Before you read the article, make sure you start with a completely solved Rubik's cube. Read the whole article, and learn the basic concepts, and make sure you learn the move sequences that are at the end of the article ("Basic Move Sequences") before you mix up the cube. It's much easier to see what each move sequence does when you start with a solved cube. You can do a move sequence, and then see what it does by looking at what happened to the cube.
Note that if you don't have a solved Rubik's cube, you can always take the cube apart to fix it manually. To do this, start by prying out an edge piece (edges are the pieces that have 2 visible sides to them) out. Corner pieces (corners are the pieces that have 3 visible sides to them). The center pieces (only 1 visible side) for each side of the cube cannot be removed. Once you have the first piece out, you can carefully remove the other pieces and manually reassemble all the pieces to the solved condition.
This article will not attempt to make you a speed cuber. World class speed cubers can solve a given cube in about 15 seconds. When you first start trying to solve the cube it will likely take you several minutes, or even more.
However, you can greatly reduce your time by learning how to recognize patterns on the cube, which will tell you what move sequence to do at what times, and then learning to simply execute those move sequences faster. Of course, you need a quality cube as well -- one where the sides move freely and easily.
Once you have gotten to a place where you can solve the cube, there are many published methods for speed solving the Rubik's cube. Some of these include:
There is plenty of information available on the web about these methods, and other methods as well.
However, before you worry about speed cubing, you need to worry about learning the basics. This is what we are going to try and cover here. If you have never solved a Rubik's cube before, and want to get a roadmap to what you need to learn, this is it.
Lastly, a warning. Learning to solve the cube reliably will take lots of experimentation and practice. It's not simple, and there are lots of things to learn. So be patient (and stubborn) and your chances of developing the necessary skills will be much improved.
- The Basic Process - Stage 1
The first thing you need to do is subdivide the problem. You are not going to simply twist the cube a few times and find it solved (unless it was almost solved already). The way I originally learned to do this was by solving the top layer first. The following pictures will show you one example of this (the pictures show the exact same cube from 2 different vantage points):
Note that solving a top layer should be pretty easy, even for a beginner. Solve the edges first, and then the corners. Here are some routines you can use to help you solve the top layer:
If you are trying to solve the top layer first, the first thing you need to do is to decide what color you are going to have on top. When first starting out, it's easier to always have one particular color on top. This will make pattern recognition easier for you. The first thing you need to do is to get the edges into place. In other words, I usually get the white-orange edge, the white-green edge, the white-red edge, and the white-yellow edge in place. This is very simple to do.
Getting the edges in place can be done with very simple manipulations of the cube. Which move you are using depends on the situation you have. The first two examples below are quite simple. The third example is made a little more complex because we want to put the red-white edge piece in the right place, but we already have all the other edge pieces in place, so we need to get the red-white edge piece in place without upsetting the others.
When you are done, make sure that you have all the edges in the exact right place and rotation. Then you can work on the corners. In all of the example sequences below, you have certain pieces on the top surface, the white one, which are already solved, and you are trying to get the corner pieces into the right place.
Here are some examples of moves to use to get the corners in place, once the edges are all set.
There are more variants of these moves that you can learn with practice.
Just a Bit More on the Other Methods - The Basic Process - Stage 2
Once you solve the first stage, regardless of the method you use, you then advance to the second stage. In the old fashioned layer by layer method, you solve the second layer, and will end up with a cube that looks something like this (same cube shown from 2 views):
The Petrus Method has this in common, where he solves the complete 2nd layer before moving to deal with the bottom layer. The Roux method is quite different, and leaves the cube in the following state (same cube shown from 2 views):
Notice in the first picture that on the side with the red center all the orange pieces are correctly oriented, and on the side with the yellow center all the green pieces are correctly oriented, including the green-white edge. Notice in the second picture that on the side with the orange center all the red pieces are correctly oriented, and on the side with the green center all the yellow pieces are correctly oriented, including the yellow-white edge.
If you study this carefully, you will see that there are only 6 edges out of place, as well as four of the center pieces. A bit of a peculiar shape, I agree, but this is the path that the Roux Method will take you down. With that in mind, let's keep things a bit simpler to think about for the rest of this article. We'll continue now with our strategy of solving the cube a layer at a time. Having solved the first layer, let's discuss techniques for solving the second layer.
