Breaking an Old Code. -And beating it to pieces. Daniel Vu - 1 -

Transcription

1 Breaking an Old Code -And beating it to pieces Daniel Vu - 1 -

2 Table of Contents About the Author Notation Time for Some Cube Math...Error! Bookmark not defined. Layer By Layer Method Step One- Cross Step Two- Solving the White Corners Step Three- Solving the Middle Layer Step Four- Orient the Yellow Edges Step Five- Corner Orientation Step Six- Corner Permutation Step Seven- Edge Permutation The Petrus Method Step One- Creating the 2x2x2 Block Step Two- Creating a 2x2x3 Block Step Three- Orienting the Remaining Edges Step Four- 2x3x3 Block (First Two Layer) Corners First Method Step One- Placing White Corners Step Two- Orienting yellow corners Step Three- Permuting Yellow Corners Step Four- Placing Three White Edges Step Five- Placing Four Yellow Edges Step Six- Final White Edge Step Seven- Middle Layer Teddy s Corner- First Method Step One- White Corners Step Two- Yellow Corner Permutation Step Three- Yellow Corner Preparation

3 Step Four- Yellow Orientation Step Five- Middle Ring Step Six-Centers Step Seven- White Edges Step Nine- Yellow Edge Orientation What Next? Getting Faster in General Patterns! Blindfolded Cubing Orientation of Corners Orientation of Edges Current World Record Statistics Pictures Cube Care Disassembling the Cube Assembling the Cube Links Solutions Tools Purchasing Puzzles

4 About the Author My name is Daniel Vu. I am a fourteen year old student about to enter high school. I have been doing the cube for half a year now and many people believed I started the Rubik s Cube fad at my school, though I believe it was more through the help of the Pursuit of Happiness, which starred Will Smith doing the Rubik s Cube. I rank fairly high on my school s leader board for speed solves, estimating around second place if we actually had a physical board to show it. I would be behind my teacher, who did it 20 years ago, so it does not come to much surprise. I created this book to help others see all factors of the Rubik s Cube and get them to be less ignorant. I know, it is an impossible task but it is worth a shot. Most people at my school scream Oh my gosh, that guy can solve five cubes blindfolded behind his back in 20 seconds! which, by the way, is probably physically impossible for even the professional. I m here to teach not only how to solve the cube one way, but three ways. I will attempt to show you ALL aspects of the cube, which will be very tough, especially with my inexperience. But as my knowledge of the cube grows, so will this book. So sit back, relax. Uhh, no, go get a dang cube first! Jeeze, what are you going to do without a cube, actually read?? Ha, let us begin

5 Notation There are a variety of ways to notate the ways to solve a Rubik s Cube. Each notation has its pros and cons, and if you decide to learn from other people, it may be helpful to know the keys for each of the notations. The first notation I will show you is the Singmaster notation. It is the system I have seen most widely used, and is very easy to use. For the most part, the letters represent the first letter of each side. U- Up D- Down L- Left R- Right B- Back F- Front It is important to capitalize these letters, as a lower case letter represents a double layer turn. In the case of r, not only would you turn the right face, but you would grab the middle layer next to it. The default letter by itself means a single turn CW. However, when an apostrophe follows it, it means a CCW turn. If the letter is followed by a 2, that means you would turn that layer twice. For the most part, when people needed to dictate a single middle layer turn that didn t include its outer layer, then they would simply write down the lower case letter with its capital letter inverse, such as r R. However, in the case of the Corners- First Method, this is highly aggravating to notate. Thus, the Harris notation allows us to notate each individual middle layer. The rest of the outer layers are still done in the same fashion, so there is no need to repeat the same table

6 M refers to the middle layer between L and R. M would be equal to r R, and M would be equal to r R. E refers to the middle layer between U and D. E would be equal to d D and E would be equal to d D. S refers to the middle layer between F and B. S would be equal to f F, and S would be equal to f F. I don t exactly know the origin of this letter, but I use it anyways. Along with these notations, some algorithms find the need to use cube rotations. It would be a pain to say r L all the time, so the cubing community have decided on using the 3d coordinate axis plane to dictate cube rotation. If you know about the 3d coordinate plane, you would know that the Z axis goes straight in front of you, the X axis goes from left to right, and the Y axis goes from up to down. If you imagine each axis like a skewer, and you prodded each axis into the cube, and you spun the skewer, the cube should spin in the same fashion. If my explanation was horrible, don t worry, (too much) I have a diagram of the 3d axis

7 Should the diagram not be enough, the same explanation with animations can be found on my website. And if my explanation is what is throwing you off, Dan Harris has an excellent table on his website, which can be found in my the chapter in the back of the book called links, showing you animations and explanations. Test time, alright people, if you have a solved cube and have not messed it up at this point, good for you. Not really, but don t mess it up yet. To test if you really know how to notate turns, try to follow this algorithm. (R D R D) 4 times Do the designated algorithm 4 times and what do you get? You should get a solved cube, so congratulations! You have cheaply solved a cube! Woo! If you can t figure out notation, you re an idiot, but don t worry, here is another diagram that shows the different layers. Each letter is colored on the cube. U L F D R B When performing the layer turn, it is important that you look directly at the face and determine it from there. U is not going in the same direction as D, so just watch out for that

8 At times, I may talk about the pieces themselves. On a regular (non Rubik s cube) cube, there are 27 pieces. (3x3x3). Now, 1 of those pieces is a center core, and 6 are face centers. That leaves 20 pieces that we will actually care about. 12 of those pieces are edges, which contain two colors on each piece, and the remaining 8 are corners, which contain three colors on each piece. 12 Edges 8 Corners Let us also label each piece so that we can easily talk about what is affected by a certain algorithm. Before, I have simply stated the cubie s position by saying its 3d position. But that will become bothersome for this section, so let us number each corner and edge piece by a certain system. This system is also similar to the system to learn how to solve a cube blindfolded, so it s best you learn it now. Just count the pieces on top layer CCW and go back to yellow and start there CCW again. orange- 1 blue- 2 green- 3 red- 4 yellow- 5 white- 6 blue (down face)- 7 piece you can t see- 8 Same method. Top Layer Red- 1 Blue- 2 Orange- 3 Green- 4 ML Green-5 Blue-6 Orange-7 Piece you can t see- 8 LL Yellow- 9 White- 10 Back-Bottom- 11 Left- Bottom

