3x3x3 Beginner's Guide:
A Beginner's Guide to Solving the Rubik's Cube. v1.10:
by: Caleb Lau
Introduction:
Anyone can solve a Rubik's cube. With that in mind, this tutorial was designed and written so that someone with no experience whatsoever would be able to understand and apply the skills discussed here. In my opinion, this is the simplest way to solve. It does not involve much thinking, however, I do recommend that you try to understand what you are doing in every step.
An essential part of learning anything new is practice. So let's see...um, the best way to put it: PRACTICE, PRACTICE, PRACTICE. Ready? Let's begin! (Please be patient, as the applets may take some time to load).
Method Overview:
First of all, let me clarify the most common misconception of the speedcubing world. There is NO secret formula to solving the cube.
There are, in fact, many ways of solving the Rubik's cube, whether it be by building blocks of colors, or working layer-by-layer. In this guide, we will use a simple, seven step, layer-by-layer (LBL) method: (Note: I did not develop this method. I am only giving it to you in my own words. One reason as to why this method is a great way to start out is that if, after you learn and master this method, you want to get even faster, it can easily be expanded to an advanced Fridrich-style approach.)
1. Form a cross on the bottom layer
2. Complete the bottom layer by inserting corner pieces
3. Complete the middle layer (1 algorithm plus mirror)
4. Form a cross on the top layer (orient the edges) (1 algorithms plus inverse)
5. Orient corners on the top layer (1 algorithm plus mirror)
6. Permute top layer corners (1 algorithm plus mirror)
7. Permute top layer edges (1 algorithm plus mirror)
As you can see, you will need to memorize 5 algorithms (a set or sequence of moves or turns that gets your cube from a specific starting state to a specific ending state) and their mirrors/inverses in order to solve the cube. A mirror is the same algorithm executed as a reflection across the cube. For example, the mirror of a clockwise turn on the right side would be a counterclockwise turn on the left side. An inverse is the same algorithm but executed in the referse order, reverse direction. For example, I'll assign two turns, turns 1 and 2. The original algorithm is 1 2 (both clockwise) and the inverse in 2 1 (both counterclockwise).
Basic Information and Standard Notation:
I would highly recommend that before you read the rest of this guide, you would just play around with the cube. Scramble it. Try to understand the movements. Notice how the center pieces never change their location in relation to the other centers. Notice the differences between corner (3-color) and edge (2-color) pieces. Please, please do these things. In my opinion, they are very important to the learning process and will help you greatly when it actually comes time to solve. You can know all the algorthms in the world, but when it comes down to solving for speed, you must be able to visualize and understand your turns.
I will be referring to two different kinds of movements: orienting and permuting. Orientation involves the turning or flipping of a piece without changing its overall position. Permuting involves the movement of the piece itself in relation to other pieces. For the time being, if you don't understand, don't worry. You will.
Lastly, I want to talk about standard notation, a nomenclature that will allow me to communicate certain turns on the cube. On every cube, by definition, there are six sides. In standard notation, we call these faces Up, Down, Left, Right, Front, and Back (U,D,L,R,F,B respectively). Every letter, by itself, stands for a clockwise turn (when looking directly at that face.) Every letter followed by an apostrophe represents a counter-clockwise turn (when looking directly at that face.) Every letter followed by the number "2," represents a double turn (180 degrees). The system is actually very simple, so now that we have established this, let's look at an example:
1. Turn the Front face clockwise
2. Turn the Right face clockwise
3. Turn the Up face clockwise
4. Turn the Right face counter-clockwise
5. Turn the Up face counter-clockwise
6. Turn the Front face counter-clockwise
Understanding the notation is very important when you begin to learn algorithms. For future reference, some algorithms will use the "x", "y", and "z" terms. These represent full cube rotations (no turning) around the respective axis. Also, lower case letters represent double layer turns. Not all algorithms use these terms, so if you are having trouble understanding, use the applets.
Step One: Form a Cross on the Bottom Layer:
The first step involves solving the four edge pieces on the bottom layer. (This forms a cross shape.) A cross is considered "solved" when the corresponding center pieces match-up with the edge pieces. The first applet shows how a solved cross should look. The second applet shows a "bad" cross, one that would not be considered solved and how to fix it.
There is no set way to solve a cross on the cube. It is the most intuitive part of the solve and if mastered, can be accomplished in no more than 7 moves every time. I would highly recommend picking a color to solve the cross on and sticking with it for every solve. Also, Because center pieces never change their position, you can consider them solved. This unique characteristic allows them to be used as reference points. So, solve a white cross around the white center piece.
