If you've spent enough time online, you've probably seen videos of people solving Rubik's cubes blindfolded. You've also probably seen the comments that invariably follow, saying the video must be fake: that it must have been played in reverse or that the stickers have braille. Well, it is actually quite possible for anyone to solve a normal cube blindfolded, and here I'll tell you how.
Note: This writeup assumes you are already comfortable solving a Rubik's cube with your eyes open. You should also be familiar with standard Rubik's cube notation.
Before we start:
A Rubik's cube is composed of 20 movable cubies (the individual pieces that make up the cube), each of which have two characteristics that define its solved position. The permutation of a cubie refers to its location on the cube, while orientation refers to how the cubie is flipped or twisted in place. Both the orientation and permutation of each cubie must be correct for the cube to be solved. In addition to the 20 cubies, there are 20 points in space in which a cubie can be located. Note that at any time, the UF (edge at the intersection of the up and front faces) position doesn't have to be filled with the UF cubie.
Solving a Rubik's cube blindfolded requires being aware of what the solved state of the cube will be. Always solving with the cube in a certain orientation (always having a certain color up and another in front) makes this easier, as you don't have to remember which sides need to be which color. As the centers of each face cannot move relative to each other, they define the orientation of the cube. The color of each center will define the color of that face. Before you begin blindfold cubing, you should choose how you will hold the cube. I solve with white up and green in front with an American color scheme, so I will use that in my explanation, but use orientation you prefer.
A brute force blindfolded solution, involving memorizing the location of each sticker and updating a mental picture of the cube after each turn would involve an immense feat of memory beyond the ability of most people. Simpler methods solve the cube in very small portions, moving only a few cubies at a time so the mental picture doesn't have to be updated as often. The method explained here solves the cube by orienting the cubies, then permuting them while maintaining proper orientation. There are, of course, other methods for solving a cube blindfolded, this just happens to be the method I know. This method requires a bit more thinking than other popular solutions, but is very fast and is used by current and former world record holders.
The purpose of these two steps is to orient the corners and edges without changing the position of any cubies. As these can be executed independently, the order is not important, as long as orientations are done before permutations.
There are eight corner cubies. Note that each of these cubies will always have either a white or yellow sticker (but never both), as these are the colors of the U and D faces. The goal of this step is to get all the U or D stickers on the top layer facing up, and all on the bottom facing down.
Each cubie will either be correctly oriented, or will need a clockwise or counterclockwise twist. The twist is defined by how the cubie would need to turn along the axis created by the diagonal of the cube that runs through the cubie. On a scrambled cube, there will often be several corners correctly oriented. A regular scramble will usually require three to five corner twists. Note that, because of the limitations of the mechanism of the cube, corner twists will always come in pairs, with one corner twisting clockwise and the other twisting counterclockwise (or in triplets all twisting the same direction, which are really just two overlapping pairs).
On a solved cube, perform the following algorithm (those familiar with Petrus method should recognize this as two Sunes):
R U R' U R U2 R' L' U' L U' L' U2 L
This twists the cubie at ULF counterclockwise and the cubie at ULB clockwise while leaving the rest of the cube unchanged. With the help of setup moves, this algorithm can be used to orient all the corners of a scrambled cube. Setup moves are used to move a cubie to where an algorithm can be applied, then undone to return the cube to its original state, except for the change made by the algorithm.
Consider the case where the cubie at UFR needs to twist counterclockwise and DRB needs to twist clockwise. To use the above algorithm in this case, the setup would be U B2, and the whole sequence would be:
U B2 R U R' U R U2 R' L' U' L U' L' U2 L B2 U'
In this case, U B2 moves the two cubies that need changing to the proper position to be worked on by the corner twisting algorithm, the algorithm is applied, then the setup is undone by applying its inverse, B2 U'. This brings the cube back to its initial state except for the twist of the two corners.
Unlike corners, not all edges will have a certain sticker. Edge orientation will thus be described in terms of both U/D stickers and F/B stickers. Any edge cubie will have at least one of these stickers. For edges in the top or bottom layer, they are oriented if a U or D sticker is facing up or down, or a F or B sticker is facing to the outside. For edges in the middle layer, they are oriented if a U or D sticker is facing to the left or right, or a F or B sticker is facing the front or back.
A scrambled cube will usually have between four and eight cubies that are oriented incorrectly. Again, because of the limitations of the cube mechanism, flipped edges always come in pairs.