9 Time for Some Cube Math Most people assume that the cube has 43 quintillion possible positions. And it is true, but how many know how to get to that number? I ll teach you. First, let me get you the basic formula for this problem. (8!*3^8) * (12!*2^12) 2*2*3 math, it is not hard. Now, there are a few things you need to know. * means to multiply. The underline means to divide. All of these were taught in fourth grade The! means the factorial of A factorial basically means to get all the numbers under it and multiply it. So the factorial of 8 would be 8*7*6*5*4*3*2*1. The ^ means To the power of. Such that 3^8= 3*3*3*3*3*3*3*3, it s just easier to read. Now, 8! shows the corner permutation. It is similar to a problem like, If you have 5 friends, how many possible ways can you seat them? To solve a problem like that, you find the factorial of the number of friends, or in our case, number of corners. That gives you all possible permutations of corners. Now, there are 3 possible orientations of every corner. And by every, I mean all 8. That means you multiply the corner permutations by 3^8. It is 3 because of the 3 orientations and to the power of 8 because there are 8 corners. Now that we covered the basics of corners, we apply the same theory for edges. There are 12 edges, and 2 orientations for each of them, so 12!* 2^12. Easy enough. Now to apply some real numbers. (8!*3^8) * (12!*2^12) (40,320 * 6,561) * (479,001,600 * 4,096) * *10^12 Total * 10^20 Goal- 4.3 * 10^19 We overshot it, wonder why? Because we re thinking theoretically, the number we got was for a random, computer based cube in which impossible cases occur. However, we are aiming for a real, solid Rubik s Cube number, so take a look at certain rules. 1. Choose any corner and void it for a second. If a whole cube is solved, then that corner must be also solved. It is like the triangle sum theory. If there are two angles that add up to 160 in a triangle, the remaining angle was must 20. Because of this rule, we divide the possible number of combinations by It is impossible to switch the positions of ONLY two pieces. It just is, no matter how hard you try to recreate it. Because of this rule, we divide the possible number of combinations by There is always an even number of unoriented edges This is obvious to every Petrus method user and every blindfolded cuber. So we divide the number by 2. So again, we will apply some real numbers * 10^20 2*2*3= 12 Total * 10^19 And that s how you get it. So if you re slow at solving it, back your knowledge up with this formula and you ll surely impress you re boss

10 Layer By Layer Method Popular User of this Method- Everyone? The layer by layer method is very popular due to its simplicity. This system is a great way to start learning how to solve the cube. It is easy for the mind to comprehend. But even though it is a simple method, it can be evolved into a higher level method, such as the Fridrich method or VB method. The description of this method after this is for a beginner s layer by layer method. It gives you basic algorithms that would allow you to solve for any position. However, as you evolve the method, you will need to learn more algorithms that are defined for certain situations. This method includes one middle layer algorithm, two last layer edge orientation algorithm, two corner orientation algorithms, one corner permutation algorithm, and one edge permutation algorithm. This makes a total of seven algorithms. However, the full Fridrich system uses a total of 121 algorithms. The overall system breaks down as follows. - Cross - Corners - Middle Layer Edges (First Two Layers) - Last Layer Edge Orientation - Last Layer Corner Orientation - Last Layer Corner Permutation - Last Layer Edge Permutation Step One- Cross It is important that anyone who reads this book knows how to solve at least one side before reading this book. This step will be easy if you know how to place edges before I tell you. Learn how to make the cross first. After learning how to make the cross shape, you will have to learn how to create the cross correctly. Each white edge piece must be connected to its correct center. Please examine these pictures. Basic White Shape Correct White Cross Incorrect White Cross This is the overall shape you are aiming for, but you must also get the correct edges in the correct spots. This is an example of a correct cross. The edges match with their centers, and it must be done on all four sides. Notice how the edge does not match with its center? This is incorrect. Do not attempt to simply move the top face; you will destroy the correct red edge. Re-insert the green piece

11 When you are creating the cross, it is not necessary to hold the white edges next to its centers. But in the end, all four white edges should be next to its center. Remember that I may not be using the same color code as you so it is important that you follow the colors of your cube and not just copy the pictures. If you are having trouble with solving the cross, Dan s Cube Station has an excellent cross examples page. And if you are still having trouble with solving the cross, Tyson Mao has a video explaining a unique way to solve the cross. It is good for beginners, but eventually, you should learn to solve the cross in less than 8 moves. =compet Step Two- Solving the White Corners After completing the cross, you must insert the white corners into their correct positions. A corner that has the colors White/ Red/ Blue needs to be between the Red and Blue centers. The basic move that moves the corner piece into position is to move the corner piece under the destination piece and execute either D R D R or D L D L. If the white is on the bottom, you will need to move the corner piece under the destination piece, and execute R D R and execute one of the first two moves. This should be an easy step and should not require too much explanation. Step Three- Solving the Middle Layer This is the first algorithm that you will learn. For my real life students, I tell them a story line, rather then having them learn a straight out algorithm. So the story line goes like this - Align the edge with its center so the first layer, the center, and the edge make a T. - Find the destination piece by seeing which side the color the bottom color is. - Move the edge piece AWAY from the destination piece (Moving the D layer) - (If it is the red/blue edge and you aligned with the red center in the first step, and blue is on your right, then you would move D ) - Move the destination piece down to the D layer (Moving the R or L layer) - Move the edge piece back to its original position (Moving D layer) - Move the white corner back to its original position (Moving R or L) - Move the connected edge and corner piece to its appropriate spot. And that solves one edge. This sums the algorithm to be either D L D L D F D F or D R D R D F D F

