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Thread: CLL Transformation Table

  1. #1
    Member Athefre's Avatar
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    Default CLL Transformation Table

    For CLL cases with at least one oriented corner it's possible to move one of those oriented corners to its correct position and transform to another case. This reveals why two seemingly completely different cases have a similar sequence of moves. Because there must be a correctly oriented corner, G and H cases can't be a starting point and can't be led to unless more moves are allowed. A2 and most of the D, E, and F cases have more than one set of possibilities and I've distinguished them by noting the location of certain colors on the unsolved corner within the layer to be adjusted. The moves in parentheses are optional and are only here to end the corners in the same position for each of the six orientations. My list follows Robert Yau's CLL document.

    &pzl=2&case=LU'R'UL'U'RUx2&pzl=2&case=R'LU'R'UL'U'RUx2

    Cases:
    Spoiler:

    A2: x' R2 U2 R' U' R U2 x R' U R'
    • Pair at Unsolved Corner:
      • L(U2) > E3
      • R > E3
      • R'(U2) > E5
      • L' > E5

    • Opposite Pair at Unsolved Corner:
      • R(U') > D6
      • R' > D6
      • L(U) > D6
      • L'(U2) > D6
      • x(U2) > F2
      • x' > F2

    • No Pair at Unsolved Corner:
      • R(U') > D3
      • R' > D2
      • L(U) > D3
      • L'(U2) > D2

    A6: R' U L' U2 L F' U L' U2 L F' R
    • R > E2
    • R'(U2) > E2
    • L(U2) > E2
    • L' > E2

    B1: R' U' R U' R' U2 R
    • R(U) > B1
    • R' > B1
    • L > B1
    • L'(U) > B1

    B2: L' U L' U L U' L U x U' L U
    • R(U2) > F4
    • R'(U) > E4
    • L > F4
    • L'(U') > E4

    B3: B' L U L' U2 R' U2 R
    • R(U2) > F6
    • R'(U') > B4
    • L > F6
    • L'(U) > B4

    B4: L U2 L' U2 L' B L B'
    • R(U2) > B3
    • R'(U') > F6
    • L > B3
    • L'(U) > F6

    B5: R' U L U' R U L'
    • R(U) > D4
    • R'(U') > F3
    • L(U') > D4
    • L'(U) > F3

    B6: (U') R' U' R U' R' U R' F R F' U R
    • R(U) > D3
    • R'(U) > E5
    • L(U') > D3
    • L'(U') > E5

    C1: L U L' U L U2 L'
    • R(U') > C1
    • R' > C1
    • L(U) > C1
    • L'(U2) > C1

    C2: R' U2 R U2 R B' R' B
    • R(U') > F6
    • R' > C3
    • L(U) > F6
    • L'(U2) > C3

    C3: B R' U' R U2 L U2 L'
    • R(U') > C2
    • R' > F6
    • L(U) > C2
    • L'(U2) > F6

    C4: R U' R U' R' U R' U' x U R' U'
    • R(U) > E4
    • R' > F4
    • L(U') > E4
    • L'(U2) > F4

    C5: L U' R' U L' U' R
    • R(U') > F5
    • R'(U2) > D5
    • L(U) > F5
    • L' > D5

    C6: (U) R' F R2 F' R U2 R' U' R2
    • R(U) > E3
    • R'(U2) > D2
    • L(U') > E3
    • L' > D2

    D1: R' U R' U2 R U' R' U R U' R2'
    • U Sticker on L or R:
      • R > E1
      • R'(U2) > E1
      • L(U2) > E1
      • L' > E1

    • U Sticker not on L or R:
      • R(U2) > F1
      • R' > F1
      • L > F1
      • L'(U2) > F1

    D2: x' R' U2 R' U' R U2 R' F R2
    • U Sticker on L or R:
      • R(U') > C6
      • R'(U2) > E3
      • L(U) > C6
      • L' > E3

    • U Sticker not on L or R:
      • R > A2
      • R'(U) > E3
      • L(U2) > A2
      • L'(U') > E3

    D3: R' U2 R U' R' U2 R U' y R U R'
    • U Sticker on L or R:
      • R > E5
      • R'(U') > B6
      • L(U2) > E5
      • L'(U) > B6

    • U Sticker not on L or R:
      • R(U) > E5
      • R' > A2
      • L(U') > E5
      • L'(U2) > A2

    D4: R U' R' U' y R' F R
    • U Sticker on L or R:
      • R(U2) > F3
      • R'(U') > B5
      • L > F3
      • L'(U) > B5

    • U Sticker not on L or R:
      • R(U) > E6
      • R' > F3
      • L(U') > E6
      • L'(U2) > F3

