Back in secondary 2, I remember my class had a Rubik’s cube fever. Back then, I learned how to solve it, but it was largely memorising (spatial reasoning works for first two layers, but it was almost impossible for me to grasp the third layer). In later years, I kept coming back to Rubik’s cube and every time I do so, I gained a better understanding of why the solution works; group theory changed my perspective of the how the algorithms work. However, time and time again, I would forget how to solve the cube. So I’m writing this so I can refer to this in the future to remind myself how to solve it.

The way I solved it is not meant for speed-cubing. Although some of the moves can be optimised by finger tricks.

- Form base layer cross.
- Solve three corners without screwing up the cross.
- Solve three edges in the second layer using the last corner, without screwing up the base layer.
- Solve last corner in the first layer, and then use algorithm to solve last edge in the second layer.
- PLLE (Permuate last layer edge): Form cross on top layer. Use only 1 algorithm: orientate such that FU is incorrect, FRUR’U’F’, chain if it’s L. (max 2 moves)
- PLLC (Permute last layer): Change the colour of the top face. Use only 1 algorithm: orientate such that sticker faces you. (When sticker faces you, corner of free hand nearer to you is fixed), (RUR’ UR U2 R’). Execute mirror using left hand if needed.
- OLLC (Orientate last layer corners) Use 1 algorithm: orientate such that two corner swap at the top is facing you: R’FR’ B2 RF’R’ B2 R2.
- OLLE (Orientate last layer edges) Use 1 algorithm: orientate such that sticker that needs to go to the edge opposite the fixed edge is facing you. Depending on where the fixed edge is, execute the following: R2 U’ FB’ R2 F’B U’ R2 if fixed edge is on the left side. L2 U F’B L2 FB’ U L2.You might want to consider this to switch opposite edges: LR U2 R’L’ F’B’ U2 FB

An interesting type of cube are those with pictures, because the center pieces can be oriented wrongly.

- Change U ccw and L cw : (L’R D’U LR’) U (L’R D’U LR’) U’
- Rotate U 180 : (LR U2 R’L’) U (LR U2 R’L’)

Other sizes:

- 2×2 cube is straight forward, just need to use step 6 repeatedly.
- 4×4 cube can be made into 3×3 by combining centre two edges. Need to worry about parity of edges.

References:

http://www.alchemistmatt.com/cube/rubikcenter.html

http://www.learn2cube.com/

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