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Rubik's Cubes

How do you solve a Rubik's Cube?

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June 22, 2017 6:22AM

Please see sources and related links (below). You can learn to solve the Rubik's Cube at those sites but the answer below explains it well also.

Solving the Rubik's Cube

Please Note: This answer is only for the standard 3x3 Rubik's Cube

The first thing you must realize is how a Rubik's cube works. There are 26 "cubies" that seem to turn. However it is important to know that the centre cubes never move. They are fixed. These are called centre pieces, and there are 6. Yes, they turn around an axis but never move. Upon examination you will realize that not all cubes are the same. There are also corner pieces, which there are 8 of. Each of them have three stickers on them and are a part of two separate faces. Then there are edge pieces, of which you will find 12, which have two stickers on each. I recommend taking apart your cube, examining how it works. To do this, simply turn one face (a side, with 9 cubes) 45 degrees. Then, with your finger, pry up one of the edge pieces that were moved. Continue from there. Pull the rest apart. Putting it back together isn't very hard; just remember to put it in the solved position. This is because chances are when you don't, 12-1 odds are it can't be solved, because there are some permutations (positions) that are normally impossible. (As a side note, don't complain how hard it is to put back together because the 4x4, 5x5, and on, are much harder).

An algorithm is a set of moves. You might say, ah, so if I learn this magical algorithm, I can solve the cube? Well, not quite. You see, there are over 43 quintillion permutations of the cube (43,000,000,000,000,000,000+). One set of moves can't solve it. Instead, there are several steps that orient (place each cube in the right place) and permute (solve the cubes completely so they are in there spot facing the right way in relation to the others). But there are many algorithms that vary slightly in each step depending on the permutation of the cube. You are going to need to know the following things. To simplify the algorithms, here are the letters that will stand for each face: U (up face, on top); D (down, bottom); F (front, so facing you); B (back); L (left); and R (you guessed it! Right). So just so you know, that is U, D, F, B, L, R. don't ask which goes with which color because none do. It is just how you are holding it at one time. Now you need to know the different types of turns: the quarter turn and the half turn. When making a turn, always look at the centre piece and you will be able to see if it is a clock-wise or counter-clockwise turn. The quarter turn is a turn of a face one quarter of the way around clockwise or 90 degrees. Then of course a half turn is a turn of a face halfway around axis (180 degrees, and it doesn't matter which way you turn it. However, if you want to get very fast, this is something you should think about). There is no need for a three-quarter turn because it can be shown and done as a backward quarter turn, and of course a full turn is not a move at all. In algorithms, a quarter turn is represented by just the letter of the face. So F alone means turning the front face clockwise a quarter turn (90 degrees). Or for example F R U means turning the front face a quarter turn, then the same for the right face and up face - but note: it MUST be done in the order it is in the algorithm or it will never work. A half turn is notated the same except there is a 2 after the letter. So F2 means turn the front face a half turn (or two quarter turns). All that's left now is the counter-clockwise quarter turn, which is indicated with an apostrophe after the letter. So F' means turn the front face counter-clockwise a quarter turn. That is all the notation you will need to know for now, and for these instructions. Well that's enough of that. Yes, yes, how to solve a 3 by 3.

STEP 1: The First layer.

DO NOT skip to here. There are no algorithms for this layer. It is intuitive (you learn it by doing it). However, you still need to read the above paragraphs, as it may help you. By the first layer, that means completely solving the U face (the top 9 cubes). Most people start with the same face every time and it's usually the white face. But irregardless of what you chose, the procedure is the same. You must first make the cross on the top. This means that the four edge pieces are solved on the first layer (and of course are on the same side as their corresponding centre piece). How to do this however is hard to explain, as it is intuitive.

You are going to need to remember the order of the colors. With white on top (and of course yellow on the bottom), the colors are, starting at blue moving left: blue, red, green, and orange. This may seem obvious but it is a good thing to remember, especially if you want to learn to solve a cube that is even, like 2x2, 4x4, etc. So white is opposite yellow, blue opposite green, red opposite orange. Remember that.

