小１にルービックキューブを教えてみた 〜群論スポーツの教育とパターン認知〜

2022年11月6日(日)
分科会@京都大学清風荘
文部科学省 科学研究費補助金 学術変革領域(A) 社会変革の源泉となる革新的アルゴリズム基盤の創出と体系化
2022年度第2回領域集会
https://afsa.jp/generalmeeting2022autumn/

Transcript

1. . .
   

   View Slide

2. (?) YouTube
   ( )
   ( )
   

   View Slide

3. A (?) vs
   ( )
   ( 1)
   e.g. T-Method CFOP
   CFOP vs Roux vs ZZ vs Petrus vs
   Q.
   

   View Slide

4. 3x x
   ( CFOP)
   

   View Slide

5. 40
   ( ) ( )
   x x (New Takahashi Method)
   CFOP ( LLL = -look OLL 2-look PLL)
   x x ( x x , x x , x x , )
   (WCA 17 )
   2x x ( )
   

   View Slide

6. 40
   ( ) ( )
   x x (New Takahashi Method)
   CFOP ( LLL = -look OLL 2-look PLL)
   x x ( x x , x x , x x , )
   (WCA 17 )
   2x x ( )
   

   View Slide

7. https://www.megahouse.co.jp/rubikcube/ ( )
   RUBIK CUBE
   

   View Slide

8. ( )
   ( )
   ⾒
   x x =
   ( )
   

   View Slide

9. View Slide

10. ( )
    ( )
    

    View Slide

11. ( )
    ( )
    

    View Slide

12. ( )
    ( )
    ( )
    ( )
    

    View Slide

13. ( )
    ( )
    ( )
    ( )
    

    View Slide

14. ( )
    ( )
    ( )
    ( )
    

    View Slide

15. R
    L
    U
    D
    B
    F
    Front
    Back
    Right
    Left
    Down
    Up
    Singmaster
    notation
    

    View Slide

16. R
    Right
    R’
    M
    Middle
    = R + L’
    U2
    °
    180°
    =
    U
    Up
    U
    Up
    

    View Slide

17. https://jperm.net/3x3/moves x x U = U 180°
    ( )
    

    View Slide

18. ( )
    https://alg.cubing.net/
    D L D' B R U L D B L U' B R U' B D' F D F' U'
    

    View Slide

19. 40
    ( ) ( )
    x x (Takahashi Method)
    CFOP ( -look OLL 2-look PLL)
    x x ( x x , x x , x x , )
    (WCA 17 )
    2x x ( )
    

    View Slide

20. https://www.asahi.com/articles/ASNB13CJJN9XUHBI01H.html https://business.nikkei.com/atcl/gen/19/00290/071300012/
    

    View Slide

21. 2020 = 話 (1980 )
    : :
    2020 40 2020 40 40
    3,080 10% /2,800
    

    View Slide

22. Ernő Rubik 20 90
    ( (Rubik s Cube) )
    GAN MoYu QiYi Dayan Yuxin
    YJ
    

    View Slide

23. 2,860 ( )
    ver. .
    , ( )
    GAN13 MagLev
    Stickerless UV-Coated
    ¥ 12,100
    QiYi QiHang
    3x3x3 W
    ¥ 450
    MoYu Cubing Classroom
    RS3M 2020 Stickerless
    ¥ 1,550
    (2022/10/27 )
    DaYan TengYun
    3x3x3 M Stickerless
    ¥ 3,300
    MoYu WeiLong WR
    MagLev Stickerless
    ¥ 3,300
    QiYi X-Man Design
    Tornado V3 M Flagship
    ¥ 4,900
    

    View Slide

24. ( ) ( )
    ( )
    ( )
    ( )
    E
    

    View Slide

25. View Slide

26. ( )
    

    View Slide

27. AFSA
    pyraminx 933,120
    skewb 3,149,260
    2x2x2 3,674,160
    3x3x3 43,252,003,274,489,856,000
    square-1 8,617,338,912,961,650,000,000
    4x4x4 7,401,196,841,564,900,000,000,000,000,000,000,000,000,000,000
    megaminx 100,669,616,553,523,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
    5x5x5 282,870,942,277,741,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
    6x6x6
    157,152,858,401,024,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,0
    00,000,000,000,000,000,000,000,000,000,000,000,000
    7x7x7
    19,500,551,183,731,300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00
    0,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
    3x x
    4x x 5x x 3x x
    2-3 4x x 5x x
    

