Pretty Rubik´s Cube patterns with algorithms

Are you tired of solving your Rubik´s Cube always the same way or are you looking for a new challenge? Try to reproduce or invent some pretty patterns! In this section I´m going to present some of my favorite Rubik´s Cube patterns algorithms with preview images, like the famous Superflip, the checkerboard, the snake patterns, the cross, the cube in a cube and other nice motives. If you got bored solving the Rubik’s Cube always the same way and want new challenge try to reach one of these patterns without watching the algorithms supplied. 
In case you don´t know what these letters mean you should get started by reading the Rubik´s notation. If you don´t have a Magic Cube go ahead and use the online Rubik´s Cube solver program where you can apply rotations or even solve the cube online.

The Superflip

U R2 F B R B2 R U2 L B2 R U’ D’ R2 F R’ L B2 U2 F2 
The SuperFlip is the “most scrambled” Rubik’s Cube pattern. Every piece is where it’s supposed to be but the edges are oriented wrong. Computer programs need the highest amount of steps (20) to solve this state.

The Checkerboard

F B2 R’ D2 B R U D’ R L’ D’ F’ R2 D F2 B’:
Corner pieces are in place, oriented the correct way, but the edges are shifted to the the adjacent face to form this nice-looking design.

The easy checkerboard

M2 E2 S2 
( = U2 D2 F2 B2 L2 R2)
The most simple algorithm, it only takes three double layer moves to make it.

Wire

(R L F B) x 3 – R2 B2 L2 R2 B2 L2

Tablecloth

R L U2 F’ U2 D2 R2 L2 F’ D2 F2 D R2 L2 F2 B2 D B2 L2

Spiral pattern

L’ B’ D U R U’ R’ D2 R2 D L D’ L’ R’ F U
Looks great on bigger puzzles

Speedsolving.Com Logo

R’ L’ U2 F2 D2 F2 R L B2 U2 B2 U2

Vertical stripes

F U F R L2 B D’ R D2 L D’ B R2 L F U F

Opposite corners

R L U2 F2 D2 F2 R L F2 D2 B2 D2

Cross

U F B’ L2 U2 L2 F’ B U2 L2 U

Cross 2

R2 L’ D F2 R’ D’ R’ L U’ D R D B2 R’ U D2

Twisted cube in the big cube

F L F U’ R U F2 L2 U’ L’ B D’ B’ L2 U

Cube in a cube in a cube…

U’ L’ U’ F’ R2 B’ R F U B2 U B’ L U’ F U R F’

Anaconda

L U B’ U’ R L’ B R’ F B’ D R D’ F’

Python

F2 R’ B’ U R’ L F’ L F’ B D’ R B L2

Black Mamba

R D L F’ R L’ D R’ U D’ B U’ R’ D’

Green Mamba

R D R F R’ F’ B D R’ U’ B’ U D2

Four spots

F2 B2 U D’ R2 L2 U D’

Six spots

U D’ R L’ F B’ U D’
The same with middle layer turns:
E S E’ S’

Twister

F R’ U L F’ L’ F U’ R U L’ U’ L F’

Center-Edge-Corner

U’ R2 L2 F2 B2 U’ R L F B’ U F2 D2 R2 L2 F2 U2 F2 U’ F2

Tetris

L R F B U’ D’ L’ R’

Henry’s Zig Zag with Checkerboard

R2 L2 F2 B2 U F2 B2 U2 F2 B2 U

Facing Checkerboards

U2 F2 U2 F2 B2 U2 F2 D2

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Rubik’s Cube and Juggling

People are always looking for new and exciting ways to make solving a normal 3x3 rubik's cube more interesting. Some of the most popular techniques, currently implemented by the WCA as official event , involve solving the cube one-handed, with feet, or blindfolded. However, for the purpose of impressing large audiences, more efficient skills have been developed. One of the most common of these is solving the Rubik’s Cube whilst juggling. This can be done in a variety of different ways, such as juggling two balls with one hand and solving a cube with the other, all the way to solving 3 individual Rubik’s cubes whilst juggling them.

