How to Solve the Rubik's Cube Blindfolded:
How to Solve the Rubik's Cube Blindfolded. v1.01
by: Caleb Lau, Mitchell Stern, and Henry Liu
Topics Covered:
Introduction
Description of Method
Step 1: Orientation of the Corner Pieces
Step 2: Permutation of the Corner Pieces
Step 3: Identifying Permutation Parity and Fixing It
Step 4: Orientation and Permutation of Edge Pieces Simultaneously
Memorization Techniques
Complete Example Solve
Conclusion and Credits
Introduction:
Despite what many people might think, blindfold cubing is actually very simple to learn. There are two types of blindfold cubing. One of which where both memorization and execution are timed, and the other which only execution is timed. Only the first type, where it is crucial to both memorize and execute quickly, will be discussed in this article.
As you can see, making any single move on a 3x3x3 moves many pieces. This shows that a normal solving method is impractical for blindfold cubing, as the cuber would have to update their memory after each move. The theory behind blindfold cubing is to only use algorithms which affect a few pieces on the cube, and have no side effects, such as this one:
Another important part of blindfold cubing is setup moves. For example, let's say you would like to flip the FL and UB edges using the above algorithm (which flips the UF and UB edges). All you have to do is F, the algorithm, then the inverse of your setup move, F'. Even though the cube gets messed up during the setup move, F, everything is returned to its original position (besides the pieces affected by the algorithm) after performing the inverse of the setup move, F'.
Once you understand these two fundamental concepts of blindfold cubing, you are ready to begin.
Description of Method:
The two major methods used for solving the cube blindfolded are 3-cycle and piece-by-piece (a common one is Pochmann's method). These methods both yield a very high potential for speed. Although both methods have their pros and cons, in the end, the choice of which method to use is made mainly based on personal preference.
Because of this, we wanted to combine the methods and create a hybrid that would be both easy to memorize and very quick to execute. With this method, we use a 3-cycle method for the corner pieces and a piece-by-piece Pochmann's method for the edges. Parity is fixed with a modified piece-by-piece method.
With the hybrid method, we believe that extremely fast times can be achieved. This is because it reduces the time needed to memorize the cube while also making the edge orientation and permutation extremely easy to execute (these are usually the longest steps with a 3-cycle approach). Corners are not that hard to memorize either.
One thing to understand before even starting out with the guide is color scheme. Most cubers have a standard color scheme that they use for solving the cube blindfolded. This color scheme is consistent and is used for all solves. For example, many cubers solved with Yellow on top and green in the front. They will always memorize and execute holding the cube this way. This makes the cube much easier to memorize and it reduces processing (thinking) time. It is recommended that you find a color scheme that works for you and stick with it. It also helps if you choose one branched off how you solve a cube normally (i.e. If you solve with a white cross on the bottom, then you can choose a color scheme such as Yellow top, and Blue front.)
Let's get started!
(Note: This guide will assume that you know the basics of PLL algorithms used in the well-known Fridrich method.)
Step 1: Orientation of the Corner Pieces:
This is an easy step to both memorize and execute.
Determining Orientation
To determine the orientation of a corner at UBR, consider the following:
1) If the U/D sticker of the corner is on U, the corner is correctly oriented.
2) If the U/D sticker of the corner is on B, the corner is twisted clockwise.
3) If the U/D sticker of the corner is on R, the corner is twisted counterclockwise.
Finding a corner's orientation should be intuitive, and after a while, you should be able to determine any corner on the cube's orientation without having to rotate the cube.
The Algorithms
Using 2 simple 8-move algorithms, you can orient 2, 3, or 4 corners on U at the same time.
These algorithms are:
The first algorithm twists the UBR corner counter-clockwise, and the second algorithm twists the UBR corner clockwise.
Notice that after executing either algorithm, only the UBR corner of the U layer has changed, but the rest of the cube is messed up.
Using these algorithms, and simple conjugation with setup moves, you can orient 2, 3, or 4 corners on the U face.
(Note: In order to preserve orientation of corners (before or after you have oriented them), you are restricted to R2, L2, F2, B2, U, U', U2, D, D', and D2 (only U and D face can have quarter turns) when performing setup moves. Then you are allowed to execute the algorithms. In order to undo the original setup move (Setdown), perform the inverse of the setup move(s).
Setup and Setdown Example:
Setup moves: y R D2 L'
Setdown moves: L D2 R' y'
An Example and The General Method
For example, let's say the UBR corner is twisted counter-clockwise, and the DBL corner is twisted clockwise.
1) First we would place both corners on U by using the setup move L2.
2) Orient the UBR corner using the second algorithm.
3) Now, move the UFL corner, which is twisted clockwise, to the UBR slot using U2.
4) Orient that corner using the first algorithm.
5) Now we have to do U2 to restore the rest of the U layer.
6) Undo the original setup move of L2 by doing L2.
As you can see, the general method of corner orientation is:
1) Get the corners you wish to orient onto either U or D using setup moves.
2) Do the appropriate cube rotation(s) so that one of the incorrectly oriented corners is at UBR, and all of the corners you would like to orient are now on U.
3) Orient the UBR corner using one of the algorithms previously mentioned in this section.
4) Turn U so another incorrectly oriented corner is in the UBR slot.
5) Repeat steps 3 and 4 as many times as needed.
6) Turn U back to its original position.
7) Undo the setup rotations from Step 2.
8) Undo the setup moves from Step 1.
Note that when orienting corners, you should orient in pairs of clockwise/counter-clockwise (1 or 2 corner(s) of each orientation), or orient in triples of the same orientation (i.e. 3 clockwise, or 3 counter-clockwise). Any other pair or triple will result in a completely scrambled cube after orienting the corners.
An Alternate Method
Alternatively, you can simply orient corners in pairs. The advantage of this method is that the cube does not get messed up after using an algorithm.
These are the two algorithms necessary for this method.
The first algorithm twists the RFU corner clockwise, and the RBU corner counter-clockwise.
The second algorithm twists the RFU corner counter-clockwise, and the RBU corner clockwise.
With these 2 algorithms and simple setup moves, you can easily orient all of the corners pairs at a time.
However, there is one tricky case* when using this method:
With this method, it may be hard to orient three pieces at a time. For example, RFU, RBU, and LBU are all twisted counter-clockwise.
1) Perform the first algorithm from above.
2) Do U to get the other 2 incorrectly oriented corners in the right position.
3) Perform the second algorithm from above.
4) Do U' to undo the setup move from Step 2.
*In a situation like this, it may be better to use the first corner orientation method described.
The first method is more intuitive, and allows for more variation. However, the second method is more straightforward. It is suggested that you experiment with both of the methods shown above and choose the method that you feel most comfortable with. These methods are both interchangeable as well so it is very possible to implement both styles.
Step 2: Permutation of the Corner Pieces:
There are 8 corner pieces on a 3x3x3, making this a fairly easy step to memorize, and a quick step to execute. For corner permutation, we will be using a 3-cycle method, meaning that 2 corner pieces will be solved after each algorithm.
There are two main algorithms that are used:
The first one performs a corner cycle of UFR->UBL->UBR, and the other algorithm (its inverse) performs the cycle of UFR->UBR->UBL.
With that said, it should make sense now that each time a cycle is executed, 2 corners can be solved (and ultimately 3, unless you encounter a parity, which will be covered in the next step). This can be done with correct setup moves, moving the corners that we wish to be permuted to the UFR, UBR, UBL positions, and the correct algorithm corner cycle. When you are performing setup moves for corner permutation (CP), limit them to R2, L2, F2, B2, U, U', U2, D, D', and D2, for this is the only way to preserve corner orientation.
