## Introduction: Solving Rubik's Cube

A Rubik’s Cube is a hand held puzzle. Each of the six faces has nine squares of six different colors. The faces can either rotate clockwise or counter-clockwise, so after just a few turns there are multiple colors on each face. Remember, centers cannot move, so they define the color of each face. The puzzle is getting all of each color on the same face.

__Here is an overview on how we will be completing the puzzle__:

- Solve the white face
- Complete the first layer (edges along the white face)
- Complete the second layer (middle of the cube)
- Solve the yellow face (side that is opposite of the white face)
- Complete the third layer (edges along the yellow face)

In these instructions, algorithms are provided to put pieces in a desired location. Interpreting the algorithms can be done by using this key:

- U = Up (top face)
- D = Down (bottom face)
- F = Front
- B = Back
- L = Left
- R = Right

[ U ] = "Turn the top face a quarter turn clockwise"

[ L' ] = "Turn the left face a quarter turn counter-clockwise"

[ R2 ] = "Turn the right face 180 degrees, or two quarter turns"

NOTE: For the purposes of usability, these instructions are for solving the second and third layers. The first layer takes a sizeable learning curve to understand how to solve the first layer. Instead of reviewing all the possible short algorithms needed to start the first layer, these instructions are on how to complete the puzzle once familiar enough with the cube to solve the first layer. These first two steps are a summary on how to solve the first layer.

## Step 1: Solving for White Edges

Look for edges with white. Solve these edges by matching their non-white color with their respective centers, and rotating them up to match the white center as well.

## Step 2: Solving for the White Corners

Now look for corners with white. Solve these by rotating a white edge down, and moving a corner that matches next to it. This part takes familiarity with the puzzle, but is easy to pick up. When the white face is complete, check to make sure that the first layer is also complete.

## Step 3: Solving the Second Layer

There are multiple possibilities in how your cube could be arranged right now. In order to solve the second layer, we will focus on the red and blue face. Keep on turning the third layer (furthest away from the white face) until you get a red T or blue T shape. Use the images to help see which one you have. Then apply the appropriate algorithm move a piece that will move a piece from the third layer to an edge on the second layer.

**[Algorithm 1]:** D F D' F' D' R' D R

**[Algorithm 2]: **D' R' D R D F D' F'

## Step 4: Completing the Second Layer

Keep on using either algorithm 1 or 2 when ever your cube matches a picture in step 3. When the red and blue faces are completed, apply algorithm 1 or 2 to other colored faces, keeping sure that your cube is oriented correctly. The front and right faces are not fixed to certain colors, it is respective to how you are holding the cube. Also, remeber ththe algorithms provided specifically positions the piece into the given location.

## Step 5: Solving for Yellow Edges

Again, there are a number of possibilities that your cube could be arranged right now. Look at your cube and observe how the yellow pieces are currently arranged. You will be using either algorithm 3 or 4 to rearrange the yellow pieces (refer to images). The end result should be having yellow pieces in a cross shape.

**[Algorithm 3]: **F U R U' R' F'

**[Algorithm 4]: **F R U R' U' F'

## Step 6: Correcting the Corners

Now, you need to identify that the corners on the yellow side are in the correct position. All three colors of the face that a corner is connected to must be featured on that corner for it to be correct. It does not have to oriented correctly. If you identify incorrect corners, then you can switch their position with another corner using algorithm 5. You can also just rotate the yellow face to put the corners in the correct location

**[Algorithm 5]: ** L U' R' U L' U' R U2

## Step 7: Rotating the Third Layer Corners

Now you will need to rotate the corner pieces in order to complete the yellow side. The following two algorithms (6 and 7) will help you do that. Examine your cube and see how many corners need to be rotated. If three need to be rotated, use the correct algorithm (either 6 or 7). Otherwise, apply either algorithm 6 or 7 to orient exactly 1 corner correctly. Then use the correct algorithm to fix the other three.

**[Algorithm 6]: **R U R' U R U2 R' U2

**[Algorithm 7]: **R' U' R U' R' U2 R U2

## Step 8: Positioning the 4 Third Layer Edges

Now your yellow side should be completely solved. The only pieces that need to be solved now are edge pieces in the third layer. If there are three edges that are incorrect, apply the appropriate algorithm (8 or 9) to completely solve Rubik's cube. If all four edges are incorrect, apply either algorithm 8 or 9 to fix one edge, then apply the appropriate algorithm to fix the other three.

**[Algorithm 8]: **R2 U F B' R2 F' B U R2

**[Algorithm 9]: **R2 U' F B' R2 F' B U' R2

## Step 9: Solved!

The Rubik's Cube should now be solved. Show off your completed cube to your friends!

If you want to see each step done live, watch this video.