This is my attempt at a simple system for solving a Rubik’s cube blindfolded. The goals are: minimal and easy memorization, few algorithms, easy setup moves, little recalculation, and few rotations of the entire cube.

A blindfold solve has 2 phases, memorization and execution. Each of those phases consists of 4 sub-phases. Memorization consists of memorizing the orientation of the corners, the permutation of the corners, the orientation of the edges and the permutation of the edges. Execution consists of fixing each of those sub-problems.

Determining Orientation of the corners

Orientation means fixing the corners so that they are twisted correctly, relative to the solved puzzle.

There are 8 corners. They are numbered counter-clockwise starting on the up layer with the front left corner, which is corner 1.

1 UFL (up front left)

2 UFR

3 UBR

4 UBL

5 DFL

6 DFR

7 DBR

8 DBL

I start with White as Up and Red as Front.

Each of the eight corners is assigned a value for their orientation. 0 means they are correctly oriented (in my color scheme, that means the they have white or yellow facing up on the up layer or down on the down layer.) 1 means they are a clockwise turn from oriented. 2 means they are a counter-clockwise turn from oriented (or 2 clockwise turns from oriented.)

I represent the orientation of the corners in my mind as two groups of 4 numbers, like (1210) (0020), the first set representing the up layer and the second representing the down layer.

Determining Permutation of the corners

Permutation means moving the pieces into their correct positions, relative to the solved puzzle. The basic idea, for both corners and edges, is to start with a piece that is not in its correct place and put it into the correct place. Of course, there was a piece in that place, so you put that one where it belongs. That piece has then displaced another piece, so that needs to be taken care of. This continues until the pieces are all where they belong. Sometimes you will find that when you put a piece into place, the piece it displaces goes into its correct position. This means you are at the end of a cycle. In my system, you may also reach the end of a cycle when you start a cycle with a particular piece, and return to that piece, after following the displacements. When a cycle is completed, you may pick any piece that is not in the correct position to start the next cycle. I move the beginning cubie of the next cycle into position with setup moves (important!). If there are no more pieces in the wrong places, you have finished determining the permutation.

I memorize permutations by cycles. My "target" position is UBR. I look at the cubie at UBR and determine where the cubie there belongs, ultimately. I memorize the number, from the chart above, for that position.

I then go to that position and look at the cubie there, and memorize the number for that position. If one of the cubes belongs in UBR, I stop that cycle (remembering it) and then start a new cycle based on putting some other cubie, like UFR into the "target"...then I continue to build another cycle. That cycle should end with the same number it started with. A cycle might look like: (7 4) (2 5 8 6 1 2)...the first cycle had UBR in position after 4, so I moved the cube in position 2 into UBR and continued.

Determining Orientation of the edges

I number the edges:

1 UF

2 UR

3 UB

4 UL

5 FL

6 FR

7 BR

8 BL

9 DF

10 DR

11 DB

12 DL

I examine each position, in order and determine if it is oriented corrected. If it isn’t, I remember its position number.

The way to determine if it is oriented correctly is:

There should be an even number of edge pieces that need orienting.

Determining Permutation of the edges

My target position for edge permutations is UR. I examine the cubie in UR and determine where it belongs and remember that number. I continue the process, just as I did for corners. If I find the cubie that belongs in the target, I stop that cycle and begin a new cycle by putting another cubie (like UL) into the target (with setup moves.)

I finish that cycle with the number that chose to replace UR.

Note:  Setup moves in all cases are selected so that the cube the rest of the cube

remains preserved after you complete your operations.  There may be other

setup moves possible, but make sure that you don't edge up twisting corners

when you are trying to setup edge permutations...etc.

Now we are ready to solve the cube.

We need to do the two orientation phases first.

Orienting edges

I use "Rubik’s maneuver". I put edges that need to be flipped into UB... and then do RM. Parity will be preserved when I am finished.

RM = M U M U M U2 M’ U M’ U M’ U2

M means  to move the "slice" that is between L and R toward you.

