Benjamin Popp HOW TO SOLVE A RUBIK’S CUBE A GUIDE FOR BEGINNERS Benjamin Popp How to Solve a Rubik’s Cube A Guide for Beginners 1 Benjamin Popp Table of Contents Introduction . . . . . . . . . . 3 Before you Begin . . . . . . . . . 4 Task I: Solving the Upper Layer . . . . . . 6 Task II: Solving the Middle Layer . . . . . . 10 Task III: Solving the Bottom Layer . . . . . . 11 Appendix A: Pattern Quick Reference . . . . . . 15 Appendix B: Extended Lower Layer Patterns . . . . . 16 Appendix C: Internet References . . . . . . 18 How to Solve a Rubik’s Cube A Guide for Beginners . 2 Benjamin Popp Introduction This instruction set will help any beginner solve the Rubik’s Cube. The Cube can be intimidating to people who do not understand it, but it is easier to solve than it looks. With this guide and a little practice you can solve the Rubik’s Cube in less than five minutes. The Cube will be solved in three basic tasks: solving the top layer, solving the middle layer, and solving the bottom layer. The process of solving the Cube is the simplest when broken into these three sections. Things You Will Need    The Rubik’s Cube or other off-brand Cube puzzle. This guide makes the most sense when you actually have a Cube available. If you do not have a Cube with you, it might be a good idea to wait and try using this guide once you have a Cube. Time The first time solving the Cube with this guide could take about an hour. Once you are accustom to the notation and the general steps, solving the cube will become a faster and more natural process. This Guide The first time through, this guide will be very helpful. The second time you might only need the figures; Appendix A is a condensed solution set for the middle and lower layers. Note: What if something doesn’t work quite right? All notes and tips to help along the way will appear in a box with a yellow heading like this one. How to Solve a Rubik’s Cube A Guide for Beginners Common problems are solved in boxes with a blue header like this one. 3 Benjamin Popp Before You Begin Figure i: 6 Center Cubies Over the years, the Rubik’s Cube solving community created standard notation and words to talk about the Rubik’s Cube. This guide will use the standard notation as described below. Cubie One of the miniature cubes in a Rubik’s Cube Center Cubie One of the six fixed centers with one visible color (Figure i) Corner Cubie One of the eight rotating cubies with three visible colors (Figure ii) Edge Cubie One of the twelve rotating cubies with two visible colors (Figure iii) Face One side of the cube; the White face is the face with a White center, the Up face is the face with the center directed upward, etc. (Figure iv) Layer All the cubies that are on a face; the upper layer is the nine cubies with colors on the Up face, the front layer is the nine cubies with colors on the front face, etc. Turn Moving the cube in your hands, but not changing the cube in any way. Usually this will keep the same face on top and change the front and side faces. Twist Changing a face with respect to the other faces. ______________________ Figure ii: 8 Corner Cubies ______________________ The six faces are defined as: (U)p, (D)own, (L)eft, (R)ight, (F)ront, and (B)ack Figure iii: 12 Edge Cubies In this guide, all figures will appear with six sides, three of which are seen as if mirrors were around the cube. The three connected sides will always be the Up face, Front face, and Right face. Cubies that are not important for a specific step will appear in gray to simplify the figures. How to Solve a Rubik’s Cube A Guide for Beginners 4 Benjamin Popp Use the pattern from the Figure… Note: During certain steps you will be asked to perform a pattern in a Figure. This pattern will always be found directly below its Figure and is written in parenthesis. A capital letter means to twist a face clockwise; a capital letter with an apostrophe (‘) means to twist that face counterclockwise; a capital letter with the number two (2) after it means twist that face twice. For example: ( U F’ R2 ) Twisting a face does not change the colors on that face; it changes the colors on the faces around it. Which way is clockwise for a face? Look directly at a face and imagine a clock on it, then twist that face in the direction the hands of the clock would move. Notice that this means that if you are