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It’s called Devil’s algorithm but I believe it is not know yet whether it exists or not https://getgocube.com/play/devils-number/ https://getgocube.com/play/de

It’s called Devil’s algorithm but I believe it is not know yet whether it exists or not https://getgocube.com/play/devils-number/ https://getgocube.com/play/devils-number/

988747 4y ago
Somewhat related: I was playing with cube recently, and, starting with solved state, I started doing sequence of two moves that came to my mind: rotate right side down, then the bottom, clockwise. After maybe a 100-150 repetitions (I did not count, just did the moves mindlessly for couple minutes) I went back to solved state. I wonder if there are more such sequences, and how long it takes to go back to original state. The obvious difference from Devil's algorithm was that the 2x2 sub-cube remained untouched the whole time, only the edges were messed up.
- lupire 4y ago
  Every sequence behaves this way (For all sequences S, there exists n_S such that S ^ n_S equals S^0, the starting state.) Proving this is an introductory problem in Rubik's theory. Try it!
- zeroonetwothree 4y ago
  Because there are only finitely many states, repeating one move will inevitably get you back to where you started from. Also check out Lagrange’s theorem in group theory
hvdijk 4y ago
It has to exist: it's a mindbogglingly large but finite number of possible permutations, and to go from any one permutation to any other takes a finite number of moves. Therefore, if you can enumerate all possible permutations in some way, any arbitrary way will do, you have a Devil's algorithm by going through them in that order. The question is not whether a Devil's algorithm exists but what the shortest one is.
- owalt 4y ago
  Worth noting that the Devil's algorithm is not a sequence of turns you repeat over and over, but one that takes you through every possible cube state. You "abort" it partway through when you reach your desired state.
  - hvdijk 4y ago
    It is both: it is a sequence of turns that if you repeat them over and over, will take you through every possible cube state. But it is possible that the shortest such sequence is trillions of moves long.
    - vikingerik 4y ago
      There are 43 quintillion cube states, so "trillions" is understating by at least a factor of 10^6. I'm not sure if the 43 quintillion are reachable in a loop of that many moves, or if you need to backtrack through some states to reach others and thus need more moves than that.
      - hvdijk 4y ago
        "Trillion" has two meanings. I'm Dutch, we use the traditional meaning of 10^18, what you call quintillion :)

It’s called Devil’s algorithm but I believe it is not know yet whether it exists or not https://getgocube.com/play/devils-number/ https://getgocube.com/play/devils-number/

988747 4y ago

Somewhat related: I was playing with cube recently, and, starting with solved state, I started doing sequence of two moves that came to my mind: rotate right side down, then the bottom, clockwise. After maybe a 100-150 repetitions (I did not count, just did the moves mindlessly for couple minutes) I went back to solved state. I wonder if there are more such sequences, and how long it takes to go back to original state. The obvious difference from Devil's algorithm was that the 2x2 sub-cube remained untouched the whole time, only the edges were messed up.

lupire 4y ago
Every sequence behaves this way (For all sequences S, there exists n_S such that S ^ n_S equals S^0, the starting state.) Proving this is an introductory problem in Rubik's theory. Try it!
zeroonetwothree 4y ago
Because there are only finitely many states, repeating one move will inevitably get you back to where you started from. Also check out Lagrange’s theorem in group theory

hvdijk 4y ago

It has to exist: it's a mindbogglingly large but finite number of possible permutations, and to go from any one permutation to any other takes a finite number of moves. Therefore, if you can enumerate all possible permutations in some way, any arbitrary way will do, you have a Devil's algorithm by going through them in that order. The question is not whether a Devil's algorithm exists but what the shortest one is.

owalt 4y ago
Worth noting that the Devil's algorithm is not a sequence of turns you repeat over and over, but one that takes you through every possible cube state. You "abort" it partway through when you reach your desired state.
- hvdijk 4y ago
  It is both: it is a sequence of turns that if you repeat them over and over, will take you through every possible cube state. But it is possible that the shortest such sequence is trillions of moves long.
  - vikingerik 4y ago
    There are 43 quintillion cube states, so "trillions" is understating by at least a factor of 10^6. I'm not sure if the 43 quintillion are reachable in a loop of that many moves, or if you need to backtrack through some states to reach others and thus need more moves than that.
    - hvdijk 4y ago
      "Trillion" has two meanings. I'm Dutch, we use the traditional meaning of 10^18, what you call quintillion :)