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Jan 20, '08 6:15 AM
for everyone

Doing The Cube

The infamous Rubik’s cube is solvable from any mixed up position. In fact, there are mathematical theorems that say the cube can be solved from any mixed up position in 22 turns. However, no one has been able to prove this theorem…yet. So we will approach a much simpler method to solving the cube. But first, we need to get a few things understood first.

The moves are fairly simple. Each move consists of a quarter turn and a single slice (a slice being one row or column of the cube). They are as follows.

	Back anti-clockwise		Left anti-clockwise
	Back clockwise		Left clockwise
	Bottom anti-clockwise		Right anti-clockwise
	Bottom clockwise		Right clockwise
	Front anti-clockwise		Top anti-clockwise
	Front clockwise		Top clockwise
	Middle Right clockwise		Middle Right anti-clockwise

So let’s get started. The first step to solving the cube is to solve for the top layer. You should pick a color that will always stand for your top layer. This way, you will always have the same colors to identify with when solving the cube. I will work with blue as my top layer.

To solve the top layer you should use the following formula: p XsX’s’ p’. ‘p’ stands for precondition, and it means that you move your cubies around until a certain precondition is met. For instance, if I wanted to move the bottom middle cubie of the front face, to the right middle cubie of the top face, my precondition would be to move the bottom slice clockwise once. ‘X’ stands for exchange, and it means to exchange one cubies position for another cubies position. Continuing with the previous example, (after satisfying the precondition) the exchange would be to move the vertical middle slice of the right face anti-clockwise one turn. This would place the bottom middle cubie at the right middle cubies position on the top face. ‘s’ stands for slice, and it means to rotate the slice that the exchanged cubie is on. So for our example, I would move the right face clockwise once. In essence, this saves the cubie that we are working with, and allows us to undo everything else. “X’” (read X-Not) means to undo the exchange. Which would mean to move the vertical middle slice of the right face clockwise once. This is the opposite motion of ‘X’, hence “X’”. “s’” means to undo the slice. In our case, this would mean to move the right face anti-clockwise once. This will put the cubie we are trying to exchange, back into its desired position. The last step in the process is “p’”, which means to undo the precondition. Continuing with our example, this would simply be done by move the bottom slice anti-clockwise one turn.

p	X	s	X'	s'	p'

You need to follow this algorithm until you get an entire face to one solid color. Don’t worry about aligning any other cubies than the ones containing your color.

The next step is to orient the cubes so that they correspond with the center cubie of each face. When we’re finished, it should look something like this:

Keep in mind that your colors and my colors may differ. The important thing is to understand that the center cubies are like landmarks. They never move, so we must orient our colors around them. In the above picture all that I’ve done is arranged my side cubies so that they line up with their center pieces. This can be done in several ways, but the easiest is to find the piece you would like to move from the solved layer, turn that slice down, turn the bottom slice left, then turn the other slice back up. This will separate the cubie you want to move from the top face (the one that is a solid color), allowing you to reposition it like you did before.

Here’s an example. Say that I needed to separate the middle cubie of the front face. I would move the front vertical slice down; bottom left; front vertical slice up. Now the cubie is floating around, giving me the opportunity to place it wherever I want. The neat thing is, that when you place that first cubie in it’s oriented position, you will have knocked another cubie out of place, allowing you to put it where it needs to go, and so on and so forth. This isn’t always the case, but it’s neat when it happens.

Once you have the cube looking like the above, it is very algorithmic to solve. The next step is to solve for the second layer:

To do this, you just need to know two algorithms. The first algorithm will move the yellow square to the red square’s position:

The second algorithm will flip the colors of an edge piece:

To make this algorithm a little easier to remember, just notice that it is the same algorithm as the first, but done twice, and with a bottom right move in between them. This is all you need to know for orienting the second layer.

The last step is to solve for the bottom layer. This is probably the most difficult step because it involves a lot of analyzing and repetition. The first step of this process is to orient the four corner pieces. This means that you need to look at each corner piece on the bottom and make sure that the colors on that cubie correspond to the colors on the face to the right and left of it. Below is an example of a correctly oriented corner piece.

The above cubie is oriented because its colors include red, yellow, and green; which are the colors on the faces to the left, right, and bottom.

In orienting these pieces you may find that you need to switch two of them, like in the picture below.

This is done with the following algorithm.

Once all the corner pieces are oriented, the next step is to rotate them so that they are inline with their corresponding faces. The following algorithm will rotate the bottom right corner piece on the right face, left one turn.

But Don’t Do This Yet!

There are real important factors you have to take into consideration before using this algorithm. Not only will this rotate the bottom right corner piece left, but it will also rotate three other corners as well. For that reason, we have do this in certain sequences with different orientations.

To start let’s examine the following scenarios.

In these pictures I am using green as the color of the bottom face. These pictures represent the possible scenarios that you might end up with when trying to orient your corner pieces. In order to properly align your cubies, you need to examine the bottom face, compare them to the three patterns (green is just an example of a bottom face color), and then use the ‘X’ side as your right face. Then you should use the previous algorithm for rotating the corner cubie. Repeat this entire process of examining the bottom face, orienting, then rotating, until all your corner cubies are aligned with their corresponding faces.

The next step is to properly orient the remaining edge pieces. To do this, first look to see if any of the edge pieces are already in the proper spot. A properly oriented edge piece will look something like the following.

In this example, the yellow and green cubie is properly oriented, but the others are not. If you are in a position similar to the above, skip down to the next paragraph. If none of your cubies are oriented, pick any face as your right face, keeping green (in the above example) as the bottom face, and do the following algorithm until you get one aligned.

Once you have a cubie oriented, use the oriented cubie (if you have more than one, just pick one) as your right face, keeping green (in the above example) as the bottom face. Then, repeat the above algorithm until all of the other cubies are oriented.

Now that you have all your cubies oriented, the next step is to align their colors. To find out how you need to orient your cube, look at the following bottom face scenarios and use the ‘X’ as your right face.