Sunday, February 6, 2011

How to... Solve a Rubik's Cube

If you are looking for a guide on how to solve a Rubik's Cube, how to master it, all the algorithms you may need to memorize and the intuitive method that you should familiarize yourself with: Youtube, and Google. If you would like my favorite videos and websites: Dan Brown/Pogobat's original Rubik's instructional videos (follow related videos or search for more of his Rubik's related videos, Solve-The-Cube.Awardspace (text instructions, with pictures), and Badmephisto (A little of everything, find the link for his Youtube channel for some great tutorials).

Another note worthy note, this is relating to a Rubik's Cube. Not a Rubiks Cube, or a rubiks cube, or a rubikscube, or a Rubix's Cube, or a rubix's cube, or a Rubixs Cube, nor Rubixscube, nor Rubix Cube, nor rubix cube, nor rubixcube, nor Robick's Cube, nor any other made up cube or misspelling of Rubik's Cube. I will be looking at the Rubik's Cube, invented by Erno Rubik. To be honest, I'm not sure if the 'Cube' should be capitalized in all cases of the proper spelling of the object, but I like it that way.

I received my first Rubik's Cube as a gift from my Grandfather, Christmas 2007 I think. I have not practiced efficiently, and often go through spouts of use followed by weeks to months of shelf time. At the moment my best time I have recorded is twenty seven seconds, something rather impressive considering when I started I was proud of a two minute time. Also, at the moment my average time is around forty seconds. I'm usualy impressed to find myself in anything above thirty; but time is not very important for most people. Most people just want to focus on getting it finished.

The first step to solving this demon cube, as one of my friends calls it, is understanding what you need to be doing. There are several methods, and several ways to go about those methods. There is no one set way to solve any scramble. A reverse scramble (solving the cube by using the opposite movements of the scramble) is the only way to ensure that your solve would be the same as someone else's, and this is assuming they are also doing a reverse scramble on the same scramble. Most people who approach the Rubik's Cube without knowledge of how it works will want to solve face by face. This is practically impossible. The problem that one who is trying this will run into, is once they fix part of the cube they will mess it up in the process of fixing another part of it. This is avoidable, through the use of a layer-by-layer method. This may be difficult to do without algorithms though, even if you have someone explain to you the ideas you are working with.

Some people can solve a Rubik's Cube with only intuition, no instructions from others needed. The majority of the population requires some help through the use of algorithms. I've has many people tell me that this is cheating, using instructions. Even if I have poured hours over them studying, I cannot genuinely solve a Rubik's Cube according to them because I need some help. After putting a large amount of time into learning how to use this device well, I can say I can do a full intuitive solve; kind of.

I understand how each step works, and I do not use any algorithms for the first two layers (by the way; if you don't understand what I mean by layer-by-layer, just keep reading. It will make sense) and technically do not need any for the last layer if I am using a very basic method. The conflict into if I am solving it intuitively or not comes into the fact that the intuitive algorithms that I have worked out, turned out to be the same as the ones I learned through instructions. I managed to figure out how to solve the last layer in a very simple manner only to find out even though I did figure it all out for myself, it was just a different perspective on what I already knew. This is why I say I can kind of do a full intuitive solve. It doesn't mean anything when you're looking at the numbers though. If I'm going for time, I use algorithms that I've learned for the last layer.

These algorithms that I am mentioning, are instructions relating to what side or sides of the cube should I spin. The Rubik's Cube should be thought of as a cube, and at the same time as having three slices vertically, horizontally, and what ever is the technical term for depth related. For the basic methods, you will be taught to use L, R, U, D, F, and B. This are, respectively: left, right up, down, front, and back. In many cases there will be a dash ( ' ) after the letter, indicating counter clockwise. I am in the habit of saying prime to indicate a counter clockwise rotation. It's faster and easier to say. If there is just the letter, you assume it is a clockwise rotation. Each of these rotations are clockwise assuming you are facing them, so if you run into a R rotation the top-right-front corner will rotate to the top-right-back, and the bottom-right-front corner will rotate into the top-right-front corner's position. If this doesn't make sense, take a look at some instructional videos. They'll clear it up quickly.

