Permutation Algorithms for begginners

[mikatzz]

I know it's kinda small question for one thread but uhm,

I still haven't learn Permutation Algs really good and I'd just like to know the basic PLL algs, whit what you could solve the cube. I mean in the Collection of Permutation Algorithms there are 50 positions and 50 algs, but if i'm right, PLL can be solved whit 3-4 algs?

 

[cmhardw]

2 algs actually, the A and U PLL cases are sufficient to solve any PLL case. Use these rules below to ensure that you always can use only these two algs to solve the PLL case.

1) If you can form a corner three cycle by spinning the U layer of the cube you must do so.
2) If you cannot form a corner 3 cycle by spinning the U layer, then turn the U layer such that all 4 corners are in the incorrect locations.

After satisfying these rules you can now solve using only the A and U PLL algs, though you may need to use each one more than one time.

Chris

 

[AvGalen]

A-Perm: R' F R' B2 R F' R' B2 R2
U-Perm: R U' R U R U R U' R' U' R2 (or F2 U' L R' F2 R L' U' F2)

This is how to decide how to hold the cube before performing the A-Perms (alternative to Chris). I am assuming Up-Down = Yellow-Wite (light), Front-Back = Red-Orange (fire), Right-Left = Green-Blue (sea).
If all corners are not permuted, rotate the cube so two opposite colors are on the corners on the F-face (fire or sea), perform A-Perm, repeat if needed.

This is how to decide how to hold the cube before performing the A-Perms: A completed side goes on the back.

Example:
Scramble: L' U' L F2 R' D R U R2 D' R2 U' F2
Corner PLL 1: R' F R' B2 R F' R' B2 R2
Corner PLL 2: U R' F R' B2 R F' R' B2 R2
Edge PLL 1: U R U' R U R U R U' R' U' R2
Edge PLL 2: R U' R U R U R U' R' U' R2
AUF: U

 

[Kenneth]

Another approach is to learn to use "half PLL's".

Take these:

X = R L U2 R' L'
X' = R' L' U2 L' R'

Y = R U' L U2 R' U L'
Y' = L' U R' U2 L U' R

Now if you do for example : X + Y or X' + Y you will get a PLL. Then to get more out of this you can for example do : X (Fx) Y Where (Fx) is any U turn (U/U'/U2) and/or any cube orentation around the y-axis (y/y'/y2). Then you can for example do X (y) X' and solve the H-PLL.

Not all PLL's are solveable using this method but many. Do experiments and you will find the PLL's and also how to solve them =)

 

[Jilvin]

I think there's 3 algs that are needed for PLL. Basically you separate this step into two sections: the corners, and the edges.

1. Corners

No corners permuted: R' F R' B2 R F' R' B2 R2 (from AvGalens post, gets 2 corners paired up.)

2 corners permuted: put these corners facing away from you and perform the same algorithm (R' F R' B2 R F' R' B2 R2)

2. Edges:

4 edges out of place: do F2 U L R' F2 R L' U F2 (gets it so only 3 edges are out of place)

3 edges out of place (face solved side away from you)
a. Front edge needs to be in right face: F2 U' L R' F2 L' R U' F2
b. Front edge needs to be in left face: F2 U L R' F2 R L' U F2

Hope that clarifies some things.

EDIT: If you really want to go further, I have algorithms that solve the following:

No corners permuted: First, line it up so two opposite corners to their correct faces using a U turn, and perform the following:

F R U' R' U' R U' R' F' (R U R' U') R' F R F'

 

[David Pritts]

When people want to know the most minimal way of executing PLL, I always give them 2 algorithms.

1) To solve corners, use the T-permutation ((R U R' U') (R' F) (R2 U') (R' U' R U) (R' F'))

Look at all 4 sides and see if any side has 2 corners of the same color... for example, you might see that on the green side of the cube, both of the corners are orange. So, rotate the upper face so that those 2 orange pieces are on the orange side (ie, solve them). Then either 2 things can happen: (1) The other 2 corners on the top face will need to be switched, which the T-permutation will do (just hold the cube such that the 2 corners needing switching are on the right side, on the top).) OR (2) All 4 corners will be solved already.

If there are no 2 corners of the same color on any side, execute a T-permutation and then there will be. Then, one more T-perm will fix the remaining 2 corners.

2) To solve the edges, use a 3-cycle. ((R2 U) (R U R' U') (R' U') (R' U R'))
This rotates the front 3 edges (ie, the back one remains in place) clockwise. If these 3 pieces need to be rotated counter-clockwise, execute the algorithm twice (or you could do the inverse, but this is just easier for a minimalistic solution).

If all 4 edges are wrong, execute the 3-cycle above, and the result will be that you are now one more 3-cycle from being solved... so follow the above directions.

David

 

[David Pritts]

btw, Kenneth.. that looks cool

 

[David Pritts]

Also, mikatzz: the link you posted (entitled "Collection of Permutation Algorithms") is not actually a collection of permutation algorithms(PLL), but a collection of orientation algorithms (OLL).

In total, there are only 21 LL permutations.

 

[AvGalen]

Jilvin, you really only need 2 PLL algs

3 edges out of place (face solved side away from you)
a. Front edge needs to be in right face: F2 U' L R' F2 L' R U' F2
b. Front edge needs to be in left face: F2 U L R' F2 R L' U F2

You only need one of those and perform it twice (but I would recommend learning both anyway)

 

[alltooamorous]

I have a video up that shows beginner's PLL. It basically teaches you to limit your last layer by using the A Perm (Corner switcher) so you will only have edges out of place. From there you can use the U perms to solve the cube. If you are interested, the link is in my signature.