Rubik's Cube Algorithms PDF: A Guide to Solving the World's Most Popular Puzzle
The Rubik's cube is a three-dimensional puzzle that consists of six faces, each divided into nine smaller squares of one of six colors. The goal of the puzzle is to twist and turn the faces until each one has only one color. Sounds simple, right? Well, not quite. The Rubik's cube has over 43 quintillion possible configurations, but only one solution. To solve it, you need to know some algorithms, which are sequences of moves that achieve a certain result.
rubik 39;s cube algorithms pdf
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Algorithms are very useful for solving the Rubik's cube, because they allow you to manipulate specific parts of the cube without affecting others. By applying different algorithms, you can gradually solve the puzzle layer by layer, from the first layer to the last layer. Learning algorithms can also help you improve your speed, memory, and logical thinking skills.
In this article, we will show you how to solve the Rubik's cube using some basic algorithms, and where to find PDF files with more algorithms for different levels of difficulty. Whether you are a beginner or an expert, you will find something useful and interesting in this guide. So grab your cube and let's get started!
How to Solve the Rubik's Cube
Before we dive into the algorithms, we need to establish some notation for describing the faces, moves, and pieces of the cube. This will help us communicate more clearly and avoid confusion.
Notation
We will use letters to represent the six faces of the cube: Front (F), Right (R), Down (D), Up (U), Left (L), and Back (B). A letter by itself means to turn that face 90 degrees clockwise with respect to the center of the cube. For example, F means to turn the front face clockwise. A letter with an apostrophe (F') means to turn that face 90 degrees counter-clockwise. A letter followed by a number 2 (F2) means to turn that face 180 degrees.
To refer to an individual piece or a face of a piece, we use one letter for the center pieces, two letters for the edge pieces, and three letters for the corner pieces. The letters indicate which faces of the cube that piece belongs to. The first letter gives the side of that piece we are referring to. For example, in this picture:
The red square is at FUR, yellow at RUF, blue at URF, and green at ULB.
. First Layer
The first step to solving the Rubik's cube is to make a white cross on the top face of the cube. To do this, you need to find the four white edge pieces and place them between the white center and the matching side center. For example, the white and green edge piece should go between the white and green centers, like this:
To move an edge piece to its correct position, you may need to use one of these algorithms:
Case
Algorithm
The edge piece is on the bottom layer, facing down.
R' D' R D
The edge piece is on the bottom layer, facing sideways.
F2 U R' L F2 R L'
The edge piece is on the middle layer, facing sideways.
U R U' R' U' F' U F
The edge piece is on the top layer, but not aligned with its center.
U until it is aligned, then F2
The edge piece is on the top layer, but flipped.
F' U L' U' L F
Once you have the white cross, you need to solve the four white corner pieces. To do this, you need to find the corner piece that matches the colors of the side centers around it, and move it to the bottom layer. Then, you need to use this algorithm to bring it up to the top layer:
R' D' R D (repeat until solved)
For example, if you have this corner piece:
You need to move it under the white, red, and blue centers, like this:
Then, you need to apply the algorithm R' D' R D until it goes up to the top layer, like this:
Repeat this process for the other three corner pieces. When you are done, you should have a completed first layer, like this:
Middle Layer
The next step is to solve the four middle layer edges. To do this, you need to find an edge piece on the top layer that does not have a yellow sticker, and move it above the side center that matches its color. For example, if you have this edge piece:
You need to move it above the green center, like this:
Then, depending on which direction you need to move it to match its other color, you need to use one of these algorithms:
Case
Algorithm
The edge piece needs to go to the left.
U' L' U L U F U' F'
The edge piece needs to go to the right.
U R U' R' U' F' U F
For example, in our case, we need to move the edge piece to the left, so we use the first algorithm: U' L' U L U F U' F'. This will result in this:
Repeat this process for the other three edge pieces. When you are done, you should have a completed middle layer, like this:
Last Layer
The final step is to solve the last layer, which consists of four yellow edges and four yellow corners. To do this, you need to apply two steps: orientation and permutation. Orientation means to make all the yellow stickers face up, and permutation means to put them in their correct positions.
To orient the last layer edges, you need to look at the top face and see how many yellow stickers are facing up. There are four possible cases:
Case
Algorithm
No yellow stickers are facing up.
F R U R' U' F'
One yellow sticker is facing up.
F R U R' U' F' U F R U R' U' F'
Two yellow stickers are facing up, forming a horizontal line.
F R U R' U' F'
Two yellow stickers are facing up, forming a vertical line.