The Good

There are many people who have uploaded legitimate videos onto YouTube of them solving the cube whilst juggling, one of the earliest examples being David calvos' 3 cube juggle in which he juggles two solved cubes with one hand, and solves a third with the other. The video dates back to late 2011 and since then has received 1,300,000 views. In 2012, David Calvo also appeared on Spanish TV show El Hormiguero where he solved four cubes under water, which was the current Guinness World Record.

Another example of an amazing juggling feat was performed by well-known Rubik's cube solver and juggler Ravi Fernando. In 2013 he successfully solved three Rubik’s Cubes whilst juggling them. He solved the cubes one at a time but continued to juggle all three until they were all solved. The entire feat took him about 6 minutes, and was one of the first of its kind. There were, as expected, many comments from people who believed the video was faked all across the web, but solvers and speedsolvers alike backed Ravi’s solve and the video is now considered legitimate. Since 2013 this video has amassed nearly 1,500,000 views.

The Bad

One of the most viral Rubik’s Cube juggling videos was posted in mid-March 2016. Juggler known as “RuboCubo” uploaded a video in which he was recorded performing the same task as Ravi’s video 3 years before, but this time in under 20 seconds. The media quickly grabbed a hold of the video and made articles on it, most saying that it was probably reversed.

The telegraph, Sploid, Metro and Mirror all wrote about the topic, quoting reddit users from the reddit thread on the matter. Some puzzlers were quick to point out that the video was not real, and whilst the media and other sites were still unsure, both Reddit and the Speedsolving forums (who  also had a thread on the video) began to try and discover how the video was faked. At first, many people were quick to point out that the video was reversed, however upon closer inspection and reversing the posted video, this was figured out to be incorrect. Others suggested that the solver had memorised a low move solution for each cube, but the difficulty of performing the moves in regards to the orientation of the puzzle when caught and the time he would’ve had to recall the move he had to perform from memory proved too large, and had it been the case it would’ve still been just as impressive. It was only when a user pointed out that the solver was standing behind a “Rushes” banner, a UK digital FX company, that the truth was uncovered. Approximately one week after the solve, the same YouTube channel uploaded a “How it was actually done” video proving that the whole thing was an amazingly well-done video edit. In the description of the video, it is written:

“The skill on display here is expertise in seamless digital effects work — not physical solving of the Rubik’s cubes.”

Regardless of the truth about the solve, the video was incredibly well done and the graphic effects shown helped to promote the company. The video was very highly regarded and received multiple comments from well-known faces within the puzzling community, such as Youtuber RedKB, puzzle designer Tony Fisher, and even the inventor of the juggling technique (Mills Mess), Steve Mills.

Unsolvable cube

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Unsolvable Rubik’s Cube

When you take  apart a Rubik's cube and put it back together randomly you have only a 1/12 chance that your scrambled configuration  is solvable. In case of other Rubik's cube variations where the orientation of the center piece counts the chances are even smaller.

If the online Rubik's scrambler throws the ‘Invalid scramble’ error you must double check your puzzle and make sure you entered the color of every field correctly.
If you keep getting this error then you must to disassemble and built it in solved position because probably it has an unsolvable state.

some impossible scrambles

Not every random scramble can be solved by legal moves because of the parity which refers to whether a permutation is even or odd (can that permutation be represented by an even or odd number of swaps):

• Corner orientation
  Every corner piece has three possible orientations. It can be oriented correctly (0), clockwise (1) or counterclockwise (2). The sum of corner orientations always remain divisible by 3, no matter how many legal turns you make. See the first two cases on the image.
• Edge orientation
  Every legal rotation on the Rubik's cube always flips an even number of edges so there can’t be only one piece oriented wrong. See the third example.
• Piece swaps
  Considering the permutation of all the corners and edges, the overall parity must be even which means that each legal move always performs the equivalent of an even number of swaps (ignoring orientation). See the last example.