- Simple Techniques for Solving a 2nd Layer
There are two moves that I am likely to use in solving the middle layer. They are the Right Handed Edge Mover and the Left Handed Edge Mover. To demo these moves, we will flip the cube, so our solved top layer is going to become the bottom layer. Then, these moves as shown here will help you move edges off the top layer into the middle layer in the correct orientation. Here they are:
Right Handed Edge Mover Basic
Use the mouse to grab the cube and rotate it. Three edge pieces have changed locations. Make sure you find them all. In the first animation, the pieces that have moved are the yellow-white edge, the red-white edge, and the yellow-orange edge piece. Notice how two edges from the top layer have moved, and one from the middle layer (the yellow-orange one) has moved.
Of particular interest is that the yellow-white piece moved from the top layer to the middle layer. Taking advantage of this will be quite helpful in solving the middle layer.
Left Handed Edge Mover Basic
As with the Right Handed Edge Mover, 3 edge pieces have moved. Once again, use your mouse to rotate the cube and find them all. Using your real cube, make sure you do each of the above Basic Move Sequences 3 times in a row to see what it does. Done correctly, this should return you to a solved cube.
To get a feeling about how to use this we will provide an example of one of the edge movers (we will use the reverse of the left handed edge mover) in action. Notice that the piece that we are moving into place is on the back side, and it is the red-green edge piece. Also, we have moved the completed layer to the bottom to fit in with the demonstration.
- Finishing the cube
Now you want to work on the final stage of this effort. The first time you read this article, make sure you read through this section to get perspective on what the steps are. Once you have a flavor for how it works, go through it again with a cube in hand. Try each of the moves out on a solved cube to see what they do. You should go through each of the moves multiple times to develop a deeper understanding of the impact of each.
The first thing you need to accept is that you will temporarily upset the work that you have done, but the move sequence will then repair the damage by the time you are done with the sequence. Do not lose track of where you are during these sequences, because you may end up having to start over.
The easiest way to keep track of where you are is to always hold the cube in your hand with the the same surface facing you and the same surface on top. Rotate sides of the cube for sure, but never rotate the cube itself in your hands. You are just asking for trouble if you do!
- Building a Portfolio of Basic Move Sequences to Finish
The way to solve this final stage is by learning Basic Move Sequences. Make sure you learn these sequences using a completely solved cube. It will be too difficult to recover if you are working with a cube where you have solved 2 layers, and try to see what they do. Doing this with a solved cube is definitely the way to go. The Basic Move Sequences will give you 3 skills:
- Switching the position of 2 corners
- Rotate 2 corners, without changing anything else
- Moving and flipping the edges in groups of 3, without changing anything else
With these 3 skills, you can solve any cube. So let's dig in, and look at the details, but let's first start with a couple of important definitions:
Out of Postion vs. RotatedTo help you visualize a cube with pieces out of position, here are two pictures of a cube with corner pieces in the wrong position (both pictures show the same cube from different angles).
Notice how the red-blue-green corner piece is in the place which belongs to the red-blue-yellow piece and vice versa. Let's take this a bit further, and look at a couple of pictures where 3 edge pieces are out of position (both pictures show the same cube from different angles):
You can see that the cube is completely solved, except that there are 3 edge pieces out of place. Let's also take a look at a couple of examples of rotated pieces. Here is an example showing two rotated (aka flipped) corners (both pictures show the same cube from different angles):
If you look carefully, you will see that the orange-blue-yellow piece sits in between the orange, blue, and yellow sides, but it's orientation is wrong (it is rotated). The same is true for the red-blue-yellow piece. Now lets look at a couple of rotated edge pieces (both pictures show the same cube from different angles):
You can see that there are two edge pieces that are in the right location, but once again the 2 sides of the edge do not match up with their corresponding center piece.
Now that we have defined these terms, let's move on to the next step!
Switching the position of 2 corners
Now we will show a method for causing two corners to swap position. In addition to swapping the position of two corners, this move will also cause movement of the edges on the last layer as well. That is why we do this as our first step on the last layer. Since we have not yet solved the edges, we don't care if they move.
When we begin working on the remaining edges, and on the orientation (or rotation) of the corners, we will use move sequences that do not affect any other pieces on the cube, other than the ones we are working on.
When you begin to work on the placement of the corners, you will either have 2, 3, or 4 corners out of place (or 0, of course, in which case you can skip this step). The best way to start is to take two of the corners that belong on one side that are next to each other (for example, the 2 red corners), and move them to the red side. If you have white on top, this will be the yellow-red-white corner and the green-red-white corner.
Then you can see if the yellow-red-white corner is on the yellow side or the green side. If it's on the green side, then the two corners are swapped. Note that if the 2 red corners are out of place, try this same exercise with one of the other colors, yellow, green, or orange.
If 2 corners are out of place you will need to do this move one time to get those 2 corners in place. If 3 or 4 corners are out of place then you will need to use the move two different times to get everything into place.
