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Is it possible (theoretically, of course) to expose each legal rubik's cube position only once with a single sequence of quarter-turn and half-turn moves? Assume a 3x3x3 cube, and ample computing power.

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Already asked: Is it possible to use one sequence of moves to solve the Rubik's cube from any position? Shortcut to the answer is here: http://bruce.cubing.net/ham333/rubikhamiltonexplanation.html

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  • $\begingroup$ Incorrect. The question states "expose each legal rubik's cube position only once", a completely different question. The other question asks for the shortest repeating block which can produce every position (not necessarily only once). $\endgroup$ – boboquack Dec 16 '17 at 4:35
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    $\begingroup$ But the "Devil's Algorithm" as explained in that question is exactly the answer to this question, as it visits every legal position exactly once. $\endgroup$ – Jaap Scherphuis Dec 16 '17 at 4:38
  • $\begingroup$ Yeah this answers my question. My curiosity is satiated. Thank you. $\endgroup$ – Chris Dec 16 '17 at 5:19
  • $\begingroup$ So it's possible with only quarter turns in one direction (per face) and by rotating only only five of the faces. $\endgroup$ – Jasen Dec 17 '17 at 2:28

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