Combining all these laws we get 1/3 * 1/2 * 1/2 = 1/12

Experienced cubers realize that something’s wrong when they the last layer of the puzzle.

These scrambles can’t be solved, you have to take your cube apart to fix it.

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God’s Number

Mathematicians love the Rubik's cube. There’s no denying it. They are amazed at how such a seemingly simply puzzle can hold so many secrets. There is always something new to learn about the cube (if you are willing to learn, of course). Perhaps the biggest secret of all, one that took over 30 years for mathematicians to crack is God’s Number.

God’s Number, as many cube enthusiasts will already know, is the maximum number of moves required to solve any of the 43,252,003,274,489,856,000 combinations of the cube. It has been proven that this number is 20, however the discovery is fairly recent (July 2010). The term “God’s Number” was coined because the mind of a being able to find the shortest sequence of moves to solve any scramble sequence would have to be thousands of times more powerful than our own, able to test millions of different combinations in the blink of an eye, something that mathematicians believe only a Deity could possess.

This number may seem low, but theoretically it should be even lower. Only around 490,000,000 combinations require the full 20 moves to be solved. Although 490 million is a huge number, it is only a fraction of the 43 quintillion possible combinations (0.0000011328955% to be precise). The chances of generating a random scramble that can only be solved in 20 moves, no more no less, is around 1 in a billion. However, the number of combinations that can be solved in 19 moves is approximately 1.5 quintillion. This means that God’s Number is much closer to 19 than 20, but unfortunately even if only 1 scramble sequence was impossible to solve in less than 20 moves, God’s Number would still be 20.

The Super-Flip

Perhaps the most famous of the rare scrambles that require exactly 20 moves to solve is the super-flip position (pictured). This is achieved by performing the following sequence of moves – R L U2 F U’ D F2 R2 B2 L U2 F’ B’ U R2 D F2 U R2 U from any orientation. The position is recognisable as every single corner is solved in its place, while every single edge is flipped in its place. This was also the first position that was found that could not be solve in less than 20 moves, raising the lower bound of God’s Number to 20 in 1995.

History of God’s Number

Work began on the search for God’s Number back in 1981, when a man named Morwen Thistlethwaite proved using a complex algorithm he devised himself that 52 moves was enough to solve any of the 43 quintillion different scrambles. This number began to fall slowly as better, more efficient methods were devised for solving the huge number of possible combinations in the fewest moves possible.

Of course, not all 43 quintillion combinations were tested individually by computers. Many ingenious patterns were spotted to reduce this number to a fraction of its original quantity. For example, if you were to perform the super-flip algorithm on a Rubik’s Cube and rotate the entire cube by 180 degrees, you would have theoretically created another of the 43 quintillion combinations without increasing the number of moves required to solve it. The reason for this is because 43 quintillion is the number of positions, not the number of completely unique patterns. If you were to hold the white face on the top and the green face on the front, that would be one position. If you were to rotate the puzzle so you are still holding the white face on the top but instead you had the red face on the front, you would have another position. Therefore, by multiplying the number of different possible “top faces” (6, one for each colour) by the number of different possible “front faces” for each different “top face” (4), you would be left with 24 different ways to position the cube for any given state. This automatically reduces the enormous number of 43 quintillion possible positions that would actually need to be tested to 1,802,166,800,000,000,000 (a mere 4% of the original number). By factoring in other similarities such as mirrors, this number reduces further, making God’s Number much easier to calculate.

Two different “positions” out of the 43 quintillion possible

God’s Number can also be implemented for other twisty puzzle, such as using an original Rubik's cube with certain restraints, or using smaller or bigger puzzles. God’s Number for a Rubik’s Cube solved using only quarter turns (where no face can be rotated more than 90 degrees at a time either clockwise or anticlockwise) has been proven much more recently (2014) to be 26 moves.

