by Alberto De Bortoli @albertodebo github.com/albertodebortoli
v0.2-beta
25th January 2013
Here I explain my technique to solve the Rubik's Cube. I consider it the simplest, easiest and quickest way to learn-how-to-solve a cube. Mastering this technique you'll be able to solve a cube in c.a. 1 minute and 40 seconds. Here is a video where I made it in 1:45.5. Not too good but still decent to impress someone. Practice and you'll master it. Follow rigorously every single word in this guide, if you miss a sentence or a step you're not going to do it and you'll give up shortly.
--- --- ---
| 1y| 2y| 3y|
--- --- ---
| 4y| 5y| 6y|
--- --- ---
| 7y| 8y| 9y|
--- --- ---
--- --- --- --- --- --- --- --- --- --- --- ---
| 1b| 2b| 3b|| 1r| 2r| 3r|| 1g| 2g| 3g|| 1o| 2o| 3o|
--- --- --- --- --- --- --- --- --- --- --- ---
| 4b| 5b| 6b|| 4r| 5r| 6r|| 4g| 5g| 6g|| 4o| 5o| 6o|
--- --- --- --- --- --- --- --- --- --- --- ---
| 7b| 8b| 9b|| 7r| 8r| 9r|| 7g| 8g| 9g|| 7o| 8o| 9o|
--- --- --- --- --- --- --- --- --- --- --- ---
--- --- ---
| 1w| 2w| 3w|
--- --- ---
| 4w| 5w| 6w|
--- --- ---
| 7w| 8w| 9w|
--- --- ---
fig. 1: This is the map of a cube. y = yellow, r = red, b = blue, g = green, w = white, o = orange.
We name pivot face the face of the cube to use as reference for the sequence of moves we are going to apply. You should keep this face always in front of your eyes while learning.
Here are all the available moves that can be applied to the cube. Consider the red face as pivot.
- RIGHT_down: move
3r-6r-9rto3w-6w-9w - RIGHT_up: move
3r-6r-9rto3y-6y-9y - LEFT_down: move
1r-4r-7rto1w-4w-7w - LEFT_up: move
1r-4r-7rto1y-4y-7y - MID_down: move
2r-5r-8rto2w-5w-8w - MID_up: move
2r-5r-8rto2y-5y-8y - UP_left: move
1r-2r-3rto1b-2b-3b - UP_right: move
1r-2r-3rto1g-2g-3g - DOWN_left: move
7r-8r-9rto7b-8b-9b - DOWN_right: move
7r-8r-9rto7g-8g-9g - MID_left: move
4r-5r-6rto4b-5b-6b - MID_right: move
4r-5r-6rto4g-5g-6g - ROT_right: move
1r-2r-3rto3r-6r-9r - ROT_left: move
1r-2r-3rto7r-4r-1r
#Algorithm
- Complete a face (colors on the edges must be correct)
- Fix centers on each face (max 2 moves)
- Fix the angles of the face opposite to the completed one
- Fix the colors of angles of the face opposite to the completed one
- Fix the remaining edges
Easy, just a little practice. The obtained face is the pivot.
Trivial.
If the angles of the face opposite to the pivot face are not in the correct position regardless of the colors, swaps are needed between 7b-7w-9o, 9w-9g-7o, 3y-3g-1o, 1b-1y-3o.
Moves:
-
comboAngles_right: RIGHT_down, DOWN_right, RIGHT_up, DOWN_right, ROT_right, DOWN_left, ROT_left
-
comboAngles_left: LEFT_down, DOWN_left, LEFT_up, DOWN_left, ROT_left, DOWN_right, ROT_right
Algorithm:
-
put the former pivot face face up (in the example pivot face goes from red to white): simply rotate the cube to change the pivot face, no moves are needed;
-
repeat comboAngles_right (or the symmetric one comboAngles_left) as long as the angles are put in the correct places regardless of the colors.
N.B. These moves don't break the former pivot face.
