 2002, with ZBLL as its final step (SpeedSolving Wiki).
The idea of solving the last layer in one step is older than the name. According to SpeedSolving Wiki, also in 2002, Lars Petrus suggested merging the final steps of the Petrus method into one, and Bernard Helmstetter was the person who found the first set of algorithms. That is why some cubers would rather call the set something else, but ZBLL is still the most common name (SpeedSolving Wiki).
In short: ZBLL = orient the corners + permute the whole last layer, at the same time. It merges two steps, "make the yellow face" and "line up the sides", into one.
How to read the pictures
- Yellow on top, green in front. In the pictures, the right face is orange.
- Each picture has two cubes: the left one is the case you have, the right one is after the move sequence. Only the top layer is coloured. The bottom two layers are grey because they are already solved.
- The pictures only show the top, front and right faces. Yellow stickers on the left and back faces are described in words.
If R, U, R' and U2 are new to you, see Rubik's Cube notation for beginners. Rw means turning the two right-hand layers together; many sites write it as a lowercase r.
When can you use ZBLL?
You can only use ZBLL when the four top-layer edges are already oriented, which means the top already shows a yellow cross the moment you finish the first two layers (SpeedSolving Wiki). If you have followed the beginner method, that is exactly the state after the yellow cross step:
- You start with (input)First two layers all correct
- Result you will get after finishing this stepYellow cross on top
The difference is that with ZBLL, the yellow cross is not made with an algorithm of its own. It has to be there already when the first two layers are done. There are three ways to get to that state:
- Normal CFOP, with luck. According to SpeedSolving Wiki, if you do not orient the edges on purpose, ZBLL only comes up in about 1 in 8 solves.
- The ZZ method. The first step of ZZ (EOLine) orients every edge right at the start, so every solve ends with a yellow cross. Wikipedia mentions ZBLL as the last step of ZZ, solving the last layer in just over 12 moves on average (Wikipedia). See also the post on the ZZ method.
- The ZB method, with ZBLS. When you pair the last corner and edge of the first two layers, you use an algorithm that both inserts the pair into its slot and orients the top-layer edges (see the ZBLS section below).
How many ZBLL cases are there?
ZBLL has 493 cases, counting the 21 PLL cases (SpeedSolving Wiki). The ZB method page on SpeedSolving Wiki gives 472, plus 21 if you count PLL (SpeedSolving Wiki). Wikipedia also says ZBLL needs 493 algorithms (Wikipedia).
The cases are sorted by the pattern of the four corners, exactly like the seven corner orientation cases (OCLL) of 2-look OLL, plus a PLL group for when all four corners already show yellow on top. Each group is split again into 6 subgroups of 12 cases each (SpeedSolving Wiki).
We counted them again by computer: we listed every last-layer arrangement with the edges oriented, then merged any that differ only by a U turn before or after. The result matches the number 493:
- Sune: 72 cases
- Antisune: 72
- U: 72
- T: 72
- L: 72
- Pi: 72
- H: 40 (fewer, because the H pattern is symmetrical, so many cases are the same after a U2)
- PLL: 21
According to SpeedSolving Wiki, a ZBLL algorithm is 12.08 moves long on average if you count the shortest solutions (SpeedSolving Wiki).
One example per group
You may already know a few ZBLL cases without realising it. Each corner orientation algorithm from 2-look OLL, when it happens to finish the whole last layer, is a ZBLL case from that group. Here is one example for each group.
Sune group
How to spot it: exactly one corner has yellow on top. Turn U so that corner is at front left: the front-right corner has its yellow sticker facing the front.
R U R' U R U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
The post on the Sune and Antisune algorithms goes into these two groups in detail.
Antisune group
How to spot it: again, one corner has yellow on top. Put that corner at front left: the front-right corner has its yellow sticker facing right. In the picture below, the yellow corner is at back right.
R U2 R' U' R U' R'
See it in 3D, before and after
- You start with (input)
- After the formula
U group
How to spot it: two neighbouring corners have yellow on top (the two at the back in the picture). The two front corners both have yellow facing the front.
R2 D R' U2 R D' R' U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
T group
How to spot it: two neighbouring corners have yellow on top. The other two have yellow facing outwards, in opposite directions. In the picture, the two yellow-on-top corners are on the right, the front-left corner faces the front and the back-left corner faces the back.
