• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 40,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

5 edge commutators

Theo Leinad

Member
Joined
Mar 31, 2017
Messages
54
WCA
2016CUEV04
Hello everyone
I'm in the seek of all the 5 edge commutators (EO preserve preferably) like this one:

R2 F2 R2 U' x 2

(all the cycle shifts are already taken into account)

So if you have any commutator (8 mover or fewer even better) is really well appreaciated.
 

Alsamoshelan

Member
Joined
Aug 29, 2018
Messages
8
Hello,

Here are 59 5-edge commutators finded by a program that I've created :

U' L D' U B' D
F' U' B' F R B
L' L2 D' U B' D U'
R' U U2 D B U D'
L' U' D F D' U
L' B L R' U' R
F U B F' L' B'
L B F' D' B' F
B' D U' L D' U
U' D B' D' U R
D' R L' F R' L
F' B U2 U' B' F R'
L' B' L R' U R
F R' L D' R L'
L' F' B D' B' F L2
R' L D L2 L R F'
R' B' R' L U L' R2
U R L L2 B' L R'
R' B' F2 F' D B F'
U D' B D U' L'
F' D' B' F L B' B2
U L R' F' R L'
D' R L' F R' L
R' F' B U F B'
L' U' D F D2 D U
R' L B L' R D'
B F' U F B' R'
D' U F' D U' R
D2 D' L R' B' L' R
B' F L' B F' D
U' U2 L U' D F' D'
U' R U2 D' U' F' D
R B' L R' U L'
F' U' D R D' U
U D' B' U' D L
U R D U' B' D'
U B F' L' F B'
U B' D U U2 L D'
D R U D' F' U'
B R L' D' R2 R L
B L' F B' U F'
U F' B L' B' F
R' U' R L' B L
F B2 B D' B F' R
L' R B' R' L U
L D' L' R F R'
U L R' F' L L2 R
L U' L' R B R'
L' F R' L D' R
D B' F L' F2 B F
L' R B R' L U'
U' D F2 F U D' L
D R' D U D2 F U'
R2 B F' U B' F R
B' F R' B F' U
B' D U' L D' U' U2
R2 R' L' F' L R' D
U' D L' D' U B
U' R' D D2 U F D
I don't know what they do exactly but these are 5-edges commutators.
This program searched between 1 and 7 moves. It would be easy for him to look for algorithms with longer moves if you want. Also it took about 2 minutes to find these 59 algorithms, if you want I could try to find much more 5-edges commutators like these ones. ;)
 

Alsamoshelan

Member
Joined
Aug 29, 2018
Messages
8
100 5-edges commutators with 6 moves :

1 : U' D R U D' F'
2 : D R' U D' F U'
3 : D L R' B' R L'
4 : U B' U' D L D'
5 : L U' D F' D' U
6 : L' F' B D B' F
7 : U' R D' U F' D
8 : L R' B R L' D'
9 : R' D U' B U D'
10 : L' R D' R' L B
11 : D U' R' D' U F
12 : R L' U R' L F'
13 : D B' F L' B F'
14 : F' D' U L D U'
15 : U D' L D U' F'
16 : F' R F B' D' B
17 : L R' D R L' F'
18 : L U' R L' B R'
19 : L' F' L R' D R
20 : U D' L D U' F'
21 : L R' F' R L' U
22 : D U' L' D' U B
23 : R' D' U F D U'
24 : D L R' B' R L'
25 : U L R' F' R L'
26 : R L' F' R' L D
27 : L' R U' R' L F
28 : U' D B' D' U R
29 : B' U B F' L' F
30 : L' R F' L R' D
31 : R B' F D' B F'
32 : L' U R' L F' R
33 : R L' F R' L D'
34 : F L R' D' L' R
35 : B D' F B' L F'
36 : B' R' L U L' R
37 : R' B' F D B F'
38 : U R D U' B' D'
39 : L R' U L' R B'
40 : R' D' R L' F L
41 : B' U' B F' L F
42 : L' U D' B D U'
43 : U' D F' U D' L
44 : D' L D U' F' U
45 : B' L B F' D' F
46 : L' B' F U B F'
47 : L R' F L' R U'
48 : F R F' B U' B'
49 : L R' F' R L' U
50 : U' B' F R B F'
51 : R' F' B U B' F
52 : B' L' F' B D F
53 : F L' B F' D B'
54 : U R L' B' L R'
55 : F R L' U' L R'
56 : D F U D' L' U'
57 : D U' B' D' U R
58 : U' R D' U F' D
59 : R' B L' R D' L
60 : B L' F B' U F'
61 : D' B' U' D L U
62 : D' F D U' R' U
63 : L R' F L' R U'
64 : D R' D' U F U'
65 : D' F B' L F' B
66 : F B' D B F' R'
67 : F B' R F' B U'
68 : D' F' B R F B'
69 : D' L' U' D F U
70 : B U' B' F R F'
71 : B' R L' D R' L
72 : U D' B' D U' L
73 : L' B R' L U' R
74 : R L' F L R' D'
75 : F' R' F B' D B
76 : F' U' D R U D'
77 : F' U' F B' R B
78 : D R L' F' L R'
79 : L F L' R U' R'
80 : U F U' D R' D'
81 : D B' F L' B F'
82 : R U' R' L F L'
83 : U' B U D' R' D
84 : R' L U' R L' B
85 : L' R U R' L F'
86 : U' L' U D' B D
87 : F' B D F B' L'
88 : F' B U' F B' R
89 : R B' L R' U L'
90 : B R' L U' L' R
91 : D' B D U' L' U
92 : D L' U D' B U'
93 : R L' F R' L D'
94 : D F' B R' B' F
95 : L' R F' L R' D
96 : L' D' L R' B R
97 : F L R' D' R L'
98 : R' D U' B U D'
99 : U F' D U' R D'
100 : R B' F D' F' B
 

Alsamoshelan

Member
Joined
Aug 29, 2018
Messages
8
I will find a way to test the preservation of EO. ;)

Before that, some other algorithms :

0 algorithm with a height < 6 founded.