Step Two: Complete the Bottom Layer by Inserting Corner Pieces
This next step after the cross involves completing the first layer (the bottom layer). Because there are only a few restrictions to moving the slices, this is also a very intuitive step. However, for a beginner, I will include a few shortcuts to solving the first layer, just to save you some time. Once again, the first applet shows you how it should look, the others are examples or tips.
Make sure that the corners are positioned in the right spots. That means that the Red-Blue-White corner piece goes in the spot between the Red, Blue, and White center pieces, the reference points. The entire bottom slice should be solved (see first applet).
Step Three: Complete the Middle Layer
This nest step involves learning an algorithm, and its mirror, that move an edge from the U layer to its proper location. Use the applets as guides to the algorithms.
In the first algorithm, notice how the edge piece in the UF position is placed into its proper slot in the FR postion. The same applies to the mirror algorithm. Use the algorithms to solve the four middle layer edges. Once again, the first applet shows how a properly solved first-two-layers should look. (For future reference, this is how it will be for all steps.)
This can also be an intuitive step (as it is in a Fridrich approach). If you try to understand what is going on, you will notice that the first four turns in the algorithm match up the edge piece with its corner piece. The next four turns put the pair into its proper spot together.
There will be some cases in which you have none of your middle layer edge pieces in the U layer. In this case, some of your edge pieces are in the middle layer. Take them out by simply putting something else into their spot. Then, the piece will come to the U layer, where you can use the algorithm to insert it in to the right spot.
Step Four: Form a Cross on the Top Layer
At this point, you should be able to see two-thirds of the cube already solved, the bottom two layers. This, and the next three steps, will guide you through solving the last layer. You will need to memorize an algorithm and its inverse (the exact opposite). It shouldn't be too hard. To get a cross on the top, you have to properly orient the edges on the U layer. In this step, ignore the corner pieces and only worry about the orientation of the edge pieces.
Two of the three cases are shown below. They are inverses of each other. The other case of edge orientation has no edges are oriented properly. In this case, you can execute one of the algorithms below, resulting in the other case. Execute other algorithm to solve the cross.
Step Five: Orient the Corners of the Top Layer
This step requires you to learn one algorithm and its mirror even though there are seven cases of corner orientation. The algorithm below only solves two cases. It turns three corner pieces either clockwise or counterclockwise, depending on which mirror you choose. However, if you reapply the algorithm a few times, you will be able to properly orient all the corners (last applet). Once you get used to the algorithm and know how to apply it, you should be able to orient all the corners while only executing it twice. But note, as you are learning you may have to use it three or four, maybe even five times.
The last applet shows how you can apply the same algorithm (in this case also the same mirror) to solve one of the other cases of corner orientation.
Step Six: Permute the Corners of the Top Layer
At this point, you should have a fully oriented top layer. There is not much to say about this step because it is not very intuitive. Just follow the algorithms, and visualize. My hint: Pick a corner and place it in the right position (in relation to the first two layers. Then you execute one of one of the following algorithms (which are inverses) to permute the other three corners. When placing this original corner, make sure that the other three corners are not in the right location, it they are, then pick a different corner.
The diagrams are of the U layer and the arrows represent the movement of the corner pieces. Also, these algorithms use moves defined as x,y, and z. Once again, these represent whole cube rotations. Use the applets if you do not understand.
Diagrams courtesy of Dan Harris.
Whoohoo!! Finally, the last step. Once again, there is not much to say about this step. It is not very intuitive and the algorithms should be executed as quickly as possible. Once the corners have been placed properly (previous step), you can permute the edges. Use the following diagrams and algorithms to help you. If you completed step six, this one should be pretty self-explanatory. However, there are two other cases of edge permutation. One: switch opposites. Two: switch adjacent. These cases can both be solved by applying two of the algorithms below. Apply one of them to your cube to get one of the shown cases, then apply the algorithm that solves that case.
Diagrams courtesy of Dan Harris.
Conclusion:
If you cannot solve the cube with this method, your cube may have been rendered impossible to solve (either by removing pieces or removing stickers and putting them back in the wrong spots.) It is up to you to fix it. You can take apart the whole cube and reasslemble or if you or someone peeled stickers reviously (because you felt like cheating), resticker the cube.
I hope you had fun with this tutorial, I know I did. With a little of practice and some time, you should be able to solve at around the 45-50 second range, probably even faster. If you still have questions or suggestions, please feel free to contact me.
Happy cubing!
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