See speedcubing.com for help with notation.

Setup moves will be required to bring each piece to UB. You will setup, do RM, invert setup.

Note: we do not orient edge 1 (UF). When we complete the orienting the others,

it will flipped correctly.

The setup moves for edge orientation:

position 1   no setup move needed

                2  R B

                3  no move needed

                4  L' B'

                5  d' B'      (d' means bottom two layers counterclockwise)

                6   d B

                7   B

               8   B'

               9   D2 B2

             10  D B2

             11  B2

             12  D' B2

  To undo the setup moves, you simply reverse everything, for example, if the setup move is d' B', you must undo it with B d.

Orienting Corners

Each corner that needs orienting will be brought with setup moves to UFR. If its orientation is 1,

we will do the "out" orientation

Out= L D R' D’ L' D R D’ (turn cube 90 degrees clockwise or Z) R' D’ L D R D’ L' D (turn 90 CCW or Z')

If the orientation is 2, do Out twice.

or do: In= L U' F2 U F2 U L U' L2 D F2 D' F2 once

The setup moves for orienting corners are:

     Position 1- no setup move required

                     2- no seutp move required

                     3- R'

                    4- B' R'

                    5- D R

                    6- R

                    7- R2

                    8- D' R2

 Note: we do not orient position 1.  When we finish the others, it will be oriented correctly. 

Permuting Edges

Follow the cycle that was memorized. Put the first number of the cycle into UL (this requires care in setup moves, which will be discussed later.) Do the T permutation.

T permutation = (R U R’ U’) (R’ F R2 U’ R’ U’ R U) (R’ F’)

Setup moves for each edge:

1 UF R2 U R2

2 UR ----

3 UB R2 U’ R2

4 UL

5 FL d' L (d' means to move the bottom two layers counterclockwise)

6 FR d' L’

7 BR d L

8 BL d L’

9 FD D' L2

10 DR D2 L2

11 DB D L2

12 DL L2

Permuting Corners

The T permutation is also used for Permuting Corners. The T permutation swaps UL and UR edges while also swapping the UFR and UBR corners.

I permute corners before I permute edges. Each time I do a T perm to fix the corners, the two edges swap. If I have to do an even number of T perms to permute corners, the edges will be back in the right place at the end of the permute corner phase.  If there is an odd number of T perms during the corner phase, I  do one more T perm to swap the edges back and fix parity. Then I go on and do the edges.

The idea is to go through the memorized cycle and put the piece that is in the memorized position in UFR and then do the T permutation. That places it in UBR and then, after the next one is in position 2 ...and the T is done, it will be where it belongs.

Setup moves for the corners:

I solve in the following order: Edge Orientation, Corner Orientation, Corner Permutation, fix Parity (if necessary), Edge Permutation.

Parity fix- if my Corner Permutation takes an odd number of T perms, I do one more to fix parity (see note above)

An easy scramble solved, step by step:

F' B' D2 F' D R D' U' L2 R' D L' B' L' B2 D2 L' B2 R' B' L B D' B R'

(thanks to Wynne Chyou for the images)

I hold Red in front, White on top. All edges are flipped properly on Up Layer. Edge 6 is flipped on layer two (green-red edge).

Edge 12 (blue-yellow) is flipped on down layer. I remember 6 12.

I look at corner orientation. On the top layer, I see that everything is correct except Corner 4 (white-orange-green)...it is turned clockwise. I remember (0 0 0 1). On the down layer, I see Corner 5 (white-red-blue) is twisted counterclockwise, which is 2.

Corner 6 (white-green-red) is clockwise, which is 1. Corner 7 (yellow-blue-orange) is clockwise twisted, which is 1. Corner 8

(yellow-blue-red) is also twisted clockwise, which is 1. The down layer is (2111).

Corner orientation is (0001) (2111). I typically do not bother to remember the corner in the position 1 (UFL). When I twist all of the other corners, it will be correct.