Equal to 7 moves (but take care : some of these ones are "fake" 7-moves as #3) :
1 : U D2 L D U' F' D
2 : L R F' L R' D L2
3 : D R' U D' F U U2
4 : R2 U' L' R B L R
5 : U F' B L' B B2 F
6 : B' F D' B2 F' B' R
7 : F' B U B' F' F2 R'
8 : D L R' B B2 L' R
9 : D2 L' R F R' L D
10 : F D' U' U2 L' U' D
11 : D U' L D D2 U B'
12 : R B' F' B2 U' F B'
13 : D' F' B' B2 R F B'
14 : R' F' R' R2 L' U L
15 : R L B' L R' U L2
16 : L2 R' L' B L' R D'
17 : L' B' L R' U R' R2
18 : L' D R L' F' L2 R'
19 : U' R L' B' B2 L R'
20 : B F' R B2 B F D'
21 : D L' R F' L R2 R
22 : B2 L B' F U' F' B'
23 : B U D' R' U' D2 D'
24 : F' U D D2 L D U'
25 : B' R' F B F2 U F
26 : R' U D' F D U U2
27 : D2 D B F' R F B'
28 : F' R' L D' D2 R L'
29 : L2 B' R' L U L R
30 : R' B' L' R' R2 D L
31 : U' B B2 U D' R D
32 : D' F B' L B' F' B2
33 : U' B F' L F B2 B
34 : L' U' D F D' U' U2
35 : B2 F' U' B' F R B'
36 : U L R' F' L' R' R2
37 : B L F' B D' F B2
38 : F B2 B U F' B L'
39 : B L B F' D' B2 F
40 : F D' U L' D' U' D2
41 : R F B' D' B2 B' F'
42 : U2 D U L U D' B'
43 : B F' R B2 F B D'
44 : B' F' R B F' U' F2
45 : R' U' L2 L R B L
46 : B F2 L B' F U' F
47 : U D' R U D U2 B'
48 : L R' B L' R2 R' D'
49 : F' B U F B2 B R'
50 : B R L' D' R2 R L
51 : L' D L R' B' R' R2
52 : L L2 R D' L R' B
53 : F L B F' D' B2 B
54 : B D U D2 R' D U'
55 : B F D B F' R' B2
56 : U' U2 F D U' R' D'
57 : B F' R B B2 F D'
58 : U2 U' R' L F' L' R
59 : U' D' D2 L' U D' B
60 : B2 F' B' D' B' F L
61 : L U U2 D F' D' U
62 : D U' L2 L' D' U B'
63 : D U' B' U2 D' U' R
64 : D' L D' U B' U' D2
65 : B' F D B F F2 R'
66 : L B F' D B' F L2
67 : B' U' D L U D D2
68 : R D' U F' U' D' D2
69 : B' F2 U' B F' L F'
70 : R' D U' B U D D2
71 : L' F2 B F D B' F
72 : U D' L2 L U' D F
73 : B' F D F' B R R2
74 : U D' L' L2 U' D F'
75 : R' D' U F' F2 D U'
76 : D' U F F2 U' D R
77 : U R U D U2 B' D'
78 : R L U L R' F' L2
79 : L2 L B F' D B' F
80 : U' D R' D' U' U2 F
81 : R' U' D B' B2 D' U
82 : R2 L U L' R B' R
83 : U' R L' B L2 L' R'
84 : L' B' F U' U2 B F'
85 : D' U R' R2 D U' B'
86 : R2 U R L' B' L R
87 : L' D' U B D2 U' D'
88 : F' B' F2 L B F' D'
89 : F F2 R' B' F D B
90 : L2 F' B D B' F L
91 : B' F D2 D B F' R
92 : L L2 R F' R' L D
93 : R L' F F2 R' L D
94 : U' D L2 L' D' U B'
95 : R D2 D' L R' B' L'
96 : D' D2 U' L' D' U B
97 : L L2 B F' D F B'
98 : U' F U' D' U2 L' D
99 : B D' F B2 B L F'
100 : F B2 L B F' D' B
Equal to 8 moves (but apparently there are a lot of fake 8-moves) :
1 : F' U U' R' L D L' R
2 : R' B F' U F B' U U'
3 : L' F R2 R2 L R' D' R
4 : F R' L' L2 D' R L L2
5 : R L' L2 L2 B' L R' U
6 : L' L B' L' F' B D F
7 : R' L D L2 R L2 L' F'
8 : U' D2 D' R D' U2 U' F'
9 : D' L R' U L' R B' D
10 : L U U2 L2 R L B R'
11 : F' R2 R2 D F B' L' B
12 : F U' B F' F2 F2 L B'
13 : R2 D2 U' D' B D' U R
14 : F2 B D' F2 B' F' L F
15 : L' R D R' F F' L B'
16 : L F B' D' F' B L' R
17 : F B F2 R' F2 B' F' D
18 : L R' B' U' U R L' D
19 : B F' L' F2 F2 B' F U
20 : D2 U L U' D2 D' F' D
21 : B' L' D2 D2 B F' D F
22 : U L D2 D' U U2 F' D'
23 : D' D2 B' F' F2 L' F' B
24 : R2 U' D F D' U R2 L'
25 : L2 L L2 B' F U' F' B
