Solving a 3 x 3 Rubix Cube

Rotation conventions

Before we look at the algorithm to solve a 3 x 3 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 3 x 3 Rubix cube has 18 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 3 x 3 Rubix cube

Step 1. Get the plus at the bottom.

Forming a plus ( cross ) on the bottom layer is the first step. This step is somewhat easy and does not need any specific algorithmic rotation of the faces.
With some practice you should be able to get a plus on the bottom layer. Though a plus ( cross ) of any color can be made, I chose white for demonstration.

Note : All the 4 non-white tiles of the edge pieces of the plus should match in colour with the center tile of the middle layer.

Bottom_Cross


Step 2. Solve the bottom layer.

For solving the bottom layer, the remaining four corner pieces should be moved in their correct positions so that the earlier obtained white plus now becomes a white square at the bottom.

The algorithm in this step moves the piece at the top-right corner to the bottom-right corner without disturbing the plus ( cross ) at the bottom.
So before applying the algorithm, rotate the face(s) to move the white corner piece in the top-right corner without disturbing the plus. This is quite easy to do.

Once the piece is in the top right corner do
R U R' U' i.e ( Right -> Up -> Right Inverted -> Up Inverted ).
Continue with the steps in this algorithm till the top-right corner piece is correctly moved in the bottom-right corner.

Note : This step has to be repeated for all the 4 corner pieces. After all the corner pieces in the bottom layer are placed correctly, the bottom layer is complete.

Bottom_Corners


Step 3. Solve the middle layer.

To solve the middle layer 4 edge pieces need to placed in their correct position.
The tiles of these 4 edge pieces should not have the color of the top layer ( yellow here ).
Do

  1. Rotate the top layer such that
    one tile of the edge piece in the middle matches the tile of the center piece on the front face
    Example below : The green tile of the edge piece in the top layer matches with the center tile on the front face.
    and
    the other tile matches with the tile on the left face or the right face.
    Example below : The red tile of the edge piece in the top layer matches with the center tile on the right face.

  2. If the edge piece in the top layer should move to the left of the center piece in the middle layer apply
    U' L' U L U F U' F'
    ( Up Inverted ) -> ( Left Inverted ) -> ( Up ) -> ( Left ) -> ( Up ) -> ( Front ) -> ( Up Inverted ) -> ( Front Inverted )

  3. If the edge piece in the top layer should move to the right of the center piece in the middle layer apply
    U R U' R' U' F' U F
    ( Up ) -> ( Right ) -> ( Up Inverted ) -> ( Right Inverted ) -> ( Up Inverted ) -> ( Front Inverted ) -> ( Up ) -> ( Front )

Middle_Layer


Step 4. Get cross at the top.

Once the middle layer is solved, the next step is to get a plus ( cross ) at the top.
To form a plus (cross) at the top hold the Rubix cube in such a way that you see an inverted L at the top left.

Apply the algorithm
F R U R' U' F'
( Front ) -> ( Right ) -> ( Up ) -> ( Right Inverted ) -> ( Up Inverted ) -> ( Front Inverted )
to get a horizontal line. Once a horizontal ( yellow ) row is formed in the middle, apply the same algorithm to get the yellow cross.

Get_Top_Cross


Step 5. Match the edge pieces of the cross at the top with the center pieces on all the 4 sides.

  • Step a)
    2 edge pieces of the cross at the top will always be aligned ( i.e have same color ) with the center tile of the side faces.
    If there are not aligned, rotate the top cross 90 degrees till 2 middle edges pieces are aligned.

  • Step b)
    Hold the Rubix cube such that one aligned face is at the back and one is on the right.

  • Step c)
    Do the below rotations
    R U R' U' R U U R' U
    ( Right ) -> ( Up ) -> ( Right Inverted ) -> ( Up ) -> ( Right ) -> ( Up ) -> ( Up ) -> ( Right Inverted ) -> ( Up )

Align_Top_Cross


Step 6. Correct the positioning of the corner pieces in the top layer.

In this step, the corner pieces in the top layer should be moved in their correct corners.
i.e The three tiles of the each of the corner pieces should match the center tile on the top and the two center tiles on the side faces.

  • Step a)
    Without rotating any of the faces, hold the Rubix cube such that any corner piece that is positioned ( may not be correctly oriented ) is at the top right corner.

  • Step b)
    Apply the algorithm
    U R U' L' U R' U' L
    ( Up ) -> ( Right ) -> ( Up Inverted ) -> ( Left Inverted ) -> ( Up ) -> ( Right Inverted ) -> ( Up Inverted ) -> ( Left )

Top_Corner_Positions


Step 7. Correct the orientation of the corner pieces at the top layer.

Once the corner pieces in the top layer are correctly positioned, their orientation should be corrected to match the adjacent tiles.

  • Step a)
    Without rotating any of the faces, hold the Rubix cube such that the ( correctly positioned ) piece with incorrect orientation is at the top right corner.

  • Step b)
    Apply the algorithm
    R' D' R D
    ( Right Inverted ) -> ( Down Inverted ) -> ( Right ) -> ( Down )
    Repeat these 4 rotations till the piece is correctly oriented.

    Note :
    1. Sometimes the piece would get oriented correctly before completing ( R' D' R D ), don’t stop. All the 4 rotations need to be made.
    2. You may think that algorithm messes up the middle and the bottom layer of the cube. Don’t worry when all the 4 corner pieces are correctly oriented, the Rubix cube would be fixed.

  • Step c)
    Once the orientation of the corner piece is fixed, hold the cube as it is and rotate only the top layer to bring the piece to the top-right corner whose orientation needs to be corrected.
    Repeat steps b) and c).

Top_Corner_Orientations

Step Key Points Algorithmic Rotations
1. Form a plus at the bottom layer. Device your own method
Nothing specific
2. Fix the 4 corners in the
bottom layer.
Before applying the rotations bring the correct corner
piece at the top-right corner.
Move the top-right corner piece moves to bottom-right corner.
R U R' U'
3. Fix the middle layer. Align the edge piece in the top layer with
the center tile of the front face.
Top tile of the edge piece should match
the center tile of the left face / right face.
To move right : U R U' R' U' F' U F
To move left :   U' L' U L U F U' F'
4. Form a plus at the top layer. Hold the cube such that an inverted “L” is at the top left.
Sequence : Inverted L => Horizontal Row => Plus
F R U R' U' F'
5. Align the edge pieces of the plus
at the top layer.
Hold the cube such that the right-face center tile and back-face
center tiles are aligned with the edge pieces of the plus
R U R' U' R U U R' U
6. Correct the positioning of the corner pieces
in the top layer.
Hold the cube such that any correctly positioned piece is
at the top-right corner
U R U' L' U R' U' L
7. Correct the orientation of the corner pieces
in the top layer.
1. Hold the cube such that any correctly positioned piece is
at the top-right corner.
2. Apply the algorithm
3. For correcting the remaining pieces just rotate the top layer
for bringing the piece in the top-right corner.
R' D' R D


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