PERMUTATION LAST LAYER - PLL

PERMUTATION LAST LAYER  -  PLL 

There are a lot of algorithms to solve the Rubik's Cube introduced by many people. Most are for the TOP layer. 

those PLL algorithms use to solve a Rubik's cube with less time-consuming than normal pattern.

Normally we take white as the base colour ( Down) then yellow will be the TOP layer Upper side colour.

TOP Layer Algorithms:

How to make the TOP layer all pieces yellow on the upper side?

1. Need to make a Cross of the TOP layer

        Use FRUR'U'F' when its a line from left to right

                

or

        Use FURU'R'F' when it's an L shape from left to back

When you have a fish shape in the top layer:

        use R U R' U R 2U R' 

 The Cube must be like that when we do the above algorithm. if no yellow colour facing the front and do the same algorithm twice ( with the fish head towards left-front)

TOP layer Corner fix?

use  R' F R'  BB RF'R' BB R'R' 

find whether the cube has headlights ( two matched edges and keep them back when doing the above algorithm. if no headlights, keep comparing right side to back and do the above algorithm until fixing corners are (maybe twice)

Fixing Edges;

RR URU R'U'R'U'R' UR'   

- for the clockwise rotation ( use when we need to move edges clockwise)

 RU' RURUR U'R'U' R'R' 

- for the Anti-clockwise rotation ( use when we need to move edges anti-clockwise)

swap opposite edges;

use 2M' U 2M' 2U 2M' U 2M'

PLL - PERMUTATION LAST LAYER - more!

Without a traditional TOP layer solution, we can use the following algorithms to fix a cube without delay. 

            F -Front        B - Back

            R - Right       L - Left

            U - Up            D - Down

1.  When we have imparity corners and edges like the below image; 

Hold the cube as shown by the notations and do the following algorithm.

x (R2) F R  F' R (U2)  r' U r (U2)

x - Rotate the cube along the x-axis clockwise

r ' - Both middle and Rgiht Layers are to be rotated anti-clockwise

Here, We need to swap the two corners of the right side and the two edges of the right and the back sides. 

The RIGHT-BACK corner is rotated clockwise and the RIGHT-FRONT corner is turned anti-clockwise.

And, The right side edge moves to the back side and Vise-Versa.

for the less time-consuming, we have to practise more and more to solve the cube as fast as we can and also need Hawkeye. otherwise, we will not be able to see this pattern and go for the most time-consuming method that we have already practised.

or keep blue side to back and do R' F R'  BB RF'R' BB R'R'. then we will have a method once of the number 2 or 3.

The following are the most common practice methods used to solve a Rubik's cube with more time-consuming but not always. we used some algorithms to make numbers 2 and 3 methods and use those algorithms then to solve.

By using the " R' F R'  BB RF'R' BB R'R'  " algorithm one time or a few times, we get the cube in the form of the following number 2 or 3 methods.

2. When we have imparity edges like the below image; 

2R URU R'U'R'U'R' UR'

We use this method when we solve a cube in Corner First then the Edges method. 

by keeping one correct corner to the right-back or both correct corners to the back and using R' F R'  BB RF'R' BB R'R'. we get this position.

Here all colours are matched in the backside. for the right, front and left sides, the edges need to move along the clockwise rotation which means, the Red piece needs to move towards the right side, the Green piece needs to move towards the front side and the Orange edge piece needs to move towards the left side.

3. When we have imparity edges like the below image; 

RU' RURUR U'R'U' 2R

This is the exact opposite of number 2, the Anti-clockwise movement of edges to fix the cube.

as shown in the figure, the Orange edge moves to the left, the Green edge moves to the front and the Red edge moves to the right when we do the above algorithm.

4. When we have imparity edges like the below image;

 2M' U 2M' 2U 2M' U 2M'

Sometimes we will have imparity like the above image. opposite edges swapped each other ( Green-Blue and Red-Orange).

Either we can use 2M' U 2M' 2U 2M' U 2M'  to fix at once

or 

use R' F R'  BB RF'R' BB R'R'   if you hard to remember so many patterns and algorithms, it will redirect again to method 2 or 3.

but it is more effortless if you remember the 2M' algorithm than others.

5. When we have imparity corners and edges like the below image;

2R F (R U R U’ R’) F’ (R U2 R’ 2U' R U)

If you ever have something like the above image when solving a cube, use the algorithm mentioned above to fix the cube at once. or

use R' F R'  BB RF'R' BB R'R'   to fix click here to see how with details.

Here two corners of the right side need to swap, while swapping them, the right-back corner rotates clockwise and the front-right corner rotates anti-clockwise. meanwhile, the front and the left edges are swapping each other to fix the cube. 