Rw U R' U' Rw' F R F'
See it in 3D, before and after
- You start with (input)
- After the formula
L group
How to spot it: two diagonally opposite corners have yellow on top.
F' Rw U R' U' Rw' F R
See it in 3D, before and after
- You start with (input)
- After the formula
Pi group
How to spot it: no corner has yellow on top. The two left corners both have yellow facing left, and of the two right corners, one faces the front and one faces the back.
R U2 R2 U' R2 U' R2 U2 R
See it in 3D, before and after
- You start with (input)
- After the formula
H group
How to spot it: no corner has yellow on top. The two left corners face left and the two right corners face right.
R U R' U R U' R' U R U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
With 2-look OLL, cases like these are just luck: once OCLL is done, PLL simply disappears. ZBLL turns every case into that kind of "luck", because you already know the algorithm for the exact case in front of you.
Same corner pattern, different case
This is the most important thing to get about ZBLL. Two cases can have exactly the same top face but different stickers on the sides. With 2-look, you do the same corner orientation algorithm, then still need a PLL. With ZBLL, each case has its own algorithm and you are done straight away.
The examples below are all built from Sune and Antisune, 15 moves long, using only R and U. They are not the fastest algorithm for each case, but they are easy to remember if you already know Sune, and they are enough to show the idea.
Pi group: Sune, U, Sune
The top looks like the Pi group above: no corner has yellow on top. But if you do the Pi algorithm from 2-look, the yellow face is done while the sides are still off, and you need one more PLL. Do Sune twice with a U in between, and the whole layer is solved:
R U R' U R U2 R' U R U R' U R U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
U group: Sune, U, Antisune
Two yellow corners at the back, the two front corners both facing the front, just like the U group above. The U algorithm from 2-look does not finish this case and leaves a PLL behind. This sequence solves it completely:
R U R' U R U2 R' U R U2 R' U' R U' R'
See it in 3D, before and after
- You start with (input)
- After the formula
T group: Antisune, U, Sune
Two yellow-on-top corners next to each other, the other two facing out to the sides:
R U2 R' U' R U' R' U R U R' U R U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
Notice: this sequence and the U group one use exactly the same two algorithms, Sune and Antisune, just in a different order, and they give two different groups.
L group: Sune, U2, Antisune
Two yellow-on-top corners diagonally opposite each other:
R U R' U R U2 R' U2 R U2 R' U' R U' R'
See it in 3D, before and after
- You start with (input)
- After the formula
In all four examples, the 2-look corner orientation algorithm only finishes the yellow face, while the combined sequence finishes the whole layer. That is why ZBLL needs you to read the side stickers carefully too, not just the top.
ZBLL compared with OLL + PLL and COLL
There are three common ways to solve the last layer once you have a yellow cross:
- OCLL then PLL (two looks). The fewest algorithms: 7 corner orientation algorithms and 21 PLLs. This is what most CFOP cubers use.
- COLL then EPLL. COLL orients and permutes all four corners at once, keeping the edges oriented. SpeedSolving Wiki counts 42 COLL cases including mirrors, or 24 without them (SpeedSolving Wiki). After COLL, only the edges need swapping.
- ZBLL (one look). The fewest moves and the fewest pauses, but 493 cases.
A quick comparison:
| Method | Looks | Cases to memorise |
|---|---|---|
| OCLL + PLL | 2 | 7 + 21 |
| COLL + EPLL | 2 | 42 + a few edge PLLs |
| ZBLL | 1 | 493 |
The biggest win with ZBLL is not just fewer moves, it is cutting out one pause to look. The price is memory: SpeedSolving Wiki notes that only a small number of people have ever memorised the full ZBLL set (SpeedSolving Wiki).
ZBLS and the ZB method
The ZB method has three parts: solve the first two layers except one corner-edge pair, then ZBLS, then ZBLL (SpeedSolving Wiki).
ZBLS (Zborowski-Bruchem Last Slot, once called ZBF2L, also known as EOLS) inserts the last corner-edge pair into its slot while orienting the top-layer edges. That way every solve ends with a ZBLL. SpeedSolving Wiki says ZBLS has 302 cases, which comes to 125 algorithms if you treat inverses and mirrors as one (SpeedSolving Wiki). Together with ZBLL, the whole ZB method needs around 800 algorithms; Wikipedia gives the figure 795 (Wikipedia).