12 The only other thing you might need to remember is that when the edge piece is in the right spot but oriented incorrectly, then you will have to use a random piece and insert the random piece into the right spot, and repeat with the right piece. And if the piece is in wrong spot, use a random piece to switch it out and use the edge piece in the right spot. Step Four- Orient the Yellow Edges This step is easy as long as you are willing to say weird phrases out loud. For orienting the yellow edges, there are 4 possible configurations of the yellow edges. There is the L configuration, the Line, the Dot, or the cross, (which is equivalent to the correct orientation) L Configuration Algorithm: F U R U R F Line Configuration Algorithm: F R U R U F If you happen to get the dot configuration, simply apply one of the two algorithms, reexamine, and apply the appropriate algorithm. Step Five- Corner Orientation This step confuses more people, due to the increased number of possibilities. In total, there are eight possible configurations, which include the solved position. What also makes this a confusing step is that most people only give you two algorithms to learn. These algorithms rotate three corners either clockwise or counter-clockwise. I call these algorithms Fish A and Fish B. It is easy to see why when you see their default state

13 Fish A- Rotates Three Corners Counter- Clockwise Fish B- Rotates Three Corners Clockwise R U R U R U2 R R U R U R U2 R As stated before, these algorithms are here to solve the other 5 positions as well. I have created a table that will tell you how to hold the cube as well which algorithm to use to solve it. It would be best to figure these out yourself, not only does it give you self satisfaction, but it teaches you how to use these algorithms properly instead of simply applying these algorithms blindly. Parallel Cross A-A Headlights B-A Siamese Fish B-A Non- Parallel Cross A-A Chameleon A-B If you hold it like in these diagrams and execute the planned algorithms, the yellow side will be done. Step Six- Corner Permutation My students and I have had a few debates on how to use this algorithm. Even though this algorithm mainly switches out the corners, it does also switch out the back edge and the right edge. Based on this, my students have gone further than I have and managed to mirror my algorithm in order to switch out the right and the front edge. This would have been simple, but I just found it beneficial to me to learn a totally new algorithm that would one: be shorter in length and two: focus all the turning in my right hand. But for now, simply learn this algorithm for its corner property. To start, find a pair of correct corners and hold them in your left hand. For corners, either it is completely correct or only two corners are in the wrong spot. It doesn t matter if they are diagonal or not, it is only possible for two to be wrong without

14 either you being wrong or something being wrong with your cube. If the wrong pieces are diagonal to each other, you will need to repeat the algorithm twice holding it in any position. Corner Switcher- Switches the Top/Right/ Front and Top/ Right/ Back corners. L U R U L U R After applying this algorithm, you will need to repeat Fish A. Then the corners will be switched. Step Seven- Edge Permutation Edge permutation is a very easy step, because while there are five different configurations including the correct permutation, this step only requires two very easy algorithms. These algorithms are easy to learn, once you learn one of the algorithms, you only have to change two of the steps in order to learn the second one. The first algorithm will cycle three edge pieces in a clockwise fashion, and the second algorithm will cycle the edge pieces in a counter- clockwise fashion. The basic algorithm is as follows 3 Edge Cycle R2 F B R2 F B R2 Insert a U into the blank Insert a U into the blank Always hold the correct edge in your left hand. If you have three edges that are in the wrong spot, then listen. If you have four pieces you need to fix, hold on for my next note. Trace the direction in which each piece needs to go and decide whether the general direction is clockwise or counter- clockwise. Then, that decides the direction of the U turn that you will need to make and insert into the blank spots in the algorithm. If the pieces need to cycle clockwise, then you will insert a clockwise U into the spot, and if the pieces need to cycle counter-clockwise, then you will insert a U into the spot

15 If you need to cycle four pieces, then there are two possible configurations. Either you will have to switch out the opposite edges (which I call the cross switch), or you will have to switch out adjacent edges (which I call the Z- permutation). Both of these can be solved by applying the clockwise or counter-clockwise edge cycle, re-examining, and then moving on from there

16 And that sums up the CFOP method. Moving on from this method, there are several ways to speed your times up. - Learning how to combine the first layer corner step and the middle layer edge step will theoretically speed up your speed. I have not had that luck, but I will continue to work toward that goal. The overall plan is to separate badly connected corners and ML edges, then reconnect them in the correct manner, and insert them back into their spots. Jessica Fridrich and Dan Harris both run their own individual sites that give excellent examples of F2L algorithms. But many suggest that you learn these algorithms out for yourself. Not only will they be personalized to your own needs, but you will feel much better about creating them yourself. So far, I have only tried to teach my sister this step, and she is having some trouble learning how to start. One tip to start this is to avoid messing up the cross, and only use empty slots. - Creating the cross in less than eight moves is great. Competitions often allow a 15 second pre-inspection time, where you should try to find the fastest way to create the cross, and maybe another corner. - Learning all the permutation algorithm: Usually permutation of the edges and permutation of the corners are combined using carefully crafted algorithms. There are around 21 of them, so it is not too difficult, but it still does take awhile. - Learning all of the orientation algorithms: I only gave you two orientation algorithms, which are not really designed for the diagrams I gave you. They are sufficient to solving edges, but in order to solve edges and corners at the same time, it is necessary to learn more algorithms. There are 56 different configurations of orientation, not including their mirrors