God’s Algorithm for 2x2x2 Cubes

God’s Number for the 2x2 puzzle (having only 3,674,160 different positions) has been proven to be 11 moves using the half turn metric, or 14 using the quarter turn metric (half turns count as 2 rotations). Unfortunately God’s Number has yet to be calculated for the 4X4 cube, or higher.

The Devil’s Number

As we have discussed on the Mathematics of the Rubik’s Cube page, every algorithm (permutation) has a degree in group theory. Every sequence of moves, if repeated enough times, will return the cube to the original state. For example a simple face turn needs 4 repetitions, the R' D' R D algorithm needs to be applied six times, going through 24 states.

The question is to find an algorithm which needs the biggest number of repetitions to return to the starting position.

For this we need an algorithm that goes through all 43,252,003,274,489,856,000 possible positions of the cube without repeating any of them. In the mathematical field of graph theory, a Hamiltonian path (also called as traceable path) is a path in a graph that visits each vertex exactly once.

This algorithm is called the Devil’s Algorithm and its length is called the Devil’s Number.

Fewest move challenge in official competitions

In official Rubik's competition organised by World cube Association (WCA), there is an event called Fewest Move Count(FMC), which involves taking a random computer generated scramble and solving it in as few moves as possible. A computer would be able to find more efficient solutions possible that takes the least amount of moves in seconds, however in this event competitors have 1 hour to try and find the most efficient solution that they physically can. The World Record for this event is 20 moves, shared by Tomoaki Okayama (Japan) and Rami Sbahi (USA). These two solves did however take place at two different competitions. Despite the world record coincidentally matching God’s Number, it is almost impossible that either solution to either scramble was the most efficient that could be found by either human or computer.

To conclude, God’s Number is a fascinating theory. It shows us how such a simple looking puzzle can have over 5 and a half times more combinations than there are grains of sand on the Earth, and it also proves that computers will always be infinitely better than humans at almost any task.

Computer programs

The Cube Explorer program by the German mathematician, Herbert Kociemba is able to find the optimal solution in 20 steps using the half turn metric (half turns count as one move). Test our program which is using the same algorithm. It’s looking for the solution in 20 moves but if the program doesn’t return any result below the time threshold then it switches to 24 steps which is also very close to the God’s number.

Cube museum

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Rubik’s Cube Museum

In March of 2012 the Hungarian governor Fürjes Balazs announced official the plans of a Rubik’s Cube museum which will exhibit the last 1100 years of the Hungarian intellectual performance. Following the announcement, the Hungarian Prime Minister Orbán Viktor and Rubik Erno signed the memorandum of cooperation.

According to the plans the construction of the Rubik's cube shaped museum will begin on the 40th anniversary of the invention in 2014, which is also the 70th birthday of the inventor Rubik Erno. The museum might open for the public in 2017 next to the Rákóczi Danube bridge in Budapest.

The Prime Minister said that the Rubik’s Cube is the symbol of the Hungarian intellectual spirit and the Government is confident that the new Rubik’s Cube Museum will become the symbol of the Hungarian renaissance in the 21st century.

Next year the government will announce an international architectural competition for the project. They are also planning a moving exhibition for the 40th anniversary of the Magic Cube which will present the history and diversity of the cube around the world.

After the announcement the Prime Minister and Rubik Erno signed the memorandum of cooperation in which the inventor approves that the museum can have the shape of the cube patented by him and the government welcomes any proposal and idea of Rubik Erno.

Update 2015

We posted about the Rubik’s Cube-shaped museum in 2012 but its fate is still uncertain because the construction was supposed to start already. The Hungarian government has allocated 3.5 million Euros for the project and they’re planning to announce an international tender to carry our the project. The location and the floor area of the building is still uncertain

We hope we’ll find updates soon.

The inventor

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Rubik Ernő, the inventor of the Magic Cube

The inventor of the Rubik’s cube (1974),Rubik’s Magic, Rubik’s magic: Master Edition , Rubik’s Snake and Rubik’s 360 , Rubik Erno was born in 1944 during World War II. He is a Hungarian inventor, architect and professor of architecture.

