Rubik’s Cube

Via Cedric Beust, circa 2003. Aims to be easy to memorize (few small moves).

Cube handling notes:

  • The cube has three pairs of opposite faces: Up/Down, Front/Back, Left/Right. Reorient as needed.
  • Move syntax uses one letter to reference a side, and optional direction marker. For example, T rotates the Up face clockwise, T' rotates anticlockwise.

The solve, first few steps left as an exercise to the reader:

  1. Pick a colour to start, this is Up.
  2. Solve Up edges.
  3. Solve 3 Up corners.
  4. Solve 3 middle edges, using the remaining Up corner as a “working” column.
  5. Solve last Up corner.
  6. Flip the cube, original Up colour is now Down.
  7. Finish middle layer. Align last cube to match front colour and then: Move Up front to right front URU'R' U'F'UF Move Up front to left front U'L'UL UFU'F'
  8. Orient Up edges. Flip front + right: FUR U'R'F' Flip front + back: FRU R'U'F'
  9. Position Up edges. Rotate Up to try and match two, then, Swap left + back: UR'UUR UR'UR
  10. Position Up corners. Sequence leaves back left untouched. Swap front left -> front right -> back right: ULU'R' UL'U'R
  11. Orient Up corners. Keep the cube positioned with a consistent side as front, repeat sequence until oriented and then rotate Up layer only to bring a different corner to front-right. Parity will fix the rest of the cube when you’re done. Rotate front right: RF'R'F RF'R'F

Chinese Cube Instructions

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

- Solve Down edges, corners
- Middle layer edges: align edge to match Front or Right
  - Up Front to Front Right: FUFUFU'F'U'F'
  - Up Right to Front Right: R'U'R'U'R'URUR
  - Flip Front Right: RU2R' U RU2R' U F'U'F
- Up Cross
  - Flip Up Front & Up Back: FRUR'U'F'
  - Flip Up Front & Up Right: FURU'R'F'
- Up Face
  - Rotate 3 CCW, lock Up Back Left: R'U'RU'R'U2R
  - Rotate 3 CW, lock Up Front Left: RUR'URU2R' 
- Swap Up Corners
  - "Headlights" right face to front face: R2F2R'B'RF2R'BR'
  - "Headlights" front face to right face: RB'RF2R'BRF2R2
- Swap Up Edges
  - Lock Up Back, swap CCW: RU'RURURU'R'U'R2
  - Lock Up Back, swap CW: L'UL'U'L'U'L'ULUL2

TBD: Use this to generate some diagrams, and format this a bit more robustly.

Heise Method

No “algorithms” per se, focuses on building an intuitive feeling on how the cube works.

  • Make four 2x2 squares
  • Match squares and orient edges
  • Solve remaining edges and any 2 corners
  • Solve last 3 corners

8355 Method

Beginner method with few algorithms. Referenced several times is “Sexy move” RUR'U'.

  • Cross on Down
  • 3 Down corners
    • Position target corner in U above its desired location in D, and repeat sexy move until placed and oriented.
  • 3 E-slice edges, using Keyhole method
    • Position a target edge piece such that its Up color matches the Front face
      • Position keyhole under the desired location
      • Keyhole up/away from target, rotate Up to place target on the keyhole, return keyhole down.
      • This is either RU'R' if keyhole is to the right, or L'UL if keyhole is to the left.
  • Remaining edges
    • Keep keyhole in front-right
      • Rotate Up to aim keyhole edge correctly relative to other correct Up edges
      • Rotate F' or R into place, rotate U to position another incorrect edge in that position, and restore keyhole with F or R'
      • To swap the last two edges, position the gap for the final Up edge as expected based on its orientation in the keyhole, and then either FR/UF: UF'UFU'FUF, or FR/UR: U'RU'R'U'RU'R'. (Intuitively, you’re moving the gap to last spot, and then bubbling the edges back and forth to fit them all in place.)
  • Final 5 corners
    • Flip cube Up/Down
    • If the keyhole corner UFR belongs in Down, rotate D until it is above its correct position, and repeat sexy move until placed and oriented. This will break the top of the cube, but only temporarily - just keep the orientation correct.
      • Rotate D to place next corner, and repeat.
      • When only 2 corners remain unplaced, repeat sexy move until the rest of the cube fixes itself, then rotate cube so unsolved corners are on Down layer.
      • Using a solved corner as the keyhole, repeat above to solve the cube:
        • if corners need to swap, sexy once to move corner up, rotate Down to the other corner, and sexy until placed, then rotate Down back and sexy until complete.
          • if corners just need to rotate, sexy to rotate the first, then rotate Down and sexy the other one til correct, and rotate Down back to complete.

Speed Cubing Method

https://lar5.com/cube/

  • Build 2x2x2 corner
  • Expand to 2x2x3
  • Orient unsolved faces as U and R
  • Fix “bad” edges, who orient “wrong” on to the two unsolved faces (whichever color they share)
    • Correct FR and UL with F'U'F
  • Finish 2 layers, only turning the unsolved faces
    • a. one corner + two edges
    • b. final corner + edge
  • Orient cube so unsolved face is U
  • Position corners
    • “Niklas” swaps UFR and UBR: LU'R'UL'U'RU2
    • Swapping two diagonally opposite corners uses two Niklas.
  • Twist corners
    • “Sune” selects a front corner, targeting its sticker on the front face, and rotates the other three corners.
      • UFR: BUB'UBU2B'U2
      • UFL: BU'B'U'BU2B'U2
    • If 0 correct corners, target any U sticker
    • If 1 correct corner, target the correct corner on the face with no U stickers
    • If 2 correct corners, target non-U sticker of a twisted corner
  • Position edges
    • Inspect top layer outer faces.
    • If one edge is correct, orient it to B, and perform “Allan”: F2U' LR' F2 L'R U'F2 - This rotates counter-clockwise UL -> UF -> UR, to rotate clockwise change the U' turns to U.
    • To swap two pairs of adjacent edges (F,R and L,B), “Bert”: F2B2 DR2 F2B2 L2 F2B2 D' F2B2
    • To swap two pairs of opposite edges, “Arne”: R2F2B2L2 D L2B2F2R2