F R U R' U' F' U2 F R U R' U' F'
For example, if you have this case:
You need to use the second algorithm: F R U R' U' F' U F R U R' U' F'. This will result in this:
To orient the last layer corners, you need to look at the top face and see how many yellow stickers are in the correct position. There are seven possible cases:
Case
Algorithm
No yellow stickers are in the correct position.
R' F R' B2 R F' R' B2 R2
One yellow sticker is in the correct position.
R' F R' B2 R F' R' B2 R2 (repeat until solved)
Two adjacent yellow stickers are in the correct position.
R2 D R' U2 R D' R' U2 R'
Two opposite yellow stickers are in the correct position.
R2 D R' U2 R D' R' U2 R'
Three yellow stickers are in the correct position.
R' F R' B2 R F' R' B2 R2 (repeat until solved)
Four yellow stickers are in the correct position, but not oriented.
R' F R' B2 R F' R' B2 R2 (repeat until solved)
Four yellow stickers are in the correct position and oriented.
No algorithm needed, you are done!
For example, if you have this case:
You need to use the third algorithm: R2 D R' U2 R D' R' U2 R'. This will result in this:
To permute the last layer edges, you need to look at the top face and see if the edge pieces are in their correct positions. If they are not, you need to use one of these algorithms:
Case
Algorithm
The edge pieces need to be swapped in a clockwise direction.
R U R' U R U2 R'
The edge pieces need to be swapped in a counter-clockwise direction.
R U2 R' U' R U' R'
The edge pieces need to be swapped across from each other.
R U2 R' U' R U' R' U2 R U2 R'
For example, if you have this case:
You need to use the third algorithm: R U2 R' U' R U' R' U2 R U2 R'. This will result in this:
To permute the last layer corners, you need to look at the top face and see if the corner pieces are in their correct positions. If they are not, you need to use this algorithm:
U R U' L' U R' U' L (repeat until solved)
For example, if you have this case:
You need to use the algorithm: U R U' L' U R' U' L. This will result in this:
Congratulations, you have solved the Rubik's cube!
Rubik's Cube Algorithms PDF Resources
Now that you know how to solve the Rubik's cube using some basic algorithms, you may want to learn more algorithms for different methods, variations, and challenges. There are many PDF files available online that contain algorithms for solving the cube faster, easier, or more creatively. Here are some of the best PDF files for beginners, intermediate, and advanced solvers:
Where to find PDF files with algorithms for solving the cube
One of the most popular and comprehensive websites for Rubik's cube algorithms is . This website has algorithms for various methods, such as CFOP, Roux, ZZ, Petrus, and more. It also has algorithms for different types of cubes and puzzles, such as 2x2, 4x4, 5x5, Megaminx, Pyraminx, Skewb, and more. You can download PDF files for each category or browse them online.
Another great website for Rubik's cube algorithms is . This website has a lot of information and resources for speedcubing, which is the practice of solving the cube as fast as possible. It has algorithms for different methods, such as CFOP, Roux, ZZ, Petrus, and more. It also has algorithms for different situations, such as OLL, PLL, F2L, COLL, ELL, and more. You can download PDF files for each category or browse them online.
A third website for Rubik's cube algorithms is . This website is run by Feliks Zemdegs, who is one of the fastest and most famous speedcubers in the world. He has created a series of tutorials and videos for teaching how to solve the cube using the CFOP method. He also has PDF files with algorithms for different stages of the method, such as F2L, OLL, and PLL. You can download the PDF files for free or sign up for a premium membership to access more features.
How to use PDF files to learn and practice algorithms
PDF files are very convenient and portable ways to learn and practice algorithms for solving the cube. You can print them out, save them on your computer or phone, or access them online. Here are some tips on how to use PDF files effectively:
Choose a PDF file that suits your level and goal. For example, if you are a beginner who wants to learn the basic method, you can use a PDF file that has the essential algorithms for solving the cube. If you are an intermediate solver who wants to improve your speed, you can use a PDF file that has more advanced algorithms for optimizing your moves. If you are an expert solver who wants to challenge yourself, you can use a PDF file that has exotic algorithms for different variations and puzzles.
Study the algorithms carefully and understand how they work. Don't just memorize the moves blindly, but try to visualize how they affect the cube and why they achieve the desired result. You can use online tools such as to see how the algorithms work step by step.
Practice the algorithms repeatedly until you master them. You can use a timer or a metronome to measure your speed and accuracy. You can also use a scrambler or a generator to create random cases for you to solve. You can find these tools online or download apps for your devices.
