Introduction: This tutorial assumes that the reader already understands the basic concepts of cube notation and algorithms.
The idea of solving a Rubik’s Cube while blindfolded sounds intimidating, but with proper methods, the tasks is easily accomplished by anyone. For the blindfold solve, the solver memorizes the initial configuration of the cube. After the memorization is completed, the solver then proceeds to solve the cube without looking at it again. It is very difficult, and probably impossible by all but few, to actually keep track of all 20 stickers that shift when one turns a single face of the cube. Instead, the basic idea of blindfold solving is to solve the cube in very small portions, only two or three pieces at a time, thus reducing the need for continual updates of your “mental picture.” The Idea: This method of blindfold solving takes place in two main steps. First, the pieces are all oriented. Then, the pieces are all permuted. Orientation is done first so that when the pieces are permuted into their proper locations, they end up facing the right way. Setting Up The Cube: Unlike regular solving, blindfold solving is most easily done with the same center faces on top and in front at all times. The colors, as always, are arbitrary. World record holder, Leyan Lo, for example always solves with the yellow face on top and the blue face in front. Shotaro Makisumi, with his Japanese color-scheme cube, solves with the blue face on top and the green face in front. I personally solve with the white face on top and the green face in front. For this tutorial, I will explain how to solve the cube blindfolded while setting the white face on top and the green face in front while using a cube with the American color-scheme (white opposite of yellow). For many blindfold solvers, numbering the pieces is a good tool that assists in the memorization of the cube state. Numbers, like colors, are completely arbitrary. There is no difference between permuting corners (3, 5, 7) and permuting corners (llama, walrus, duck). Like the color orientation, go with whatever works for you. Orienting the Corners: First, we must orient all the pieces. This tutorial explains corner orientation before edge orientation. However, it should be noted that the order in which these processes are done is irrelevant. As long as the pieces are oriented before they are permuted, you will be fine. If it is more comfortable to orient the edges first, go ahead and do it that way. The idea is that we want to orient all the corners without affecting their placement or any of the edges. In blindfold cubing, there are a variety of algorithms that one can use. The more algorithms one knows, the more options a solver has. This tutorial will present three methods of orienting corners. Now, we want to orient the corners in such a manner that when we apply the permutation algorithms, the end up in the correct orientation. Note that every corner will have a white or a yellow sticker. This should be fairly obvious: the cube consists of 8 corners. Four of the corners are on the top, and since our top color is white, four of them will have white stickers. Similarly, four of the corners are on the bottom, and since our bottom color is yellow, those four corners will have yellow stickers. Since white and yellow or opposite colors, no corner can have both a yellow and a white sticker. At the end of the orientation, we want all corners on the top layer to have white or yellow stickers facing up. On the bottom layer, we want all corners to have white or yellow stickers facing down. Scramble a cube, and notice that some of the corners are already correctly oriented—they have yellow or white stickers facing directly up or down. Many of the corners will require a twist for this to happen. Not the same corners require clockwise twists, and other corners require counter-clockwise twists. On a solved cube, perform the algorithm (L’ U’ L U’ L’ U2 L)(R U R’ U R U2 R’). You’ll notice that the algorithm twists two corners in the top layer. The bottom right corner is rotated clockwise, whereas the top right corner is rotated counter-clockwise. Now, perform the exact inverse of that algorithm: (R U2 R’ U’ R U’ R’)(L’ U2 L U L’ U L). You’ll notice that that algorithm solves the two twisted corners in the top layer. More specifically, the bottom right corner is twisted counter-clockwise and the top right is twisted clockwise. Experiment with the mirror images of these algorithms. (R U R’ U R U2 R’) (L’ U’ L U’ L’ U2 L)and (L’ U2 L U L’ U L) (R U2 R’ U’ R U’ R’)should do similar things, but to the top left and bottom left corners in the top layer. Now, experiment with the following algorithm B2 (L’ U’ L U’ L’ U2 L)(R U R’ U R U2 R’) B2. You’ll notice that it twists the bottom right corner in the top layer clockwise and the top left corner in the bottom layer counter-clockwise. B2is what we call a “setup move.” While orienting the cube, we can perform