In more advanced methods you will run into algorithms that have lower case letters, meaning that side and one over. A u' is the top layer and the layer below it (so all but the D) spun counter clockwise. You may also find M, E, and S. These are, also respectively, middle (between L and R), equator (between U and D), and standing (between F and B). A final instruction you may run into is x, y, and z. These are rotations around the x, y, or z axis. All of these which have been listed in this paragraph may also have a dash after them, making for a total of thirty-six different instructions.

The algorithms will look something like: R' D' R D (this is repeated twice for rotation of the front-right-top corner and if repeated six times the cube will return to as it was). Most of the algorithms are much longer than four instructions though, I think the longer ones I use are around twenty? I could be wrong.

Now that the terminology and a bit of theory has been explained, your brain may of started to glaze over the text. I'm going to go into the actual solving, and how I like to.

The first step that almost every method asks for is you solve the cross of any colour. It does not matter what colour you start with, but that will be designated your D layer. On a Rubik's Cube, the cross is a center piece surrounded by four edge pieces of the correct colours and orientation. It is important to ensure you have opposite colours correct, and that you do not need to switch two colours (which is easily done but if not you will run into problems quickly). This step is easy, and ideally will take only eight movements. Often it only takes seven. If you know where all the pieces you need are, this can be done in only one or two seconds if you are going at full speed. I usually get it done in five seconds or less I think. I've never timed individual steps of speedcubing (which, if I have not mentioned already, is the practice of solving a Rubik's Cube as fast as possible).

I should of mentioned colour orientation before, for it's something that is important to take note of. A Rubik's brand Rubik's cube will have the colour layout with green and blue opposite, orange and red opposite, and white and yellow opposite. It does not matter how you remember these, but they can be difficult to do at times. I have never had a problem remembering green and blue, because I've always thought of them to be the most different colours out of the six. Sleeping Beauty came up with the concept that white and yellow are opposite because they are colours related to the sun. It may not be a sound fact, but it helps me remember. This just leaves orange and red, which are fairly similar I think.

To finish the first layer there are four corners that need to be put into place. There are algorithms you can use for these, but most people can do it intuitively. I use the same idea as corner rotation, as I do for many aspects in solving a Rubik's Cube, for putting the corners in place. When I first started speedcubing I used the idea of "I need to put this corner here, but in doing so I lose this edge piece that needs to stay in place, so I will move this edge piece that I would lose out of the way first, put the corner piece in place, then move the edge back." When explaining how to put the corners in, I often use that for my explanation.

The centers of the second layer will already be in place correctly, and lined up with the pieces that were originally put in place for the cross. This will result in four edges needing to be corrected. Sometimes some of them are already in place for you even, but this does not happen very often. Using the most basic methods, here you will run into your first need of an algorithm. There is one algorithm that is used to move edge pieces from the top layer into the second layer, and it can be mirrored if the piece is facing the wrong way. The best way to find pieces that need to be moved down into the middle layer is by finding edge pieces in the top layer that do not have the colour of the U center (the opposite colour to the colour we started with making the cross).

An alternate method to this, is leaving one of the first layers corners unsolved. Then you use a three step algorithm, or even better just a three step concept. I like to think of it as "open the door, walk in, close the door." The door is the empty edge piece that is above an unsolved corner. If you have an unsolved corner and an unsolved edge piece in the second layer, the D or E can be rotated so they line up. By opening the door, you are moving the unsolved edge piece into the top layer, usually by a R or L' rotation. By walking in, you are putting the edge piece that needs to be there into the piece that was previously occupying the spot that the unsolved edge piece was in. Finally, by closing the door, you are doing the opposite movement of opening the door (so a R' or L) and putting the correct edge piece into place, therefore solving that edge piece. The center pieces of the second layer (which I should probably mention is the E slice or layer) may now be lined up with the cross on the bottom layer (the D) if desire. This is repeated three times until there is only one F2L slot left, one unsolved corner in the first layer and one unsolved edge in the second layer. This corner may be fixed just as it would originally, as long as you avoid moving any of the edge pieces of the second layer out of place (which is not very difficult). The edge piece is fixed with an algorithm. Alternatively, since you are working with an F2L slot you could just use F2L method to fix it.

F2L, first two layers, is a method that involves fixing the corners of the first layer and the edges of the second layer together. This way instead of fixing eight pieces (the four corners, the four edges), you must only deal with four F2L sets. The number of moves needed are a bit more than if you were to use algorithms to correct the second layer; F2L is very efficient like that. It can be learned through algorithms (there are 58 F2L situations you can run into I think, I could be wrong, but therefore 58 algorithms) or it can be done intuitively. Once you know the concept of how to use F2L, the intuitive method comes to many people quite easily. Now that I think of it, the 58 situations may not include situations looking at the bottom-left-back and the bottom-right-back slots, which I know can be used because I use them and I think perfect F2L requires them to be used.

The concept is related to corner rotation. Rotate the bottom-right-front corner (clockwise or counter clockwise, I won't be putting the time into giving most algorithms if you have not noticed yet, so explanations like this may not make much sense to people who are not familiar with Rubik's Cubes) and observe the edge piece above it. What piece is now in it's place? Work out where it would of been, which is easy to do if you're starting with a solved cube, and consider what way the edge was facing before it 'dropped' into place. Now try this with the opposite rotation, but make sure the original position of the edge piece that was just 'dropped' is occupied by the piece that you want in place. If you do this a few times, with some experimentation, you should be able to pick up on some basic F2L concept and figure out most of the situations. This is for F2L slots on the right side, just use left handed rotations or mirror the algorithm you used for the right side for left sided F2L slots.

Just because it's fairly simple, I think I'll provide the algorithm for what I described. As an example, or for a shortcut for anyone who wants to try learning F2L by my explanation: R U R' U' R U R' U' (this is the first corner rotation) U (putting the desired edge piece into place) R U' R' U R U' R' (the second rotation, excluding a final U because it is not needed). That's R U R' U' R U R' U' R U' R' U R U' R' if you want to see it uninterrupted. Do you see why it may be better to learn this intuitively, rather than algorithms? This algorithm only has R and U based movements so it is rather confusing looking. Try using my worded instructions before the algorithm, if you are going to try both. Note, if you use the algorithm correctly it should bring your cube back to what you started with.

A final note about F2L; you should learn to solve each layer individually before attempting F2L. It's a good thing to know, layer-by-layer. Initially F2L will raise your times if you are timing yourself, but once you are good with the method you should be faster than before.

The later layer, well it's just a mess. There are several methods you can use. I have several of my own methods that I've deprived from learned methods. I'll start with the basic method.

The most basic method that I can think of, involves first correcting the edges. First you use a fun-to-pronounce algorithm (F R U R' U' F' or FRU RUF or if you're adventurous even FRURUF) that will ensure all the edges are facing upwards. Then you correct the cross so it lines up with the E centers, just as the original cross did. This is done with a fancy algorithm that only uses R's and U's like the F2L related algorithm I provided. Then you must locate a corner piece that is in the correct corner and use it as the 'nose' for your fish OLL (well, an algorithm that can be used in OLL; something I will explain soon) and in doing so you will rotate the positions of the other corners. This may be needed to be done twice if you do not look at where the pieces are and see if you need to use the mirror of this algorithm. If the pieces are out of place clockwise, and you use an algorithm that rotates them clockwise, it will be needed to be done twice. If you use an algorithm that rotates them counter clockwise, it will only be needed to be done once. Efficiency makes for the win. Then corner rotation ensues, and you are finished.

Corner rotation comes up in initial corner placing, F2L, and this. It is important you know how to do it properly and for every corner; even the up-left-back corner. I think I could write a decent sized post just on it.

Changing the position of the corners and rotating them can be done with a method that I've put together, taking ideas from situations in F2L where the corner is in the wrong corner position (ex, the bottom-right-front instead of the bottom-left-front) but it doesn't work very well and often takes many more moves than what would be needed. There are few situations where my method is better.

At this point your Rubik's Cube should be solved. The problem is, there are better ways than the most basic method that I have just described (which on the most part is my intuitive method for the last layer). For effiency you want to use OLL and PLL.

First up, OLL or orientation of last layer. This takes the last layer and positions all the pieces so the colour of the U is facing up, but the pieces may not be in the correct position. This means that (if yellow is your U colour) the top will look all yellow from a top view, however from a side view you will see the edges and corners of the U layer do not match up with the E layer. Corners will needed to be switched with other corners in the U layer, edges may need to switch also. Sometimes three or four will needed to be switched. If you have three corners and three edges that needed to be switched, you have a G-Permutation (part of PLL). They're nasty.

There are fifty-seven OLL's you may run into, and one solved case. I may be wrong with these numbers. This means there are fifty-seven algorithms that you want to memorize, ideally. OLL may also be done in a two or even three step method (though three usually just means I messed up on two step). This means that instead of needing to know all of these algorithms, you just need to know a few that will encourage you into a set of situations that you will know or learn. Instead of learning fifty-seven algorithms, you just need seven or eight; and even then you should know some of them from previous methods such as the fish situation I mentioned already.

There is no set way to OLL if you are using two step. Personally I use my own two step method, which is a bit faster than most two step methods but I have incorporated more algorithms. As I learn more I incorporate them in too, and eventually I should be able to do it in one step. My method encourages different situations than what you will find to be encouraged by most two step OLL methods that are found online. These are just situations that I know well and have found how to get to quickly. Even though you are given several algorithms to work with, you do not need to use the algorithm you have been given. For several situations I use algorithms that I have figured out myself that may not be faster but they are what I am use to so they are faster for me. This, technically, makes this semi intuitive OLL; but I'm not going to go about telling that to people just to have to explain what it means and for them to come to the conclusion that most of what is used in the method I used is learned. Not intuitive.

Past OLL is PLL, or fermentation of the last layer. This takes the corners and edges and almost magically rearranges them with the use of algorithms. There are only twenty-one situations, and one solved situation, that will be found here and it is best to learn one step PLL first. Just like OLL, PLL can be done in two steps. The two steps are focusing on the corners, and then the edges. I tend to do this for G Permutations, which are slightly evil. They are the last algorithms in PLL that most people learn, because they are complicated and difficult to remember often. After some work they become easy to use (but I have forgotten two of them and probably only need a few minutes of time to learn them again but I just have not gotten around to it), and the pictures describing them become sensible. Initially the pictures look like jumbles of arrows and lines.

And even with all these methods described, there are more ways. One method that I only use when I am thinking to use was created by Lars Petrus. It involves solving a 2x2x2 section. Then this is expanded into a 2x2x3 section. From there I'm not sure what is ment to be done exactly. I turn this into a 2x3x3 (cross and F2L complete) section. For me, this is followed by the last layer, and what ever method I desire to use. Lars Petrus's method involves ensuring that the edges are correct in only three extra moves (something I have not figured out or tired to do really) and therefore this method uses very few movements.

There are many ways to solve a Rubik's Cube. For most people they are happy just to have it finished. Many people ask why I solve my Rubik's Cube several times a day at school; and the answer is simply because I'm not happy with a simple solve. I want to do it faster. I'm going to continue to do it again better.


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