One algorithm for orienting edges is known as Rubik's Move, which will flip the UF and UB edges. In standard notation, it is:
M U M U M U2 M' U M' U M' U2
The use of this algorithm is the same as that for corner orientation. Use setup moves to place incorrectly oriented edges at UF and UB, apply the algorithm, then reverse the setup.
Imagine four boxes and four blocks, one of each marked with the letters A, B, C and D. Consider the scenario where box A contains block B, box B contains block C, box C contains block D and box D contains block A. In this situation, the block in box A needs to move to box B, the block in B needs to move to C, C needs to move to D and D to A. A path, ABCD, can describe this situation.
This path can be broken down by cycling pieces. Consider if the first three blocks are cycled between their boxes, with the block in A moving to B, B to C and C back to A. Box B will now contain block B, box C will contain block C and box A will contain block D. The path can now be reduced to AD. For any arbitrary path of length greater than three, cycling three positions will remove the last two positions in the cycle from the path. (In the general case, cycling n positions will solve the last n-1 positions of the cycle.) For a path of length three, a cycle will solve all three positions of the path. Paths of length two will be dealt with later.
Each of the eight corner positions, and the cubies that occupy them in the solved state, should have a label to identify them. In my case these labels are numbers, but any set of names to identify them is fine. Permuting corners 1, 2 and 3 is no different from permuting corners Alex, Bob and Charlie.
Select a corner position to start defining your corner permutation path. If the proper cubie is in that position, that position is solved and you should move on to another position. If an incorrect cubie is in that position, it is now the first position in your path. Look at the cubie in the first position, and move to the position in which it belongs. This is the second position in your path. The proper cubie won't be there, as it was in the last position, so you will have another position to move to, and a new position in your path. Continue doing this until you return to the position you started with, completing your path. If your path covers eight positions, you are done, otherwise you need to move to the next position not in a path and start a new path. Once all cubies are accounted for, either solved or as part of a path, you are finished.
Corner paths will be broken down by cycles, as explained above. Two algorithms that cycle groups of three corners clockwise and counterclockwise are:
R' F R' B2 R F' R' B2 R2
L F' L B2 L' F L B2 L2
Notice that these algorithms are simply mirrors of each other.
The corners were previously oriented, and must remain that way for the cube to be solved properly. In order to maintain orientation, restrictions must now be placed on movements. As there are three stickers on each corner cubie, movement must be restricted along two axes to maintain orientation. Take a solved cube and mix it using only double turns on the front, back, right and left faces, and free turns on the up and down faces. Note that the corners remain oriented throughout. These restrictions (F2, B2, R2, L2) will be used during setup moves for corner permutation cycles. Additionally, the corner permuting algorithms only maintain orientation when performed on the U or D faces. Use the restricted setup moves to place the three corners from your path in the U or D face, cycle them, then undo your setup.
Paths with odd length will be reduced completely with three-cycles, while paths with even length will leave two cubies to be permuted. A pair of two-length paths can be solved with three-cycles or with Fridrich PLL algorithms that switch two pairs of corners. If you are left with a single pair of incorrectly placed edges, you have the parity case, which will be explained later.
Edges are permuted using cycles in the same way corners are. The paths are determined by following the positions of incorrectly located cubies, and broken down by three-cycles. Two edge three-cycle algorithms are:
F2 U R' L F2 R L' U F2
F2 U' R' L F2 R L' U' F2
These algorithms cycle groups of three edges clockwise and counterclockwise, respectively.
Again, the edges were previously oriented, and now limited moves must be used to maintain orientation. As edges only have two stickers to keep oriented, only one axis must be restricted. A cube scrambled with only double turns of R and L and free turns on U, D, F and B will maintain edge orientation. The algorithms here maintain orientation only on the U, D, F and B faces. Use the restricted setup moves (R2, L2) to position three edges from your path, cycle them, then undo your setup.
Again, paths with odd length will reduce completely with these algorithms. Even length paths will leave pairs of edges that need to be permuted. Two pairs of edges can be solved with three-cycles or Fridrich PLLs. If you are left with a single pair of edges, you should also have a single pair of incorrectly permuted corners from the previous step, and you have the parity case.
In half of blindfolded solves, your cycles will leave you with two corners and two edges to permute, the parity case. This is a results of another of the limitations of the Rubik's cube mechanism, corner and edge permutations are not independent. A single pair of corners cannot be switched without switching a pair of edges.