6. When we have imparity edges like the below image;

If we come across imparity edges like the above image when solving a cube, need to use a special algorithm like 

R' U' R U'  R U R U' R'  U R U  (R2)  U' R'  

to solve it.

or

use R' F R'  BB RF'R' BB R'R'   to fix click here to see how with details.

Here we got edges swapping positions but not opposite. instead, we have to swap the front - the left edges and the right-back edges simultaneously.

The back and the Front takes clockwise rotation and the right and the left edges take anti-clockwise rotation.

7. When we have imparity corners like the below image; 

            xR2D2 RUR' D2 RU'R x'

in No:7, only 3 corners have an issue with imparity and are willing to move along an anti-clockwise rotation as shown in the above image.

The Red-Blue-Yellow corner should move to the Front-Right corner, the Orage-Blue-Yellow corner towards the Right-Back corner and the Orange-Green-Yellow corner to the Back-Left corner ...

As shown in the image, two corner colours are matched on the right side. keep them as it is, and do the above-mentioned algorithm to fix the cube.

or keep them ( two matched colours) on the back

and use  

R' F R'  BB RF'R' BB R'R'   

once to a few times to match all corners. then we can use No2 or 3 algorithms to fix the cube. 

click here to see how with details.

8. When we have imparity corners and edges like the below image; 

xR'UR' D2 RU'R' D2R2 x'

exactly opposite algorithm than in No.7. and the movement to edges also. here Clockwise rotation needs to fix the cube by using the above algorithm.

 

The Orange-Blue-Yellow corner is towards the Back-Left corner. the Red-Blie-Yellow corner to the Back-Right corner and the Green-Red-Yellow corner to the Front-Right corner...

9. When we have imparity corners like the below image; 

x' (RU'R'D) (RUR') (D'R) (UR'DRU'R'D') x

No double corners are matched. but it is easy to fix using the above-mentioned algorithm. Keep the yellow side up and rotate the whole cube along the x-axis anti-clockwise. 

The green-Red-Yellow corner piece and the Orange-Blue-Yellow move anti-clockwise and The Orange-Green-Yellow and the Blue-Red-Yellow pieces move clockwise when following the above algorithm.

10. When we have imparity corners and edges like the below image; 

        Following T-perm is found sometimes when We going to solve a Rubik's cube.

          (RUR'U'R') F (R2U'R'U') (RUR') F'

Here, two corners of the TOP-Front-Right and the TOP-Right-Back are swapped. and Edges of the Left and the right also swapped. 

We can swap the mentioned corners and edges simultaneously by doing the above algorithm (The yellow colour should be up when using the algorithm).

11. When we have imparity corners and edges like the below image;      

(R’ U’ F’) 

(R U R’ U’ R’)

 F 

(R2 U’ R’ U’ R U R’)

 U R 

Keep the solved edge, and corners to the left side then, imparity edges and corners are in the front and the back.

Then, do the above algorithm to fix the cube.

when doing the algorithm, the opposite edges of the Front and the back will be swapped. meanwhile, the front-Right corner and the back-right corner will be swapped(the front corner rotates anti-clockwise, back corner rotates clockwise).

12.a. When we have imparity corners and edges like the below image;  

J-permutation or J-perm

R U R' F’ R U R' U’ R’ F R2 U’ R’ U'

J perm is one of the PLL methods for an easy solution to a Rubik's cube. By using the above algorithm, we can fix the upper layer at once. Hold the cube as shown above image, and use the mentioned algorithm once. two imparity corners of the right side will be swapped and the edges of the front and right sides also swapped simultaneously. 

when the cube holds like above, we can see only the left side is fixed and one corner of each other side is not placed correctly but actually, only two corners of the right side and two edges of the front and the right sides are moved with the algorithm used.

’ U L’ U2 R U’ R’ U2 R L

 12. b. When we have imparity corners and edges like the below image; 

R’ U L’ U2 R U’ R’ U2 R L U'

This is the exact mirror image of the above 12. a when (vertically flipped image- only imparity corners and edges.) other colours are not much important. but the algorithm is not a mirror or opposite as used in 12. a

But there should be a slight difference when we going to use the algorithm, if the cube holds the above and used the algorithm, the cube will not be fixed, instead same type of imparity with different colours will be got.

So, If we want to fix this arrangement, the cube should be held like the image below.

Keep the all-matched colour to the Front side and use the algorithm to fix the cube at once.

13. a.When we have imparity corners and edges like the below image; 

There are two types of similar arrangements which are exactly opposite mirror images.

a. 

(R’ U2 R U2 R’)  F  (R U R’ U’ R’)  F’ (R2 U')

shows the back side corners are swapped and the left and the edge of the Front side also. let the cube-like above and follow the algorithm mentioned above we can fix the cube.

b.

This is the exact mirror image of part a.