26 : F B R' B' F D' D2 F2
27 : L' F' B D F' F' B' F'
28 : B' F L B F' U2 U2 D'
29 : F2 B2 R' F B' D B' F
30 : D' U F' U' D R2 R2 R
31 : U2 U' B U U2 D L' D'
32 : F2 U2 F2 R' F2 U2 F2 R'
33 : R D U' B' U2 U' D2 D
34 : R' L' F' R' L D R R
35 : R' L B L2 R L2 L' D'
36 : R2 L' R U' R L' B L2
37 : U' F U2 U' D' L L2 D
38 : L' R F R L' R2 L2 D'
39 : D L' D U' D2 U2 B U'
40 : U2 U' D' R U' D B B2
41 : R' R2 L R2 F L' R U'
42 : R' R R' F R L' U' L
43 : D2 D U' F' D U' R U2
44 : U R2 L' R L2 F' L' R
45 : B' U D' R L2 L2 D U'
46 : B2 B F R' F' B' B2 U
47 : B U D' B B' R' U' D
48 : D2 D' F' B R F B' D2
49 : B F F' L' R D' R' L
50 : D' F' B L2 L2 R B' F
51 : R2 R2 B D' U R' D U'
52 : D' R U U2 D2 D' B' U
53 : L' D U' F D U' D2 U2
54 : R U2 U R' L F L2 L
55 : R2 R F' R L' U L' L2
56 : R' D' D2 R2 L' R' F' L
57 : U D' D2 F' D' U L U2
58 : D R D D2 U F F2 U'
59 : U' R2 R2 F' B L B' F
60 : L' D U2 U F D' U' U2
61 : L' U2 U D F' D' U L2
62 : D2 U' D' B' D' U R2 R'
63 : R B B' F' R' L D L'
64 : R' R2 U2 U R' L F L'
65 : F' D' B' F L B D D'
66 : F' F F' B L B' F U'
67 : L U' D U U' F' U D'
68 : U2 B' U' U2 D' R U D
69 : F R' R2 L' U' L' R' L2
70 : L' B R' B' F D F' L
71 : D F B' D2 D2 L' B F'
72 : U D' F F2 U2 D U R
73 : R2 R' L' D' L R R2 B
74 : U' D B' F2 F2 U D' R
75 : L' R F R' L F' F D'
76 : F' L' B' F L L' U B
77 : F2 B F R' B' F D' D2
78 : R2 F R L' U' L R' R2
79 : B U B' F L' R' L F'
80 : D F2 B F R' B F B2
81 : L R R2 D' D2 R L' F'
82 : B F' R F B' U D' U'
83 : F' F2 D' U2 U' L' U' D
84 : L' D U' R' D' U F L
85 : D U' R D' D' U D F'
86 : F D2 D2 R B F' U' B'
87 : D' U F' D' U L D2 U2
88 : R B D' U R' D U' R'
89 : R B R' L U' B2 B2 L'
90 : R' L B L' F' F R D'
91 : L2 L2 R' U L' R B' L
92 : R D U U2 B B2 D' U
93 : U B U D' U2 D2 L' D'
94 : B' U D' R2 R' U2 D U
95 : F' D U' R' D2 D U F2
96 : U' D' U2 R' U' D2 D' B
97 : F' R L' U R2 R' R2 L
98 : B D2 D U R' U U2 D
99 : L2 B' F U F' B L2 L'
100 : U' B2 B F R B' F' B2
Equal to 9 moves (same remark) :
1 : U2 F2 F2 U F' U D' L D
2 : D2 B' D U D2 R U D' U2
3 : F L' R U' L' L2 U U' R'
4 : L D D2 U2 U U2 B' U' D
5 : F2 F' D U' R' D2 D' D2 U
6 : D U' B' F2 F' B U D' L'
7 : U' B' D' U L L2 R L D
8 : R L' U2 U' R' R2 L R2 F'
9 : F2 F2 L' B' F U F' B2 B'
10 : R' L2 R2 L U' L R' F2 F'
11 : R2 R' L' B R' U U' L U'
12 : D D D U F' U' D' D2 R
13 : B2 B2 D' F' B R B' F2 F'
14 : L B' L2 L R D R2 R' R2
15 : U' D F B B2 L' B F' U
16 : U' U2 D' U' F' D U' R U
17 : D' U D R L R2 F' L' R
18 : L' R2 F B' U2 U' B F' R2
19 : D L2 L2 U L U' D F' D2
20 : R B L L2 R' L L U' L'
21 : R' L' U2 U' L' R' R2 B' L2
22 : U' F B F2 R' B' F U D
23 : U2 R' D2 U' D U2 F U D
24 : F B' L L2 R R' B F' D
25 : U F B' R' B2 F' B' B' B
26 : R2 R' F' L2 L2 B U' F B'
27 : U' F F' B B2 U D' R D
28 : L' R' L F' B U F2 B' F'
29 : R D R L' L2 R2 B' L2 L
30 : F F2 B L' F L L' B' U
31 : F B B2 F2 L' F' B D F2
32 : D' R R2 L D L' R F' D
33 : L D D' B B2 F U' F' B
34 : U L D U' F' R R2 R D'
35 : R B L' L2 R' U' L' F' F
36 : R L' U U2 L B2 B2 R' F
37 : U F U' L L' D R' D D2
38 : D2 U D L' U U2 D2 D' F
39 : R2 R R2 B F' U' B' F2 F'
40 : F2 F L' R' L2 D R' R2 L'
41 : U D' R U2 U' D' D2 U2 B'
42 : U' L U2 U D F' U U D'
43 : F' D' B' F2 B2 F R F2 B'
44 : D' R U' D F F' B B2 U
45 : U B' U2 U D2 D' L D D2
46 : D' D2 B' F L' D' D F' B
47 : D' B F' L2 R L L F B'
48 : R' L' L L B' B2 L' R D'
49 : U' D' R' U' D F2 F2 B U2
50 : D' D2 F' F U' B U D' R'
Eventually, algorithms with a random height between 6 and 12 :
1 : D R' L B' L' R
2 : R B R' U U' L U U2 L'
3 : F B' L B F' D'
4 : B' F R D' D B F' U'
5 : D' D L L' U B' F R' B F'
6 : F' R' U' D B U D' F
7 : B' U D' R D U'
8 : D U' L D' U B'
9 : U' R R' F2 F' U' U B' R' F' B U2
10 : U2 U D B' U D' R
11 : U' L' R' R B L R' U' R U
12 : R' U U' B2 B' F B2 D F' B
13 : B U D' R' D U'
14 : U L' D' U B U' U D U2
15 : F2 B B2 R F B' D' B2 F
16 : U' L' U D' B D2 D'
17 : D2 D' L2 L' D' U B' U'
18 : B F' U' B' F R
19 : D' B F' R B' F
20 : R L' D R' L B'
21 : R L B R L' D' R2
22 : R' D R' L B' L' R2
23 : B' L B' F U' F' B2
24 : F' L' R U' R' L F2
25 : R D2 U D F' U' D
26 : F' B' R' B' R R' F D B B L2 L2
27 : D' L R' B L' R
28 : L' F' R R R2 R L' U R' L2
29 : D' R L' F R' R2 L R2
30 : L' R' B2 B L R' U R2
31 : B' U' B F' L F' F2
32 : B' L' B F' D F
33 : L R' F' L' R U
34 : R' U' D B F' F U D'
35 : D' L' R2 R' F R' L' L2
36 : D' B' F' F2 L F' U2 U2 B' B2
37 : F' B R' F' F R2 F B B2 D'
38 : D B B2 B2 D' U R' U'
39 : F F' U' L L2 R B R' L
40 : B' L' F' B D F
41 : B B2 F2 U U' F' R' B F' U
42 : R U D' F2 F D U'
43 : B' D F' B R R2 F
44 : R2 R L D' L' R F
45 : U' B' D' U R D
46 : R D' L' R F R2 L
47 : B L R' U2 U L' D' D' D2 R
48 : L B' R L' D R'
49 : B' R2 R' B F' U' F2 F'
50 : B D D2 B' F L B F2 F B'
51 : U' L' D' U B D
52 : D' U2 D2 U F' D U D2 L
53 : B' R F2 B' F' D' F' B2
54 : F R2 R L D' R L' U' B' B U
55 : L' R' D R L' F' L L
56 : R2 R2 R' D2 U D F' U2 U D R2
57 : D U D2 R' D2 U' D' B
58 : L2 F' L R' D' D2 L R2 R'
59 : L' D' L' L2 R' B R
60 : R L' F' R' U' U L D
61 : D' U B B2 U' D L
62 : R L' B' L R' U' U2
63 : F F B' R2 R' B F' U' F'
64 : D' U2 U U2 B' D U' L
65 : D' D2 B' U D2 D' D' D D2 R U'
66 : L' U F' F D' B D U'
67 : B B' R2 L R D' R L' F
68 : B' L' R D R L' R L2 R
69 : R' R2 D2 D' U' B' D' U
70 : R R' F' B R' F B' D
71 : D U' F2 B' F2 D' U R
72 : D2 D2 B' F' F2 U B F' L'
73 : L' L D L U D' B' U'
74 : R' R U2 D' U' F' U' D R
75 : F R' B' B' F' B' U B'
76 : U' R L2 L' R2 F R L'
77 : D' B D2 U' D' L' U
78 : U B2 B U' D L D'
79 : D R B R' L U2 U L' D'
80 : F F2 B D' B2 B F L
81 : U' B' U' U2 D' R D
82 : L' B' F U B' B2 B' F F2 B
83 : F F2 D F B' L' B
84 : R' B' F D B' F' B2
85 : R' D' L' R F L' L2
86 : D' R L' D R' L' L2 B' D
87 : D' R L' F L' R' L2
88 : B' F U B F' L'
89 : D U' F' D' U L
90 : U D' F U' D R'
91 : L' R' F L R' D' R2
92 : U2 R' U D' F U D
93 : F' B L' F' F2 B' U U' U
94 : D' U2 B2 B' B' U D' D' B' U D' R
95 : D' L' R F' F2 R' L2 L'
96 : D U' L' D' U B
97 : U' D B2 B U D' R
98 : U D' R D U' B'
99 : U L R' F' R L'
100 : R F B' D L' L D2 L2 L2 F F2 B
My program is very primitive yet, I will improve it in order to avoid fake n-moves and to check EO preservation. ;)
 
Last edited:

Alsamoshelan

Member
Joined
Aug 29, 2018
Messages
8
I thought that there is a sort of "universal" conventional definition : an edge is oriented if and only if we can put it into its original slot without F, F', B and B' moves.
But after all, it's just a convention and maybe the author of this threat uses another one.
 
Joined
Sep 3, 2017
Messages
105
Location
USA
I thought that there is a sort of "universal" conventional definition : an edge is oriented if and only if we can put it into its original slot without F, F', B and B' moves.
But after all, it's just a convention and maybe the author of this threat uses another one.

Another definition of edge flip counts the number of quarter turns required to return the edge piece to the solved position and orientation. Even flip requires an even number of q-turns. Odd flip requires and odd number of q-turns.
 

abunickabhi

Member
Joined
Jan 9, 2014
Messages
6,687
Location
Yo
WCA
2013GHOD01
YouTube
Visit Channel
Hello,

Here are 59 5-edge commutators finded by a program that I've created :

U' L D' U B' D
F' U' B' F R B
L' L2 D' U B' D U'
R' U U2 D B U D'
L' U' D F D' U
L' B L R' U' R
F U B F' L' B'
L B F' D' B' F
B' D U' L D' U
U' D B' D' U R
D' R L' F R' L
F' B U2 U' B' F R'
L' B' L R' U R
F R' L D' R L'
L' F' B D' B' F L2
R' L D L2 L R F'
R' B' R' L U L' R2
U R L L2 B' L R'
R' B' F2 F' D B F'
U D' B D U' L'
F' D' B' F L B' B2
U L R' F' R L'
D' R L' F R' L
R' F' B U F B'
L' U' D F D2 D U
R' L B L' R D'
B F' U F B' R'
D' U F' D U' R
D2 D' L R' B' L' R
B' F L' B F' D
U' U2 L U' D F' D'
U' R U2 D' U' F' D
R B' L R' U L'
F' U' D R D' U
U D' B' U' D L
U R D U' B' D'
U B F' L' F B'
U B' D U U2 L D'
D R U D' F' U'
B R L' D' R2 R L
B L' F B' U F'
U F' B L' B' F
R' U' R L' B L
F B2 B D' B F' R
L' R B' R' L U
L D' L' R F R'
U L R' F' L L2 R
L U' L' R B R'
L' F R' L D' R
D B' F L' F2 B F
L' R B R' L U'
U' D F2 F U D' L
D R' D U D2 F U'
R2 B F' U B' F R
B' F R' B F' U
B' D U' L D' U' U2
R2 R' L' F' L R' D
U' D L' D' U B
U' R' D D2 U F D
I don't know what they do exactly but these are 5-edges commutators.
This program searched between 1 and 7 moves. It would be easy for him to look for algorithms with longer moves if you want. Also it took about 2 minutes to find these 59 algorithms, if you want I could try to find much more 5-edges commutators like these ones. ;)


All the algs are pretty bad here.
Here is the one that I have hand-crafted:
https://github.com/abunickabhi/5style/blob/master/5-style-edge.pdf

https://algsets.jonatanklosko.com/alg-sets/5c712ae91a3b515e307eea47
 
Joined
Sep 3, 2017
Messages
105
Location
USA
I did some back of the envelope calculations:

The number of sets of 5 edge cubies:

12! / 7! = 95,040

Each of these edge sets may be permuted:

5! / 2 x 2^4 = 60 x 16 = 960

giving:

95040 x 960 = 91,238,400 edge permutations of five or fewer cubies.

similarly

12! / 8! x 4!/2 x 2^3 = 1,140,480 edge permutations of four or fewer cubies.

Thus

91,238,400 - 1,140,480 = 90,097,920 cube positions with five unsolved edge cubies.

This is not that big a state space that modern computers could not completely explore it.

Woops, the above is in error. The order one picks the 5 cubies to scramble doesn't matter:

The number of sets of 5 edge cubies:

12! /(7! x 5!) = 792

Each of these edge sets may be permuted:

5! / 2 x 2^4 = 60 x 16 = 960

giving:

792 x 960 = 760,320 edge permutations of five or fewer cubies.

similarly

12! /( 8! * 4!) x 4!/2 x 2^3 = 47,520 edge permutations of four or fewer cubies.

Thus

760,320 - 47,520 = 712,800 cube positions with five unsolved edge cubies.
 
Last edited:

abunickabhi

Member
Joined
Jan 9, 2014
Messages
6,687
Location
Yo
WCA
2013GHOD01
YouTube
Visit Channel
You have left out some cases.

Working with the sticker logic,
there are a total of 24 edge stickers.
Assuming buffer to buffer, we have 22 targets for the first edge to move to,
20 targets for the second edge to move to,
18 targets for the third edge to move to,
16 targets for the fourth edge to move to,
giving us 22x20x18x16= 126,720!

As simple as that.