You can tell if you have the parity case by looking at your path lengths. An even number of paths with even length does not have the parity case, while an odd number of even length paths leads to the parity case.
To solve the parity case, the four remaining pieces could be moved into one layer using the restricted setup moves (F2, B2, R2, L2 - you're dealing with corners, so two limited axes) and a Fridrich PLL applied to swap both pairs. This setup is usually not easy to do. A simpler solution is to swap the two remaining corners and another two edges, then fix the two last edges along with the two edges just swapped. This can be done with the T PLL:
R U R' U' R' F R2 U' R' U' R U R' F'
This algorithm swaps a pair of corners and a pair of edges. To solve parity with this, place the two corners in the U or D face with the restricted setup moves while keeping track of which edges will get swapped, perform the algorithm, then undo the setup, leaving you with four edges to permute. These last edges can be finished with the method explained in the edge permutation section.
Solving parity with the T permutation by swapping corners first is better than swapping edges first because the setup moves for edges are less restricted, which could lead to corner orientation getting messed up, as both edges and corners get switched in this step.
Although it may seem daunting, memorizing the state of a Rubik's cube out of the 43 quintillion possibilities isn't really that difficult, compared to some people's accomplishments.
The most basic memorization method would be to use a string of numbers. Permutations can be remembered by assigning a number to each of the cubie positions, and remembering the paths as strings of numbers. Orientations can be remembered by defining each orientation state with a number. A correctly oriented edge is 0, while an incorrectly oriented edge is 1. Following the edges in the order they are numbered for permutations, the orientation can be remembered as a 12 digit binary number. Corner orientation can be remembered in a similar way with 0 for the correct orientation, and 1 and 2 for the two twisted states. This method would lead to a string of at most 40 numbers, which isn't so bad, considering some people can memorize pi to thousands of digits.
Other memorization methods can be used to speed this step. For edge permutations, I remember the paths visually by tracing the positions with my fingers. Corner permutations are done with numbers, as there are only eight of them, and that's not much worse than a phone number. Other people remember permutations by associating a character or word with each position, then forming a story with the characters as they appear in the paths. Edge orientations can be remembered by breaking down the 12 digit binary number described above to three 4 digit numbers, one for each layer, which can further be converted to decimal, giving three numbers from 0 to 15 representing the edge orientation. In this way, memorization for edge orientation can be reduced by 75%. Edge orientations can also be remembered visually. As I solve corner orientations first, I look at them last. I take a visual snapshot of the cube, then put on the blindfold and THINKREALLYFAST.
After each step is completed, the progress you have made shouldn't later be undone, so the information you had memorized is no longer needed. Once corners are oriented, they should remain that way for the rest of the solve, so you can forget the corner orientations you had remembered. As you perform permutations, you can drop positions from your path as they are solved.
Memory is also important for setup moves, as they must be undone in the exact reverse of how they were performed. Saying your setup moves outloud as you do them can help. Just be sure you know which cubies you're working on at each point, and you should be able to remember how you got them into position.
Here I have only listed enough basic algorithms to complete a solve. Knowing more algorithms makes blind solving easier by reducing the necessary setup for each step, allowing them to be completed faster. This also speeds memorization, as you will get through each step quicker, and be less likely to have forgotten the information, so you memorization doesn't need to be as thorough. Detailing all the algorithms useful in blindfolded cubing would make this already long writeup far too long. Anyone that is seriously interested can feel free to message me for a big list of algorithms.
Blindfolded cubing does take some practice, so you probably shouldn't try a whole solve immediately. First try scrambling a few cubes, then solving them with this method with your eyes open, being sure you understand how the cycles work and how to keep orientations. After this point, if you understand the method but are having trouble remembering everything, do some partial solves, completing edges then orienting and permuting corners blindfolded, or doing all orientations, then solving permutations blindfolded. Try to find a memorization method that works for you.
You can do the steps here in a different order, as long as orientations come before permutations. Steps can even be mixed. If during the corner permutation you realize the parity case would be easy to solve at that point, go ahead and do it, then carry on with the step you're on.
Once you've mastered the cube, it's time to compare yourself with others. The 2006 US national championships will be held in early August in San Francisco, and all competitors are welcome - US national championship website. Information on other competitions can be found at speedcubing.com
Enjoy your cubing!
Anyone that understands what I'm saying here and has suggestions for making this more readable, please give your advice.
Special thanks to Leyan Lo for inspiring me to get faster and particularly Tyson Mao, through whom I learned to blind solve.