He graduated from the Technical University, Budapest Faculty of Architecture in 1967 and began postgraduate studies in sculpting and interior architecture. From 1971 to 1975 he worked as an architect, then became a professor at the Budapest College of Applied Arts.

In the early 1980s, he became editor of a game and puzzle journal called …És játék (…And games), then became self-employed in 1983, founding the Rubik Stúdió, where he designed furniture and games. In 1987 he became professor with full tenure; in 1990 he became the president of the Hungarian Engineering Academy. At the Academy, he created the International Rubik Foundation to support especially talented young engineers and industrial designers.

At present he is mainly working on video game development and architectural topics and is still leading the Rubik Studios.

He is known to be an introvert, barely accessible and hard to contact or to get hold of for autographs. He typically does not attend speedcubing events. He also gave a lecture and autograph session at the “Bridges-Pecs” conference in July, 2010

However many Rubiks replicas have been sold, in the 80’s he was the richest people in Hungary.

Hungarian inventions

There are many world famous Hungarian inventions but a lot of them wasn’t patented in time or the Hungarian inventor lived in a foreign country. The reason why Hungarians are so proud of Rubik Erno is because he has always lived in Hungary and didn’t let someone else steal his invention.

Among the most famous Hungarian inventions we have to mention the non-explosive match (Irinyi János), Vitamin C (Szent-Györgyi Albert), Dynamo (Jedlik Anyos), Ballpoint Pen (Bíró László József), Hydrogen bomb (Teller Ede), Holography (Gabor Dénes), Computers, with linear programming (Neumann János), Soda water (Jedlik Ányos), Telephone exchange (Theodore Puskas), Torpedo (Luppis János), Water-cooled Reactor (Wigner Jeno)

Advance method

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Rubik’s Cube solution with advanced Friedrich (CFOP) method

The first speedcubing world championship was held in 1982 in Budapest and it was won by Minh Thai(USA) with a 22.95 seconds solution time. Since then the methods have evolved and we are capable of reaching solution times below 6 seconds. If you want to improve your cubing speed, all you need is a high quality,well lubricated rubix cube  with good corner cutting and optimal tensioning so the pieces don’t pop. Practice finger tricks, the art of turning the cube like you can barely see the movements. You’ll also need a rubik's cube timer to keep track of your evolution, and a lot of practice of the method described in the tutorial below.

Cross

F2L

OLL

PLL

When talking about the advanced technique of solving the rubik's cube we have to mention the Petrus system and the Friedrich method (or full CFOP) which is used by the big majority of speed cubers these days. This advanced technique developed by Jessica Friedrich divides the puzzle into layers and you have to solve the cube layer by layer using algorithm in each step, not messing up the pieces already in place. These steps are the following: cross F2l OLL and PLL, as seen on the illustration above.

The method developed by Jessica Friedrich involves memorizing a lot of algorithms, but there is a logical connection between them. After a lot of practice you will develop the ability to execute these operations intuitively.

Steps of the advanced method

First step: form a white cross

I assume that at this point you are familiar with the notations of the rubik's cube and you can solve the cube with beginner's method. If not then I strongly recommend you visit these pages to avoid any confusion.

It’s up to you which face you want to start with, let’s make a convention that for the sake of this tutorial we’ll start with the white face. Our goal is to form a cross at the bottom of the rubik's cube in a way that the sides of the white edges match the lateral centre pieces. Experienced cubers foresee the steps when they inspect the cube and they plan this step. In most cases you’ll need 6 rotations to complete this phase, and you should never need more than 8.

White face always down

Hold your cube in your hands with the white centre facing down to improve your solution time. With a lot of practice you won’t need to see the white cross because you will know what’s going on down there according to the color scheme of your puzzle, your moves and what you see on the top. This way you don’t have to turn your cube around, saving this way a lot of time. Some speedcubers prefer solving the cross on the left side but if you choose to make it on the bottom you’ll have a nice lookahead and is more suitable foe finger tricks. The only bad thing is that it’s weird for beginners and you can’t notice in time if you messed the cross up.

