Sunday, November 30, 2008
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How To Solve a Rubik's Cube
This article will present a beginner's guide to learning the Rubik's cube. Follow the steps in this guide, and you should be able to solve the cube reliably. It will take time and practice to become fast, but you will be in a position to solve those cubes at your friends' houses that have been sitting on the bookshelf unsolved for the last 6 years.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 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 MethodsFor 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.
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.
The Basic Process - Stage 2Once 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
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.
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:
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.
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.
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!
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:
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: