3x3x3 Rubik's Cube

The 3x3x3 Rubik's Cube (commonly just referred to as a "Rubik's Cube) was the first widely sold puzzle to be invented and its invention was the catalyst of the invention of all other special Rubik's Cube, larger Rubik's Cubes, and Rubik's Cube shape modifications.

It has a total of 20 movable pieces to rearrange. The 3x3x3 Rubik's Cube has 43 quintillion (

4.3
∗

10

19

{\displaystyle {4.3\*10^{19}}}

) possible permutations.

The 3x3x3 Rubik's Cube consists of 26 pieces: 6 centers (which have one color each), 8 corners (which have 3 colors each), and 12 edges (which have two colors each). There is no piece in the middle of the 3x3x3x Rubik's Cube because the middle is where the core turning mechanism is contained.

There are six faces with the following colors on them: white, yellow, green, blue, red, and orange (note that some 3x3x3 Rubik's Cube not manufactured by the Rubiks company may have different colors on them). All Rubik's Cubes have those same colors on their six faces. It was invented by Hungarian sculptor and professor of architecture Ernő Rubik in 1974.

Ernő Rubik was the first person to solve a Rubik's Cube and did so while it was still in its prototype stage. It took him 3 months to solve it for the first time.

There are quite a few indirect advantages of solving a Rubik's Cube that can help your brain become sharper. Solving a Rubik's Cube can better your eye-hand coordination, improve your concentration in general, and ensure that you are able to process your thoughts faster.

Cases which your cube cannot be solved is called a parity. This can happen on any twisty puzzle. The most common parity is an edge flip or corner twist.

If your cube ever pops assemble it into its solved state. This is because there is a 0.08333333333 or 1/12 chance of it being solvable again. If you dont assemble it into its solved state that you will have many paritys.

## Notation

Here is the Rubik's Cube notation that is used in sequences called algorithms to solve it. A letter means a turn 90 degrees clockwise.

An apostrophe or "i" after a letter means invert or prime. This means the move is to be performed in the opposite direction or 90 degrees counterclockwise. A "2" beside a letter means to perform the move two times, rotating 180 degrees. There are two Rubik's Cube notations: one is the basic notation and one is the advanced notation.

A Rubik's Cube has six faces and each one is represented with a letter: R, L, U, D, F, or B. When you see these letters in algorithms, it means to rotate that face 90 degrees clockwise.

### Advanced Notation

Rubik's Cube notation is used for solving Rubik's Cubes faster and for simplifying algorithms. In basic notation, the letters are always capitalized because a lowercase letter indicates turning two layers at once (rotate both the corresponding face and the central layer above it), which is used in advanced notation.

Double layers turns are also sometimes marked with a "2" in front of the letter to indicate grabbing two layers or with a "w" behind the letter. In advanced notation, there are also middle layer turns or slice turns. Middle layer rotations or slice turns are not simply the rotations of two opposite layers because these moves reposition the center cubelets too. Whole cube reorientations are occasionally seen in advanced notation.

Although whole cube reorientations are never strictly necessary for solving a Rubik's Cube, they are sometimes used in advanced algorithms. "x" means to rotate the whole cube along the axis that connects R and L, rotating 90 degrees clockwise in the direction of a R move. "y" means to rotate the whole cube along the axis that connects U and D, rotating 90 degrees clockwise in the direction of a U move. "z" means to rotate the whole cube along the axis that connects F and B, rotating 90 degrees clockwise in the direction of a F move.

### Piece Notation

Piece notation is used to represent pieces on a Rubik's Cube. This makes it much easier to talk about pieces on a Rubik's Cube. Each piece can be represented with a letter or group of letters. The center piece of each face is represented with the letter name of the face. For example, the center piece of the F face would be represented with the letter "F". Edge pieces are represented by the letter of the two faces it is attached to. For example, the edge between the U face and the F face would be represented with "FU". A corner piece is represented by the three faces it belongs to. For example the corner attached to the F face, R face, and U face would be represented with "FRU".

## Solution

To solve a Rubik's Cube several algorithms need to be memorized. Fortunately, after memorizing the 3x3x3 Rubik's Cube algorithms, there are much less algorithms that need to be remembered for solving larger cubes. There is a basic/beginner's solving method and an advanced solving method (CFOP). It is recommended that you learn the beginner's solution method before moving on to CFOP. Click here for an online Rubik's Cube Solver.

#### White Cross

Hold your cube with the white face facing up. The first step is to make the white cross (making a cross with any color works, but solving the white cross first is more common). This step is mostly intuitive and it would be better for you to try to do it on your own.

You will feel more of a sense of accomplishment that way. Remember that the center pieces on a 3x3x3x Rubik's Cube never change position so they indicate the color of the face. Hold your cube with the face with the white center/Rubik's logo facing up.

When moving an edge piece up, remember to consider the color of the two faces that you are moving it to. If you are moving it to the spot between the white face and the red face make sure that the edge has both white and red on it. This step is complete when you have made a white cross, with all edge pieces in the right position.

#### White Corners

Hold your cube with the white face facing up. The next step is to fill in the white corners on the white cross. Once again, before moving the corner up, consider the color of the center pieces of the centers that you are moving it between. If you are moving a corner to a spot between the white, blue, and orange face, make sure that that corner has all of those colors on it. This step is complete when the white face is solved, with all corners in the right position.

#### Second Layer

Hold your cube with the white face on the bottom. In this step, you move down all of the edge pieces on the top to their corresponding positions on the right or on the left. Before applying the algorithm, take note of the color of the faces you are moving the piece beside. If you are moving a red and orange edge piece down, make sure you are moving it to the spot between the red and the orange face. This step is finished when the entire second layer is complete with all the edge pieces in the right position.

#### Yellow Cross

Hold your cube with the white face on the bottom. There are three possible cases for the top layer. If a case on the top layer has a few more yellow pieces than a pattern but does not make it another pattern, it is treated as that same pattern. The following algorithm can get you from one case to the next, but repeating the algorithm is not always the fastest: F R U R' U' F.

#### Orienting the Last Layer and Permuting the Last Layer

This is commonly referred to as OLL and PLL. Orienting the last layer involves solving the top face (which is the yellow face if you started with the white face) and having all the top face pieces facing up, but not necessarily with the pieces in the right position. It is unlikely that you will solve the whole cube with the OLL step and if it occurs, it is just fortuitous. Permuting the last layer involves putting all the last layer edges and corners in the right position, solving the cube. The following are two methods of performing this.

##### Method One

The first step is to get all the yellow edges in the right position.

Use this algorithm to switch the edge facing you and edge to the left of that one: R U R' U R U2 R' U

Do this until all of the yellow edges match the color of the center piece they are above.

The next step is to get all of the yellow corners into the right position. Do not worry about whether or not the yellow part of the corner is facing up.

If you have one yellow corner in the right place, meaning that it has the color of the three faces it is attached to on it, apply this algorithm to cycle the other three corners to put them in the right place: U R U' L' U R U' L (note that applying this algorithm once cycles the three corners clockwise, applying this algorithm twice cycles the three corners counterclockwise, and applying this algorithm three times returns the cube to its original state before the algorithm was applied). If no corners are in the right place, apply that algorithm until a corner is in the right place.

The next step is the step that solves the cube but is also a difficult step that flummoxes many people. Hold the cube so that an unsolved corner is in the top right corner facing you. Do the following algorithm until the corner is solved: R' D' R D. Do a U move (rotation of the top face) to get to the next unsolved corner. Do the algorithm R' D' R D to solve that corner. Continue the process until all the corners are solved. All that is left is now is to perform a U, U', or U2 move to put the top face in the correct position. Remember that after applying the R' D' R D algorithm, you must rotate the top face (U face) to get to the next unsolved corner. It may seem that you messed up the whole cube, but after you apply the algorithm for all the corners, you will have solved the top layer. Interesting note: if you apply the R' D' R D algorithm continuously, you will eventually return to the cube to the state it was in before the algorithm was applied.

##### Method Two

The first step is filling in the top layer cross and making all of the top layer pieces face up. The algorithm is the same for all of the cases: R U R' U R U2 R'. You just have to memorize the cases.

After getting all the last layer pieces facing up, it is time to put all the last layer corners in the right position. Hold your cube with two corners that need to be switched facing you in the top right and top left corners and apply the following algorithm: R' F R' B2 R F' R' B2 R2 U'. The U' move can be applied before the algorithm as well.

The last step is cycling all of the edge pieces to put them in the right spot. Remember that after you get one edge piece into the right position, hold the cube so it is in the back in order to not mess up its placement when cycling the other three edges. After you cycle all of the edges to the right spot, your cube is solved!

## References

https://www.ruwix.com

https://www.google.com

http://w.astro.berkeley.edu/~converse/rubiks.php?id1=basics&id2=notation

https://www.rubikspace.com

https://www.youcandothecube.com

## Patterns

There are many patterns that you can create with the Rubik's Cube, using some algorithms.

 Cube in the Cube

## Shape Modifications

Shape modifications are puzzles that are similar to an existing puzzle but have their shape or core turning mechanism altered.

## Videos

The following videos may also be helpful in learning how to solve a Rubik's Cube.

https://www.youtube.com/watch?v=7Ron6MN45LY