any setup moves necessary to position the pieces. First, perform the setup move. Then, perform the algorithm. Finally, reverse the setup move. Setup moves are used to bring other pieces into locations such that we may act on them with the algorithm. Experiment with a variety of setup moves, and gradually familiarize yourself with corner orientation. With the provided algorithms and a couple of setup moves, you should be able to orient all the corners of the cube. Make sure you familiarize yourself with the algorithms and that you understand exactly what they do. Try orienting all the corners of a scrambled cube. I will now explain another method of orienting corners. This method of orienting corners requires slightly more intuition, but is very powerful. Try the following algorithm on a solved cube: R’ (D R D’ R’ D R) U’ R’ (D’ R D R’ D’ R) U. Understanding exactly what this algorithm does is essential to its application. First of all, you’ll notice that this algorithm twists two corners in the top layer. The bottom right corner is twisted clockwise and the bottom left corner is twisted counter-clockwise. The mechanism of this algorithm is very powerful. The first R’places the bottom right corner in the top layer into the bottom layer. The next part,(D R D’ R’ D R), twists the corner while creating some junk on the bottom layer as well. U’ R’moves the bottom left corner in the top layer into the bottom layer and(D’ R D R’ D’ R)twists that corner counter-clockwise while reversing the junk on the bottom. Uthen reverses theU’move which moved the corner over in the first place. The fundamental moves in this corner orientation method are (D R D’ R’ D R)and(D’ R D R’ D’ R). The first one performs clockwise twists while the second one performs counter-clockwise twists. Now, attempt the algorithmR’ (D’ R D R’ D’ R) U’ R’ (D R D’ R’ D R) U. You will notice that the sections in parentheses are reversed, and so is the effect on the corners. The corner that was previously twisted clockwise is now twisted counter-clockwise and vice versa. Now attempt the algorithmR’ (D R D’ R’ D R) U2 R’ (D’ R D R’ D’ R) U2. You will notice that this algorithm is the same as the first, except there is aU2move instead of aU’. The effect is that it twists the diagonal corners instead. Notice how theU2moves brings the diagonal corner into position and then theR’move pushes it into the bottom layer. Now, try the following algorithm: R’ (D R D’ R’ D R D’) U’ R’ (D R D’ R’ D R D’) U’ R’ (D R D’ R’ D R D’) U2. First, notice that the portions of the algorithm in the parentheses are all identical. Next, notice that those portion are the same as the fundamental clock-wise twist algorithms, but with an addedD’at the end. Now, notice that the firstR’pushes a corner into the bottom layer. The part in the parenthesis twists the corner clockwise. U’ R’moves the next corner over and we also twist it clockwise. We repeat this a third time, and finally,U2puts all the corners back in their original locations. The algorithm has twisted three corners all clockwise. Attempt the same thing, but substitute(D’ R D R’ D’ R D)into the algorithm to perform a counter-clockwise three-cycle. For the advanced blindfold solver, algorithms such as [(R U R’ U’)(R U2 R’ U2)]x2,[(R U2 R’ U2)(R U R’ U’)]x2, and their inverses can be very powerful. Other multi-corner orientation algorithms exist as well but they should not be attempted until the solver is fully comfortable with the basic set of algorithms. With these tools and a combination of setup moves, you should now be able to orient all of the corners of the cube. Attempt to orient all the corners of the cube with your eyes open. Then, attempt to memorize the corner orientation of the cube and try to orient them blindfolded. Memorizing the corner orientation should not be too difficult, but if you need assistance, please see the next section. Now, all the corners should be oriented. Again, this means that only white or yellow stickers on the corners point directly up or down. Keep in mind that throughout this procedure, it is imperative that you are aware of the locations of your top and front sides. Memorizing: Everyone has his own memorization techniques. I will present the techniques that I use, but sometimes techniques that you develop on your own will ultimately be more powerful. Everyone’s mind works differently. You’ll notice that I included two different methods of orienting the corners. I personally use both of them. Leyan and Macky only use the second one. Corner orientation is the last thing I memorize. I memorize the steps in reverse order of the actual solve. When you have adjacent pairs that need to be twisted clockwise and counter-clockwise, there are two different shapes. In one of them, the two stickers of interest, in this case, yellow or white, will be on the same side. For other cases, they’ll be facing away from each other. Sometimes, it is easier for me to remember what algorithm