So how do you make that cross? Try and figure out for yourself. You may get it, but chances are it is not the most efficient way. What you should do is solve them one at a time, in order, to start off (remember? So it's going to be the white-blue piece, then the white-red piece, white-green, white-orange). However, when you understand how to make the cross, it really doesn't matter. Let's try it. Take your cube, and if it isn't already, scramble it. Go ahead. Just turn different sides randomly. Thirty to forty turns should be enough but you don't need to count. First you need to hold your cube with white on top. Now you must find the white-blue piece. With practice you will get good at quickly locating pieces. If it is in the U face, and the white sticker on it is facing up, then it's easy - it's already solved. At this point, there is no need to match the blue part of the piece to the blue centre piece. If it is in the top layer and the white is not facing up, then it can be solved in two moves. First of all, notice that every piece (except for centre pieces) is part of two faces. So this edge is in the U face, but also another face. Turn the cube so that that face is the front face (white is still U of course). Then to solve simply turn F R (it is the easiest, however F' L' works too). If it is in the D face (on the bottom of the cube when white is on top), the answer is similar. If the white sticker in the white-blue piece is facing down, find the second face it is part of, hold the cube so this second face is the F face (white still U) and turn F2. Solved. If it is not (and the blue part is facing down), then again hold the cube so the second face the white-blue cube is a part of is the F face and turn F' R (or F L'). There is one more scenario - where the cube is in the middle layer (all cubes between the U and D face, but not including the U and D face). Look at it - it can be solved in one move. Hold the cube so that the 'cubie' is in the front and right faces. It will be solved either by turning F', or R. Only one will work, but you will understand soon enough how this works.

And that is how you will solve the other 3 pieces too (white-red, white-green, white-orange). But remember - you cannot move the white-whatever edge pieces that have already been solved, or you'll have to solve them again. You will need to play around with it a bit. Also, you must remember that once you have solved the first one, the rest have to go into the right place. Remember, blue, red, green, orange? Okay, I'll stop asking that. For example: the 'cubie' is oriented correctly (in the right spot) but not permuted (so the white is not in the up face as it should be). The easiest solution is to hold the cube so that 'cubie' is in the front-up faces, and then turn F U' R (or F' U L'). If it is in the D face with white facing down, hold the cube so that the corresponding centre piece of the non-white part of that 'cubie' is the front face (ex. if it's the white-green 'cubie', then hold green as F face, which is the face that has the green centre piece). Without turning the whole cube, now turn the D face so that the 'cubie' is in the front face as well. Now turn F' U' R (or F U L'). Now if it's in the middle layer, simply turn the top layer the required way so that you can turn the piece in to its desired position (wit Hough affecting the other pieces of the cross).

You should understand solving the cross. The thing I want you to remember is that until you have to solve them, pieces that are irrelevant at any step (for example, when solving the cross, the position of the top layer corner pieces, or any other pieces for that matter that aren't in the cross), you do not need to pay attention to. And thus is pretty much the logic behind this method for solving. It is, of course, not of my invention, however. The method is the classic and easiest to learn. The principle is that by completing the first layer, it isolates the rest of the cubes to the middle and last layer (last layer meaning the cubes that make up the D face). Then be moving the U pieces, making a change to the rest of the pieces, and replacing the U pieces in a different way, to some extent that is the reasoning on how the second and then third (middle and bottom) layers are solved. This may sound confusing, but you will see the wisdom behind it once you learn the ways of the cube.

And now - the four U corners.

This will complete step 1! It's not hard - just remember that you can't move the cross you've already made. Try it.

Okay, it's alright to have trouble. There is a simple trick to it however, and once you understand it, it will always be easy. First, let's suppose you have the cross complete and want to solve the white-blue-red corner piece. There are of course 8 places the piece could be, and another 3 way it could be permuted in that place. Odds are 1 in 24 that this piece will already be solved. First thing you want to do (read this even if it does happen to be solved) is to get it into the last layer (LL). If it already is, read this, but you won't have to do anything just yet. If it isn't, then hold the cube so that that corner piece (white-blue-red) is in the F and R faces (with white still on top, so also the U face). Then turn R'D'R. Now you can put it back in the FL (first layer, top layer, or U face). Don't forget where this cubie is. Next you have to find where that cubie goes only one place. So it goes between the white-blue and white-red edge pieces. Hold the cube so that spot (which at this point contains any random corner piece) is in the F, R, and U faces. Got it? So then, turn the D face so that the white-blue-red cube is underneath this spot, or in the F, R, and D faces. There are 3 permutations for a corner cube, so there are three ways it could be facing.

-------------1) White is in the F face. Turn D' R' D R

-------------2) White is in the D face. Turn R' D R F D2 F'

-------------3) White is in the R face. Turn R' D' R

Now you just repeat this for the other 3 FL corner pieces and your done step 1!

I am writing this as plain as I possibly can. But it looks more complex than it really is. Is that really possible? Of course it is. Because practice and knowledge is not easy to explain. If you get used to doing these maneuvers you will eventually not need the mini-algorithms provided. As I said, the FL (step 1) is really intuitive. But you can't explain how to do something intuitively! You just have to do it. This should help you start out. You may not be that good at it yet. It does get harder, but everyone was once a beginner at the cube. Even the Rubik's record holder, Erik Akkersdijk, with a time of 7.08 seconds he completed the Rubik's 3x3 in 2008, was once a beginner. So with that, let's solve the second layer.

