I remember seeing somewhere that there existed some permutation of a rubiks cube, that when applied to any configuration of the cube, would solve it (although not always in the same number of moves). As in, a permutation x (probably with a ridiculous number of moves) existed which could solve any cube as long as it was applied enough times. Is this true? If so, how do we know, and how can rubik's cube permutations be represented in cyclical form?

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TopNewestI haven't heard of any such permutation.Although,I do know of 2 other permutations which can be used once reaching a particular stage.For example,after solving the first two faces and the top phase,you could use a permutation to get a 'U' pattern on every side.Suppose :- F-front;B-back;R-right;L-left;U-up;D-down where you rotate the respective faces clockwise as if they are facing you and if the letter is followed by an 'i', rotate that face anti-clockwise as if it is facing you . Caution must be taken so as not to change the face that was originally facing you.Permutation-------Ri,F,Ri,B,B,R,Fi,Ri,B,B,R,R – Roshan Rollands · 4 years, 1 month ago

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It is true. I don't know how it works, but it does.

x R' U R' D2 R U' R' D2 R2 x' F U L S

Repeat that algorithm a bunch and it will solve – Aiden Lu · 1 year, 1 month ago

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Yes such an algorithm is known as a Devil's Algorithm. It is a set of moves that when repeated a necessary number of times will return a solved cube despite any initial configuration.As Beakal said the optimal number of moves for solving the Rubik's cube(God's Number) using various appropriate algorithms is 20. As for the Devil's Algorithm it has been shown that the shortest Devil's Algorithm (The Devil's Number) required to solve a 2x2x2 cube is between 102060 and 2886840. As for a standard Rubik's cube the Devil's Number is quite ridiculous as you said and is known to be between 34,326,986,725,785,600 and 43,251,683,287,486,463,996. If you are some sort of bored immortal speed cuber Goddess with a photographic memory,there is a Devil's algorithm that will allow you to solve a cube within \(2.9 * 10^{11}\) years,that is assuming a speed of 5 turns per second and If you are to be finished by now you would also have to start before the creation of the universe. – Thaddeus Abiy · 4 years ago

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no,but the maximum number of moves it will take to solve any cube,if done at its highest efficiency is only 20 moves,though the agorithm are different. – Beakal T Tiliksew · 4 years, 1 month ago

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– Beakal T Tiliksew · 4 years, 1 month ago

if the permutation algorithm repeats itself as you said,its bound to solve some,but definitely not all,Log in to reply