    View Slide

28. AFSA (FMC)
    Computer Scientists (NP ?)
    WCA( ) 17 FMC (Fewest
    Moves Challenge) ⾒
    ೔ຊޠ຋༁ https://kawam1123.github.io/translation/FMC/FMC-Tutorial/v3/
    https://fmcsolves.cubing.net/fmc_tutorial_ENG.pdf
    Fewest Moves Tutorial: Solving a Rubik’s Cube with as few moves as possible v3.03
    by Sebastiano Tronto
    Basics
    (Heise, , F L, , , NISS, , )
    FMC ( )
    

    View Slide

29. NP by ( )
    https://arxiv.org/abs/1706.06708
    

    View Slide

30. ( )
    6 {F, B, U, D, L, R}
    1 2 3
    4 U 5
    6 7 8
    9 10 11 17 18 19 25 26 27 33 34 35
    12 L 13 20 F 21 28 R 29 36 B 37
    14 15 16 22 23 24 30 31 32 38 39 40
    41 42 43
    44 D 45
    46 47 48
    48 (Facet)
    12 ( 2 ) 8
    ( 3 )
    n
    n
    AAAB83icbVDLSgMxFL1TX7W+qi7dBIvgqsxIUZdFNy4r2Ad2hpJJM21oJhOSjFCG/oYbF4q49Wfc+Tdm2llo64HA4Zx7uScnlJxp47rfTmltfWNzq7xd2dnd2z+oHh51dJIqQtsk4YnqhVhTzgRtG2Y47UlFcRxy2g0nt7nffaJKs0Q8mKmkQYxHgkWMYGMl34+xGYdh9jgbiEG15tbdOdAq8QpSgwKtQfXLHyYkjakwhGOt+54rTZBhZRjhdFbxU00lJhM8on1LBY6pDrJ55hk6s8oQRYmyTxg0V39vZDjWehqHdjLPqJe9XPzP66cmug4yJmRqqCCLQ1HKkUlQXgAaMkWJ4VNLMFHMZkVkjBUmxtZUsSV4y19eJZ2LundZb9w3as2boo4ynMApnIMHV9CEO2hBGwhIeIZXeHNS58V5dz4WoyWn2DmGP3A+fwBVzJHk
    Z
    n
    AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE1GPRi8dK7Qe0oWy2m3bpZhN2J0IJ/QlePCji1V/kzX/jts1BWx8MPN6bYWZekEhh0HW/ncLa+sbmVnG7tLO7t39QPjxqmTjVjDdZLGPdCajhUijeRIGSdxLNaRRI3g7GdzO//cS1EbF6xEnC/YgOlQgFo2ilRqOv+uWKW3XnIKvEy0kFctT75a/eIGZpxBUySY3pem6CfkY1Cib5tNRLDU8oG9Mh71qqaMSNn81PnZIzqwxIGGtbCslc/T2R0ciYSRTYzojiyCx7M/E/r5tieONnQiUpcsUWi8JUEozJ7G8yEJozlBNLKNPC3krYiGrK0KZTsiF4yy+vktZF1buqXj5cVmq3eRxFOIFTOAcPrqEG91CHJjAYwjO8wpsjnRfn3flYtBacfOYY/sD5/AEytI3B
    Sn
    AAAB7XicbVBNSwMxEJ2tX7V+VT16CRbBU9mVoj0WvXisaD+gXUo2zbax2WRJskJZ+h+8eFDEq//Hm//GbLsHbX0w8Hhvhpl5QcyZNq777RTW1jc2t4rbpZ3dvf2D8uFRW8tEEdoikkvVDbCmnAnaMsxw2o0VxVHAaSeY3GR+54kqzaR4MNOY+hEeCRYygo2V2veDtFafDcoVt+rOgVaJl5MK5GgOyl/9oSRJRIUhHGvd89zY+ClWhhFOZ6V+ommMyQSPaM9SgSOq/XR+7QydWWWIQqlsCYPm6u+JFEdaT6PAdkbYjPWyl4n/eb3EhHU/ZSJODBVksShMODISZa+jIVOUGD61BBPF7K2IjLHCxNiASjYEb/nlVdK+qHqX1dpdrdK4zuMowgmcwjl4cAUNuIUmtIDAIzzDK7w50nlx3p2PRWvByWeO4Q+czx8aj47V