On to the Corner Permutation. The corner in UBR is the one that belongs in position 8 (DBL). Remember that. Now look at position 8.

The corner there belongs in position 6 (DFR). Remember 86. Look at position 6. It contains the corner that belongs in position 1 (UFL).

Remember 861. Go to position 1. It contains the corner that belongs in the target position (UBR). I ignore that...I do not remember 3...instead, I pick the handiest other corner, which is 2. Remember 2. So far, we have 8612. I examine position 2, and it contains the corner that belongs in position 5. Remember 5. Position 5 contains the corner that belongs in Position 2. Remember 2.

The Corner Permutation is 861252. I remember them 2 at a time. 86 12 52...an even number of digits (6), so there is no need for a parity fix.

Notice that whenever a cycle is complete (which means I get to the position 2 corner, or I have repeated a number in the current cycle (like 2 in this example), that cycle is finished. In this example, corners 4 and 7 are already in the correct place, so we did not need to cycle them.

Now we figure out the Edge Permutation. Examine Edge 2 (UR). It contains the edge which belongs in position 3 (UB). Remember 3.

Go to position 3. It contains Red-White, which belongs in position 1 (UF). Remember 1. Go to position 1. Position 1 contains the edge for position 4. Remember 4. The edge in position 4 belongs in 12.

Remember 12. The edge in 12 belongs in 10. Remember 10. Now we see that the edge in 10 is good old number 2 (don't remember him). That means that cycle is over. At this point we can pick any edge that needs cycling, and hasn't been cycled. In this case, that could be edge 5 or edge 6. Let's pick 6. Remember 6. The edge in position 6 belongs in position 5. Remember 5. The edge in 5 belongs in 6. Remember 6. That's the end of the second cycle (because we repeated 6). So, the edge permutation is:

3 1 4 12 10 6 5 6

Notice that this is an easy scramble...4 edges are in their correct positions: 7,8,9,11.

The entire set to be memorized is:

6 12

(0001)(2111)

86 12 52

3 1 4 12 10 6 5 6

I will discuss the mnemonics that I use later.

Now we are ready to put on the blindfold and solve the cube.

First the edge orientation:

Setup for 6: d B (remember d means turn the bottom 2 layers clockwise).

Do RM (from above), that is M U’ M U’ M U2 M’ U’ M’ U’ M’ U2

Undo the setup: B' d' (6 should be oriented correctly)

Setup for 12: D' B2

Do RM

Undo setup: B2 D

Notice again that I ignored the state of the edge in position 1 (UF). It takes care of itself.

Moving on to corner orientation:

(0001)(2111)

I need to twist the corner in position 4.

Setup for 4: B' R' brings it to UFR

Do the algorithm Out (from above)...L D R' D’ L' D R D’ (turn cube 90 degrees clockwise) R D’ L D R’ D’ L' D (turn 90 CCW)

Undo the setup: R B

Twist the corner in position 5.

Setup for 5: D R brings it to UFR

Do the algorithm In (from above)...L U' F2 U F2 U L U' L2 D F2 D' F2 ...or you can do Out twice instead.

Undo the setup: R' D'

Twist the corner in position 6.

Setup for 6: R

Do algorithm Out (from above).

Undo the setup: R'

Twist the corner in position 7.

Setup for 7: R2

Do algorithm Out (from above).

Undo the setup: R2

Twist the corner in position 8.

Setup for 8: D' R2

Do algorithm Out (from above)

Undo the setup: R2 D

Everything is oriented.

Time to permute corners. Remember that it was 86 12 52.

Corner 8 is at UBR, but we want it to be in 8! So we will bring position 8 up to UFR. Then we will do a T permutation to swap UBR and UFR. Then we will undo the setup move and corner 8 will go back to position 8. Like this:

Put Corner 8 in place.

Setup position 8 (bring it to UFR): D F2

T permutation. that is: (R U R’ U’) (R’ F R2 U’ R’ U’ R U) (R’ F’)

Undo setup: F2 D'

Put Corner 6 in place.

Setup position 6 : D' F2

T permutation.

Undo setup: F2 D

Put Corner 1 in place.

Setup position 1: F2 D' F2

T permutation.

Undo setup: F2 D F2

Put Corner 5 into UBR.

(it is in position 2 when the cycle ended)

T permutation.

Put Corner 2 into UBR, while Corner 5 goes into position.

Setup move: F2

T Permutation.

Undo setup: F2

Put Corner 2 into position.

T Permutation.

Corners are all in the correct positions. If I had done an odd number of T perms, I would have done one more to fix parity, but that didn't happen.

Now the endgame....permute the edges. The process is the same as the corners.

Remember: 3 1 4 12 10 6 5 6

Edge 3 (White-Orange) is in our magic position (UR or 2). We will put the edge that is now in position 3 (White-Red) into position 4 (UL, that is the swap spot), and swap positions 3 and 4.

Then the setup move will be undone and the white-orange edge will be in its home position.

Fix Edge 3:

Setup move to put position 3 into position for swap: R2 U' R2

T permutation.

Undo Setup: R2 U R2

Fix Edge 1:

Setup move: R2 U R2

T permutation.

Undo Setup: R2 U' R2

Fix Edge 4:

T permutation. (it is already in the swap position)

Fix Edge 12:

Setup move: L2

T permutation.

Undo setup: L2

Fix Edge 10:

Setup move: D2 L2

T permutation.

Undo setup: L2 D2

At this point the edge that belongs in position 2 (UR) is in position. That means a cycle is complete, but we know from our memorization that there is more work

to be done...we just continue our process...by the memorized numbers.

Swap edge that is at position 6 into UR:

Setup move: d' L'

T permutation.

Undo setup: L d

Fix Edge 5:

Setup move: d' L

T permutation.

Undo setup: L' d

Fix Edge 6:

Setup move: d' L'

T permutation.

Undo setup: L d

You should take off your blindfold and find a solved cube (unless I have a bug in my document)...

Memorization: I memorize corner orientation, edge orientation, and corner permutation as numbers. For the edge permutation, I encode it into a sentence.

Each position is a letter at the beginning of a word.

I use the following letters:

1 G

2 -

3 P

4 R

5 T

6 L

7 S

8 B

9 D

10 M

11 C

12 N

Why those letters? They are related to people in certain rooms in the building in which I work. For example, Sarah is in the room ending in 7.

So, the edge permutation in the example is (P G R N M) (L T L) and I make a sentence as I go:

Peter Green reads no mathematics. Len thinks logically.

I allow the insertion of words that begin with vowels to help with sentence construction...I ignore them, of course, when I am executing the solve.

A simple, meaningful sentence makes memorization easy for me. I sometimes lock into themes, like people and the school subjects that they are taking.

Final comments for now:

This system, because it uses 2-cycles, will not allow you to break the world record for solving blindfolded. I would say this is analogous to using a plain vanilla layer method to solve the 3x3x3 normally. It is a good start, but there are many ways to improve and become faster.

I have solved a non-lucky cube in 4:46 using just this method...and can average about 7 minutes. The method can easily be modified to speed up the solution times. For example, you could orient edges two at a time by bringing edges to the UF position with setup moves. You can also orient corners by bringing corners that need twisting to UFL. The method above does twist UFL, but it is always the same UFL.

You can also easily modify permutations of corners and edges into a 3-cycle approach, when you are ready. With corners you can setup corners into UFL and 3-cycle from UBR to UFR to UFL. With edges you can setup an edge into UF and 3-cycle from UR to UL to UF.

Links to my other pages (not related to cubing):

http://home.earthlink.net/~bmcgaugh/eloiq.htm

http://home.earthlink.net/~bmcgaugh/thinkf.htm

http://home.earthlink.net/~bmcgaugh/pred3.htm

Revision log:

September 2, 2005-  added setup moves for orientations

September 5, 2005- slight algorithm change.

April 15, 2007- fixed problem with corner setup moves.