STEP 2: The second layer

By this you will complete, as you may have guessed, the first two layers.

There are just two algorithms you need to know for this step. I will expect you to understand the way of the cube a bit, so this section is going to be shorter than the first. You will think it is easier, but it isn't really. It is easier to learn and complete, for some people, but is harder because there is those two algorithms to memorize. Don't worry - they're not too long, and one is just the opposite of the other.

NUMBER ONE thing you have to make sure going into this step is that the middle layer centre pieces are lined up with the completed first layer. If it isn't, turn U until it is.

You only have to solve the four middle layer edge pieces in this step, so here we go.

These four pieces are: blue-red, red-green, green-orange, and orange-blue. You don't need to do this every time, but right now let's start off with blue-red. First locate your piece. There is a 1 in 16 chance it is in the right place permuted correctly. But right now, even if it is, let's assume it isn't (but follow as red-green if it is). It is either in the middle layer or bottom. If it is in the bottom here is what you have to do. Turn the D face so that the cube matches up with its corresponding centre piece, and then hold that side as F. So what I mean is the color that is not facing down (on the blue-red cubie) turn D so that that color is on the same face as its centre piece. Got it?

Okay. Now there are two scenarios. F is either blue which means the cube is going to have to go up and LEFT into its spot, or red which means it is doing to have to go up and RIGHT into its spot. The algorithms for this step:

-------------1) Going up and LEFT: turn D L D' L' D' F' D F

-------------2) Going up and RIGHT: turn D' R' D R D F D' F'

And look at that! It's in place. Just do that for the other three and you will have completed step two.

Did it work? Yes? No? Well it may not have. It's fifty-fifty sometimes. But why? Sometimes you'll notice that the cube you want to place is not in the bottom layer - it's in the middle layer. Try and figure out how to fix this.

No luck? The easiest way to go about this is as follows. Why not, instead of trying to take that cubie out, just put another cubie in there using the algorithms? Sure, it works, however it means you'll have to do an algorithm twice (it doesn't matter which one). So once you put another random cubie in, your needed cubie is in the bottom layer. Tip - just to make it easier, make sure the piece you insert to bring your desired cubie out has yellow on it. It makes it easier for you. That's because the edge pieces left are either needed in this step or are part of the yellow face, so by not putting one of the needed pieces in there, you won't have to just take it out again when you do need it.

And that's it for step 2! That's not too bad. Okay. One more layer to go. You're probably thinking that because there are only EIGHT more cubes to orient and permute, that this should be the easiest part of all. Well, not so. Yes, there are only 8 to go (centre cube doesn't count), but to solve them you CANNOT mess up the first two layers. That is why the last layer has been divided into four steps: Forming the last layer cross, Orienting the last layer corners, Permuting the last layer corners, and Orienting the last layer edges. They're not too bad though. Just take it one at a time.

Step 3: Forming the last layer cross.

You will notice that the LL edge piece matches up with its centre piece. However you may by chance achieve this but it is not a part of this step. They can be in any order - in fact you won't even be paying attention to this order until the very last step of solving the cube.

More importantly you will notice that white is no longer on top - yellow is. SO from now on YELLOW is U face.

It's a 1 in 7 chance that this is already complete (notice how your odds just keep getting better? That's because you are isolating cubies). If it's not, well, I'm not going ask you to try it because you'll scramble your cube. It's different this time. All the desired edge pieces are on the bottom layer, but you can't fix them without knowing the algorithms. So there are four scenarios.

-------------1) The cross is formed (1 in 7 chance). Move on to the next step.

-------------2) Two edges are correct and they form a LINE (2 in 7 chances). Hold the cube so this line appears horizontal and turn F R U R' U' F'

-------------3) Two edges are correct and they form and L (3 in 7 chances). Hold the cube so that the two edges of the L are in the B and L faces as well as top (or, more simply, hold it so the pieces form a backward L) and turn F U R U' R' F'

-------------4) No edges are complete (1 in 7 chance)! The only part of the cross that is there is the centre piece, which is always there. Perform either step one or two (holding it any way you like). Then you will have to perform the other one accordingly (so if you chose step 2, after executing it you will have to do the algorithm for step 3 and vice versa.

And there you have it. The LL cross, complete.

Step 4: Orienting the last layer corners.

