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(?) YouTube ( ) ( )

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

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3x x ( CFOP)

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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 ( )

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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 ( )

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

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( ) ( ) ⾒ x x = ( )

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( ) ( )

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( ) ( )

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( ) ( ) ( ) ( )

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( ) ( ) ( ) ( )

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( ) ( ) ( ) ( )

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

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

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

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

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

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

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

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

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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

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( ) ( ) ( ) ( ) ( ) E

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( )

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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

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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 ( )

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

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( ) 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

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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 ( )

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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

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(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

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

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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)

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

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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/

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

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(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 ( )

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(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 ( )

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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

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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

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

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( ) ( ) ( ) ( ) ( ) E

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

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

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

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

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

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

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( !) ( !) (U L U L) (U R U R ) (U L U L) ! ! ! ! ! !

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6 x x ! ! ! !

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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 )

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! ! ! ! ! ! ! !

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

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

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Daisy Daisy Cross

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F F

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U ⾒

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( )

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

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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

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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

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= 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

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= 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

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

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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

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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

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

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

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

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(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

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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

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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

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No content

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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

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( , , , , MagLev, ) MagLev 90 ( )

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

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

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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

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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/ !

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

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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 ( )

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( ) ! ! ( ) ! ( ) ! ( ) ! ( ) ! U

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PLL OLL by by by

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