looking at the Front face of the Cube, the Up face clockwise and Down face clockwise appear to be opposite directions. The above translates to twisting the Up face clockwise, the Front face counterclockwise, and the Right face twice. Figure iv: The Six Faces How to Solve a Rubik’s Cube A Guide for Beginners 5 Benjamin Popp Task I: Solving the Upper Layer If you have not scrambled your Cube, do so now. Before you begin this task your Cube must be in total disarray. It will not stay scrambled very long; soon your Cube will have all of the White face solved and half of the Red, Blue, Orange, and Green faces solved. Also make sure you have read the “Before You Begin” section and you understand the basic Rubik’s Cube vocabulary. 1. Turn the Cube so the white face is the Up face. Figure 1.5A Note: You can actually start with any face Up you want, but this guide is easier to understand if you solve White first. The White Cross (R) 2. Find the white-red edge cubie. 3. If that cubie is in the upper layer the lower layer, turn the Cube until the cubie on the Front face and twist the Front face either direction. This places the cubie in the middle layer. ______________________ Figure 1.5B 4. Turn the Cube so the cubie is in the Front and Right sides. 5. If the cubie has white on the Front face, twist the Right face clockwise (Figure 1.5A). If the cubie has white on the Right face, twist the Front face counterclockwise (Figure 1.5B). ( F’ ) My colors are laid out different from yours! Most modern Rubik’s Cubes have White opposite Yellow, Red opposite Orange, and Green opposite Blue. If your colors are different, you can still use this guide; just look at the introduction section and decide which of your colors is which based on the center cubies. How to Solve a Rubik’s Cube A Guide for Beginners 6 Benjamin Popp 6. Repeat steps 2-5 for the white-green edge cubie; before step 5, twist the Up face so the green cubie will be placed next to the red cubie (Figure 1.6). Note: If you have trouble getting white edges into the upper layer correctly, just try all the possibilities. If a twist produces an undesired effect, undo that twist and try twisting the Up face before continuing. 7. Repeat steps 2-5 for the whiteorange edge cubie, placing it beside the white-green cubie (Figure 1.7). My centers line up wrong in step 9! 8. Repeat steps 2-5 for the white-blue edge cubie, placing it beside the white-red cubie (Figure 1.8). Some of your white edges are in the wrong place. See the note above. 9. Twist the Up face to align the four white edge cubies with the four side center cubies (Figure 1.9). Figure 1.6 Figure 1.7 Figure 1.8 Figure 1.9 How to Solve a Rubik’s Cube A Guide for Beginners 7 Benjamin Popp The White Corners Note: Figure 1.10 Do NOT choose a white corner cubie that is already in place with white on the Up face in step 10. You know a cubie is in place when its colors match the centers around it. 10. Choose two adjacent sides, such as red and blue. Find a corner cubie with those colors and white. If it is in the upper layer, turn the Cube so the cubie is in the Front-Right-Up corner and use the pattern in Figure 1.10 to move it to the bottom layer. 11. Twist the Down face to place the cubie directly beneath its desired location. ( R’ D’ R ) ______________________ Figure 1.12 12. Turn the Cube so the cubie is in the Front-Right-Down corner and perform the pattern in Figure 1.12 continuously until the piece is correctly positioned. 13. Repeat steps 10-12 for each of the four white corner pieces. ( D’ R’ D R ) The pattern in Figure 11 was unhelpful… Those four twists will get the piece where it needs to go in the direction it needs to be, but you might need to use the pattern up to five times before the piece is correct. Also make sure you are twisting the faces the right way; clockwise for the Down face is opposite of clockwise for the Up face. How to Solve a Rubik’s Cube A Guide for Beginners 8 Benjamin Popp Figure 1.14 14. Double check to make sure the Cube looks like the Figure 1.14 before moving on. The upper layer completed When you made it this far, take a deep breath and relax a little; you just finished one third of the Rubik’s Cube! That is farther than most people can get. If you have time, go ahead and mix up the Cube and solve the first layer again. Take this opportunity to become comfortable with how the cubies move together; the more you understand the Cube, the easier it is to work through the next two layers. Try to understand how the patterns listed in Figures 1.10 and 1.11 work instead of just memorizing them; it will make Cube solving more natural and less mechanical. How to Solve a Rubik’s Cube A Guide for Beginners Note: The method detailed here is just one of many ways to solve the first layer. If you want to solve the Cube for speed, solving the upper layer should become natural so you can focus on the parts that lie ahead. 