    S48
    AAACK3icbVDLTsJAFJ3iC/FVdelmIjFxRVokypLgxiUGeURamukwwITpIzNTE9L0f9z4Ky504SNu/Q+nUBMFTjLJmXPvyb33uCGjQhrGh5ZbW9/Y3MpvF3Z29/YP9MOjtggijkkLByzgXRcJwqhPWpJKRrohJ8hzGem4k+u03nkgXNDAv5PTkNgeGvl0SDGSSnL0etOpQktSjwjYdGKznPz+LA/JsevG94lz0Y+rq/RyPzU4etEoGTPAZWJmpAgyNBz9xRoEOPKILzFDQvRMI5R2jLikmJGkYEWChAhP0Ij0FPWRGmvHs1sTeKaUARwGXD1fwpn61xEjT4ip56rOdFGxWEvFVbVeJIdVO6Z+GEni4/mgYcSgDGAaHBxQTrBkU0UQ5lTtCvEYcYSliregQjAXT14m7XLJvCxVbivFWj2LIw9OwCk4Bya4AjVwAxqgBTB4BM/gDbxrT9qr9ql9zVtzWuY5Bv+gff8ANWSnGw==
    S8
    ⇥ S12
    ⇥ Z8
    3
    ⇥ Z12
    2
    AAAB6HicbVDLSgNBEOyNrxhfUY9eBoPgKexKUI9BD3pMwDwgWcLspDcZMzu7zMwKIeQLvHhQxKuf5M2/cZLsQRMLGoqqbrq7gkRwbVz328mtrW9sbuW3Czu7e/sHxcOjpo5TxbDBYhGrdkA1Ci6xYbgR2E4U0igQ2ApGtzO/9YRK81g+mHGCfkQHkoecUWOl+l2vWHLL7hxklXgZKUGGWq/41e3HLI1QGiao1h3PTYw/ocpwJnBa6KYaE8pGdIAdSyWNUPuT+aFTcmaVPgljZUsaMld/T0xopPU4CmxnRM1QL3sz8T+vk5rw2p9wmaQGJVssClNBTExmX5M+V8iMGFtCmeL2VsKGVFFmbDYFG4K3/PIqaV6UvctypV4pVW+yOPJwAqdwDh5cQRXuoQYNYIDwDK/w5jw6L86787FozTnZzDH8gfP5A57jjNQ=
    G
    AAAB6HicbVDLSgNBEOyNrxhfUY9eBoPgKexKUI9BD3pMwDwgWcLspDcZMzu7zMwKIeQLvHhQxKuf5M2/cZLsQRMLGoqqbrq7gkRwbVz328mtrW9sbuW3Czu7e/sHxcOjpo5TxbDBYhGrdkA1Ci6xYbgR2E4U0igQ2ApGtzO/9YRK81g+mHGCfkQHkoecUWOl+l2vWHLL7hxklXgZKUGGWq/41e3HLI1QGiao1h3PTYw/ocpwJnBa6KYaE8pGdIAdSyWNUPuT+aFTcmaVPgljZUsaMld/T0xopPU4CmxnRM1QL3sz8T+vk5rw2p9wmaQGJVssClNBTExmX5M+V8iMGFtCmeL2VsKGVFFmbDYFG4K3/PIqaV6UvctypV4pVW+yOPJwAqdwDh5cQRXuoQYNYIDwDK/w5jw6L86787FozTnZzDH8gfP5A57jjNQ=
    G
    AAAB6HicbVDLSgNBEOyNrxhfUY9eBoPgKexKUI9BD3pMwDwgWcLspDcZMzu7zMwKIeQLvHhQxKuf5M2/cZLsQRMLGoqqbrq7gkRwbVz328mtrW9sbuW3Czu7e/sHxcOjpo5TxbDBYhGrdkA1Ci6xYbgR2E4U0igQ2ApGtzO/9YRK81g+mHGCfkQHkoecUWOl+l2vWHLL7hxklXgZKUGGWq/41e3HLI1QGiao1h3PTYw/ocpwJnBa6KYaE8pGdIAdSyWNUPuT+aFTcmaVPgljZUsaMld/T0xopPU4CmxnRM1QL3sz8T+vk5rw2p9wmaQGJVssClNBTExmX5M+V8iMGFtCmeL2VsKGVFFmbDYFG4K3/PIqaV6UvctypV4pVW+yOPJwAqdwDh5cQRXuoQYNYIDwDK/w5jw6L86787FozTnZzDH8gfP5A57jjNQ=
    G
    