No picture for this one. Basically what you do is orient the four LL corners so that there are in the right spot. 1 in 5 chances is this is already completed for you. There is one algorithm for this step and you will have to perform it either once or twice (or not at all if it happens to be complete).

Here's what you do. Chose any corner in the LL, for example, yellow-red-blue, and turn U so that it, to some extent, lines up with the two other colors beside yellow on the cubie, so red and blue if you chose the yellow-red-blue cubie. The yellow will not necessarily face U at this point. Hold the cube so that this cubie is in the F, U, and L faces. Now look at the other 3 corners. Which ones are complete? Which are not? If two are complete and two are not, hold the cube so that the two incomplete ones are part of the U and R faces. Then perform the following algorithm, which in effect switches those two pieces:

-------------1) Switch two cubies that are in U, F, and R and U, B, and R respectively. Turn L U' R' U L' U' R U2

That's the only algorithm for this step. But what if three of the corners are unsolved? Well suppose if this is the case, then, while holding your cube the same way, the cubie that is in the U, B, and R faces will either need to go to the U, F, R place or the U, B, L place. Hold the cube so that you switch these cubes, then there are two more that need to be switched and perform the algorithm stated above ( 1) ) accordingly. There you go! Time for step five.

Step 5: Permuting the last layer corners

All these corners are in the right spot right? But they are not solved. So they are oriented, but not permuted, and that is what we are going to do in this step.

This is similar to forming the last layer cross - there are only 2 algorithms you need to know. Except this time there are more scenarios, and the algorithms are longer. Let's just jump right into the different scenarios of what your cube might look like at this point.

-------------1) The four corners are all complete, and the yellow is complete. Proceed to last step.

-------------2) One corner is complete, but all the others are not. In a way the yellow looks like a fish. Hold your cube so that the completed corner piece (the nose) is in U, F, L position. Got it? Now look at the corner piece that is in U, F, R position. Of course it isn't solved, so there are two ways it could be, and there is an algorithm for each way.

-------------------a) The yellow sticker on this cubie is in the F face. Turn R U R' U R U2 R' U2

-------------------b) The yellow sticker on this cubie is in the R face. Hold the cube so that This cubie is now in U, R, L position (turn the whole cube 90 degrees clockwise). Now turn R' U' R U' R' U2 R U2 (notice how it is exactly opposite of the last algorithm?)

-------------3) Two opposite corners are complete, and the yellow in a way forms a figure 8. Hold the cube so that the yellow of one of the incomplete pieces is in the front face AND that incomplete cubie is in U, F, and L position. Perform algorithm for step 2a) and then you will see you have to follow 2b).

-------------4) Two adjacent corners (corner that are close and share being part of two faces) are solved and the other two are not. Look at the yellow stickers on these cubies. They are either both facing the same direction, or are faced away from each other.

------------------a) If they are facing away hold the cube so that those two cubies are in U, F, L, and U, B, L respectively. Now perform algorithms for 2a) and then 2b).

------------------b) If they are facing the same way, hold the cube so that the two cubies's yellow stickers are both in the front face, then perform algorithm from 2a) then follow and perform 2b).

-------------5) No corners are correct. Only the cross is there. Perform an algorithm from 2) and it will look like one of the other steps.

Follow this and you will have completed step 5! But you will notice that the cube is not solved. Not quite!

Step 6: Orienting the last layer edges

The last step. Only two more algorithms! And again, they are similar to each other.

There are different scenarios. Let's go.

-------------1) All edges are oriented, and the cube is complete! You're done!

-------------2) One edge is complete, but the three others aren't. Hold the cube so that the completed edge piece is on the left (in the U and L faces). Look at the unsolved edge piece in the F and U faces. Decide where it has to go. It is either straight back into the B face, or to the right into the R face. Follow either step 2a) or b) depending on your scenario. Yes, there are two other edge pieces unsolved, but don't worry about them, performing the right algorithm from below will solve them too.

--------------------a) The unsolved edge in the F and U face has to go to the B and U face spot (and edge in L and U faces is solved). Turn R2 U F B' R2 F' B U R2

--------------------b) The unsolved edge in the F and U face has to go to the R and U face spot (and edge in L and U faces is solved). Turn R2 U' F B' R2 F' B U' R2

-------------3) None of the edges are solved. Perform algorithm for step 2a) (it doesn't matter how you hold the cube) and then follow step 2b).

There you go! Complete! That is the easiest solution to the Rubik's 3x3x3. If you want, you can print out the algorithms that you need, so you can practice them. You will probably memorize the first layer first, then the second layer, and after a while the third layer will come. Don't give up on it though!

(see the related links)