## 3x3x3 Solution

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## Permutation Cases

This is the last step of my solution and it occurs right after all the pieces have been oriented correctly. I have included a notation to denote the finger tricks that I use for each of these moves. Each set of moves inside a pair of parenthesis is a finger trick routine that can be done at an accelerated pace using your fingers. Since there are fewer cases for this step I am going to try to include videos of me doing all of them. I only have some of the videos up but this should give you an idea of how I do these finger tricks, and it should help you see how I might do some of the orientations as well. All of the pictures of the cube positions are from Jessica Fridrich's page, though I have edited some of them. Please keep in mind that all of these finger trick routines I figured out to fit my hands, so if they feel uncomfortable or awkward then try to figure out a way you can do the moves that suits you better. Try to use this page more as a learning tool than to directly copy how I do it.

### The Tricks

Keep in mind that a lot of time I twist the cube to get the cube into a better position during some of these finger tricks. Keep that in mind if you run into one that does not fit your hands well, perhaps twisting the cube and doing the trick from another angle will help

Here is a key to the notation I'll be using. Note, do each of these turns as if you are looking directly at the face you are turning.

Clockwise Turns Counter-clockwise Turns Double Turns
 R = Right face clockwise L = Left face clockwise F = Front face clockwise B = Back face clockwise U = Up (top) face clockwise D = Down (bottom) face clockwise
 R' = Right face counter-clockwise L' = Left face counter-clockwise F' = Front face counter-clockwise B' = Back face counter-clockwise U' = Up (top) face counter-clockwise D' = Down (bottom) face counter-clockwise
 R² = Right face twice L² = Left face twice F² = Front face twice B² = Back face twice U² = Up (top) face twice D² = Down (bottom) face twice
I've updated my p13 finger trick (the perm at the bottom of the page) which used to be my slowest algorithm out of all 53. The new trick is a bit complicated to explain just using notation so I have included cube rotation notation. Below is a table that explains cube rotations simply. There are three cube rotation moves, x, y, and z. When you see one of these moves simply turn the entire cube the same direction you would turn the corresponding face in the table below.

Cube
Rotations
 x = R y = U z = F
For all of these moves the permutation picture is what you should have on the U face unless otherwise noted. The second to last permutation on this page you must be able to do backwards. This is because there are 4 ways that you can have that particular case come up: normal as in the picture, backwards (flip all arrows to point in the opposite direction) and reflections of both of those. I also strongly recommend knowing the moves that I give you the backwards move for you. In these cases I also recommend knowing the reflections for both the normal and backwards moves. Doing this will help you to complete these cases in quicker times no matter how they come up.

### Case

1) R² U F B' R² F' B U R²
 no video avail.
I don't actually use any finger tricks for this move. With a little practice and some dexterity this move can go fairly quickly (2 seconds or less).
1) R² U' F B' R² F' B U' R²
 no video avail.
I don't actually use any finger tricks for this move. With a little practice and some dexterity this move can go fairly quickly (2 seconds or less).
1) (R² B²) (R F R') (B² R F' R)
 Video: slow fast
It takes a while to get used to (B² R F' R) but practice it slowly and you're hands will start to get used to it.
1) (R' F R') B² (R F' R') (B² R²)
 no video avail.
This one is pretty straight-forward
1) ( (R B') (R' B) ) (F R' F B') (R' B R) (F² U)
 no video avail.
This move goes very quickly and it looks cool if you do it at about half speed. View the first two triggers as one
motion, it will go faster that way.
1) R² (B² F²) (L² D') R² (B² F²) (L² U)
 no video avail.
If you start with the 3rd layer corners not aligned with their correct positions the last U will change. Practice with this some to get used to it. For the (B² F²) hold the cube with your base hand fingers only on the middle slice between F and B and turn both faces at the same time with your other hand.
1) (F R' F') L (F R F') (L² B') (R B) (L B') (R' B)
 no video avail.
1) (U' L²) (D F²) (D' L²) B² (D' R²) (D B²)
 no video avail.
Throughout this move I am slowly rotating the cube counter-clockwise as viewed from the top face.
1) (R' U R' U') (B' D B' D' B²) (R' B' R B R)
 Video: slow fast
1) (L² F' L) D² (R' B R) D² L B (L F L' B')
 no video avail.
It can be difficult to include the last B' in the last trigger sometimes but I always try to.
1) U' B' U² B U' (R' F R) B' (R' F' R) (U' B)
 no video avail.
The first U' is to correct for the last layer being out of position after the rest of the algorithm. It may not always be necessary to do this move.
1) B² (L U L') B² (R D' R D R²)
 Video: slow fast
To get the full effect of the last trigger turn the cube upside down just before you get to it (see the video). The
last trigger can be performed extremely quickly (at times less than 0.5 second).
1) R B U' (B' R D) B' (L' B' L) B² (D' R²)
 no video avail.
The D' in (B' R D') is somewhat difficult to perform quickly (compared with the ease of most triggers) but I always try to use it in the trigger anyway.
1) (F U F') L² D' ( (B U') (B' U B') ) (D L²)
 no video avail.
Treat the two middle triggers as one hand motion. It is essential that you know the reflection for this move.
1) L² D' (B U' B U B') (D L²) (F U' F')
 no video avail.
The first trigger goes pretty quickly. It is essential that you know the reflection for this move.
1) (R U' R2) (F2 U' R F2 R') (U F2) (R2 U R') (U')
1a) (R U' R2) (F2 U' R F2 R') (x2 y) (D R2) y (r2 U L') (U')

2) (L D') (B L') D² (R F' R') (D² L²) (B') (L' D L')
 Video#2: slow fast
(4-23-03)
I just recently figured out the finger trick to #1 (Thanks Justin Vining for the move). The last U' should be treated as an optional move. #1a lists the move noting where I do cube rotations. In order to do the 5 move trigger, turn the first F2 turn clockwise. Also, begin to do the rotation (x2 y) during the 5 move trigger. When doing r2 in the last trigger (r2 U L') in #1a try to turn both the L face and r at the same time, where r means to turn R as well as the middle face at the same time.
#2 is my old way of doing this move which is ridiculously slow (at least for my hands). See the video for further clarification on that move.
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