It would be more intuitive to solve it on the top and turning upside down when it’s done, but you’ll need to learn it this way if you want to reach times below 20 seconds. To encourage you I have to tell that the knowledge of the next step (F2L) will help you a lot in the understanding of the manipulation of the cube upside down. You will discover the advantages of this perspective and you will admit that this is the best way of doing it. And if you really want to master the Rubik’s Cube I recommend you to examine the cube and try to plan all the necessary steps and execute them without watching.

Some examples – Basic idea

The examples below show a couple situations you can meet. The first one is very easy, you just have to turn the edge piece to the correct position. The second shows how to reorient a piece. The third example demonstrates how to place two pieces in one step. The last step shows the steps to fix the Superflip (the “most scrambled Rubik’s Cube”) in only 6 moves.

F2

U’ R’ F R

F R2 D2

Superflip: R F L B R D

This first step of solving the white cross is actually an intuitive stage of the solution process. We couldn’t even cover every possible situations because at this stage there are so many cases. Almost everyone could get this far without learning algorithms. But you’ll need to practice forming the white cross to make it efficient. Do it smoothly, without stopping and with the cross facing downwards. If this works well, you can proceed in our tutorial to the second step: F2L

Step 2: First two layers – F2L

The first two layers (F2L) of the Rubik’s Cube are solved simultaneously rather than individually, reducing the solve time considerably. In the second step of the Friedrich method we solve the four white corner pieces and the middle layer edges attached to them. The 41 possible cases in this step can be solved intuitively but it’s useful to have a table of algorithms printed on your desk for guidance.

To be efficient try not to turn your cube around while solving and look ahead as much as possible. Familiarize with the algorithms so you can do them even with your eyes closed.

In the beginner’s method solving the white corners and the second layer edges were two separate steps, but in this stage you should already know this. In the advance Friedrich method we’re going to pair them in the top layer, then insert them where they belong. The simple example below demonstrates a lucky situation where the red-blue edge piece goes where it belongs while we solve the white corner. If the red-blue corner is somewhere else, then first we need to get it to the back-top position.

Be intuitive or learn algorithms?

An intuitive approach of this situation would suggest to solve this case in the following steps: to take the two pieces to the top layer, then joining them to insert where they belong to: (R U2 R’) (F’ U2 F) (U’ R U R’). However the following algorithm is much quicker because it’s the same series of movements repeating: (R U R’ U’) (R U R’ U’) (R U R’ U’)

Let’s see the possible situtations you might meet in this stage. Cases grouped by the position of the white corner and the edge that needs to be attached to it:

1st: Easy cases

These are the lucky cases which can be solved in 3-4 moves.

R U R’

F’ U’ F

U’ F’ U F

U R U’ R’

2nd case: Corner in bottom, edge in top layer

The first two should be familiar from the beginner's method:

(U R U’ R’) (U’ F’ U F)

(U’ F’ U F) (U R’ U’ R)

(F’ U F) (U’ F’ U F)

(R U R’) (U’ R U R’)

(R U’ R’) (U R U’ R’)

(F’ U’ F) (U F’ U’ F)

3rd case: Corner in top, edge in middle

(R U R’ U’) (R U R’ U’) (R U R’)

(R U’ R’) (d R’ U R)

(U F’ U F) (U F’ U2 F)

(U F’ U’ F) (d’ F U F’)

(U’ R U’ R’) (U’ R U2 R’)

(U’ R U R’) (d R’ U’ R)

4th case: Corner pointing outwards, edge in top layer

In this case we usually bring the cube to a basic case, reorienting the white corner in the first stage.

