# Rubik's Cube

**Cubing Notation**

When solving the Rubik's Cube, we will use various algorithms. Each algorithm requires a specific orientation of the cube, and a specific sequence of rotations. However, to convey the rotations of each algorithm, we need a standardized set of notations.

The faces:

F | Front |

B | Back |

L | Left |

R | Right |

U | Up |

D | Down |

For example, B indicates a 90° clockwise rotation of the back face, while B' indicates a 90° *counter*-clockwise rotation of the back face.

FRU would mean rotating the front, the right, and the upper face clockwise, in that order.

As a more complicated example, FR'U' indicates a clockwise front face rotation, counterclockwise right face rotation, and a counterclockwise upper face rotation.

Using the method below, we solve "layers" of the cube separately. We start with layer 1 and end with layer 3.

**Layer 1:**

Create a cross on the 1st layer such that the colours of the 4 edge pieces match up with the colours of the corresponding layer 2 centre pieces (i.e. in the figure to the right, the colours of "a" and "b" should be the same once we finish). There are many ways to get this pattern. Practice and patience are your best friends in getting this essential step.

Now we complete the corners of the 1st layer:

Observe the diagram given in Algorithm #1. Looking at the 3rd layer, first find the correct corner piece that goes into position "b". Then, rotate this piece to position "a".

**Algorithm #1:**

Inserting a corner piece: Say we want to put the piece "a" in position "b". In this cube orientation, repeat

R' D' R D

Until you get the corner in the right place and orientation. You may need to repeat these rotations up to 5 times for each corner piece.

Repeat algorithm #1 for each corner. You are now done layer 1!

You may have to run this algorithm many times. Have fun! :)

**Layer 2:**

Our goal is to match up the edge pieces. We will use a pair of algorithms that can move pieces from the 3rd layer into the 2nd layer. Observe the diagrams below. In order to use the two following algorithms, we need to find a specific piece on the 3rd layer, and then rotate it to position "a" so that we get a T shape on the front face.

If you make a mistake and put a piece in the wrong orientation or position, don't worry. Repeat either Algorithm 2 or Algorithm 3 to bump out the piece.

**Algorithm #2:**

Inserting a layer 2 piece, 1

^{st}variant: Here, "a" has the same colour as "c", and you need to put piece "a" into position of "b". Do,

D L D' L' D' F' D F

**Algorithm #3:**

Inserting a layer 2 piece, 2

^{nd}variant: As above, but we would like to insert "a" into a different location. "b" is now on the right hand side. Do,

D' R' D R D F D' F'

Use Algorithm #2 and #3 to insert all the layer 2 pieces. That is all for the 2^{nd} layer.

This handout was prepared for the Rubik Club at Toronto Public Library in 2013.