Example 1:
UBL->UBR->DFL
1) Setup move: F2
2) Cycle: (R' F R') B2 (R F' R') B2 R2 (1st algorithm listed above)
3) Setdown move: F2
Example 2:
DFL->UBR->DBL->DFR->DBR->DFL
1) Setup moves: L2 y
2) Cycle: (R' F R') B2 (R F' R') B2 R2
3) Setdown moves: y' L2
4) Setup move: z2 y2
5) Cycle: (R' F R') B2 (R F' R') B2 R2
6) Setdown moves: y2 z2
As you can see setup moves can also include cube rotations, but there are numerous ways to achieve the same results. Some are just more efficient than others.
Also, when you have to do multiple cycles, 2 corners will be solved and the 3 corner will be permuted to the first corner's position, and the cycle after that will start with that position [See second Example]. I'll leave it to the readers as to why/how this works. Once you figure it out, you'll be able to have your own interpretation. Reading the Numbers memorization method could help clear things up.
Experiment with different cases and get used to the setup moves, as they are the hardest part of CP. As for determining where and how to start CP, it does not really matter--as long as you can memorize efficiently and determine execution efficiently. It is highly recommended that a "number" memorization method is applied to this step (in the memorization section). It can also help provide a clearer understanding of CP.
Awkward case:
Whenever you have 3 corners in a cycle, 2 or 3 of which are diagonal from each other, setup moves for conventional cycles can be very long, and thus not very effective. For example, the cycle UBL->UFR->DFL would require 4 setup moves using the algorithms listed above.
However, another useful algorithm for CP is:
This algorithm swaps the UFL/UBR corners, and the UFR/DFR corners. To fix the case listed above, do:
1) Setup move: D
2) Another temporary setup move: U2
3) (F R' F' R) (F R' F' R) (F R' F' R)
4) Setdown move: U2
5) (F R' F' R) (F R' F' R) (F R' F' R)
6) Setdown move: D'
Using this fake 2-cycle logic, you can solve these awkward cases with ease.
Step 3: Identifying Permutation Parity and Fixing It:
Permutation parity occurs when all you have is a single pair of corners left to be switched. With the 3-cycle method, it is not possible to swap only two corners. Parity occurs about half the time you attempt to solve blindfolded: sometimes it’s there, and sometimes it’s not. First off, you should get to know the nature of the T-perm fairly well, as the method we’ll be discussing here deals with T-perms. Also keep in mind that the setup moves here have the same restrictions as they do in corner permutation.
Only One Pair of Corners Need to be Switched:
Corners DLF and URB need to be switched.
Edges UR and UL are switched.
A) This can be fixed simply by lining up the two corners and performing a T-perm. But note that this also switches the location of two edges. So when you use this method you have to make sure to memorize with two edges swapped and begin solving edges from their relocated positions (Solving edges is Step 4). This mental note shouldn't be difficult as long as you don’t make the two edges in remote locations. Using this method, it is recommended that you always just swap edges UR and UL. (once again, this is a T-perm)
B) Another option is just to leaving the corners alone [for now]. Remember which corners need to be switched and leave the corners until you have finished your edges down to the last two that need to be swapped and perform a T-perm fixing both the edges and the corners solving the cube. However, this may result in the need to make some setup and setdown moves (which can prove to be difficult sometimes).
Either way produces the same result, however, it is recommended that method “A” is used. If this does not work, then you may have a cube that has been rendered impossible to solve.
Two or More Pairs of Corners Need to be Switched:
A) When there is an even number of pairs that need to be switched, then, technically, this is not a parity case. Because performing the T-perm twice (or any even amount of times) with the same edges will result with solved edges in the end. So there will be no relocation of any edges in the end if done correctly. There are different permutation algorithms that deal with 4 corners only that can make this easier, but use at your own discretion and risk (setup and setdown moves can prove to be difficult).
B) When there is an odd number of pairs, then solve each pair using the T-perm as you would if there’re even numbers. You’ll eventually end up with only 2 corners left to be switched, which is the first case stated above. Make sure that when you are switching corners with the T-Permutation, you are switching the same edges until you are left with only two corners that need to be switched. Meaning when you reach back to the first case (only 2 corners left) there should be no relocated edges yet.
Again, this should cover any parity case you encounter. If this does not work, then you may have a cube that has been rendered impossible to solve.