    View Slide

31. https://www.sfu.ca/~jtmulhol/math302/lectures.html
    https://www.kyoritsu-pub.co.jp/book/b10007945.html
    ( ) : 25( ) pp. -
    https://www.mathsoc.jp/assets/file/publications/tushin/2503/2503yokoyama.pdf
    ( )
    

    View Slide

32. https://www.sfu.ca/~jtmulhol/math302/puzzles-rc-cubology.html
    3x x
    The Fundamental Theorem of Cubology
    AAACI3icbVDLSgMxFM34rPU16tJNsAgtQpmRom6EohuXFewDOkPJpJk2NMkMSUYow3yEH+E3uNW1O3HjwoV/YqbtwrYeCDmccy/33hPEjCrtOF/Wyura+sZmYau4vbO7t28fHLZUlEhMmjhikewESBFGBWlqqhnpxJIgHjDSDka3ud9+JFLRSDzocUx8jgaChhQjbaSefeZxpIeSp4oORFb25DCqwGu4oJqPo0rPLjlVZwK4TNwZKYEZGj37x+tHOOFEaMyQUl3XibWfIqkpZiQreokiMcIjNCBdQwXiRPnp5KgMnhqlD8NImic0nKh/O1LElRrzwFTmy6pFLxf/87qJDq/8lIo40UTg6aAwYVBHME8I9qkkWLOxIQhLanaFeIgkwtrkODcl4JnJxF1MYJm0zqvuRbV2XyvVb2bpFMAxOAFl4IJLUAd3oAGaAIMn8AJewZv1bL1bH9bntHTFmvUcgTlY379sH6VF
    sign(⇢) = sign( )
    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
    v1 + v2 + · · · + v8 = 0 (mod 3)
    ( )
    ( )
    ( )
    (Parity)
    0
    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
    w1 + w2 + · · · + w12 = 0 (mod 2) 0
    1 2 1 2 2
    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
    (⇢, , v, w) 2 S8
    ⇥ S12
    ⇥ Z8
    3
    ⇥ Z12
    2
    Twist
    Flip
    

    View Slide

33. (Setup)
    Setup (Conjugate)
    x x 1260 ( R U D B D × )
    4 ( )
    3
    2
    3
    2
    [L D L, U]
    [L D L F D F, U]
    [M, U ]
    [M D M D M D M, U]
    (Commutator)
    AAACAHicdVDLSgMxFM34rPVVdekmWAQ3Dpl2bLssunFZwT6wrSWTpm1oJjMkGXEYZuM3uNW1O3Hrn7j0T0wfghU9cOFwzr3ce48XcqY0Qh/W0vLK6tp6ZiO7ubW9s5vb22+oIJKE1knAA9nysKKcCVrXTHPaCiXFvsdp0xtfTPzmHZWKBeJaxyHt+ngo2IARrI10E98mp04K72Hcy+WRXXZRpVCEyEZnjuO6hrio5BZd6NhoijyYo9bLfXb6AYl8KjThWKm2g0LdTbDUjHCaZjuRoiEmYzykbUMF9qnqJtOLU3hslD4cBNKU0HCq/pxIsK9U7Hum08d6pH57E/Evrx3pQaWbMBFGmgoyWzSIONQBnLwP+0xSonlsCCaSmVshGWGJiTYhLWzx/NRk8v04/J80CrZTst0rN189n6eTAYfgCJwAB5RBFVyCGqgDAgR4BE/g2XqwXqxX623WumTNZw7AAqz3L9Xdlxc=
    y 1xy
    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
    [x, y] = xyx 1y 1
    (BLD)
    https://www.sfu.ca/~jtmulhol/math302/lectures.html
    

    View Slide

34. = ( -Cycle)
    ) 8
    Niklas
    [R, U L U] = R U L U R U L U
    

    View Slide

35. n n
    ( = )
    (2 ) (e.g. )
    (1 2 3) = 1 2 3 1
    ( )
    ( = G g G , gn=e ( ) n)
    ( , )
    1,5,3 3 (1 5 3) (1 5 3) = (1 3) (1 5)
    