Use the following algorithm to fix the cube.

 y R U’ R’U’ R U R D R’ U’ R D’ R’ U2 R’ U'

y - Rotate the whole cube along the y-axis clockwise once. 

and then, it will show like the below image;

If the cube does not rotate along the y-axis, the algorithm should be like this;

B U’ B’U’ B U B D B’ U’ B D’ B’ U2 B’ U'

R is replaced by B, if the cube rotates along the y-axis, B becomes the Right and it will easy to rotate the cube than if not.

14. When we have imparity corners and edges like the below image; 

 F R U’ R’ U’ R U R’ F’ R U R’ U’ R’ F R F'

Here, pieces are swapped just like a cross angled to the left. the corners of the Front-Right and the Back-Left are swapped.  and edges of the Left and the Back also swapped. also known as Y permutation or Y perm.

hold the cube as shown in the above image. then, Use the above algorithm to fix the cube. 

15. When we have imparity corners and edges like the below image; 

F'UF'U' y F'L'F2 U'F'  U F'L FL

or 

Turn the cube anti-clockwise and it will show like the below image

Then use the below algorithm to fix the cube

 R’ U R’ U’ y R’ F’ R2 U’ R’ U R’ F R F

or use the below algorithm

 R’ U R’ U’ B'R' B2U'B' UB' RBR

By keeping the cube as the second image shown, it is easier than the first one.

And R’ U R’ U’ y R’ F’ R2 U’ R’ U R’ F R F is a very easy algorithm to use than others.

16. When we have imparity corners and edges like the below image;

It is called a diagonal corner swap or N-permutation.

There are two main possibilities.

a If the Rubik's Cube TOP layer has corners and edges that are imparity like the above image, that is Edges of the Left and the Right, as well as corners of the Front-Left and the Back-Right are swapped.

R U R’ U R U R’ 

F’ R U R’ U’ R’ F 

R2 U’ R’ U2 R U’ R’

b. If the Rubik's Cube TOP layer has corners and edges that are imparity like the above image, that is Edges of the Left and the Right, and corners of the Front-Left and the Back-Right are swapped.

R’ U R U’ R’ 

F’ U’ F R U R’ F 

R’ F’ R U’ R

The above two are opposite mirror images of each other but the algorithms are not much different.

17. When we have imparity corners and edges like the below image;

Corners and edges are rotated simultaneously, also called G-Permutation.  There are a few different scenarios with this permutation. 

a. Corners need to move clockwise and edges need to move anti-clockwise. It is very hard to gather for the first time unless we have a good experience with these movements. 

R2 U R’ U R’ U’ R U’ R2 U’ D R’ U R D’

b. It is so similar to part a. The only difference is that the movement of the edges is exactly opposite to the above part a. and the algorithm is also the opposite of the above one.

 D R' U' R D' U R2 U R' U R U' R U' R2 

c.  It is another imparity permutation, in which is 3 corners and three edges move simultaneously but in opposite directions. Two Front side corners with the Back-Left corner moving Anti-clockwise with the front, the Left and the Back Edges moving clockwise.

R’ U’ R U D’ R2 U R’ U R U’ R U’ R2 D

d. Here we have another Permutation issue. Two Front side corners with the back-left corner which is misplaced with anti-clockwise movement. Also, the Front, the Left and the Right edges are also misplaced with clockwise rotation. 

Corners and edges move in opposite movements with the following algorithm in order to fix the cube simultaneously. 

  

R2 U’ R U’ R U R’ U R2 U D’ R U’ R’ D

R2 U’ R U’ R UR’ U R2 U D’ R U’ R’ D

e. Here, We have another situation that two backside corners with one Front-Left corner and the Front-the Back and the Left edges are misplaced with clockwise rotation of corners and anti-clockwise rotation of edges. R2 HereU’ R U’ R U R’ U R2 U D’ R U’ R’ D

R U R’ U’ D R2 U’ R U’ R’ U R’ U R2 D’

It is not so easy to get on the first try. need to focus and practice for better improvement of speeding to solve with this type of algorithm, otherwise, it will be more time-consuming than the basic method.

There are the most difficult algorithms to remember because of two movements at the same time. so, which algorithm that we need to use for fixing the cube, is just for luck when solving the cube.

18. When we have imparity corners and edges like the below image;

diagonal edge pairs swapped each other. The Front - Right and the Left-Back edges have been swapped. 

2M U 2M U M’ 2U 2M 2U M’ 2U

or 

2M' U 2M' U M’ 2U 2M' 2U M’ 2U

By using the above algorithm, it is so easy to fix the cube.

We can use both algorithms but I prefer the second one. Because it is easy to rotate the anti-clockwise rotation of M than the clockwise rotation.

There are so many algorithms mentioned here that are helping to resolve TOP layer corner and edge issues in a Rubik's Cube.