17 The Petrus Method Popular User of this Method- Lars Petrus The Petrus Method, created by Lars Petrus, is another popular method is solving the Rubik s Cube. Because the layer by layer method creates one layer which will constantly get in the way and will always have to be restored, the Petrus method tries to avoid this conflict by geometrically building the cube, always leaving free sides to maneuver the cube until the last few steps. This theoretically reduces the number of moves to do the cube from around 100+ to around 60+. The overall breakdown of the system is as follows, - Create a 2x2x2 - Create a 2x2x3 - Orient Edges - Create a 2x3x3 (A.K.A. First Two Layers) - Orient Corners - Last Layer Permutation. As a final note, I would like to say that this system uses a fewer number of algorithms than the beginner system, making it a great choice to start with. However, I have not received/ gotten to a dignified answer. So as a warning before typing the actual system out, more than likely 7 algorithms will be needed to be learned through this system. Step One- Creating the 2x2x2 Block There are multiple ways of thinking this through. However, because I have become so used to using the cross method, I will explain a method following that state of mind. - Place two white edges. - Insert the included corner - (Do not align the edges with their centers) - Insert the appropriate middle layer edge piece next to its centers. - Slide the top layer over the middle layer block, completing the 2x2x2 block. Of course, there are other ways such as - Align a corner with middle layer edge. - Match one of the edge pieces to its center. - Connect that edge/center pair to the corner/ ML edge pair - Connect another edge to its center. - Connect the square to the new pair, completing the 2x2x2 block

18 I personally like the layer way better, but it is best to learn both, just in case of certain scenarios where pieces are already aligned and it would be simple to connect. Another note is to remember that you are free to use any colors to create the 2x2x2 block, and is advised you are color free. At the beginning, it may be harder to use any other color than white, due to the rough transition from layer by layer to Petrus, but in the end, it will truly help you in tough situations where the white pieces are scattered. So learn your cubes coloring, and try new ways of looking at it. Step Two- Creating a 2x2x3 Block I am going to have a hard time explaining how to do this step. It is the most intuitive step of this method, so I ll try to guide you as much as possible. The beginner s way to approach this step would be to. - Insert the corner piece. - Use the Move the piece out of the way fundamental move in order to move the edge pieces in. Which would be technically correct, but remember, we are aiming for speed, and that is just not a good way to approach this. A more defined way of doing it would be - Matching the corner piece with one of the edges - Matching the remaining edge with the center - Connect the two pairs to finish the square, and move into on top of the 2x2x2 to finish the block. Now, as mentioned before, the Petrus method is designed to not create pieces that are in the way. After completing the 2x2x2 block, you will have three remaining sides to turn that will not destroy the cube. This also means you will have three choices in which color to start with for the 2x2x3 block. Remember, remain color- preference free and choose which is most prepared. Step Three- Orienting the Remaining Edges. This may be a hard step to grasp at first, but it will become the easiest step in the whole system once you understand. The point of this step is to flip all the edges onto its correct side. For this step, it is important you do not limit your self to the only two remaining sides. You are allowed to turn the sides that contain parts of the block, as long as you don t harm any of the pieces and eventually return the pieces to the block

19 Normally I would give an animation or live demonstration to my students, but that is impossible for most of you. So just imagine what side will be your top. Now, you need to make the opposite colors match the bottom. That is your goal, and you can use any turns to get to that goal. (Section Under Construction) This works on the theory that the number of unoriented edges must always be even, or zero. It would be impossible for the number of unoriented edges to be odd, or it will probably be impossible for people to solve the cube blindfolded. (Their algorithms solve edges in pairs, 6 s, and 12 s) Step Four- 2x3x3 Block (First Two Layer) Once all the edges are flipped and the first two layers have their edges in place, it really is simple to insert the remaining corner. There are only two different categories, In position, oriented incorrectly or Not in position. Not in Position - Directly below: Rotated CW: D L D L D2 L D L or mirrored for CCW - Directly below: Rotated Correctly: (R U R U )*3 times In Position, Oriented Incorrectly. - Rotated CW (on the right, bottom position): R U R U R U2 R U R U R You could qualify these algorithms, but usually they are found by people manually learning the whole Fridrich system, so just suck it up and learn them! ( HA, kidding ) And the rest of the system is entirely based like the layer- by- layer method, and it would be pointless of me to retype it completely. So simply turn back to that page if you have not learned it already. After learning how solve with this system, here are some things you could probably improve on. - Becoming completely color- preference free: Trust me, I still even have trouble with this, and usually just end up either starting with white, because of the cross method, or starting with yellow, which is basically the flip of white so it is just deciding whether blue or green is on your right. But its worth becoming complete color- preference free in the end. - Learn how to check ahead of time: Competitions give you a 15 second preinspection time, so use this to plan your 2x2x3 block. The further you look in, the less pressure the step is going to be when you get there. - Learning the last layer algorithms: Though the beginnings are solved in a different fashion, the last layer is done almost identically the same. This gives you a lot of resources from both sides, so don t be an elitist, and start saying your system is 100 times better!

20 Corners First Method Popular User of this Method- Minh Thai While there are many methods, most of them are based around the core methods: The layer by layer method, the Petrus method, and the Corners Method. We have already discussed the first two methods, and how each differs in pros and cons. The corners-first method has some great advantages. I have a different corners-based method than some other, but they both generally have the same advantages. First, the method focuses on certain part of the cube at a time. Instead of having to search for two different types of pieces at the same time, you will only have to look at the corners first, then edges. Second, many people say that by using corners-first, you allow your stronger hand to do most of the turning. I personally have not found too much of a difference, but in theory, it sounds right. Third, nothing is created that would get in the way. The overall system breaks down as follows - Placing white corners - Orienting yellow corners - Permute yellow corners - 3 white edges - 4 yellow edges - Final white edge - Middle Layer Other than the yellow orientation and permutation, this system use short and easy to remember algorithms. Step One- Placing White Corners This is a very easy step and does not require any algorithm. You should be used to doing this through the layer by layer method. However, unlike the layer by layer method, you are not limited to creating the corners on a certain face, giving you the ability to reduce then number of moves it takes. Certain people have created tables for certain tables to illustrate an example of moves you could take; however, those people also say that you should find your own way, because they themselves admit that they did not optimize it. Once you find your own way, you can recheck these tables later to see if there is a faster way. Step Two- Orienting yellow corners This step is illustrated through my layer by layer method. Though the edges are not the same, the corners are still done through the same fashion, you simply have the imagine it. At this point in the book, you should have matured enough to be able learn the individual algorithms for each of the seven cases, making it much faster. I will illustrate them later in the book, so continue to read this section using the Fishes

21 Step Three- Permuting Yellow Corners See above paragraph. Step Four- Placing Three White Edges This step is very easy as long as you know your fundamental moves. There are basically three cases; Piece is in the down layer and white is on the bottom, piece is in the down layer and white is not on bottom, and the piece is in the middle layer. Piece in Down Layer, White on Bottom R E R2 E R Piece in Down Layer, D M D M Piece in Middle Layer E R E The reason behind only placing three edges is because by leaving one white edge open, you are able to use that keyhole to easily insert the yellow edges. Step Five- Placing Four Yellow Edges This step is basically the same as step four, but you are simply limited a little more. You will always have to remember to place the keyhole under the destination target before applying the moves. Here are a few pictures to help you visualize it. Piece in Middle Layer E R E Piece in Keyhole (Yellow on the bottom, blue/yellow edge) R E R2 E R

22 Step Six- Final White Edge Most people who have already solved a 5x5x5 will find this algorithm very familiar. And it is pretty easy to figure out for those who haven t. Not much to think on this, just do this or its mirror and you will have both the yellow and white face solved. Step Seven- Middle Layer E R E R E R E R This is basically the only step that I will actually teach, because there has only been one middle layer algorithm so far. There are three basic configurations of the middle layer edges, and some variations based on combinations of the basic configurations. Three Middle Layer Edge Cycle U2 M U2 M H Middle Layer Edge Switch M 2 U2 M 2 U2 Rubik s Maneuver (Changes the Orientation of Front-top edge and Back-top edge) M U M U M U2 M U M U M U2 If my guide is hard to understand, a page with no text but animations can be found here to assist you

23 And that is about it. Several ways of getting faster is to solve the white corners on the bottom. This way, you don t waste time rotating the cube to get to the yellow side, plus, if you are using finger tricks, the corners should be on the bottom layer anyways. You could also learn each individual algorithm for the seven corner orientations and a diagonal corner permutation algorithm. This way, instead of having to repeat several algorithms over and over, you can simply do one algorithm and get on. Also, this is a hybrid corner-first method that I made out so that it would use the layer by layer algorithms as much as possible. However, this is not the step that most people take, and the regular system is broken down as follows. - White corners. (Put the corners on the white side, do not worry about which corner where) - Yellow Corners Orientation - Yellow and White Corner Permutation Based on Pairs - Solving Three White Edges (Same system) - Solving Yellow Side - Solving Final White Edge - Positioning Middle Layer Edges Except for the permutation step, this corner-first method is almost identical to mine, and can be figured out intuitively if you already know the layer by layer method. However, I would suggest you try learning the other method and see which you find best suited for your own needs. The other system can be found here

24 Teddy s Corner- First Method Popular User of this Method: Teddy (Of course, who is more popular than him?) Due to some last minute arrangements, I have managed to get Teddy to type up his method and send it to me. After a few hours of thinking, I managed to understand the basics of his method, and though it would have been easy for me to simply use my algorithms, I wanted to learn his thought process and stick to his method strictly. So I analyzed each algorithm down to every change and effect, and learned how to use them. Previously, I typed a Corners- First Method called the Keyhole Method. Both this method and the keyhole method are similar, both starting with the corners obviously. But the main difference is in how they tackle the edges. The keyhole method decides to create 3 white edges, 4 yellow edges, the final white edge, and the middle ring. However, Teddy s method starts with the middle ring, then the white edges, and finally the yellow edges. I have not seen any major flaws with using this method, plus, Teddy has always managed to keep up with me in races. So I present to you this new method. The overall breakdown is as follows - White Corners - Yellow Corner Permutation - Yellow Corner Orientation - Middle Ring - Centers - White Edges - Yellow Edges Orientation - Yellow Edges Permutation Step One- White Corners This step is basically intuitive, and after the whole walkthrough from the rest of the book, it would be a waste of space for me to tell you how to place corners. I don t really have much to say for this step, other than you don t have to worry about centers. Teddy has actually set the Centers as a step, so if solving the corners on a different face reduces the number of moves, go for it

25 Step Two- Yellow Corner Permutation You already know a corner permutation algorithm for this book, and Teddy simply uses the inverse of that algorithm, and because we are only focusing on corners, it doesn t matter which one you use. The actual goal to finish off orientation is to actually get the parallel cross orientation. So for now, if you need to switch two corners on your right, just use this algorithm. Also, when using this algorithm, I usually say to add Fish A to this, but it you do not need to in this case. L U R U L U R Here is an example of a correct permutation, notice we have not done orientation yet (This may or may not be physically possible on a real cube) Step Three- Yellow Corner Preparation You are basically aiming to get the parallel cross permutation. Here is the basic algorithm you will be using. F U L U L F If you can solve a cube already and you are just want to learn this method, then solve the cube and execute this algorithm. We will pinpoint every single change from this algorithm. This switches corner 1 and 2, and also switches out 3 and 4. It also changes the orientation of the original 1 CCW and the original 4 CW. Here is a helpful diagram that Teddy has drawn for us. Before After Remember, the goal is to get the parallel cross permutation. So if you have the headlights permutation, you would hold both yellow on your left. If you have a non parallel cross, hold the matching pair on your right

26 Step Four- Yellow Orientation This is a pretty neat step. These two algorithms both orient the parallel cross permutation, but the difference is that they are built for different permutations. This would be an appropriate build up into learning COLL, where you learn how to orient the corners, while at the same time permuting them, speeding up the process and narrowing the rest of the cube to edge permutation. Imagine the two blue dots representing the corners of the parallel cross permutation. The yellow and red dots are representing a color pair, so hold the corners like this, and see which one you have. (Two Corner Switchers) (L U R U L U R ) (L U R U L U R ) F2 U2 F U2 F2-26 -

27 Step Five- Middle Ring This step is pretty simple, and can be found intuitively. I really do suggest you find it on your own, as the following explanation will more than likely be the worst thing you have ever read. The main idea is to use M and S, and any other regular layer turn. Try avoiding using E too much. Check these basic cases for help. These are only the basic cases, there may be more. M F M M2 F M F F M F2 M2 F This case is special because the regular move would destroy the other green column, so avoid this by doing an L to move it out of the way, and then do the regular move. Apply to all cases like this. Step Six-Centers Simply fix the centers; no illustration should be required for such a simple step. If you really need to break it down, simply get all the middle centers, and then the down and up layer centers. Step Seven- White Edges This step is very easy as long as you know your fundamental moves. There are basically three cases; Piece is in the down layer and white is on the bottom, piece is in the down layer and white is not on bottom, and the piece is in the middle layer

28 Piece in Down Layer, White on Bottom R E R2 E R Piece in Down Layer, D M D M Piece in Middle Layer E R E Step Eight- Yellow Edges Orientation There are only 3 possible cases of LL edge orientation. Just memorize these cases, there is no need to try learning it any other way. Rubik s Maneuver M U M U M U2 M U M U M U2 M U M U2 M U M M U M U M U M U M U M U M U M U Step Nine- Yellow Edge Orientation We already learned from the CFOP method how to rotate edges, simply use R2 F B R2 F B R2. That is about it

29 What Next? Now that you can solve the cube, what should you do next? Most people will either set it down before they get obsessed, or they will drown in the intoxication that is the cubing addiction. But simply learning how to solve the cube is only one small piece of a gigantic pie. People are breaking new records with the Rubik s Cube everyday, and they reach those records with practice. Check the records on the table in the back of the book. It is amazing on how much work they put into their hobbies, and it is inspiring. But those are just the normal records. Many people work on strange records, such as solving on a rollercoaster or while during a freefall. The possibilities are endless. Speed Solving This is the main branch of solve that most people start with. This is simply the act of solving the cube as fast as possible. People have invented numberless algorithms to speed up the basic methods so that they can reach sub-20 records. They also created finger tricks. Finger tricks are the algorithms that are based around using your fingers to spin the faces at extreme rates. Some people have mastered these finger tricks to 10 turns per second. Great Resource for Learning Blindfolded Solving Blindfolded solving is a favorite for impressing people, though it does require more work than speed solving, but it is not impossible. In competition, the cuber is allowed as much time as he needs to memorize a cube. He then places a blindfold over his eyes and solves the cube. Both the memorization section and the solving section are timed, so it is amazing how fast these cubers can analyze a single cube. A brief explanation of how this can be done can be found in the back of the book. Great Resource for Learning One- Handed Solving One-handed solve is very impressive, but a little more dangerous than the other categories. Because it is done with only one hand and not two, more work is placed on the hand, and it can cause pain for a cuber. However, with proper finger training, and a loose cube, people have managed to solve the cube one-handed faster than most people can solve normally. Great Resource for Learning

30 Getting Faster in General Many people have a million websites that tell how to get faster, but they generally all say the same things. Because of how repetitive they are, I ve grown to trust them, and even if they sound a little strange, you should try it. These steps will help you prepare both mentally and physically for competitive cubing. - Slowing down: Is the secret to getting faster really slowing down? According to most professional cubers, it is. While you don t completely go at a beginner s speed, you should keep yourself from going full speed. By slowing down, you will give your mind enough time to prepare for your next move. If you go full speed, you do cut off some time in doing a certain move. However, you waste this gained time by trying to find the next piece, so avoid doing this by slowing yourself down! You also reduce the possibility of a cube popping or a lockup, so this physically helps you. - Pre-Examinations: Give yourself 15 seconds to look at the cube and find the best move possible. No, this isn t cheating, most competitions give you 10 to 15 seconds in order to examine the cube, so don t waste this time. Know what you are looking for, and know how to place those pieces in the most efficient way possible. It is also important for you to reduce the time you need to examine the cube. While they do give you the time, you shouldn t waste it just trying to find the MOST efficient method, use the extra time to relax yourself. (See next tip) - Relax: This goes side by side with slowing down. By relaxing, you don t get cube lockups as easily. Do quick deep-breathing exercises during the examination time. People also say NOT to look at your timer. If you don t know your times, you can t get frustrated. Remember, smart people solve a cube for speed; wise people solve a cube for fun

31 Patterns! Because my school doesn t practice in speed to keep up with me, patterns are a category that they choose to master instead. Sure, it began as the simple checkered pattern or the simple center switcher pattern, but as time passed, their skills evolved into patterns such as the cube inside a cube inside a cube, and crosses of all sides. What is great about what my students have done is that instead of easily looking up algorithms on how to do each pattern, they manually built each pattern from previous algorithms they have learned, expanding on their knowledge of how they can be used. So in this section, I will explain some basic algorithms that will allow you to create these patterns. Now, we will begin describing some basic algorithms that are helpful CCW Corner Cycle (x) R U R D2 R U R D2 R2 (x ) CW Corner Cycle (x ) R2 D2 R U R D2 R U R (x) (It is simply an inverse of the previous algorithm) I am about to introduce an orientation commuter. A commuter is any sequence in the form of X, Y X-1, and Y-1. This commuter turns corner 4 CW and corner 2 CCW. We will call this commuter, W. When we apply W, it does some damage to the other parts of the cube that we don t want. However, if we do the inverse of W, then it will resolve the cube. Now, to insert real moves W= (R D R D) twice W =(D R D R) twice. Now, it is pointless to do W W, as it does no effect. However, if we do W, then U2 to move corner 4 into position 2, and do W, we change corner 4, and resolve the rest of the cube. And from there, we simply do U2 again to return the whole cube to its original position. Most of the algorithms you will need to create patterns are located on the last page of the Corners- First Method. There is pretty much no need to repeat them, I will give a brief description of each one. The ML H switch switches edge 1 and edge 3, and switches edge 9 and edge 11. (Picture at Right- Effects of W U2 W U2)