Review the algorithms regularly and test yourself on them. You can use flashcards or quizzes to help you recall the algorithms and apply them correctly. You can also mix up the algorithms and try to solve different cases with them.
Have fun and enjoy learning new algorithms. Don't get frustrated or bored if you find some algorithms hard or confusing. Remember that solving the cube is a hobby and a skill that you can improve over time with practice and patience.
What are some of the best PDF files for beginners, intermediate, and advanced solvers
There are many PDF files with algorithms for solving the cube, but some of them are more popular and recommended than others. Here are some of the best PDF files for different levels of solvers:
For beginners, a good PDF file is . This PDF file has 10 pages and covers the basic method for solving the cube in six steps. It has clear diagrams and explanations for each step and algorithm.
For intermediate solvers, a good PDF file is . This PDF file has 12 pages and covers the CFOP method for solving the cube in four steps: Cross, F2L, OLL, and PLL. It has over 100 algorithms for different cases and situations.
For advanced solvers, a good PDF file is . This PDF file has 36 pages and covers various methods and techniques for solving the cube faster and more creatively. It has over 300 algorithms for different puzzles, variations, challenges, and tricks.
Conclusion
In this article, we have shown you how to solve the Rubik's cube using some basic algorithms, and where to find PDF files with more algorithms for different levels of difficulty. We hope you have learned something new and useful from this guide.
Solving the Rubik's cube is a fun and rewarding activity that can improve your memory, logic, and creativity skills. It can also be a great way to impress your friends, family, and yourself. With enough practice and patience, you can master any algorithm and solve any puzzle.
If you have any questions or feedback about this article or Rubik's cube algorithms in general, please feel free to leave a comment below. We would love to hear from you and help you with your cube-solving journey.
FAQs
Here are some of the most frequently asked questions about Rubik's cube algorithms and their answers:
What is God's number for the Rubik's cube?
God's number for the Rubik's cube is the minimum number of moves required to solve any configuration of the cube. It is proven that God's number for the Rubik's cube is 20, which means that any scrambled cube can be solved in 20 moves or less, using the standard notation.
How many possible permutations are there for the Rubik's cube?
There are 43,252,003,274,489,856,000 possible permutations for the Rubik's cube, which is about 43 quintillion. This number is calculated by multiplying the number of ways to arrange the 8 corners (8!), the number of ways to orient the 8 corners (3^7), the number of ways to arrange the 12 edges (12!), and the number of ways to orient the 12 edges (2^11), and then dividing by 12, which is the number of invalid orientations.
What is the world record for solving the Rubik's cube?
The current world record for solving the Rubik's cube is 3.47 seconds, set by Yusheng Du from China in 2018. The current world record for solving the Rubik's cube blindfolded is 15.50 seconds, set by Max Hilliard from USA in 2019. The current world record for solving the Rubik's cube with one hand is 6.82 seconds, set by Max Park from USA in 2019.
What are some other types of Rubik's cubes and puzzles?
There are many other types of Rubik's cubes and puzzles that vary in size, shape, color, and mechanism. Some of the most common ones are:
2x2 cube: A smaller version of the Rubik's cube that has only 2 layers and 4 stickers per face.
4x4 cube: A larger version of the Rubik's cube that has 4 layers and 16 stickers per face.
5x5 cube: An even larger version of the Rubik's cube that has 5 layers and 25 stickers per face.
Megaminx: A dodecahedron-shaped puzzle that has 12 faces and 50 stickers per face.
Pyraminx: A tetrahedron-shaped puzzle that has 4 faces and 9 stickers per face.
Skewb: A cube-shaped puzzle that has 6 faces and 4 stickers per face, but rotates around its corners instead of its centers.
How can I create my own Rubik's cube algorithms?
Creating your own Rubik's cube algorithms can be a fun and challenging way to explore the puzzle and discover new ways to solve it. There are different methods and tools for creating your own algorithms, but here are some general steps:
Pick a goal or a result that you want to achieve with your algorithm. For example, you may want to swap two pieces, flip an edge, or rotate a corner.
Experiment with different moves and sequences on your cube until you find one that achieves your goal. You can use trial and error, intuition, or logic to find a suitable algorithm.
Write down your algorithm using the standard notation and test it on different cases to make sure it works as intended.
Optimize your algorithm by reducing the number of moves, avoiding unnecessary moves, or using shortcuts or tricks.
Name your algorithm and share it with other cubers if you want.
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