In your second calculation, there is no need of, 5! /2 as 11C4 (=330) takes care of all the cases.
All it is 11C4 since I am assuming buffer(DF) to be the reference piece.

126,720 comes up with your method as: 11C4 x 4! x 2^4 = 126, 720

(Keep in mind, I am not accounting for flipped edge cases, and dedges cases in big cubes, the number would be much higher there, but still not as high as your 712,800 which is just astronomical.) With mirrors and inverses, the number of cases in 5-style becomes like ~40k which is manageable with 2 years of dedicated training. Since I have to generate optimal fingertrickable algs for myself, it will take me 4 years. And I started out in 2016 yo.

Looks like your intention was to just bump up the numbers and make 5-style sound harder. :|
The number 712,800 is close to 5 times 126,720, so there are 5 times more cases if we try to go for full floating buffer 5-style.
Even I would find complete floating buffer 5-style ridiculously hard and never speculate it or make a SS thread on it lol.
 
Joined
Sep 3, 2017
Messages
105
Location
USA
You have left out some cases.

Working with the sticker logic,
there are a total of 24 edge stickers.
Assuming buffer to buffer, we have 22 targets for the first edge to move to,
20 targets for the second edge to move to,
18 targets for the third edge to move to,
16 targets for the fourth edge to move to,
giving us 22x20x18x16= 126,720!

As simple as that.

In your second calculation, there is no need of, 5! /2 as 11C4 (=330) takes care of all the cases.
All it is 11C4 since I am assuming buffer(DF) to be the reference piece.

126,720 comes up with your method as: 11C4 x 4! x 2^4 = 126, 720

(Keep in mind, I am not accounting for flipped edge cases, and dedges cases in big cubes, the number would be much higher there, but still not as high as your 712,800 which is just astronomical.) With mirrors and inverses, the number of cases in 5-style becomes like ~40k which is manageable with 2 years of dedicated training. Since I have to generate optimal fingertrickable algs for myself, it will take me 4 years. And I started out in 2016 yo.

Looks like your intention was to just bump up the numbers and make 5-style sound harder. :|
The number 712,800 is close to 5 times 126,720, so there are 5 times more cases if we try to go for full floating buffer 5-style.
Even I would find complete floating buffer 5-style ridiculously hard and never speculate it or make a SS thread on it lol.

You are correct. My calculation includes cases which are not 5 cycles. There are three cycles + two cubies flipped in place, etc. The requirement to preserve edge orientation is ambiguous since that depends on how one defines edge orientation.
 
Joined
Sep 3, 2017
Messages
105
Location
USA
I did some back of the envelope calculations:

The number of sets of 5 edge cubies:

12! / 7! = 95,040

Each of these edge sets may be permuted:

5! / 2 x 2^4 = 60 x 16 = 960

giving:

95040 x 960 = 91,238,400 edge permutations of five or fewer cubies.

similarly

12! / 8! x 4!/2 x 2^3 = 1,140,480 edge permutations of four or fewer cubies.

Thus

91,238,400 - 1,140,480 = 90,097,920 cube positions with five unsolved edge cubies.

This is not that big a state space that modern computers could not completely explore it.

Woops, the above is in error. The order one picks the 5 cubies to scramble doesn't matter:

The number of sets of 5 edge cubies:

12! /(7! x 5!) = 792

Each of these edge sets may be permuted:

5! / 2 x 2^4 = 60 x 16 = 960

giving:

792 x 960 = 760,320 edge permutations of five or fewer cubies.

similarly

12! /( 8! * 4!) x 4!/2 x 2^3 = 47,520 edge permutations of four or fewer cubies.

Thus

760,320 - 47,520 = 712,800 cube positions with five unsolved edge cubies.

I knocked together some code today and enumerated the set of cube states with five unsolved edge cubies. As it turns out the above calculation is not valid. There are 462,528 cube states with 5 unsolved edges not 712,800. The latter number includes a lot of duplicates of states with less than 5 unsolved cubies.

The 462,528 states reduce to 19,272 symmetry equivalence classes by the 24 cubic rotation symmetries. I ran representative elements of these classes through an optimal solver giving the following results. There are none less than 6 turns from solved and all may be solved in 15 or fewer moves. The 5-Cycles column are those instances where all five cubies are moved from their home position. That is, none of the five are simply flipped in place.
DepthElementsReduced(O)5-Cycles


6​



192​



8​



8​


7​

480​

20​

20​

8​

2,112​

88​

88​

9​

5,472​

228​

228​

10​

25,632​

1,068​

958​

11​

58,320​

2,430​

2,256​

12​

138,384​

5,766​

4,700​

13​

143,496​

5,979​

3,914​

14​

81,384​

3,391​

496​

15​

7,056​

294​

4​

Sum​

462,528​

19,272​

12,672​



Here are representative members of the four depth 15 5-Cycles. None of these has any symmetry so they each represent a 24 element symmetry equivalence class whose elements differ only in the orientation of the cube to which the maneuver is applied.

F' R F R' F2 R' U F L F L' F2 U' R F2 15f
D R F R2 D2 R2 D2 R' B R' B' D2 R' F' D' 15f
U R U L' B2 R2 B R L' U B R' B' U' L2 15f
D R' D L' D2 R2 D2 R2 B R B' L R2 B2 D2 15f
 
Last edited:

abunickabhi

Member
Joined
Jan 9, 2014
Messages
6,687
Location
Yo
WCA
2013GHOD01
YouTube
Visit Channel
I knocked together some code today and enumerated the set of cube states with five unsolved edge cubies. As it turns out the above calculation is not valid. There are 462,528 cube states with 5 unsolved edges not 712,800. The latter number includes a lot of duplicates of states with less than 5 unsolved cubies.

