Solving a 2 x 2 Rubix Cube

Rotation conventions

Before we look at the algorithm to solve a 2 x 2 Rubix cube, it is important to understand the rotations of the faces.

Left_Right_Rotations


Up_Down_Rotations


Up_Down_Rotations


Position and Orientation

A 2 X 2 Rubix cube has 8 pieces. Each of these pieces has a position in the cube. Unless a piece is at its final position and has the right orientation, the Rubix cube cannot be solved.


Algorithm for solving a 2 x 2 Rubix cube

Step 1. Solve the bottom layer

We being by forming a white square at the bottom. The idea is to get the first while square at the bottom, after which the remaining squares can easily be moved to complete the bottom layer.

  • Step a)
    The piece that is to be moved to the bottom-right corner is moved at top-right position.

  • Step b)
    To solve the bottom layer you could use the below algorithmic rotations.
    Note : Below 4 rotations are not always needed to place the piece at the bottom-right corner. Stop the rotations once the piece gets correctly placed at the bottom-right corner.
    R U R' U'
    ( Right ) -> ( Up ) -> ( Right Inverted ) -> ( Up Inverted )

  • Step c)
    Repeat Steps a) and b) to solve the bottom layer.

2x2_Bottom_Layer


Step 2. Get same color (yellow) tiles on the top layer.

Check: If you don’t have same color tiles on the top layer, you may have

a) Not a single yellow tile on the top.

  • Apply algorithm

b) A single yellow tile on the top.

  • Before applying the algorithm, rotate the top layer such that the yellow tile moves to the bottom-left quadrant of the top face.
    Apply algorithm.

c) Diagonally placed yellow tiles on the top.

  • Before applying the algorithm, rotate the top layer such that one of the yellow tiles moves to the bottom-left quadrant of the top face.
    Apply algorithm.

d) Yellow tiles in the same column / row on the top layer.

  • Before applying the algorithm, rotate the top layer such that the right half of the top layer has yellow tiles.
    Apply algorithm.

Algorithm
R U R' U R U U R'
( Right ) -> ( Up ) -> ( Right Inverted ) -> ( Up ) -> ( Right ) -> ( Up ) -> ( Up ) -> ( Right Inverted )
Repeat Step 2 till all the 4 tiles on the top layer have the same color.


2x2_Bottom_Layer


Step 3. Aligning all the faces of the cube.

  • Step a)
    Once we get all the 4 tiles of the same color ( ex: yellow ) we may get
    • Scenario a)
      Front / Back / Left / Right face having the same color tiles.
      Keep the face that has the same colored tiles at the back and apply the algorithmic rotations once to solve the Rubix cube.

    • Scenario b)
      None of the 4 vertical faces ( Front / Back / Left / Right ) have the same color tiles
      Apply the algorithmic rotations to get same color tiles on one of the 4 verticle faces. Keep this face at the back. Re-apply the algorithm.
      Thus in this scenario the algorithm is used twice to solve the Rubix cube.


Algorithm
R' F R' ( B' X 2 ) R F' R ( B' X 2 ) ( R X 2 ) ( B' X 2 )
( Right Inverted ) -> ( Front ) -> ( Right Inverted ) -> ( Back Inverted ) -> ( Back Inverted ) -> ( Right ) -> ( Front Inverted ) -> ( Right ) -> ( Back Inverted ) -> ( Back Inverted ) -> ( Right ) -> ( Right ) -> ( Back Inverted ) -> ( Back Inverted )

Rubix_2x2_Final_Step



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