Talk:Superflip
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QTM
[edit]The 24 moves quarter turn solution should be added if someone knows a source for it. --93.220.255.136 (talk) 20:18, 8 August 2016 (UTC)
Miscellaneous
[edit]Let S be the superflip.
(1) For any alg Y we have that Y.S.Y' = I.
(2) Did anybody notice that if S = X.T is a superflip, where X is an alg and T is a turn, then T.X is also a superflip?
Proof of (1) is a restatement of the fact that {S, I} is the center of the Cube group.
Proof of (2) follows from (1), as follows: consider that with S = X.T, we have that I.S = (T.T').S = T.(T'.S) = T.(S.T') = T.(X.T).T' = (T.X).(T.T') = (T.X).I = T.X. Here, equality means that we are talking about the same element of the Cube group, but not the same alg to achieve it!
Hence, from the article, we have the following other superflip algs:
U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2 (original)
F2 U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2
U2 F2 U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2
B2 U2 F2 U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L
L B2 U2 F2 U R2 F B R B2 R U2 L B2 R U' D' R2 F R'
R' L B2 U2 F2 U R2 F B R B2 R U2 L B2 R U' D' R2 F
F R' L B2 U2 F2 U R2 F B R B2 R U2 L B2 R U' D' R2
R2 F R' L B2 U2 F2 U R2 F B R B2 R U2 L B2 R U' D'
D' R2 F R' L B2 U2 F2 U R2 F B R B2 R U2 L B2 R U'
U' D' R2 F R' L B2 U2 F2 U R2 F B R B2 R U2 L B2 R
R U' D' R2 F R' L B2 U2 F2 U R2 F B R B2 R U2 L B2
B2 R U' D' R2 F R' L B2 U2 F2 U R2 F B R B2 R U2 L
L B2 R U' D' R2 F R' L B2 U2 F2 U R2 F B R B2 R U2
U2 L B2 R U' D' R2 F R' L B2 U2 F2 U R2 F B R B2 R
R U2 L B2 R U' D' R2 F R' L B2 U2 F2 U R2 F B R B2
B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2 U R2 F B R
R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2 U R2 F B
B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2 U R2 F
F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2 U R2
R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2 U
The same can be said of the quarterturn superflip and slice superflip.
Note that the section "Solution" starts with "This is one possible sequence of moves to generate the Superflip", but I don't think that anybody thinks that it is easy to find another such algorithm. Here, I showed easy that really is . . .
Could this be incorporated in the main article somehow? Or perhaps some clarification is needed for the term "possible sequence"?