itakigawa
November 07, 2022
430

# 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)

2022年度第2回領域集会
https://afsa.jp/generalmeeting2022autumn/

## itakigawa

November 07, 2022

## Transcript

1. . .

( )
( )

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

4. 3x x
( CFOP)

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 ( )

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 ( )

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

8. ( )
( )

x x =
( )

9. ( )
( )

10. ( )
( )

11. ( )
( )
( )
( )

12. ( )
( )
( )
( )

13. ( )
( )
( )
( )

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

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

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

17. ( )
https://alg.cubing.net/
D L D' B R U L D B L U' B R U' B D' F D F' U'

18. 40
( ) ( )
x x (Takahashi Method)
CFOP ( -look OLL 2-look PLL)
x x ( x x , x x , x x , )
(WCA 17 )
2x x ( )

20. 2020 = 話 (1980 )
: :
2020 40 2020 40 40
3,080 10% /2,800

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

22. 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
¥ 4,900

23. ( ) ( )
( )
( )
( )
E

24. ( )

25. 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

26. 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 ( )

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

28. ( )
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
Z
n
Sn
S48
AAACK3icbVDLTsJAFJ3iC/FVdelmIjFxRVokypLgxiUGeURamukwwITpIzNTE9L0f9z4Ky504SNu/Q+nUBMFTjLJmXPvyb33uCGjQhrGh5ZbW9/Y3MpvF3Z29/YP9MOjtggijkkLByzgXRcJwqhPWpJKRrohJ8hzGem4k+u03nkgXNDAv5PTkNgeGvl0SDGSSnL0etOpQktSjwjYdGKznPz+LA/JsevG94lz0Y+rq/RyPzU4etEoGTPAZWJmpAgyNBz9xRoEOPKILzFDQvRMI5R2jLikmJGkYEWChAhP0Ij0FPWRGmvHs1sTeKaUARwGXD1fwpn61xEjT4ip56rOdFGxWEvFVbVeJIdVO6Z+GEni4/mgYcSgDGAaHBxQTrBkU0UQ5lTtCvEYcYSliregQjAXT14m7XLJvCxVbivFWj2LIw9OwCk4Bya4AjVwAxqgBTB4BM/gDbxrT9qr9ql9zVtzWuY5Bv+gff8ANWSnGw==
S8
⇥ S12
⇥ Z8
3
⇥ Z12
2
G
G
G

29. 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
( )

30. https://www.sfu.ca/~jtmulhol/math302/puzzles-rc-cubology.html
3x x
The Fundamental Theorem of Cubology
sign(⇢) = sign( )
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
v1 + v2 + · · · + v8 = 0 (mod 3)
( )
( )
( )
(Parity)
0
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

31. (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

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

33. 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)

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

35. 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/

36. ࣍਺ ૯ঢ়ଶ਺

८ճஔ׵ͷੵͰॻ͚Δ
ճͰݩʹ໭Δ
ճͰݩʹ໭Δ
ճͰݩʹ໭Δ
ճͰݩʹ໭Δ

37. (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
( )

38. (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
( )

39. 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

40. GAP SageMath MacOS
\$ 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

41. ) 62
-'6-'6%#63%'#%36#%

42. ( ) ( )
( )
( )
( )
E

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

44. ( )
https://youtu.be/BVi_7pY6wtQ https://youtu.be/yjv7IlkCXMk
Speed Cubing
Speed Stacking

45. 40
( ) ( )
x x (Takahashi Method)
CFOP ( -look OLL 2-look PLL)
x x ( x x , x x , x x , )
(WCA 17 )
2x x ( )

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

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

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

49. ( !) ( !)
(U L U L)
(U R U R )
(U L U L)
! ! !
! ! !

50. 6
x
x
! !
! !

51. 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 )

52. ! !
! !
! !
! !

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

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

55. Daisy
Daisy Cross

56. F F

57. U

58. ( )

59. 40
( ) ( )
x x (Takahashi Method)
CFOP ( -look OLL 2-look PLL)
x x ( x x , x x , x x , )
(WCA 17 )
2x x ( )

60. 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

61. 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

62. = 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
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

63. = 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

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

65. 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

66. 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

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

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

69. 40
( ) ( )
x x (Takahashi Method)
CFOP ( -look OLL 2-look PLL)
x x ( x x , x x , x x , )
(WCA 17 )
2x x ( )

70. (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

71. 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

72. 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

73. 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

74. ( , , , , MagLev, )
MagLev
90
( )

75. ( + + )
IUUQTcstimer.net
csTimer
(Desktop)
Twisty Timer
(Android App)
DCTimer Lite
(iOS App)

76. 4
https://superliminal.com/cube/cube.htm
ASolver (Android app)
https://www.gancube.com/GAN-ROBOT

77. https://gigazine.net/news/20180308-rubiks-cube-solving-machine/
0.38
https://github.com/dicarlo236/cube-solver
(Two-Phase ) github

78. 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/
!

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

80. 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 ( )

81. ( ) ! !
( ) !
( ) !
( ) !
( ) !
U

82. PLL
OLL
by
by
by

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