Rubik's Cube arrived at my country in '80s, when I was a child and I always wanted to solve it. The years passed by and I had not the patience to keep trying. One day when I was in the university learning group theory, the professor asked for a work and a friend of mine said me that he saw an article about groups and the cube in a book. We made the work together and I discovered that he knew a solution for the cube. I learned it and practiced to solve the cube in about 1 minute. In the following, I will describe the method I learned from him. Later I discovered a lot of other methods, but probably because I learned this one first, I still think that it is the easiest.

Let us start with notation. Look at the figure at the left. Let us name the faces of the cube. Holding the cube in front of your eyes, the face you´re looking is called F (Front). The R (Right) and U (Upper) faces are as drawn in the figure. The opposite face to F is called B (back), the opposite to U is D (Down) and to R is L (Left).

Each little square inside each face is called a cubicle.

The first task is to solve one face of the cube such that the laterals of that face are matching correctly the center cubicles of the adjacent faces. The colored cubicles of the figure at the right show the important cubicles that must be matched at the F and R faces. The same must apply to B and L. There is no need to worry about the D face at this stage.

I will not teach how to solve one face because it is not so difficult. If you still don't know how, that's an excellent opportunity to play with the cube and acquire some practice before start to solve it all.

Second Phase

Let's introduce a little more notation. In order to start to solving the cube, we need to name the moves we will need. In the figure below, you can see the five basic moves. Each move consists of a 90 degrees turning of the cubicles painted in grey in the direction indicated by the arrow. The moves are always described considering that you are holding the cube in front of your eyes.

A prime after the move indicates the move in the opposite direction, for example, while f indicates a turning of the F face clockwise, f' will idicate the turning of the same face counterclockwise.



Now, the second phase consists in solving the middle layer of the cube. To do this you will only need to know two operators. Operator is a name for a sequence of basic moves.

The operators below will move the green cubicle at the start of the arrow to the place at the end of the arrow. They will let the grey painted cubicles and the entire upper layer intact. The move can be used either to put a cubicle in the right place or to take it off from a wrong place, for the cubicle at the end of the arrow will be put in another cubicle in the bottom layer of the cube.

    

With these simple operators you will solve both the upper and the middle layers of the cube. But to solve the last layer, we will need more complicated operators.

Third (and last) Phase

In the last step you will need to turn your cube upside down, I mean, the unsolved face will be your U face now. To solve it, we will need to introduce one more basic move, the m-move.

This move consists in turning the middle layer of the F face by 90 degrees, letting the upper and bottom layers unmoved. To complete the cube, you will need to know four more operators. Sometimes you will not need to use all of them and, depending on your luck (it happened to me only once), maybe you will use none.


First, we will solve the middle cross of the U face, as shown in the figure at right. We will not bother now about the corners. To do this we will use two operators. The first operator will be used to bring the corresponding cubicles of the middle cross to the correct place, but they may be twisted. We will untwist them after we put them in the correct places.

The operator used to align the middle cross is shown in the figure at the left. Very mnemonic, isn't it? I used to memorize the word ufruruf and them I just needed to remember to put a prime in the last three moves. This operator will change the indicated cubicles without disaligning the other two, but may twist them.

The figure at the right shows a configuration of the cube where the middle cross has all cubicles aligned correctly, but two of them are twisted. The interesting feature when you align the middle cross is that the twisted cubicles come in pairs. You will never see one or three cubicles twisted, only two or four. Let's learn how to untwist them.

Now you must pay attention because it's a tricky operator. The operator works in this way: consider that the F face is in the bottom of the figure. You must put the cubicle you want to twist in the place where you have the circle with the arrow in the figure. Then, you will make the first part of the operator, the power 4 after the (rm) indicates that you will do the two moves rm four times.

Be careful now! The o indicates that you will turn the U face WITHOUT TURNING THE REST OF THE CUBE till the next cubicle to twist reach the cubicle indicated with the circle and the arrow in the figure. DO not bother if your cube seems to be a mess at this point, when you finish the next four rm moves you will find your cube in the correct configuration. If you have four cubicles to twist, just repeat the operator with the two remaining cubicles.

At this point we're only two operators away from solving the entire cube. The next stage is to put the corners in the right place, although they may be twisted. The operator needed to do that is shown at the right. It will change the places of the cubicles as shown by the arrows without affecting the already solved middle cross.

Take a deep breath. You will use the next operator till your cube is totally solved. Don't stop and pay attention, because if you do something wrong, you will probably have to start it all again. The operator at the left only twist the indicated corner. You will use this operator repeatedly till the corner you want is totally untwisted. You will have a totally messed cube, but the corner will be correct. After that, moving only the upper layer, put the next corner to be untwisted and repeat the operator till it is totally untwisted too. You will keep doing this untill all the corners are untwisted. You will see that, amazingly, when you untwist the last corner, the cube will be solved!