Step 4: Orientation and Permutation of Edge Pieces Simultaneously:
There are 12 edge pieces on a 3x3x3 cube, as opposed to the 8 corner pieces of a cube. If we were to use a 3-cycle approach to solving the edge pieces, we would have to memorize both the orientations and the permutations of the pieces. However, with a 2-cycle (Pochmann's method) approach, we memorize both orientation and permutation at the same time.
With this approach we will be using simple PLL algorithms with the use of setup and setdown moves to position all of the edges. The setup and setdown moves are used to displace the location of the places where the pieces will be swapped.
The Algorithms
The three main algorithms for solving the edges with this method are:
These algorithms are preferred for blindfold solving, because they do not contain any double layer turns or full cube rotations, which may hinder or confuse you while blindfolded. However, any algorithms which have the same effects as these will do.
Swapping Edge Pieces with Setup and Setdown Moves
The process is really very simple:
1) Setup an edge piece to be either in the UF, UL, or UB position.
2) Perform the appropriate algorithm.
3) Setdown the edge piece using the inverse of the setup move.
If you look at the algorithms you will notice that they all swap the corner pieces located at URF and URB. They also swap the edge piece (UR) with another edge piece. Because a piece is always switched out of the UR position will can use that as a "buffer" for cycling all of the edge pieces. Let's use the T-perm for an example:
The T-perm swaps the UR and the UL piece. Note: UR switches with UL, not LU. They may be the same piece, but if you switched with LU, it would not be in the proper orientation. Swapping with UL also orients the piece properly. It is imperative that when you memorize, you memorize whether or not it is UL or LU.
Now assume the piece in our "buffer" (UR position) is supposed to be in DL position (not LD). We can swap the pieces with a simple setup move, L2. When you perform L2, you are putting the piece that is in the DL position in the UL position. Then when you execute the T-perm, you switch the two pieces. All that is left to do then is the setdown move, which is the inverse of the the setup move (in this case, L2). See the above applet.
The same applies to the other two algorithms. For example, if you need to swap UR (the piece in the buffer) with FD (once again, its important you know the difference between FD and DF), then the setup move would be l'. (see the first applet) A trick when looking for setup moves, is to use double layer turns. If we were to switch the buffer piece with DF, then we would use the setup move would be (D' L2) and execute a T-perm then setdown (see the second applet).
I will let you figure out the setup/setdown moves for swapping with the rest of the edge piece. Once you figure them out, you should have no problem switching any edge piece to and from the buffer location (UR). A key to this method is that once you know the setup move and algorithm to switch, say UR and RB, you can use that every time. The swapping process is the same every time. This reduces the execution time of the solve by reducing the amount of thinking required.
Solving a String of Edge Pieces
Now that you understand how to swap 2 edge pieces, you're probably wondering how to apply that knowledge and solve all the edge pieces. I said that swapping pieces would be easy. This is easier (if you understand swapping).
(See applets.) First, look at your buffer piece (UR) and find out where it goes. Move that piece to its proper spot, in this case BL. Afterwards, you will notice that the piece that was once in the BL spot is now in the the buffer (UR). Now put that piece in it's proper spot. Continue doing this until the piece that is in the "buffer" zone is actually supposed to be there, whether or not it is oriented properly. That is a cycle.
Solving All Edge Pieces Using Multiple Cycles
Very rarely is it possible for one to solve all the edge pieces in a single cycle. You probably noticed that. Instead you will have to use multiple cycles (usually 2). It's actually quite a simple concept, as is this entire method of solving edges. In fact, I'll explain it all in one paragraph, without the use of applets.
When the piece in the buffer location is in the UR or RU (we will worry about orientation later on) piece, all you have to do is to swap it with a piece that is not already solved. This will start a new cycle, in which you continue through until the UR or RU piece returns back to the buffer zone. You can do this until all edge pieces are solved and in position. (We can deal with orientation after that, if needed). Also, just letting you know that it is quite common that the piece in the buffer location of the first cycle is UR or RU. In this case, simply do what is described above.