32 That is what you would use if you only need to switch 2 corners. Now, if you need to change the orientation of two edges, then you would use the Rubik s Maneuver. It changes the orientation of edge 1 and edge 3 without harming the rest of the cube. If you learned the Corners- First Method, you already know this algorithm. Rubik s Maneuver (Changes the Orientation of Front-top edge and Back-top edge) M U M U M U2 M U M U M U2 Four-center switcher M 2 E M2 E Six-center switcher M Y M Y M Y M Y H Permutation (Switches 1-3 and 2-4) Z Permutation (Switches 1-2 and 3-4) (x') R U' R' U D R' D U' R' U R D2' F (x)

33 Now for some patterns, starting from easiest and progressing to hardest. Basic Checkers M2 E2 S2 Basic Mixed- Up Centers M (y) M (y) M (y) M Chris- Lines (Tribute to first one to show it to me!) To create this one, there are multiple ways to do this. To create it manually, simply do this. LL H Switch- Flip Cube on Bottom- LL H Switch- 4 Center ML Center Switch A second way to do this is do 2/3 s of the Basic Checkered Pattern, and then use the ML H switcher on one of the sides that does not have a line on them. Then repeat. And the real algorithm would be (R2 F2 L2) twice. Four Sided Cross This one is really simple, it is just a four-edge cross switcher done on both the yellow and white side. Scott Cross Not really the official name, but Scott made such a big deal about it that I named it after him. First you start by doing the z-permutation twice on both the white and yellow side. Then turn the cube on its side, and then do the Middle layer edge switcher so that some of the centers have opposite adjacent edges, and different corners. Now, use the Middle layer Edge switcher on all edges of the yellow and white sides. And then simply use the four center switchers to position the centers in the correct spot

34 I have not found a real algorithm for this one. Cube inside a Cube Front View Now for some real patterns. It is actually 2 cubes inside a cube, but we just call it this for conversation reasons. There are three basic methods for creating this pattern: Building it manually from scratch, building it manually from a solved cube, and using an algorithm. I recommend learning all three, as the experience will give you a boost in your overall view on the cube. Method One- Building it manually from scratch Start by creating a 2x2x2 block consisting of the colors white, red, and blue. (Later on, you can try your own combinations, but stick View After X2 with me for this one.) Now, place your blue/orange edge on your top-left, and your blue/yellow on your top-back. Then, place your corners in, using common sense. (Just make sure the top row is pretty much solid colors besides the 2x2x2 block.) Then use the middle layer algorithm to fill in the edges matching the colors of the corners, not centers, below corner 1 and corner 3. (For a review on numbering corners, refer back to the chapter on notations) For corner 4, you have to remember there is going to be a second cube, so you have to actually fill it with the correct edge between those centers and not the corner. In this case, you will be putting the orange/green edge in there. The final layer is tricky, because the bottom isn t a solid color anymore. Remember, Fish B turns 3 corners clockwise, and Fish A turns 3 corners counter-clockwise. I always find it easiest to do corner permutation first, then corner orientation, then edge permutation, and finally edge orientation. By doing permutation first, it will be easier to see how each cublet needs to be flipped. For corner permutation, only three corners will be flipped so that the green is on top, and the fourth one will have yellow on top. That yellow one will have green/orange on the side and will be placed under the 2 nd cube. If you already know diagonal corner switcher algorithm and a 3 corner cycle switcher, then you can probably just place the y/g/o corner under its respective spot, and then trace with your fingers which way the other three need to go. Corner orientation is easy if you already know each separate algorithm for the 7 cases on corner orientation. If you don t, you don t have to worry. Pick any corner with a wrong orientation. Put your finger on any color of that single corner. Ask yourself, Where does THIS need to go? and move your fingers where it needs to go. Repeat this until you find the color that needs to go on top. Then imagine that color would be the wrong yellow on a regular cube. Once you can imagine the case, then execute the proper algorithm, and repeat from there

35 Edge permutation is easy, just match the edges according to the corners and use common sense. Just remember that two edges are held within the 2 nd cube, so it will be detached from the corner next to it. Just remember the algorithm properly, sometimes even I forget when I usually use visual aids, but don t mess it up yet. Do NOT use FURU R F or FRUR U F when doing edge permutation. This will mess up all the work you did to your corners. Instead, use the Rubik s Manuever to place each bad edge into place 1 and 3, and execute the algorithm. Then, INVERT your set up moves. Like if you did R B to put edge 2 into edge 3, then do B R to get it back. And then you should have it. Method Two- Building it from a solved cube I have recently learned how to solve this pattern from a solved cube. First do a sixcenter switcher, with red on front and white on top. Now, do Y X2 B. Then, execute W (corner commuter) U2 W (inverse of W). Then, inverse your setup moves (B X2 Y ). Do Y, then E2 F. From there, execute a CCW edge cycle. Next, inverse your setup moves (F E2 Y) Do Y, then L2 B. Execute Rubik s maneuver, inverse setup moves. (B L2) That s the first block, and now you have to do the same for the second block. However, you should notice that you will do the directional opposite of each algorithm. As you recall, W turns corner 2 CCW, and W turns corner 2 CW. Thus, because we matched the CCW edge cycle with the CCW corner flip, we will do the same by matching CW edge cycle with CW corner flip. Do not over think it, it is quite simple! Hold the yellow side in your front and orange on top. (Referring to centers, not overall pieces.) Y E2 F CW Edge Cycle F E2 Y R B Rubik s Manuever B R Solved Method Three- Using an Algorithm L F L D'B D L² F² D'F'R U'R'F² D This algorithm will turn a solved cube into the cube inside a cube pattern. Execute 3 times, and it will re-solve the cube

