If you apply the same algorithm over and over again the cube will be solved.
I want to know what algorithm is the worst one (the one with the longest cycle)
I have found RU (cycle of 60 times)
I have found one of 72 but I can't remember it
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$\begingroup$ Cycling RU solves the cube in 60 times? I didn’t know that was possible $\endgroup$Gabe– Gabe2019-12-12 16:18:00 +00:00Commented Dec 12, 2019 at 16:18
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1 Answer
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It seems like you are trying to find
An element of the Rubik's cube group whose order is as large as possible.
One such example that satisfies this is
$(RU^2D^{-1}BD^{-1})$ which has the maximum attainable order of $1260$
In particular,
Starting from a solved cube, you need to apply this algorithm $1260$ times to get back to the beginning.
As mentioned by armb in the comments, there is a good answer here discussing the maximum orders for an $n \times n \times n$ Rubiks cube.
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2$\begingroup$ Can you prove that? $\endgroup$pgp1– pgp12019-12-11 19:46:19 +00:00Commented Dec 11, 2019 at 19:46
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16$\begingroup$ @pgp1 you can do it yourself - simply apply the algorithm 1260 times! :P $\endgroup$Quintec– Quintec2019-12-12 01:14:48 +00:00Commented Dec 12, 2019 at 1:14
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4$\begingroup$ "apply the algorithm 1260 times" proves it has order 1260, it doesn't prove that that is the maximum possible order. For the latter, see math.stackexchange.com/questions/2392906/… $\endgroup$armb– armb2019-12-12 11:06:24 +00:00Commented Dec 12, 2019 at 11:06
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$\begingroup$ @armb This is very useful, I may add this link to the answer. $\endgroup$hexomino– hexomino2019-12-12 11:08:14 +00:00Commented Dec 12, 2019 at 11:08