Superflip? How about SuperTwist?

Discussion in 'Puzzle Theory' started by blgentry, May 25, 2009.

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  1. blgentry

    blgentry Member

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    I was playing around and decided to create a condition on the cube where all edges were solved, but corners were only permuted properly, but not oriented. Using 8355 you can "solve" the cube this way, though it takes some effort to make sure all corners are un-oriented.

    It's easier if you start with a solved cube though. I do it by doing a corners only OLL on the top to unorient all corners, then fix the edges that got moved with a U perm. Then I turn the cube over and do the same thing to the other side.

    So, superflip has a number of algorithms that produce it, including some with great symmetry like: ((M' U)*4 x'z)*3

    Do you think SuperTwist has a similar algorithm? How about it's "difficulty"? I know superflip is considered one of the more difficult cases for optimal solvers to solve. I wonder how SuperTwist rates?

    Brian.
     
  2. Ethan Rosen

    Ethan Rosen Guest

    R2 B2 D B2 F2 L2 R2 D2 U' F2 R B2 F2 D2 U2 L'
     
  3. Johannes91

    Johannes91 Member

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    Do you have some specific position in mind? I count 7 unique positions with edges and CP solved and all corners twisted.

    Superflip is special because it's so symmetric.

    Here's one supertwist alg that's similar to the superflip alg you posted:
    ([B R' D2 R B', U2] z)4
     
    Last edited: May 25, 2009
  4. qqwref

    qqwref Member

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    I converted Ethan's alg to R2 B2 [D S2 M2 U'] D2 B2 [L S2 E2 R'] but I still don't understand how it works. However the bracketed sequences are very similar so maybe that is the key.
     
  5. blgentry

    blgentry Member

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    I actually didn't realize that until I ran the previous poster's alg and saw that it was different than the one that I made "by hand". Then doing rotations between steps I realized there was a "family" of supertwist positions. I didn't know it was 7, but that sounds about right. :)

    Right; only one of them and it's completely symmetric.

    I'm either reading the alg wrong, or the alg doesn't work. Is the comma significant? I tried the alg 4 times and got a scrambled cube each time. All of the corners are twisted for sure, but they are not permuted properly and the edges are flipped and/or permuted as well.

    Brian.
     
  6. fanwuq

    fanwuq Member

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    It's a commutator.

    Becomes B R' D2 R B' U2 B R' D2 R B' U2
    It twists 2 corners in U.

    Try (R U R' U R U' R' U R U2 R' L' U' L U' L' U L U' L' U2 L z2)*2.
    Double-sune from left and right.
     
    Last edited: May 25, 2009
  7. qqwref

    qqwref Member

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    Here are two I just found by hand:

    F B U F' B' L' R' U L R
    M2 U M2 U M2 U' D
    L' R' U' L R F B U' F' B'
    D' U M2 U' M2 U' M2 (31 stm)

    R U2 R2 U' R2 U' R2 U2 R U2
    F2 M B2 M'
    U2 R' U2 R2 U R2 U R2 U2 R'
    M B2 M' F2 (28 stm)
     
  8. Lucas Garron

    Lucas Garron Super-Duper Moderator Staff Member

    Last edited: May 26, 2009
  9. Swordsman Kirby

    Swordsman Kirby Member

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    Both algs are great comms, but I like the second one better because of the OLL alg. :p
     
  10. byu

    byu Member

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    [A, B] = A B A' B'
     
  11. TMOY

    TMOY Member

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    Another one: (L U L' U L U' L' U L U2 L' M2 S2 x2)^2
     
  12. blgentry

    blgentry Member

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    @fanwuq, Lucas, BYU: Thanks for the notation help. I didn't know that (obviously).

    @fanwuq: That double Sune from both sides is exactly the kind of symmetry thing I was hoping for. Very nice! :)

    Brian.
     
  13. Stefan

    Stefan Member

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    Just 14 moves: U F2 L S2 U2 D2 R2 L' B2 D2 U' S2 R2 L2

    Quite a few moves but easy to remember: (RU)35 z2 (RU)35

    Four right+left Sunes: (R U R' U R U2 R' L' U' L U' L' U2 L z)4

    And very simple: (R'Fz)140
     
    Last edited: May 26, 2009
  14. blgentry

    blgentry Member

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    Stephan, I don't understand how you figure out things like this. ...and seriously 140 steps?!? Wow. :)

    Brian.
     
  15. brunson

    brunson Member

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    That'd be 280 QTM. Got time on your hand? :)
     
  16. d4m4s74

    d4m4s74 Member

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    how bout (((U R U' R)2 D (R U R' U')2 D)2 Y2)2
     
  17. Stefan

    Stefan Member

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    I'm genius, that's all.

    Even if you change the wrong R to R' so it doesn't scramble the cube anymore, this only twists four corners.

    Why don't people just check their goddamn algs before they post them? Try these:
    http://thearufam.brinkster.net/cube/wrapplet.asp
    http://alg.garron.us/

    And blgentry, these tools are the real way I figure these things out. I do *not* really repeat random moves 140 times myself. I let the program do it in an instant. Using that, it's mostly trial and error with a little bit of thinking.
     
    Last edited: May 26, 2009
  18. cmhardw

    cmhardw Premium Member

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    Johannes, I count more than 7.

    If you ignore symmetric cases then actually I count 86 supertwist cases. I posted a long time ago about combining the superflip and the supertwist into the "super-superflip" (posted on Macky's glossary). There are 86 possible super-superflips where every piece is correctly permuted but none correctly oriented. Since the only difference between these and the supertwist is that the edges are all correctly permuted but flipped, then you should get the same number for supertwist cases ignoring symmetry.

    If you do count symmetry I count the following supertwist cases:
    1) 1 corner rotated clockwise, 7 rotated counter-clockwise
    all these cases are symmetric to eachother (8 cases)

    2) 1 corner rotated counter-clockwise, 7 rotated clockwise
    all these cases are symmetric to eachother (8 cases)

    All the next cases are ones with 4 corners rotated clockwise and 4 counter-clockwise. They are split into the following sub-cases based on symmetry. I list one example of each class.

    1) UBR, UBL, UFL, DFR rotated clockwise, and all others rotated counter-clockwise (24 cases)

    2) UBR, UBL UFL, DLF rotated clockwise, and all others rotated counter-clockwise (12 cases)

    3) UBR, UBL UFL, DBR rotated clockwise, and all others rotated counter-clockwise (12 cases)

    4) UBR, UFR, UBL, DBR rotated clockwise, and all others rotated counter-clockwise (8 cases)

    5) UBR, UFR, DBL, DFL rotated clockwise, and all others rotated counter-clockwise (6 cases)

    6) All U layer corners rotated clockwise and all D layer corners rotated counter-clockwise (6 cases)

    7) UBR, UFL, DFR, DBL rotated clockwise, and all others rotated counter-clockwise (2 cases)

    Giving 9 unique ways to supertwist corners, with the number of actual cases on the cube marked next to the example for each class.
     
    Last edited: May 27, 2009
    Cameron Pearce likes this.
  19. qqwref

    qqwref Member

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    I also counted 7 cases for 4 edges flipped each way, although I neglected the two cases where only one edge is flipped in one direction and 7 are flipped in the other. Good catch there.
     
  20. Johannes91

    Johannes91 Member

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    The 7cw and 7ccw cases are inverses of each other and 2) and 3) are mirrors/inverses. I should've been more careful and explained what I meant by "unique", but the point was just that there's more than one.
     
    Last edited: May 27, 2009

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