(R U’ R’ U) (d R’ U’ R)

(F’ U F U’) (d’ F U F’)

(U F’ U2 F) (U F’ U2 F)

(U’ R U2 R’) (U’ R U2 R’)

(U F’ U’ F) (U F’ U2 F)

(U’ R U R’) (U’ R U2 R’)

(U’ R U’ R’ U) (R U R’)

(U F’ U F U’) (F’ U’ F)

(U’ R U R’ U) (R U R’)

(U F’ U’ F U’) (F’ U’ F)

(U F’ U2 F U’) (R U R’)

(U’ R U2 R’ U) (F’ U’ F)

5th case: Corner pointing upwards, edge in top layer

(R U R’ U’) U’ (R U R’ U’) (R U R’)

y’ (R’ U’ R U) U (R’ U’ R U) (R’ U’ R)

(U2 R U R’) (U R U’ R’)

(U2 F’ U’ F) (U’ F’ U F)

(U R U2 R’) (U R U’ R’)

(U’ F’ U2 F) (U’ F’ U F)

(R U2 R’) (U’ R U R’)

(F’ U2 F) (U F’ U’ F)

6th case: Corner in bottom, edge in middle

(R U’ R’ d R’ U2 R) (U R’ U2 R)

(R U’ R’ U R U2 R’) (U R U’ R’)

(R U’ R’ U’ R U R’) (U’ R U2 R’)

(R U R’ U’ R U’ R’) (U d R’ U’ R)

(R U’ R’ d R’ U’ R) (U’ R’ U’ R)

Step 3 – Orient last layer – OLL

While solving the rubik's  with the advance friedrich method, when the first 2 layers(F2L) are solved we need to orient the last layer (OLL) so the upper face of the rubik's cube  is all yellow. We don’t care if the side colors don’t match, we are going to permute the last layer(PLL) later.

You’ll need to learn all the 57 algorithm below to complete this in one step. If this seems too many I recommend you learn the 2look OLL which uses only 9 algorithms but of course it’s slower.

Let’s group them according to their look.

Dot

R U B’ l U l2′ x’ U’ R’ F R F’

R’ F R F’ U2 R’ F R y’ R2 U2 R

y L’ R2 B R’ B L U2′ L’ B M’

R’ U2 x R’ U R U’ y R’ U’ R’ U R’ F

(R U R’ U) R’ F R F’ U2 R’ F R F’

M’ U2 M U2 M’ U M U2 M’ U2 M

R’ U2 F (R U R’ U’) y’ R2 U2 x’ R U

F (R U R’ U) y’ R’ U2 (R’ F R F’)

Line

R’ U’ y L’ U L’ y’ L F L’ F R

R U’ y R2 D R’ U2 R D’ R2 d R’

F U R U’ R’ U R U’ R’ F’

L’ B’ L U’ R’ U R U’ R’ U R L’ B L

Cross

L U’ R’ U L’ U (R U R’ U) R

(R U R’ U) R U’ R’ U R U2 R’

L’ U R U’ L U R’

R’ U2 (R U R’ U) R

R’ F’ L F R F’ L’ F

R2 D R’ U2 R D’ R’ U2 R’

R’ F’ L’ F R F’ L F

4 corners

M’ U’ M U2′ M’ U’ M

L’ (R U R’ U’) L R’ F R F’

Shape _|

L F R’ F R F2 L’

F R’ F’ R U R U’ R’

R’ U’ R y’ x’ R U’ R’ F R U R’

U’ R U2′ R’ U’ R U’ R2 y’ R’ U’ R U B

F (R U R’ U’) (R U R’ U’) F’

L F’ L’ F U2 L2 y’ L F L’ F

Shape |_

U’ R’ U2 (R U R’ U) R2
y (R U R’ U’) F’

r U2 R’ U’ R U’ r’

R’ U2 l R U’ R’ U l’ U2 R

F’ L’ U’ L U L’ U’ L U F

R’ F R’ F’ R2 U2 x’ U’ R U R’

R’ F R F’ U2 R2 y R’ F’ R F’