A cut-down version of ZBLS is VHLS: pair the corner and edge first, then insert the pair into the slot while orienting the edges. According to SpeedSolving Wiki, this is a small part of ZBLS that only covers one pairing situation.
The ZB method page on SpeedSolving Wiki also says many CFOP cubers pick up ZBLL on its own, because it fits CFOP very well, and that recently some top Chinese cubers such as Xuanyi Geng have switched to ZB completely (SpeedSolving Wiki).
Who should take on ZBLL?
- Beginners: not yet. First get solving with the 7-step guide, then move up to CFOP with 2-look OLL and PLL. - CFOP cubers who know full OLL and PLL: you can add it one group at a time and use it whenever a yellow cross turns up on its own. - ZZ cubers: it is most worth it for you, because every solve has a yellow cross. ## Where to start with ZBLL?
- Get OCLL and PLL down first. SpeedSolving Wiki recommends knowing OCLL/PLL or COLL/EPLL first, so that when you hit a case you do not know yet, you can still solve it quickly (SpeedSolving Wiki).
- Pick up COLL. Each ZBLL subgroup matches one COLL case, so knowing COLL helps you spot the subgroup faster.
- Go one 12-case subgroup at a time. Do not try a whole group of 72 at once. Pick a group, for example T, and get through all of its subgroups before moving to another group.
- Do not skip Sune and Antisune. SpeedSolving Wiki notes that many people skip these two groups because their OCLLs are already short, but they are still worth having.
- Practise spotting cases from the front-right corner. According to SpeedSolving Wiki, the easiest way to recognise a case is to look at the front-right corner and the stickers next to it.
While practising, set up a case by doing the algorithm backwards on a solved cube, like the "before" pictures in this post. Then solve it with the 3x3 timer to see whether your last layer is faster than with two looks.
Summary
Each algorithm comes with a picture of the case it solves.
- Sune group: R U R' U R U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
- Antisune group: R U2 R' U' R U' R'
See it in 3D, before and after
- You start with (input)
- After the formula
- U group: R2 D R' U2 R D' R' U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
- T group: Rw U R' U' Rw' F R F'
See it in 3D, before and after
- You start with (input)
- After the formula
- L group: F' Rw U R' U' Rw' F R
See it in 3D, before and after
- You start with (input)
- After the formula
- Pi group: R U2 R2 U' R2 U' R2 U2 R
See it in 3D, before and after
- You start with (input)
- After the formula
- H group: R U R' U R U' R' U R U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
- Pi group, another case: R U R' U R U2 R' U R U R' U R U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
- U group, another case: R U R' U R U2 R' U R U2 R' U' R U' R'
See it in 3D, before and after
- You start with (input)
- After the formula
- T group, another case: R U2 R' U' R U' R' U R U R' U R U2 R'
See it in 3D, before and after
- You start with (input)
- After the formula
- L group, another case: R U R' U R U2 R' U2 R U2 R' U' R U' R'
See it in 3D, before and after
- You start with (input)
- After the formula
Video
Want to see it in motion? The short video below from the DTD Cuber channel on YouTube adds to what this post covers. It is in Vietnamese. The video belongs to that channel and is embedded straight from YouTube.
Sources
Frequently asked questions
What is ZBLL?
ZBLL (Zborowski-Bruchem Last Layer) is a set of algorithms that solves the whole last layer of a 3x3 Rubik's Cube in one step, when the four top-layer edges are already oriented, meaning you already have a yellow cross.
How many ZBLL algorithms are there?
493 cases including the 21 PLLs, or 472 without PLL. An algorithm is about 12 moves long on average.
How is ZBLL different from OLL and PLL?
OLL and PLL solve the last layer in two steps: make the yellow face, then line up the sides. ZBLL does both at once, but you can only use it when the yellow cross is already there.
Can CFOP cubers use ZBLL?
Yes, when the yellow cross is already there after the first two layers, which happens in about 1 in 8 solves. To get ZBLL more often, you need to orient the edges during the last pair, for example with ZBLS or VHLS.
What is ZBLS?
ZBLS is the step that inserts the last corner-edge pair into its slot while orienting the top-layer edges, so every solve ends with ZBLL. It has about 300 cases.