Recent content by Cielo

  1. Cielo

    A Hamiltonian circuit for Rubik's Cube!

    Congratulations! P.S: I noticed a typo in your explanation :"The problem of connnecting up the 2048 cosets".
  2. Cielo

    Maneuver and its Inverse (question)

    S = B D2 R U B D' R D2 F U D' B2 D' L2 D' F2 R2 B2 D2 R2 M1 = B2 S M1 has two blocks: DB&DBL (now in RU&RUB), LB&LBU (now in UL&ULB). For the first one, X = z y', so after executing S M1 X, DB&DBL are "solved". As a result, DB&DBL are also "solved" if we execute X' M1' S'. In fact, DB&DBL...
  3. Cielo

    Maneuver and its Inverse (question)

    You are right. I didn't explain clearly. Maybe we can see the cube from a different point of view. That is, the center cubies can change positions (by rotation), just like edges and corners. Then "a block is solved" means the block is in the same position as it was in the initial state. For...
  4. Cielo

    Maneuver and its Inverse (question)

    My answer is regarding unsolved blocks too. I meaned to answer you question using what you have known in #1 :) What I said is that we can extend the cube group by adding rotations x,y,z. Then for a unsolved block A of S M1, we can rotate the whole cube (the rotation is X) so that we put the...
  5. Cielo

    Maneuver and its Inverse (question)

    S M1 has a block A, then there exists a sequence X (exactly, X is some rotation of the cube), and block A is among the solved cubies of S M1 X. As you posted, block A is among the solved cubies of X' M1' S', too. Since X' is a rotation, M1' S' has a block B.
  6. Cielo

    WCA Statistics Website

    I wanted to know the most sub 30 in FM, and I found that I should fill the blank with "0.30". :p
  7. Cielo

    Trick: swapping 2 edges (only) on a 3x3

    A shorter alg: r2 U' M' U r2 U y' U M U M' U
  8. Cielo

    I'm writing a group theory essay

    I've read Inside the Rubik's cube and beyond(by Christoph Bandelow) and Handbook of cubik math(by A.H.Frey & D.Singmaster). These might help. I tried and solved, turning only L-U-R. At first, I only thought of the alg I used: R' U L' U2 R U' R' U2 R2. Then I realized that L' R, then F turns...
  9. Cielo

    The Dino cube has 2 solutions.

    Never thought of this before. And the 5-move pattern is nice!
  10. Cielo

    <U, D, F2, R2, B2, L2> vs. <L, R, F2, U2, B2, D2> vs. <F, B, U2, R2, D2 L2>

    1) 10.43, (13.62), 11.85, 11.88, 11.17, 11.77, 11.88, (10.33), 12.09, 11.46, 11.08, 11.63 => 11.52 2) 10.59, (14.62), 11.23, 12.15, 11.44, 11.44, (09.87), 11.59, 10.54, 12.85, 10.51, 10.89 => 11.32 3) (09.72), (14.62), 10.85, 11.92, 12.26, 12.08, 11.42, 11.08, 12.79, 10.04, 13.14, 11.21 =>...
  11. Cielo

    [Help Thread] Void Cube Discussion

    Exactly, Roux method can deal with this "parity" without extra algs.
  12. Cielo

    [Help Thread] Void Cube Discussion

    Void cube is the cube without the centre caps ^_^ Turning a middle layer for 90° results in a center-4-cycle(invisible in this situation) and an edge-4-cycle. 4-cycle is an odd permutation. That's why parity can occur.
  13. Cielo

    God's number is...

    In fact, István Kocza is unlucky, his WR solution should have been less than 20 moves. That's because
  14. Cielo

    FMC riddle: second layer edge

    Scramble 1: F' U' F U R U R' U (1 to go with the help of hint) Scramble 2: F' U' F U R U R' U' (done with the help of hint) Scramble 3: F' U' F U R U R' U2 (done) Scramble 4: F' U' F U R U R' (done) After seeing the hints, I still can't find this one.
  15. Cielo

    Yu Nakajima Interview (by Shotaro "Macky" Makisumi)

    Here is part I, maybe you can see this?