    View Slide

36. ( GAP)
    ϧʔϏοΫΩϡʔϒྫ https://www.gap-system.org/Doc/Examples/rubik.html
    Documentation → Examples
    

    View Slide

37. SageMath(GAP )
    SageMathCell ( )
    https://sagecell.sagemath.org/
    C = RubiksCube("D L2 D' B2 R2 U2 L2 D2 B2 L2 U' B R U' B D' F2 D2 F' U'",
    colors=['white','orange', 'green', 'red', 'blue', 'yellow'])
    C.show3d()
    solve = C.solve(algorithm='gap', timeout=15)
    print(solve.replace("^-1", "'").replace("^2", “2").\
    replace("^-2", "2'").replace("*", " "))
    B L U B U' B' L' B' D' B' R' B R D B' L B' L' B2 R D' R'
    B' D B D L B' L' D' B2 D B D' L' D B' D' B L B L' B' D'
    B D L B' D B L B' L' D' B2' D' B D L' D L D' B' D' B D
    B' D B R D' R' B D2 B' D L' D' L B' U' L U D' L' B2' R
    F' R' L' U' F2' U F D2' B U'
    gap
    SageMathCell
    https://doc.sagemath.org/html/ja/tutorial/
    

    View Slide

38. ࣍਺ ૯ঢ়ଶ਺
    
    ८ճஔ׵ͷੵͰॻ͚Δ
    ճͰݩʹ໭Δ
    ճͰݩʹ໭Δ
    ճͰݩʹ໭Δ
    ճͰݩʹ໭Δ
    

    View Slide

39. (Thistlethwaite s Algorithm)
    https://en.wikipedia.org/wiki/Optimal_solutions_for_Rubik%27s_Cube
    Hofstadter, D. R. (1981). METAMAGICAL THEMAS. Scientific American,
    244(3), 20–39. http://www.jstor.org/stable/24964321
    Two-Phase / (Kociemba s Algorithm)
    https://www.speedsolving.com/wiki/index.php/Thistlethwaite%27s_algorithm
    https://www.speedsolving.com/wiki/index.php/Human_Thistlethwaite_Algorithm
    https://www.speedsolving.com/wiki/index.php/Kociemba%27s_Algorithm
    https://github.com/cs0x7f/min2phase
    http://kociemba.org/math/imptwophase.htm
    A practical implementation of "God's Algorithm" for Rubik's Cube (Korf s Algorithm)
    https://www.aaai.org/Papers/AAAI/1997/AAAI97-109.pdf
    Korf, R. E. (1997). Finding optimal solutions to Rubik's cube using pattern databases. AAAI’97, 700–705.
    https://cflmath.com/Rubik/optimal_solver.html
    ( )
    

    View Slide

40. (Thistlethwaite s Algorithm)
    https://en.wikipedia.org/wiki/Optimal_solutions_for_Rubik%27s_Cube
    Hofstadter, D. R. (1981). METAMAGICAL THEMAS. Scientific American,
    244(3), 20–39. http://www.jstor.org/stable/24964321
    Two-Phase / (Kociemba s Algorithm)
    https://www.speedsolving.com/wiki/index.php/Thistlethwaite%27s_algorithm
    https://www.speedsolving.com/wiki/index.php/Human_Thistlethwaite_Algorithm
    https://www.speedsolving.com/wiki/index.php/Kociemba%27s_Algorithm
    https://github.com/cs0x7f/min2phase
    http://kociemba.org/math/imptwophase.htm
    A practical implementation of "God's Algorithm" for Rubik's Cube (Korf s Algorithm)
    https://www.aaai.org/Papers/AAAI/1997/AAAI97-109.pdf
    Korf, R. E. (1997). Finding optimal solutions to Rubik's cube using pattern databases. AAAI’97, 700–705.
    https://cflmath.com/Rubik/optimal_solver.html
    • hybrid - try kociemba for timeout seconds, then dietz
    • kociemba - Use Dik T. Winter’s program (reasonable speed, few moves)
    • dietz - Use Eric Dietz’s cubex program (fast but lots of moves)
    • optimal - Use Michael Reid’s optimal program (may take a long time)
    • gap - Use GAP word solution (can be slow)
    SageMathͷsolveͷΞϧΰϦζϜΦϓγϣϯ
    https://doc.sagemath.org/html/en/reference/spkg/rubiks.html
    ( )
    