The 462,528 states reduce to 19,272 symmetry equivalence classes by the 24 cubic rotation symmetries. I ran representative elements of these classes through an optimal solver giving the following results. There are none less than 6 turns from solved and all may be solved in 15 or fewer moves. The 5-Cycles column are those instances where all five cubies are moved from their home position. That is, none of the five are simply flipped in place.
DepthElementsReduced(O)5-Cycles


6​



192​



8​



8​



7​



480​



20​



20​



8​



2,112​



88​



88​



9​



5,472​



228​



228​



10​



25,632​



1,068​



958​



11​



58,320​



2,430​



2,256​



12​



138,384​



5,766​



4,700​



13​



143,496​



5,979​



3,914​



14​



81,384​



3,391​



496​



15​



7,056​



294​



4​



Sum​



462,528​



19,272​



12,672​





Here are representative members of the four depth 15 5-Cycles. None of these has any symmetry so they each represent a 24 element symmetry equivalence class whose elements differ only in the orientation of the cube to which the maneuver is applied.

F' R F R' F2 R' U F L F L' F2 U' R F2 15f
D R F R2 D2 R2 D2 R' B R' B' D2 R' F' D' 15f
U R U L' B2 R2 B R L' U B R' B' U' L2 15f
D R' D L' D2 R2 D2 R2 B R B' L R2 B2 D2 15f

Nice work, in BLD however, using cube symmetry and reducing it just 12,672 cases won't work. Since each alg needs to be fingertricky, rotationless and from [R U D F M S E] set, the number of cases is 126,720/2(Inverses) = 63,360. (Some Mirror Algs are slow to execute)
Also the target shooting should be consistent which only one visit to each piece.

In the 15 mover, F' R F R' F2 R' U F L F L' F2 U' R F2, by BLD tracing, there will always be a cycle break from a buffer.
 
Joined
Sep 3, 2017
Messages
105
Location
USA
I knocked together some code today and enumerated the set of cube states with five unsolved edge cubies. As it turns out the above calculation is not valid. There are 462,528 cube states with 5 unsolved edges not 712,800. The latter number includes a lot of duplicates of states with less than 5 unsolved cubies.

The 462,528 states reduce to 19,272 symmetry equivalence classes by the 24 cubic rotation symmetries. I ran representative elements of these classes through an optimal solver giving the following results. There are none less than 6 turns from solved and all may be solved in 15 or fewer moves. The 5-Cycles column are those instances where all five cubies are moved from their home position. That is, none of the five are simply flipped in place.
DepthElementsReduced(O)5-Cycles


6​



192​



8​



8​



7​



480​



20​



20​



8​



2,112​



88​



88​



9​



5,472​



228​



228​



10​



25,632​



1,068​



958​



11​



58,320​



2,430​



2,256​



12​



138,384​



5,766​



4,700​



13​



143,496​



5,979​



3,914​



14​



81,384​



3,391​



496​



15​



7,056​



294​



4​



Sum​



462,528​



19,272​



12,672​







Here are representative members of the four depth 15 5-Cycles. None of these has any symmetry so they each represent a 24 element symmetry equivalence class whose elements differ only in the orientation of the cube to which the maneuver is applied.

F' R F R' F2 R' U F L F L' F2 U' R F2 15f
D R F R2 D2 R2 D2 R' B R' B' D2 R' F' D' 15f
U R U L' B2 R2 B R L' U B R' B' U' L2 15f
D R' D L' D2 R2 D2 R2 B R B' L R2 B2 D2 15f

I extended the above analysis to the Quarter Turn Metric and the Slice Turn Metric.

(I'm done trying to use the table editor here. You'll have to copy and paste into a spreadsheet if you're interested. The columns are the same as above.)

QTM

6 192 8 8
8 1,536 64 64
10 13,248 552 552
12 79,728 3,322 3,248
14 211,296 8,804 7,590
16 147,744 6,156 1,210
18 8,784 366 0
Sum 462,528 19,272 12,672


STM

4 96 4 4
5 288 12 12
6 1,632 68 68
7 5,424 226 208
8 20,064 836 758
9 53,568 2,232 1,976
10 136,464 5,686 4,586
11 158,496 6,604 4,204
12 78,432 3,268 852
13 8,064 336 4
Sum 462,528 19,272 12,672

And here are the depth 13s 5-Cycles:

R L F MU2 F' U F' MU2 F U MR U2 L2 • CR' 13s
R' D R' D' MR' D MR D' MR' D L B' R • CR 13s
R' F L' F' MR F2 R MU L' U' L D' F • CR' CF' 13s
R U F' U' B MU2 F' L F L' MU2 MF' U' • CF 13s
 
Last edited:

iheartgeo

Member
Joined
Jul 9, 2018
Messages
15
Hello,

Here are 59 5-edge commutators finded by a program that I've created :