Let's give weights to the angles of the face opposite to the completed one.
- 0: if the angle has colors already in place
- 1left: if the angle has colors shifted on the right by 1
- 1right: if the angle has colors shifted on the left by 1
Moves:
-
comboColors_right: LEFT_down, DOWN_right, LEFT_up, DOWN_right, LEFT_down, DOWN_left (x2) (o DOWN_right x2), LEFT_up, DOWN_left (x2) (or DOWN_right x2);
-
comboColors_left: RIGHT_down, DOWN_left, RIGHT_up, DOWN_left, RIGHT_down, DOWN_right (x2) (o DOWN_left x2), RIGHT_up, DOWN_right (x2) (or DOWN_left x2)
Examples given bottom right angle 7b-7w-9o in the pivot face. The final state will be:
angle weight after cc_right after cc_left
--------- ------- --------------- --------------
7b-7w-9o 0 0 1right
9w-9g-7o 1right 0 1left
3g-3y-1o 1right 0 1left
1b-1y-3o 1right 0 1right
angle weight after cc_right after cc_left
--------- --------- --------------- --------------
7b-7w-9o 0 0 1right
9w-9g-7o 0 1left 1right
3g-3y-1o 1right 0 1left
1b-1y-3o 1left 1right 1left
In every case an angle remains unaltered.
Algorithm:
-
put the former pivot face face up (in the example pivot face goes from red to white): simply rotate the cube to change the pivot face, no moves are needed;
-
apply comboColors_right (or the symmetric one comboColors_left) as long as the angles have weights equal to 0.
comboColors_right and comboColors_left are symmetric, both keep an angle unaltered and increase or decrease the weight of the other 3 angles by 1 (from 1right to 1left or from 1left to 1right).
This is tough, keep practicing it.
At this point only the edges need to be placed in the correct positions. We are going to do it moving the edges 3 by 3 clockwise or counterclockwise. We will use combinations of both comboColors_right and comboColors_left.
Example: Given a solved face, rotating 8b-4b-2b, the starting pivot will be as in fig. 2.
--- --- --- --- --- --- --- --- ---
| 1b| 2b| 3b| | 7b| 4b| 1b| | 7o| 4o| 1o|
--- --- --- --- --- --- --- --- ---
| 4b| 5b| 6b| --> | 8b| 5b| 2b| --> | 8o| 5o| 2o|
--- --- --- --- --- --- --- --- ---
| 7b| 8b| 9b| | 9b| 6b| 3b| | 9o| 6o| 3o|
--- --- --- --- --- --- --- --- ---
fig. 2: Simply rotate the cube to change the pivot face, no moves are needed.
Optimal state: given 3 edges to fix, the application of the following algorithm fixes all of them
Sub-optimal state: given 3 edges to fix, the application of the following algorithm fixes 1 or 2 of them
Now we need to move edges clockwise.
Algorithm to move the edges clockwise:
- apply all the moves in comboColors_right but the last 2;
- rotate the cube on the left, no moves are necessary;
- apply all the moves in comboColors_left but the last 2.
Algorithm to move the edges counterclockwise:
- apply all the moves in comboColors_left but the last 2;
- rotate the cube on the right, no moves are necessary;
- apply all the moves in comboColors_right but the last 2.
Hard thing here is that it is likely not to have optimal state that allow to fix edges simply using the algorithm described above, so you might want to apply some pre-moves to reach an optimal or sub-optimal state required to apply the algorithm.
This is even more tough than the previous step.
Swapping centers and something more...
Preconditions:
- start with a solved cube
- pick up a move in: MID_down, MID_up, MID_left or MID_right
- pick up a direction between left or right.
Algorithm:
- apply the chosen move on the pivot face
- turn around the cube by 90 degrees in the chosen direction keeping the pivot face in front
- repeat 1) and 2) three times
- RIGHT_DOWN (x2) e DOWN_right (x2)
Solution: c'mon! Make that brain work!