    View Slide

41. God s number ( )
    http://cube20.org/
    http://cube20.org/qtm/
    (Half-Turn Metric)
    Harf-Turn(90 /180 /270 )
    (Quarter-Turn Metric)
    Quarter-Turn(90 ) 1
    

    View Slide

42. GAP SageMath MacOS
    $ curl -L -O https://github.com/conda-forge/miniforge/releases/latest/download/Mambaforge-$(uname)-$(uname -m).sh
    $ sh Mambaforge-$(uname)-$(uname -m).sh -b
    $ export PATH=${PATH}:$HOME/mambaforge
    $ mamba create -n sage sage python=3.9
    $ mamba init
    (IPython)
    $ mamba activate sage
    $ mamba install rubiks python=3.9
    $ sage
    :
    $ mamba deactivate
    $ mamba activate sage
    $ mamba install rubiks python=3.9
    $ sage -n jupyter
    :
    $ mamba deactivate
    Jupyter
    

    View Slide

43. ) 62
    -'6-'6%#63%'#%36#%
    

    View Slide

44. ( ) ( )
    ( )
    ( )
    ( )
    E
    

    View Slide

45. ( ) Official Trailer
    https://youtu.be/-wrTIWx_Z6k
    https://www.netflix.com/jp/title/81092143
    

    View Slide

46. ( )
    https://youtu.be/BVi_7pY6wtQ https://youtu.be/yjv7IlkCXMk
    Speed Cubing
    Speed Stacking
    

    View Slide

47. 40
    ( ) ( )
    x x (Takahashi Method)
    CFOP ( -look OLL 2-look PLL)
    x x ( x x , x x , x x , )
    (WCA 17 )
    2x x ( )
    

    View Slide

48. New Takahashi Method (T-Method):
    https://youtu.be/Z Qc Nq bU
    

    View Slide

49. New Takahashi Method ( ⾒ )
    Daisy Cross
    Edge OLL Edge PLL Corner OLL Corner PLL
    

    View Slide

50. T-Method
    https://tribox.com/3x3x3/solution/notation/
    ( !) ( !)
    !
    (U R U R = [U, R])
    ( Anti Sexy Move )
    

    View Slide

51. ( !) ( !)
    (U L U L)
    (U R U R )
    (U L U L)
    ! ! !
    ! ! !
    

    View Slide

52. 6
    x
    x
    ! !
    ! !
    

    View Slide

53. R U R U = [R, U] = (U R U R )
    ( !) ( !)
    (U R U R ) = (R ) (U ) R U = R U R U
    U R U R
    https://www.speedsolving.com/wiki/index.php/Sexy_Move
    ( Sexy Move )
    

    View Slide

54. ! !
    ! !
    ! !
    ! !
    

    View Slide

55. ⾒ Ua
    ( ) ! !
    ( ) ! !
    ( ) ! !
    ( ) ! !
    PLL
    Sexy
    Sexy
    Anti Sexy
    Anti Sexy
    

    View Slide

56. New Takahashi Method ( ⾒ )
    Daisy Cross
    Edge OLL Edge PLL Corner OLL Corner PLL
    

    View Slide

57. Daisy
    Daisy Cross
    

    View Slide

58. View Slide

59. F F
    

    View Slide

60. U
    ⾒
    

    View Slide

61. ( )
    

    View Slide

62. 40
    ( ) ( )
    x x (Takahashi Method)
    CFOP ( -look OLL 2-look PLL)
    x x ( x x , x x , x x , )
    (WCA 17 )
    2x x ( )
    

    View Slide

63. CFOP ( , Fridrich )
    (Roux ZZ Petrus Big ⾒ CFOP?)
    https://youtu.be/MS5jByTX_pk
    Cross
    F L
    OLL
    PLL
    Cross
    First Two Layers
    Orientation of the Last Layer
    Permutation of the Last Layer
    https://www.speedsolving.com/wiki/index.php/CFOP_method
    https://www.speedsolving.com/wiki/index.php/Layer_by_layer
    

