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A Friday-afternoon puzzle about #RubiksCube:

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  • simontatham@hachyderm.ioundefined

    A Friday-afternoon puzzle about :

    What's the shortest sequence of moves on the Cube which _non-obviously_ gets you back to where you started?

    By "non-obviously", I mean that it shouldn't be possible to _prove_ the sequence is a no-op by using only the obvious properties of the quarter-turn moves that they all have order 4, and opposite faces commute.

    To be group-theoretically formal about it, consider the following infinite group H, which captures those properties of the Cube moves but nothing more subtle:

    H = ⟨ L,R,F,B,U,D | LR=RL, FB=BF, UD=DU, L⁴=R⁴=U⁴=D⁴=F⁴=B⁴=e ⟩

    A sequence of moves is _obviously_ the identity if it's the identity even when you do it in H. What's the shortest sequence of moves that is the identity in the true Rubik's Cube group, but _not_ the identity in H?

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