9 Benjamin Popp Task II: Solving the Middle Layer Note: This layer involves more complex patterns than the upper layer, but also only involves four cubies. From this point on, be careful applying the patterns; messing up a pattern could force you back to solving the upper layer. The middle layer is the eight cubies between the upper and the lower layer, NOT the eight cubies between the front layer and the back layer or the right layer and the left layer. 1. Find an edge cubie in the bottom layer with no yellow side. Figure 2.4A 2. Twist the Down face so the cubie’s side color is under the center of the same color. 3. Look at the color on the bottom of the cubie to decide if the cubie should go up and left or up and right. ( D’ R’ D R D F D’ F’ ) _________________________ 4. Perform the pattern in Figure 2.4A to move the cubie up and right, or perform the pattern in Figure 2.4B to move the cubie up and left. Figure 2.4B 5. Repeat steps 1-4 for each of the four middle layer edge cubies. You should now have at least six colors correct on the four side faces as well as the whole white face. Take another deep breath; you will soon conquer the Rubik’s Cube. ( D F D’ F’ D’ R’ D R ) All the edges in the bottom layer have yellow sides! First make sure you are looking at the edges, not the corners. Use one of the patters in Figures 2.4A and 2.4B to push a yellow edge cubie into the middle layer. This will pull a cubie you need back to the bottom layer where you can apply one of the patterns again. How to Solve a Rubik’s Cube A Guide for Beginners 10 Benjamin Popp Figure 3.2 Task III: The Lower Layer The bottom layer is the most reliant on patterns; this is because you must be careful not to ruin your work from the first two layers while fixing the third layer. 1. Turn the entire cube over so the yellow face is the Up face and the white face is the Down face. ( F U R U’ R’ F’ ) Orienting the Yellow Cross Figure 3.5 2. If you can turn the Cube to make it look like Figure 3.2, skip to step 4. 3. Apply the pattern from Figure 3.2 to the Cube. The front face color is unimportant. Return to step 2. 4. Turn the Cube to make it look like Figure 3.2 and aply the pattern from Figure 3.2. 5. If you do not have the yellow cross (Figure 3.5), return to step 2. Note: The patterns used to solve the bottom layer are freely available online from many websites and are considered public domain. Appendix C lists the website of Lars Petrus, the only known human creator of some of these patterns. How to Solve a Rubik’s Cube A Guide for Beginners 11 Benjamin Popp Note: The purpose of the next section is to get all the yellow corner cubies between the center cubies with the same colors. For example, you want the fellow-green-orange cubie between the yellow, green, and orange centers. It is not important for yellow to face up on all of the corner cubies; just get the corners between the right centers. Positioning the Yellow Corners Figure 3.8 6. Choose a color from one of the four sides: red, green, blue, or orange. Make sure there are two yellow corner cubies of the chosen color in the same side layer. For example, in Figure 3.8, both yellow-green corner cubies are on the right layer. 7. Twist the Up face to allign those two cubies with the center that shares their color. ( L’ U R U’ L U R’ U2 ) 8. If those two cubies need to switch places, turn the Cube so both cubies are on the Right face, then use the pattern in Figure 3.8. 