    D5: F' R U R' U' R' F R
    • U Sticker on L or R:
      • R(U') > C5
      • R' > F5
      • L(U) > C5
      • L'(U2) > F5

    • U Sticker not on L or R:
      • R(U2) > F5
      • R'(U') > F5
      • L > F5
      • L'(U') > E6

    D6: L' U2 L2 F' L' F L' U2 L
    • U Sticker on L or R:
      • R(U2) > F2
      • R' > F2
      • L > F2
      • L'(U2) > F2

    • U Sticker not on L or R:
      • R(U) > A2
      • R'(U') > A2
      • L(U') > A2
      • L'(U) > A2

    E1: (U) R U' R U' R U' R' U R' U R'
    • R(U) > D1
    • R'(U2) > D1
    • L(U') > D1
    • L' > D1
    • x' > F1

    E2: (U') z' U2 R' U' R2 U' R' U' R U' R'
    • R > A6
    • R' > A6
    • L > A6
    • L' > A6
    • x'(U2) > E2

    E3: R2 U L' U2 L F' L' U2 L'
    • U Sticker on U:
      • R(U) > A2
      • R'(U) > C6
      • L(U') > A2
      • L'(U2) > C6

    • U Sticker not on U:
      • R' > A2
      • R(U) > D2
      • L(U') > D2
      • L'(U') > A2

    E4: x R U' R U' R' U L' U' L
    • U Sticker on U:
      • R(U2) > B2
      • R' > C4
      • L > B2
      • L'(U2) > C4

    • U Sticker not on U:
      • R(U') > F4
      • R'(U') > F4
      • L(U) > F4
      • L' > F4

    E5: L2 U' R U2 R' F R U2 R
    • U Sticker on U:
      • R(U2) > B6
      • R' > D3
      • L > B6
      • L'(U2) > D3

    • U Sticker not on U:
      • R(U') > A2
      • R'(U2) > D3
      • L(U) > A2
      • L' > D3

    E6: (U) F' L' U' L U F
    • U Sticker on U:
      • R(U') > D5
      • R' > D4
      • L(U) > D5
      • L'(U2) > D4

    • U Sticker not on U:
      • R(U') > F3
      • R'(U') > F5
      • L(U) > F3
      • L'(U) > F5

    F1: R' U R' U R' U' R U' R U' R
    • R(U') > D1
    • R' > D1
    • L(U) > D1
    • L'(U2) > D1
    • x > E1

    F2: L F' L' U2 L2 F' L' U L'
    • R(U) > D6
    • R'(U2) > D6
    • L(U') > D6
    • L' > D6
    • x(U) > A2

    F3: (U') L' U' L U L F' L' F
    • U Sticker on U:
      • R(U2) > B5
      • R'(U2) > E6
      • L > B5
      • L' > E6

    • U Sticker not on U:
      • R(U') > D4
      • R'(U2) > D4
      • L(U) > D4
      • L' > D4

    F4: (U') x L' U R U' L U L' U R'
    • U Sticker on U:
      • R > E4
      • R'(U2) > E4
      • L(U2) > E4
      • L' > E4

    • U Sticker not on U:
      • R(U') > C4
      • R'(U') > B2
      • L(U) > C4
      • L'(U) > B2

    F5: (U) R U R' U' R' F R F'
    • U Sticker on U:
      • R > E6
      • R' > C5
      • L(U2) > E6
      • L'(U2) > C5

    • U Sticker not on U:
      • R(U) > D5
      • R' > D5
      • L(U') > D5
      • L'(U2) > D5

    F6: (U') R U L F' R U' R' U L' U L2
    • U Sticker on U:
      • R(U2) > B4
      • R' > C2
      • L > B4
      • L'(U2) > C2

    • U Sticker not on U:
      • R(U') > C3
      • R'(U') > B3
      • L(U) > C3
      • L'(U) > B3


    Thanks to Robert Yau for his CLL and Kirjava for the name.
    Last edited by Athefre; 08-16-2012 at 04:56 PM.

  2. #2
    Member riffz's Avatar
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    I don't really have much to say about this other than that it's interesting and that this deserves a bump.
    Average of 12/Official: 14.43/15.17 --- BLD PB/Official: 53.31/1:23.18
    Changing username to RobHolt shortly. Remember me!

  3. #3
    Babby
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    I wonder if this can be applied to EG cases also, in order to find better algs?
    I like cats.

  4. #4
    Member Athefre's Avatar
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    Quote Originally Posted by Escher View Post
    I wonder if this can be applied to EG cases also, in order to find better algs?
    For speed, maybe. For move count, those solutions are already found by computers.

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