36 Cube Inside a Cube Inside a Cube Really, this pattern is easy once you master the previous version. It simply involves holding it on the green side front, and yellow side top. Then, do a B W U2 W U2 B. Simple as that. Chicken Wings I don t know for sure that this is the proper term for this pattern. I have seen the name on a site but for now, I ll name these Chicken Wings. Simply do the six center switcher twice from the red side and you will have it. Chicken Feet An obvious one if you have been following through with all my other patterns, it is simply Chicken Wings with the two corners rotated

37 Blindfolded Cubing Where it all gets serious. I began trying to learn blindfolded cubing when I was three months into the cubing obsession. I have succeeded in a few blindfolded solves, but I am still not proficient at memorizing the cube, as it is a long process, usually 16 minutes for me. But I will be able to outline the basic steps for this method. It is a beginner method, requiring the use of only 1 algorithm and 1 commuter (being the same commuter you use for patterns, it shouldn t be too difficult to apply.) This method can be found at Nerd Paradise, a very good site for all nerdy subjects from Rubik s cubes to how to convert logarithms in your head. Before we begin, we must number our pieces. Each individual piece is given a number. A number 1-12 is given to each edge, and a number 1-8 is given to each corner. A brief instruction of this system of numbering was briefly explained at the beginning of the book, so I would advise you look back and review before continuing. Basically, the corners are numbered 1-8, starting from the UFL position and going CCW, then jumping to the FDL corner and continuing until 8. And the edges are numbered 1-12, starting from the UF position, going CCW, then going back to the ML edge, naming that 5, continuing CCW, and going back to the DF edge and labeling that 9, and continuing until 12. The overall method goes as follows - Orientation of Corners - Orientation of Edges - Permutation of Corners - Permutation of Edges As I said, this is a beginner method, no two sections are combined and the minimal amounts of algorithms are used. However, it is also the easiest to comprehend and is a good start for intermediate solvers

38 Orientation of Corners As stated in the introduction, a basic commuter is used to orient corners. An explanation of this commuter can also be found in the beginning of the Patterns! section. A commuter is broken down into four basic sections: the change of piece A, the setup moves replacing A with B, the change of piece B using the inverse of what was done to A, and the replacing of B with A. This can be simplified to W setup moves W (setup moves) where W is the move editing A, and W is the inverse. However, in this case, W will be (R D R D)*2 and W will be (D R D R)*2, the effect of W will turn corner 2 CCW, and W will turn corner 2 CW. For an example, we will take the case of the Siamese fish. We notice that corner 2 needs to be turned CCW, and corner 4 needs to be turned CW. This is the perfect chance to use W. So to solve, simply do W, then replace corner 2 with corner 4 by doing U2, W, and replace 4 with 2 again, U2, This will solve that certain case. For another example, take into consideration the case of Headlights. Notice that corner 2 needs to be turned CW, and corner 1 needs to be turned CCW. We could do. U W U W Or W U W U As they are both the same amount of moves, it is your choice to whether or not you use the first or second one. The point trying to be proven is that it doesn t matter in which order you do W or W, but the fact that one will solve the other. Also, it may be easier for some to always use W first, but there are also some cases where using W first may be a pain to setup. The final example involves Sune (or Fish B as some call it). This involves corners 2, 3, and 4 to be turned CW. But can we solve this using W and W? Indeed we can. One might do W U W U U2 W U W U U2 Using back to back W and W. However, note that there is an easier way to doing this. W U W U W U2 This can be done because 3 corner rotations will resolve itself to its former position. Because corner 2 is the only one affected in the U layer, doing W three times while switching corner 2 will resolve the destroyed bottom layer. Also realize that the two corners you wish to rotate are not always going to be on the same layer. But simply place them in the same layer, execute the commuters, and do the inverse of your setup moves to get them back to their original positions

39 Orientation of Edges This uses the same idea as the orientation of corners: using one algorithm to change the orientation of two edge pieces. The algorithm we will be using is called Rubik s Maneuver (abbev. RM). This algorithm changes the orientation of edges 1 and 3. Rubik s Maneuver (Changes the Orientation of Front-top edge and Back-top edge) M U M U M U2 M U M U M U2 4-Edge Rubik s Maneuver (M U)*4 (M U)*4 For this certain method, orientation is defined when the each side of each edge is either on the side of their certain color or on the side of the opposite of their color. This was my own definition, not a technical definition, but it is the easiest way to picture the cube. This has the correct orientation because the red side of edge 1 is on its side and the white side of edge 1 is on its side. This edge is incorrect, because the red of edge 1 is not on the orange or red side. This edge is correct because the orange is on the red side, (the opposite of the its color)

40 (UNDER CONSTRUCTION) Current World Record Statistics Category Record Holder Record 3x3x3 Single Tibaut Jacquinot 9.86 seconds. 3x3x3 Average Yu Jeong-Min seconds 3x3x3 Blindfolded Single Chris Krueger 1:15.60 minutes 3x3x3 One-Handed Single Dan Dzoan 17.9 seconds 3x3x3 One-Handed Average Dan Dzoan seconds Category Record Holder Record 3x3x3 With Feet Anssi Vanhala seconds 2x2x2 Single Anthony Hsu 3.55 seconds 4x4x4 Single Michael Fung seconds 5x5x5 Single Frederick Badie 1:44.47 minutes 3x3x3 Fewest Moves Mirek Goljan 28 moves Pictures Leyan Lo (Left) Former record holder of blindfolded cubing Tyson Mao (Right) Former record holder of blindfolded cubing. Formed the World Cubing Association

41 (Middle) Jessica Fridrich Inventor of the Fridrich method Lars Petrus (Right) Inventor of Petrus Method

42 Will Smith- 55 Seconds (Though, half the cube was done before timer was started) Those were the people who inspired me to keep going on -Jessica Fridrich -Lars Petrus -Tyson and Toby Mao -Shortaro Macky Makisumi -Leyan Lo -Dan Harris -Will Smith (Sort of, ha! Kidding)