Once you are done, the corners may be rotated so they don't look solved yet, but you will have them in the right location.
Lars Petrus offers a method he refers to as Niklas. Niklas will cause the 2 corners closest to you (the ones out of place in the picture above) to swap with each other, without changing the position of the two other corners. Here are the steps:
Once you have completed the move sequence, study the results. What do you notice about the 4 corners? The two in front have swapped positions and rotated. The two in back have stayed in position, and also have rotated. What about the edges? None of them have rotated, but they have all moved one position to the left. Note that if you repeat the Niklas sequence 4 times that the edges do move back to the correct position.
However, the corners are not yet right. Even though they are in the right position, they are rotated. If you keep repeating the Niklas move sequence, it will take you a total of 12 repetitions to get back to the solved position. There are many patterns that you may come to recognize, if you spend lots of long hours with the cube, and many other moves you can learn to take advantage of this, but for now, the Niklas gives you a way to swap the position of 2 corners.
Rotate 2 corners, without changing anything else
Once you have all the corners in the right location, you will find that there are 4 possible scenarios: 2, 3, or 4 corners rotated incorrectly, or all the corners are correct. Of course, if all the corners are correct, we don't need to worry about it. To make things a bit simpler, let's assume that 2 corners are correct, and 2 are wrong, as in the following picture:
To fix this, orient the cube as shown below, and follow the move sequence step by step.
Once you have done this, you will have flipped two corners without changing the location of any other piece. You should take a completely solved cube and do this sequence to see what it does. Once you have done it, repeat the exact same sequence on the same two corners and see what happens. Then do it a third time, and you will see that the two corners move back to their original position. If you start with a solved cube and do the complete move sequence 3 times, you will get back to the solved cube once again.
The beauty of this maneuver is that you can rotate the position of 2 corners without changing anything else.
Moving and rotating the edges in groups of 3, without changing anything else
Now everything should be done except a few edges. They can be oriented a lot of different ways. Once again, you should start with a solved cube to see what happens when you execute the new move sequence below. There are 3 Basic Move Sequences that will get you there.
We have already shown you the Left Handed Edge Mover and the Right Handed Edge Mover, but we need to show you a modified version of those, plus one new Basic Move Sequence. As before, repeat these move sequences 3 times to see what they do, and how they move and rotate the corners.
Note that the second cube in each example shows the same move sequence, but in the reverse direction.
- Right Handed Edge Mover Complete
The difference between this move and the Right Handed Edge Mover Basic is that the 3 edges that we are moving are all on the top layer. Since at this stage we have the two other layers solved, we need such a move to be able to keep moving forward without undoing the work we have already done. - Left Handed Edge Mover Complete
This version of the Left Handed Edge Mover has also been modified to move three edges from the top layer only. - Two Handed Edge Mover
You will need to study these move sequences so you can learn which one to use in which situations. Make sure you understand the direction in which the pieces move, and the nature of how they rotate their orientation as well. With this in mind you will know which move sequence to use at which time.
Once you understand exactly what each of these sequences does, you will need a maximum of 2 of these move sequences to solve the cube when there are only edges out of place and/or rotated on the bottom layer. However, which move sequences you need will vary depending on the exact state your cube is in when you get to this stage.
For purposes of perspective, we will take a brief look at the general technique used by the other approaches to solving the cube. You can skip this section for now, if you are tunnel vision focused on learning how to reliably solve the cube. Once you have more experience, it will be valuable to see the alternative forms of thinking that people use.
In the Petrus method, you solve a 2 x 3 cylinder first, and the cube looks like this (again the pictures are the same cube from 2 different vantage points):
We are not going to try to teach the Petrus Method here, but simply include these pictures, and the following ones of the Roux Method, to provide some perspective with regard to different approaches. In the Roux method, you solve 2/3 of 2 opposing sides first. Here is how the Roux Method looks at this stage shown from 2 different vantage points:
Notice that 2 of the 3 layers of the red side are solved (shown in the first picture above), and 2 of the 3 layers of the orange side are solved (shown in the 2nd picture above).
This is just a primer, to get you out of the starting gate. There are lots of different Basic Move Sequences that you can learn, but you really don't need to learn that many to become fast. That is much more about recognition of what the move sequences do, and when to use them.
If you want to become a speed cuber, plan on spending hundreds of hours on learning the move sequences demonstrated in this article, and perhaps a few more, and when to use them. For example, one simple variant is to take a move sequence and do it in reverse.
Learning when to use which sequence will take many hours of study. But, if you learn to do the Basic Move Sequences in this article, you will be in a good position to solve that cube lying in your basement since someone mixed it up on you 6 years ago ...
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