to apply rather than which way the piece wants to be twisted. Different methods of doing certain things on a blindfold solve act as tools. You can solve the cube with very few tools, but the more things you understand how to execute, the more ways you can do them, and the more choices you have. Sometimes, one choice will be more convenient than the other. Other memorization techniques that people do involve memorizing numbers for the corners. I personally do not do that, but it should be easy to see how this is done. Simply assign an ordering to the corners and then memorize the state of each corner. Memorizing the overall shape of the cube state can be a powerful tool. However, always remember that I’m not right, and that you should experiment. Orienting the Edges: This step is very easy and many people consider this to be easier than orienting the corners. Leyan Lo performs this step first on the cube whereas Macky and I do this second after the corner orientation. Again, it doesn’t matter which one you do first. The idea is that we are orienting the edges in such a manner that when we execute the edge permutation step, all of the edges are facing the correct way. Unlike permutation moves, setup moves during orientation have no restrictions. I will outline the restriction for permutation moves when we get there. The most difficult thing of the edge orientation is recognizing which edges are oriented incorrectly. With edge orientations, we consider the top, bottom, front, and back colors. On my cube, white is my top, yellow is my bottom, green is my front, and blue is my back. Below are several criteria that indicate a correct edge. I will explain the logic for this later. If an edge is in the top player, it is correctly oriented if the top or bottom color is facing upwards. If the yellow or white sticker is facing upwards, then the edge is correct. This applies to the bottom layer as well. If the white or yellow sticker is facing directly downwards, the edge is oriented correctly. If the edge is in the top layer, it is correctly oriented if the green or blue sticker is facing off to the side. If a green or blue sticker is facing directly upwards, then it is incorrectly oriented. The same applies for the bottom layer. If the blue or green sticker is facing to the side, then it is correctly oriented. If the edge is in the middle layer, it is correctly oriented if the white or yellow sticker faces to the side. If the white or yellow sticker faces the front or the back, then it is incorrectly oriented. If the edge is in the middle layer, it is correctly oriented if the green or blue stickers faces the front or the back. It is incorrectly oriented if the green or blue sticker faces to the side. Why are these the rules for orienting edges? When we permute edges, we will be limiting ourselves to R2andL2double turn setup moves where as theU,D,F, andBfaces are free to move however. For an edge with a white sticker in the middle layer, you will notice that if the white sticker faces to the side, we can bring it to the top layer and have the white sticker face directly up with one of the setup moves. However, if the white sticker faces in front, the setup moves that we are allowed to use will never be able to move the edge so that the white sticker is on top. The same logic is applied to all edges. Now, we will experiment with the algorithms. I use two main algorithms, but there are many edge orientation algorithms available, and as always, the more you know, the more choices you have. The main algorithm switches two opposite edges in the top layer. Perform the move (M’ U M’ U M’ U2)(M U M U M U2)on a solved cube. You’ll notice that it switches the near and far edges in the top layer. M’,for me, moves in the same direction asL’. However, you should notice thatM’andMare interchangeable in this algorithm. It does not matter which way you move the middle slice first as long as you switch directions in the middle. Furthermore, theUcan be easily substituted with aU’. It does not matter; the algorithm is symmetric. I personally preferU’because I am right handed, and so I allow my right hand to perform the sliceMmove and my left index finger to do theU’move. Now, try doing a setup move with this algorithm. Try the setup move L’ B’, perform the algorithm, and then conclude withB L. Notice thatL’B’moves the top left edge into the position formerly occupied by the top back edge. BLsimply reverses the setup move. Try a variety of setup moves such asB2or even a cube rotation. As long as you reverse your setup move, everything will be as you expect it. Now, try a four-edge flipper. The following algorithm will flip all four edges in the top layer. (M’ U M’ U M’ U M’ U)(M U M U M U M U). Notice how it flips all four edges. Again, realize thatM’andMare interchangeable as with before. Furthermore, realize that I am right handed and that I preferU’overU. As with before, experiment with some setup moves and