Shape ¯|

R U R’ y R’ F R U’ R’ F’ R

L’ B’ L U’ R’ U R L’ B L

U2 r R2′ U’ R U’ R’ U2 R U’ M

x’ U’ R U’ R2′ F x (R U R’ U’) R B2

Shape |¯

L U’ y’ R’ U2′ R’ U R U’ R U2 R d’ L’

U2 l’ L2 U L’ U L U2 L’ U M

R2′ U R’ B R U’ R2′ U l U l’

r’ U2 (R U R’ U) r

C

R U x’ R U’ R’ U x U’ R’

(R U R’ U’) x D’ R’ U R E’

L

R’ F R U R’ F’ R y L U’ L’

L F’ L’ U’ L F L’ y’ R’ U R

L’ B’ L R’ U’ R U L’ B L

R B R’ L U L’ U’ R B’ R’

P

F U R U’ R’ F’

R’ d’ L d R U’ R’ F’ R

L d R’ d’ L’ U L F L’

F’ U’ L’ U L F

T

F (R U R’ U’) F’

(R U R’ U’) R’ F R F’

W

L U L’ U L U’ L’ U’ y2′ R’ F R F’

R’ U’ R U’ R’ U R U y F R’ F’ R

Z

R’ F (R U R’ U’) y L’ d R

L F’ L’ U’ L U y’ R d’ L’

Step 4 – Permute the last layer – PLL

The 4th and final step of the advance friedrich method is the permutation of the last layer (PLL). At this point the white cross, the first two layers (F2L) are both done and the last layers pieces are oriented(OLL). When we execute this last step our rubix cube will be solved.

Again, X and Y (x,y) are whole cube rotations, while lowercase u is double layer turn.

First rotate the top layer to align as many pieces as possible then do one of the 21 algorithms listed below. If this seems too many to learn, you should try the 2 look PLL which method contains only six algorithms but takes more time to execute.

I wrote the name of each algorithm at the beginning of the rotation chain. On the images the dots mark the direction of the permutations (arrowheads).

A 1:x [(R’ U R’) D2]
[(R U’ R’) D2] R2

A 2:x’ [(R U’ R) D2]
[(R’ U R) D2] R2

U 1:R2 U [R U R’ U’]
(R’ U’) (R’ U R’)

U 2:[R U’] [R U] [R U]
[R U’] R’ U’ R2

H:M2 U M2 U2 M2 U M2

T:[R U R’ U’] [R’ F]
[R2 U’ R’] U’ [R U R’ F’]

J 1:[R’ U L’] [U2 R U’ R’ U2] [R L U’]

J 2:[R U R’ F’] {[R U R’ U’]
[R’ F] [R2 U’ R’] U’}

R 1:[L U2′ L’ U2′] [L F’]
[L’ U’ L U] [L F] L2′ U

R 2:[R’ U2 R U2] [R’ F]
[R U R’ U’] [R’ F’] R2 U’

V:[R’ U R’ d’] [R’ F’]
[R2 U’ R’ U] [R’ F R F]

G 1:R2 u R’ U R’ U’ R
u’ R2 [y’ R’ U R]

G 2:[R’ U’ R] y R2 u R’
U R U’ R u’ R2

G 3:R2 u’ R U’ R U R’
u R2 [y R U’ R’]

G 4:[R U R’] y’ R2 u’
R U’ R’ U R’ u R2

F:[R’ U2 R’ d’] [R’ F’]
[R2 U’ R’ U] [R’ F R U’ F]

Z:M2 U M2 U M’ U2 M2 U2 M’ U2

Y:F R U’ R’ U’ [R U R’ F’]
{[R U R’ U’] [R’ F R F’]}

N 1:{(L U’ R) U2 (L’ U R’)}
{(L U’ R) U2 (L’ U R’)} U

N 2:{(R’ U L’) U2 (R U’ L)}
{(R’ U L’) U2 (R U’ L)} U’

E:X (R U’ R’) D (R U R’)
u2 (R’ U R) D (R’ U’ R)