Dealing with Orientation of Edges (if Needed)
Sometimes, you will end up with some pieces that need to be reoriented. There are two main ways to fix this problem. One is to continue on and create a new cycle. This will eventually reorient the pieces properly. The second method is to use a simple commutator to orient the edges. Because the first method has already been discussed in the above areas, here I will focus mainly on the second approach.
The first applet shows how to orient pairs of edges. To use it to orient edges, we will use a similar approach to that of the solving the edges. That is, we will be using setup and setdown moves to position pieces in the proper location to allow for use of the commutator. Look at the second applet for an example of how to orient UR and DB pieces. Once again, it's quite simple. The last applet is completely optional. It is an algorithm that orients UF and UR. This may make it easier to solve with certain setup moves.
Although, you could orient without the use of these commutators (option 1), it is highly recommended to learn to use them at one point or another. Not only will it reduce your times, but it will also give you a better understanding of the use of setup and setdown moves. Plus, it is easier to memorize, at least to some.
With all of this information, you should now be able to solve all the edges pieces.
Memorization Techniques:
Below are a few techniques that we [the authors] use for memorizing the cube for a blindfolded solve. Read through all of them and pick one that you think will work best for you. Also, feel free to combine methods of memorization if you are comfortable with certain methods for memorizing certain things (e.g. numbers for corners, and visual for edges). The more you try, the more options you will have, as well. The key thing to remember is to choose what works best for YOU. We can suggest things, but it all comes down to how your mind works. Mix and match, or stick solely with one method, but have fun experimenting!
Visual
This is simply put as memorizing with a mental image. It does not necessarily mean (or require) photographic memory. As long as you just take a few "snapshot" photos of certain locations of the cube that you need to memorize, then that's all visual really is. Of course, if trained extremely well, this method has the highest potential of any listed below, however it is very difficult (but not impossible) to achieve such a high level as to simply look at the cube and be able to reconstruct it perfectly in the mind within seconds. For most cubers, this method is implemented when you have small amounts of items you need to memorize and can discard quickly after you solve it. For example, this method is commonly used when orienting corners, because of their easy identifications, and their fast solve times (which means they can then be discarded from memory as soon as you solve them, which is why it corner orientation is commonly solved first).
Shape/Pathway
This applies mostly to corner permutation, however, it could work for edge permutation as well. This method will not work for orientation, unless you can come up with one (somehow?). This method starts from the first piece of permutation and as you move along the corner/edges you wish to permute, you connect the pieces with an imaginary line. This could eventually draw out a shape within the cube, which can be easier to visualize and to remember. Or you can think of it as walking along a path, making stops to which places in a specific order. If this method is applied to corners, it is possible to use in conjunction with numbers, memorizing both the numbers and the visual shape/path.
Numbers
This is a simple assignment of numbers to each piece. The numbering system is the most traditional method, especially if you're using the 3-Cycle method (as described for corners in this guide). This method is not recommended for edge permutation using 2-Cycle. This system can be used to memorize each part of solving the cube: Orientation, or permutation (but highly recommended only for permutation). If you have been following this guide, then it is recommended that you only use this for corner permutation, and Picture/Story for edge permutation. But, as always, find what's most comfortable for you. Here is an example of the numbering system for permutation (create any sort of numbering as long it works for you):
1 UFL
2 UFR
3 UBR
4 UBL
5 DFL
6 DFR
7 DBR
8 DBL
A brief description of how to use this method:
First try to get comfortable with the pieces and their corresponding numbers, but this will come to you with experience and time. You can practice simply by scrambling a cube and calling out the number in order. Ex: Corner 1 position has corner piece 3. Corner 2 position has corner piece 6...etc.