familiarize yourself with this algorithm. There are other algorithms available. Certain algorithms will flip six, eight, or even all twelve edges. However, I feel that these two algorithms are sufficient as almost all possible cube states can be reduced to just several applications of the above algorithms. Experiment with only the first half of the four-edge flipper and see what it does. Finally, experiment with this one: M2 U M U2 M’ U M’ U M’ U2 M U M’. A list of algorithms will be provided at the end. Memorizing: Again, if you prefer, one can memorize the edge orientation state with numbers by simply ordering the numbers and then by remembering a string a binary digits. I personally prefer to just visualize where the incorrectly oriented edges are. Frequently, instead of memorizing which edges need to be corrected, I will memorize the algorithms necessary to correct them. This is very fast as I can execute the algorithm without even thinking about the edges that I’m affecting. Here’s an example. Let’s say I see three edges that need to be corrected on the top and one edge that needs to be corrected on the bottom. Instead of memorizing which edges are incorrectly flipped, I will memorize the setup move D R2or something similar. Then, I will perform the setup move, apply the four-edge flipping algorithm, and then reverse the algorithm. There are many ways to memorize the cube, so by all means just do whatever works for you. Corner Permutation: All your edges should be oriented now. Now, we will put all the corners in their correct place. For this step, I have numbered my corners to assist in the recognition of the cycles. There is no standard numbering convention. Macky, Leyan, and I all do it differently. Start with your first corner location. For me, this is the top, front, right corner. For Leyan, it’s the top, front, left, and he holds the world record, so maybe you should listen to him. If your first corner is correct, more specifically that the piece that belongs there actually is there, move on to your second corner. Otherwise, you will have a different corner in that location. Look at the corner in that location, and go to the position where that corner belongs. Since that corner is in your first location, it cannot be where it belongs. Therefore, there will be another piece in that location. Look at where that corner wants to go, and go to the next corner position on the cube. Continue this until you find the corner that belongs in the first position, then stop. That’s a cycle. If you have accounted for all eight corners, then you are done. Otherwise, you will need to go to the next corner position that has not been visited by the previous cycle, and continue again. Let’s make slot A our “first” corner position. Suppose corner B is in slot A. We then take a look at corner B’s desired position. In corner B’s position, we have corner C. We look at C’s position, and we see D. We look at D’s position, and then we see E. When we look at E’s position, we see corner A, and so we stop, and we remember the cycle (ABCDE). It not necessary to memorize the cycles with letters or numbers. As long as you know where the cycle leads, it’s fine. Now, we continue on our memorization, and we go to the corner position F. We see that in corner position F is corner position G, and we follow G to H, which leads us back to F, and so we have the cycle (FGH). Occasionally, you will have cycles with an even number of elements such as (ABCD) or (EF) or (ABCDEFGH). If we have an even number of even cycles such as (AB), (CD), (EF), (GH), then there is no parity error. Otherwise, there is a parity error and I will discuss how to correct that later. First, we will deal with cycles of odd length. When we permute corners, we generally swap them three at a time. I will illustrate other algorithms later as well. Experiment with the algorithms (L F’ L B2 L’ F L B2 L2) and(R’ F R’ B2 R F’ R’ B2 R2). Notice that these two algorithms are mirror images and they both cycle three corners. Notice that (R’ F R’ B2 R F’ R’ B2 R2)cycles the bottom right corner to the top left position, the top left corner to the top right position, and the top right corner to the bottom right position all in the top layer. Even more importantly, notice that the bottom left corner in the top layer is untouched. Before we proceed, it is important to understand the restrictions of the setup moves. While permuting corners, only the UandDfaces may make single turns. TheF,L,B, andRfaces are restricted to double turns. Consider now that we want to solve the cycle (ABCDE). First, we want to deal with the corners A, B, and C. The most common situation is that you have one corner in one layer, and two adjacent corners in the other layer. This is nice, because we can put all three corners in the top layer easily. Generally, this can be accomplished by a double turn of one of the side faces. Sometimes, a D2is necessary to move the bottom corners away from the