9. Repeat steps 6 through 8 for the color on the opposite side of the Cube. For example, if you chose green first, repeat the steps for blue. How to Solve a Rubik’s Cube A Guide for Beginners 12 Benjamin Popp Note: The pattern in Figure 3.11 rotates three corner cubies at a time and can be difficult to use. Due to this complexity, there is a little guess-and-check in the next section. If you have trouble passing this step, Appendix B lists patterns for all possible configurations for the yellow face. Go directly to step 13 if you use one of those patterns instead. Finishing the Yellow Face Figure 3.11 10. If the yellow face is solid, skip to step 13. If the yellow face has exactly one yellow corner cubie facing up, skip to step 12. Otherwise, turn the cube so the cubie in the up-front-left corner does NOT have fellow facing up. Configuration A 11. Use the pattern in Figure 3.11, then return to step 10 if the Cube does not look like either configuration in Figure 3.11. Configuration B 12. Turn the Cube so the cubie in the up-front-left corner has yellow facing up and perform the attern in Figure 3.11 until the fellow face is solid (you may have to use the pattern twice). ( R U R’ U R U2 R’ U2 ) 13. Twist the Up face to align all the corner cubies and make sure the colors line up with the colors in the other two layers. If some corner cubies have the wrong colors on their sides, you made a mistake while placing the corners; return to step 6. How to Solve a Rubik’s Cube A Guide for Beginners 13 Benjamin Popp Figure 3.14 Finishing the Side Faces 14. If one of the four side faces is solved, turn the Cube to make the side face the Left face. 15. Use the pattern in Figure 3.14, then return to step 14 if necessary. You might have to do this up to three times. ( R2 U F B’ R2 F’ B U R2 ) Congratulations! You just solved the Rubik’s Cube. Now that you understand the process, you might try doing it again using just Appendix A. If you’re interested in learning to solve the Cube faster, start working with Appendix B for an extended set of lower layer patterns or Appendix C for internet references. Note: Appendix B lists more patterns for solving the bottom layer. It can be solved using only these four; however, the more cases you remember, the faster you can solve the cube. How to Solve a Rubik’s Cube A Guide for Beginners 14 Benjamin Popp Appendix A: Pattern Quick Reference ( D’ R’ D R D F D’ F’ ) ( D F D’ F’ D’ R’ D R ) ( F U R U’ R’ F’ ) ( L’ U R U’ L U R’ U2 ) ( R U R’ U R U2 R’ U2 ) ( R2 U F B’ R2 F’ B U R2 ) How to Solve a Rubik’s Cube A Guide for Beginners 15 Benjamin Popp Appendix B: Extended Lower Layer Patterns Yellow Face Patterns V - Fix cosune sune cosune F U R U’ R’ F’ R’ U’ R U’ R’ U2 R R U R’ U R U2 R2 U’ R U’ R’ U2 R Line - Fix double sune bruno F R U R’ U’ F’ R U R’ U R U’ R’ U R U2 R’ R’ U2 R2 U R2 U R2 U2 R’ sune anti-cosune anti-sune triple sune R U R’ U R U2 R’ R’ U2 R U R’ U R2 U2 R’ U’ R U’ R’ R U R’ U R U’ R’ U R U’ R’ U R U2 R’ How to Solve a Rubik’s Cube A Guide for Beginners 16 Benjamin Popp Yellow Edge Patterns Clockwise 3-Spin Counterclockwise 3-Spin R2 U F B’ R2 F’ B U R2 U’ R2 U2 R2 U2 R2 U R2 U2 R2 U2 R2 Reverse Pair Switch Adjacent Pair Switch R2 U’ F B’ R2 F’ B U’ R2 R U R’ U R’ U’ R’ U R U’ R’ U’ R2 U R U2 How to Solve a Rubik’s Cube A Guide for Beginners 17 Benjamin Popp Appendix C: Internet References http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/f2l/f2l Dan’s Cube Station provides information about solving the Rubik’s Cube using the F2L, or First2-Layers method. Instead of solving the cube layer by layer, the F2L solves the cube by fixing the first two layers at the same time. It can be much faster than the method listed in this document. However, there are also many more patterns to remember. http://lar5.com/cube/ The website above explains the Petrus method for solving the Rubik’s Cube, invented by Lars Petrus. While fundamentally different from the method outlined here (Petrus begins by creating a 2x2 Cube and expands it), the last section of the solution is very similar. Petrus also invented the Sune pattern used in this document and the Niklas pattern which appears in Figure 3.4. http://www.geocities.com/rubiks_galaxia/PLL.html The Permutation Last Layer is a system for speeding up the lower layer by adding more patterns to move all the lower layer cubies at the same time. With this system, you would skip step 4-6 of the lower layer and just solve the face; then use one of the patterns listed on the web page above to move all the cubies to their proper positions, solving the entire last layer in only three steps. How to Solve a Rubik’s Cube A Guide for Beginners 18 Benjamin Popp