Now, how to use this in memorization:
This can be confusing at first, but once learned, it can be trained to memorize a mass amount of items in a short period of time. In this description the explaination will be done with memorizing corners. In short, you want to create a string of numbers that tells you where each corner wants to go. It's best to start with the lowest number that is not in it's correct location. Then move on to that corner's location and determine that number of that corner. Then move on to that number's correct location and determine that number of the next corner etc...Eventually you will end up at the first corner's number. Then you have completed that cycle. The 3-Cycle method will reduce 2 numbers (because you solve 2 corners) each time a cycle is executed, so this method of memorization can be done quickly, and be discarded from your memory quickly as well. This memorization works because when done with 3-Cycle, the 3rd piece will come back to the location of the piece that started the cycle. Eventually, you will also find out that the last number in your cycle is the location of where you started from (the current corner location of the smallest number that started the cycle).
When the cycle has an even amount of numbers, then there is a parity. However, as discussed before, two sets of parities (or any even amount) cancels each other out and will not result in an overall parity, if dealt with correctly (Step 3).
Example: Corner permutation: (1 3 7) (2 5 4 6)
There are two cycle of permutations in this string: (1 3 7) and (2 5 4 6). It does not matter which cycle you solve first.
Another thing you may notice is that corner 8 is not in this string of cycles. This means that it is already in it's correct location.
In cycle (1 3 7) corner piece 1 is in corner 7. And the corner piece in corner 1 needs to be permuted to corner 3. And the corner piece in corner 3 needs to go to corner 7
In cycle (2 5 4 6) apply what you've learned so far, and you'll find out that when you do the first permutation, corner 4 will end up where corner 2 was, but you'd have solved corners 2 and 5 (which can be discarded from memory now). You're then left with (4 6). In this case there is a parity because the total amount of numbers in this cycle is even (and the other cycle did not result in a parity).
Once this becomes clear, you'll be able to interpret it in your own way. Just play around a bit. Although this method has become obsolete, it is still very effective, nevertheless.
Pictures/Story
Another common method of memorization involves the use of mental story that is created with certain objects. The story is generally an over exaggerated story so it is quite easy to memorize.
A simple way of utilizing this involves the assigning of objects to different color pairs. For example, the Orange/Green color pair can be called "carrot" (this is because a carrot is orange and green and it would be easier to memorize). The Red/White color pair can be called "stop sign." The Yellow/Blue color pair can be called "flounder" and so forth. I'll let you create a list that works for you. Just finish off the rest of the color pairs.
Now that we've established the color pairs, we can begin with the story. For example, if we want to memorize the edge pieces in the cycle, we would look at the buffer and memorize from there. Here's an example of the objects in the first cycle: flounder, stop sign, carrot. With a cycle like this, we can create a simple (and dumb, yes) story to help us memorize the edge pieces. For example: "Flounder stopped at a stop sign at the intersection near the grocery store. He was on his way there to buy more carrots."
This kind of memorization can be utilized throughout the solve, however, it is only recommended that it be used for edge solving as it could get quite confusing for 3-cycle corners.
Auditory
The use of audio to assist in memorizing a cube is scarcely, if at all, used. Caleb is the only person known (to us) that actually implements it and puts it to use. However, it is suggested that you do not fully rely on audio as a resort to memorization. It is recommended mostly to use a visual approach with the audio as an addition. For example, it can be used to keep track of whether or not there is a parity.
Caleb creates a song [during memorization] that helps him count the pieces in a cycle and determine whether or not he has to fix parity. This is only done because of the fact that he gets confused with numbers. (Ya, it's a dumb excuse).
Complete Example Solve:
One of the best and easiest ways to learn is with example. So, with that said, we wanted to provide you with an example solve that should include all the aspects of our hybrid method.
COMPLETE EXAMPLE SOLVE
Conclusion and Credits:
First off, thank you for taking the time to read this guide. If you understand the concept and descriptions found throughout this guide, you should be able to solve the cube blindfolded. If you have any questions, please feel free to ask.
The writing of this guide was inspired by many others and various techniques and methods were taken from other people. The 3-cycle method described on this page can be found in Shotaro "Macky" Makisumi's Cubefreak. The 2-cycle method described on this page can found in Stefan Pochmann's Cube Corner. The wonderful applets, RubikPlayer are by Werner Randelshofer. Many thanks also to those who helped with the proof-reading of this guide.
Happy Cubing!
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