top corners. Notice,DandD’are acceptable setup moves, but sinceD2can solve every case, you might as well use it. It makes it easier to remember and you won’t make a mistake going the wrong direction. Now that all three corners are in the top layer, determine whether or not they wish to be cycled clockwise or counter-clockwise and choose the appropriate algorithm. If they want to cycle clockwise, you need to do the “right handed” algorithm. Set up the three corners correctly. This is very easy if you remember the “blank” corner. One of the corners in the top layer does not need to be cycled. If we are doing the “right handed” algorithm, put this blank corner in the bottom left corner with a U,U’, orU2move. Then, do your algorithm, and reverse your setup moves. If it is a counter-clockwise cycle, then your blank corner goes in the bottom right corner. After you have cycled A, B, and C, you may eliminate B, and C from your string. Now, (ABCDE) becomes (ADE). Simple cycle (ADE) and you are done with that entire cycle. Do this until all corners are solved. Sometimes, you will have one corner in one layer, and you will have two corners situated diagonally from each other in the other layer. This makes the setup move more difficult. However, in my misunderstandings with Leyan, I have come up with a good way of solving these situations. Consider the cycle (ABC). A and B are in the to player. A is in the bottom right corner and B is in the top left corner. C is in the bottom layer directly below A. Now, try to algorithm (R’ F R F’)x3where x3 means you repeat those moves three times. You will notice that corners A and C are swapped, B remains untouched, but the other two diagonal corners in the top layer are swapped. The idea here is that were’ going to swap two corners, then we’ll swap the other two. In the process, the corners getting swapped diagonally will be swapped twice, and they will return to their original positions. Remember, we want to swap A to B, B to C, and C to A. Since C wants to go to A, we apply the algorithm right away. Now, we do U2,which positions B in the location where A used to be, we do the algorithm again, and we’ve swapped (ABC). Remember to doU2again to undo your setup move. Because the corners in question are diagonal from each other, the setup moves in the middle of this algorithm are always double turns. Now, consider the same situation, but consider the cycle (BAC). Here, C wants to go to position B. Therefore, we must perform U2first in order to place C in B’s position, and then we doU2and swap the others. Notice that we do not need aU2to reverse the setup move at the end. In this situation, we do not swap A and C first. A does want to go to C, but C is the lone corner, and if we swap A with C first, we will destroy it when we include the swap with B. The same method can be applied if two corners are diagonally in the bottom, and the other corner is in the top layer. Think about which position the top layer corner wants to go, and do that swap first. Then do D2, and do the next swap, and then reverse your setup moves. In this process, it is sometimes necessary to position the corners with UorDmoves. Just make sure you reverse them when you’re done. There are other similar algorithms such as(R B’ R’ B)x3. They’re all basically the same. Now, we will discuss cycles of even length. How do we cycle (AB) and (CD)? Experiment with the algorithm (R’ F R’ B2 R F’ R’ B2 R2) U (L F’ L B2 L’ F L B2 L2) U’. Notice you do not have to memorize anything new. Notice that this algorithm swaps the bottom left corner with the bottom right corner and the top left corner with the top right corner. However, sometimes it may be difficult to perform the necessary setup moves in order to place the corners in this configuration. Instead, we can swap the corners in two steps using a T-permutation. This is very similar to Stefan Pochmann’s blindfold method. Let’s say we want to cycle (AB) and (CD). First, we will cycle A and B. Put A and B into the top right and bottom right corners in the to player. However, when doing these setup moves, we do not want to disturb the left and right edges in the top layer. This can be accomplished by performing a UorDmove combined with aF2orB2. Now, perform the algorithm(R U R’ U’)(R’ F)(R2 U’)(R’ U’ R U F’). Now, you have successfully swapped corners A and B, but you have also swapped the left and right edges in the top layer. Reverse your setup moves, and now position C and D in the top right and bottom right corner positions, and do the algorithm again. You will swap C and D, and you will reverse the damage done to the edges. Note, that a U2setup move will not damage your edges. Swapping the left and right edges is the same as the right and left. Sometimes, it is more convenient to swap the top right and bottom right corners, and then swap the top left and top right corners. This is also fine, but always keep in mind which edges are being swapped and be