    View Slide

64. OLL PLL OLL 57 PLL 21
    Ua Ub H Z
    Aa Ab E F
    Ga Gb Gc Gd
    Ra Rb Ja Jb
    Na Nb T V
    Y
    OLL PLL
    

    View Slide

65. = CFOP ( -Look LL = -Look OLL + -Look PLL)
    Cross F L Edge OLL Corner OLL Corner PLL Edge PLL
    F Sexy F’
    f Sexy f’
    F Sexy F’ f Sexy f’
    H Pi
    Head
    Lights T
    Sune
    Anti
    Sune
    Bowtie
    D
    OLL
    T perm
    Y perm
    Ua perm Ub perm
    H perm Z perm
    f
    Sexy = R U R’ U’
    ! !
    F
    

    View Slide

66. = CFOP (Sexy + R U R U R U R + T perm + Ua perm)
    Cross F L Edge OLL Corner OLL Corner PLL Edge PLL
    F Sexy F’
    f Sexy f’
    F Sexy F’ f Sexy f’
    D
    T perm Ua perm
    f
    Sexy = R U R’ U’
    ! !
    F
    R U2 R’ U’ R U’ R’
    Megaminx
    

    View Slide

67. Sexy T
    Cross F L Edge OLL Corner OLL Corner PLL Edge PLL
    Ua perm
    ( ) ! !
    ( ) ! !
    ( ) ! !
    ( ) ! !
    Sexy
    Sexy
    Anti Sexy
    Anti Sexy
    T-Method
    ͷखॱΑΓ
    

    View Slide

68. OK ( )
    https://youtu.be/GhmYBgLoQQg
    https://youtu.be/f_Yor-ydZjs https://youtu.be/9r_HqG4zSbk https://youtu.be/vU6HsK3hvQs
    https://youtu.be/3B_oB2YrLvk
    https://youtu.be/Ar_Zit1VLG0 https://youtu.be/f_Yor-ydZjs https://youtu.be/HWIQdX8vHcE
    https://youtu.be/pHUBJPTIGPo
    https://youtu.be/FirE9oE3fj4 https://youtu.be/9r_HqG4zSbk
    https://youtu.be/ealBmfXxEtM
    

    View Slide

69. YJ Megaminx YuHu V2 M Stickerless
    MoYu Cubing Classroom RS3M
    2020 Stickerless
    FAVNIC Magic Cube 2x2x2
    25೥͘Β͍લʹϋϯΨϦʔ͔Ͳ͔͔͜Β
    ݸਓ༌ೖͰखʹೖΕͨṖͷΩϡʔϒͨͪ
    ૈѱͳ5x5x5
    Pyraminx
    Skewb
    Impossiball
    6-Color
    Megaminx
    ๭ձٞͷAmazonͷ
    ϒʔεͰ΋Βͬͨ
    Rubik’s Revenge (4x4x4)
    ͨͩ͠ୈҰ࣍ϒʔϜ࣌ͷ
    Rubik’s Cube (3x3x3)
    ͨͩ͠ୈҰ࣍ϒʔϜ࣌ͷ
    Rubik’s cube (2x2x2)
    ͨͩ͠ୈҰ࣍ϒʔϜ࣌ͷ
    ͋͢ͳΖࣷ αϯϦΦΩϟϥ
    Ϋλʔζ Ωϡʔϒύζϧ
    MoYu Cubing Classroom Meilong
    5x5x5 M Stickerless
    MoYu Cubing Classroom Meilong
    4x4x4 M Stickerless
    

    View Slide

70. x x
    x x
    3x x
    ( )
    3x x
    3x x
    3x x
    ( T-Method )
    ( x x )
    ( x x )
    ( x x )
    OK
    

    View Slide

71. x x , x x ,
    )
    )
    ) x x
    )
    2 3
    x x PLL parity
    x x OLL parity
    

    View Slide

72. 40
    ( ) ( )
    x x (Takahashi Method)
    CFOP ( -look OLL 2-look PLL)
    x x ( x x , x x , x x , )
    (WCA 17 )
    2x x ( )
    