U' L D' U B' D
F' U' B' F R B
L' L2 D' U B' D U'
R' U U2 D B U D'
L' U' D F D' U
L' B L R' U' R
F U B F' L' B'
L B F' D' B' F
B' D U' L D' U
U' D B' D' U R
D' R L' F R' L
F' B U2 U' B' F R'
L' B' L R' U R
F R' L D' R L'
L' F' B D' B' F L2
R' L D L2 L R F'
R' B' R' L U L' R2
U R L L2 B' L R'
R' B' F2 F' D B F'
U D' B D U' L'
F' D' B' F L B' B2
U L R' F' R L'
D' R L' F R' L
R' F' B U F B'
L' U' D F D2 D U
R' L B L' R D'
B F' U F B' R'
D' U F' D U' R
D2 D' L R' B' L' R
B' F L' B F' D
U' U2 L U' D F' D'
U' R U2 D' U' F' D
R B' L R' U L'
F' U' D R D' U
U D' B' U' D L
U R D U' B' D'
U B F' L' F B'
U B' D U U2 L D'
D R U D' F' U'
B R L' D' R2 R L
B L' F B' U F'
U F' B L' B' F
R' U' R L' B L
F B2 B D' B F' R
L' R B' R' L U
L D' L' R F R'
U L R' F' L L2 R
L U' L' R B R'
L' F R' L D' R
D B' F L' F2 B F
L' R B R' L U'
U' D F2 F U D' L
D R' D U D2 F U'
R2 B F' U B' F R
B' F R' B F' U
B' D U' L D' U' U2
R2 R' L' F' L R' D
U' D L' D' U B
U' R' D D2 U F D
I don't know what they do exactly but these are 5-edges commutators.
This program searched between 1 and 7 moves. It would be easy for him to look for algorithms with longer moves if you want. Also it took about 2 minutes to find these 59 algorithms, if you want I could try to find much more 5-edges commutators like these ones. ;)

Thanks for producing these algs! I would like to understand the structure of 5-cycles. I know how to construct 3-cycles on the fly because I have internalized their structure, and would like to be able to do the same with 5-cycles. Is anyone else interested in developing the theory with me?
 

iheartgeo

Member
Joined
Jul 9, 2018
Messages
15
100 5-edges commutators with 6 moves :

1 : U' D R U D' F'
2 : D R' U D' F U'
3 : D L R' B' R L'
4 : U B' U' D L D'
5 : L U' D F' D' U
6 : L' F' B D B' F
7 : U' R D' U F' D
8 : L R' B R L' D'
9 : R' D U' B U D'
10 : L' R D' R' L B
11 : D U' R' D' U F
12 : R L' U R' L F'
13 : D B' F L' B F'
14 : F' D' U L D U'
15 : U D' L D U' F'
16 : F' R F B' D' B
17 : L R' D R L' F'
18 : L U' R L' B R'
19 : L' F' L R' D R
20 : U D' L D U' F'
21 : L R' F' R L' U
22 : D U' L' D' U B
23 : R' D' U F D U'
24 : D L R' B' R L'
25 : U L R' F' R L'
26 : R L' F' R' L D
27 : L' R U' R' L F
28 : U' D B' D' U R
29 : B' U B F' L' F
30 : L' R F' L R' D
31 : R B' F D' B F'
32 : L' U R' L F' R
33 : R L' F R' L D'
34 : F L R' D' L' R
35 : B D' F B' L F'
36 : B' R' L U L' R
37 : R' B' F D B F'
38 : U R D U' B' D'
39 : L R' U L' R B'
40 : R' D' R L' F L
41 : B' U' B F' L F
42 : L' U D' B D U'
43 : U' D F' U D' L
44 : D' L D U' F' U
45 : B' L B F' D' F
46 : L' B' F U B F'
47 : L R' F L' R U'
48 : F R F' B U' B'
49 : L R' F' R L' U
50 : U' B' F R B F'
51 : R' F' B U B' F
52 : B' L' F' B D F
53 : F L' B F' D B'
54 : U R L' B' L R'
55 : F R L' U' L R'
56 : D F U D' L' U'
57 : D U' B' D' U R
58 : U' R D' U F' D
59 : R' B L' R D' L
60 : B L' F B' U F'
61 : D' B' U' D L U
62 : D' F D U' R' U
63 : L R' F L' R U'
64 : D R' D' U F U'
65 : D' F B' L F' B
66 : F B' D B F' R'
67 : F B' R F' B U'
68 : D' F' B R F B'
69 : D' L' U' D F U
70 : B U' B' F R F'
71 : B' R L' D R' L
72 : U D' B' D U' L
73 : L' B R' L U' R
74 : R L' F L R' D'
75 : F' R' F B' D B
76 : F' U' D R U D'
77 : F' U' F B' R B
78 : D R L' F' L R'
79 : L F L' R U' R'
80 : U F U' D R' D'
81 : D B' F L' B F'
82 : R U' R' L F L'
83 : U' B U D' R' D
84 : R' L U' R L' B
85 : L' R U R' L F'
86 : U' L' U D' B D
87 : F' B D F B' L'
88 : F' B U' F B' R
89 : R B' L R' U L'
90 : B R' L U' L' R
91 : D' B D U' L' U
92 : D L' U D' B U'
93 : R L' F R' L D'
94 : D F' B R' B' F
95 : L' R F' L R' D
96 : L' D' L R' B R
97 : F L R' D' R L'
98 : R' D U' B U D'
99 : U F' D U' R D'
100 : R B' F D' F' B

The first alg is equivalent to [E’ , F].
 
Top