sure not to disturb them with your setup moves. If you do this, sometimes all four edges will be swapped. If this is the case, simply performM2 U M2 U2 M2 U M2and correct all four corners. Memorizing: Being the numerically minded person that I am, I generally rely on the use of numbers to aid in my memorization. It should be clear that if your corners are given numbers 1 to 8, you can generate a numerical cycle such as (1 5 7 2 4 3 8) which will give you all the information you need to complete the permutation of the corners. Numbers are especially useful if the permutation cycle resembles something mathematical such as (1 2 3 5 8)(4 6 7) where the first cycle consists of numbers from the Fibonacci sequence. However, numbers have generally become obsolete with the general blindfolding population and many people rely on the shapes and the patters of the permutation that the path of the corners trace out. Everyone has a different way of memorizing things and so pretty much as long as you can retain the information, it doesn’t matter how you do it. Edge Permutation: Permuting the edges is basically the exact same thing as permuting the corners. Instead, as stated above, the limitations of the setup moves are more liberal. We are allowed to make single turns on theF,B,U, andDfaces. All setup moves on the left and right sides must beL2andR2. The algorithms you will use will be the basic three-edge cycles. These should be quite familiar to you from speed cubing. Edge Parity Correction: In this tutorial, I have explained how to correct corner parity in the event you wish to switch corner A with B and corner C with D. Edge parity can be done very similarly. If you can situate your edges using the appropriate setup moves into an H-permutation (M2 U M2 U2 M2 U M2)or Z-permutation(R B’ R’ B F R’ F B’ R’ B R F2 U), then those algorithms will correct the parity for you. Note: The Z-permutation can be performed on the F,B,U, andDfaces and it will still maintain the orientation of the edges. The H-permutation can in fact be performed on any face. Try the H-permutation on theLface and notice is still preserves the orientation of your edges. Similarly, the H-permutation + U2 or (M2 U M2 U2 M2 U M2 U2)which swaps two sets of diagonal corners can also be performed on any face without interfering with the corner orientation. In general, corners that are being swapped diagonally may be swapped on any face. Otherwise, they are confined to UandD. Edges that are being swapped across and not adjacent may also be swapped on any face. Otherwise, they are confined toF,B,U, andD. Sometimes, it can be difficult to perform setup moves that arrange all four edges on the same face. In such cases, the parity can be broken down into two steps. Suppose you want to swap edges A and B and edges C and D. Using the setup moves with the appropriate limitations (double turns for the left and right sides), place edge A at the FU position and edge B and the BU position. Then, perform the H-permutation. Reverse your setup moves and then put edge C in the FU position and edge D in the BU position and perform another H-permutation. Again, reverse your setup moves. This sequence first swaps edges A and B but also swaps edges at the FL and FR positions. The second H-permutation swaps edges C and D while correcting the FL and FR edges. Corner and Edge Parity Correction: Corner and edge parity occurs when one wishes to swap corners A with B and edge C with D. If it is possible to bring A, B, C, and D all to the same face, then the appropriate PLL may be performed. It is important that if corners are being swapped non-diagonally and edges are being swapped adjacently, you probably have to perform the PLL on the U-face. However, sometimes this can be difficult to setup, especially if you are blindfolded. It is possible to break down the corner/edge parity correction into two steps. First, let us correct the corners. We will be utilizing the T-permutation, which will swap the FRU corner with the BRU corner. Position corner A and corner B into FRU and BRU. In doing so, it is important not to disturb Oh I'm sorry, you wanted to learn how to solve the cude. Let me work on that. Tyson Mao MSC #631 California Institute of Technology On Nov 25, 2005, at 11:48 PM, sri charan wrote: > --- In [email protected], crazycomputers wrote: >> > please tell me how to sove the cude > > > > > >> I can usually solve the Rubik's Cube in 2-3 minutes. >> > > > > > > > > > Yahoo! Groups Links > > > > > > ------------------------ Yahoo! Groups Sponsor --------------------~--> AIDS in India: A "lurking bomb." Click and help stop AIDS now. http://us.click.yahoo.com/VpTY2A/lzNLAA/yQLSAA/MXMplB/TM --------------------------------------------------------------------~-> Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/speedsolvingrubikscube/ <*> To unsubscribe from this group, send an email to: [EMAIL PROTECTED] <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/