    View Slide

73. (World Cube Association, WCA)
    17 ( )
    1 YY$VCF 1.02 Zayn Khanani
    2 4LFXC 1.56 Zayn Khanani
    3 1ZSBNJOY 1.66 Jasper Murray
    4 $MPDL 3.56 Jacob Chambers
    5 YY$VCF 4.86 Max Park, Tymon Kolasiński
    6 4RVBSF 5.02 Max Siauw
    7 YY0OF)BOEFE 0)
    8.65 Patrick Ponce
    8 YY#MJOEGPMEFE #-%
    15.24 Tommy Cherry
    9 YY$VCF 19.88 Max Park
    10 .FHBNJOY 29.27 Leandro Martín López
    11 YY$VCF 38.42 Max Park
    12 YY$VCF 1:08.56 Max Park
    13 YY#MJOEGPMEFE #-%
    1:08.76 Stanley Chapel
    14 YY$VCF 1:42.12 Max Park
    15 YY#MJOEGPMEFE #-%
    2:26.63 Stanley Chapel
    16 YY'FXFTU.PWFT '.$
    21 Cale Schoon
    17 YY.VMUJ#MJOE .#-%
    62/65 57:47 Graham Siggins
    Last updated: Saturday, October 29, 2022 at 8:16 PM GMT+9
    4LFXC
    1ZSBNJOY $MPDL
    4RVBSF .FHBNJOY
    x x Feet( ) 2019
    

    View Slide

74. Last updated: Sunday, October 30, 2022 at 11:51 AM GMT+9
    https://www.worldcubeassociation.org/results/rankings/333/average
    3x3x3
    (ao5)
    Max Park Tymon Kolasiński Matty Hiroto Inaba Leo Borromeo Ruihang Xu
    Feliks Zemdegs
    

    View Slide

75. Max Park Feliks Zemdegs
    https://youtu.be/-wrTIWx_Z6k
    https://youtu.be/_omMHKavyqQ
    CubingUSA Nationals 2018 3x3 Finals!
    (feat. Feliks Zemdegs, Philipp Weyer, Max Park)
    The Speed Cubers | Official Trailer | Netflix
    εϐʔυΩϡʔόʔζ: ੈքΛݟਾ͑ͯ
    https://www.netflix.com/jp/title/81092143
    

    View Slide

76. View Slide

77. Monkey League ( )
    https://youtu.be/AycjUQBwIc0
    https://youtu.be/LE8pi97s8q0
    https://youtu.be/AycjUQBwIc0
    https://youtu.be/YQ6tUBT8O_s https://youtu.be/gr-WyX3sJNc
    https://youtu.be/qw3hIb7XT0A
    Leo vs Matty Ruihang vs Tymon Ruihang vs Leo
    Leo vs Feliks Leo vs Tymon Matty vs Tymon
    

    View Slide

78. ( , , , , MagLev, )
    MagLev
    90
    ( )
    

    View Slide

79. ( + + )
    IUUQTcstimer.net
    csTimer
    (Desktop)
    Twisty Timer
    (Android App)
    DCTimer Lite
    (iOS App)
    

    View Slide

80. 4
    https://superliminal.com/cube/cube.htm
    ASolver (Android app)
    https://www.gancube.com/GAN-ROBOT
    

    View Slide

81. https://gigazine.net/news/20180308-rubiks-cube-solving-machine/
    https://www.youtube.com/watch?v=nt00QzKuNVY
    0.38
    https://github.com/dicarlo236/cube-solver
    (Two-Phase ) github
    

    View Slide

82. Solving the Rubik’s cube with deep reinforcement learning and search.
    Nat Mach Intell 1, 356–363 (2019). https://doi.org/10.1038/s42256-019-0070-z
    AI solves Rubik's Cube in 1.2 seconds (that's three times slower than a non-AI algorithm)
    https://www.theregister.com/2019/07/16/ai_rubiks_cube/
    https://deepcube.igb.uci.edu/
    !
    

    View Slide

83. Solving Rubik’s Cube with a Robot Hand (OpenAI)
    https://openai.com/blog/solving-rubiks-cube/
    https://arxiv.org/abs/1910.07113
    

    View Slide

84. 40
    ( ) ( )
    x x (New Takahashi Method)
    CFOP ( LLL = -look OLL 2-look PLL)
    x x ( x x , x x , x x , )
    (WCA 17 )
    2x x ( )
    

    View Slide

85. ( ) ! !
    ( ) !
    ( ) !
    ( ) !
    ( ) !
    U
    

    View Slide

86. PLL
    OLL
    by
    by
    by
    

    View Slide

87. A (?) vs
    ( )
    ( 1)
    e.g. T-Method CFOP
    CFOP vs Roux vs ZZ vs Petrus vs
    

    View Slide