Most "cubers" solve a Rubik's cube in about 60 moves, using special algorithms and quick fingers. But any Rubik's cube can be solved in 20 moves or less (cube20.org). Is it possible that there is a way (without computers) to look at a cube and solve it in 20 moves or less, without trying to memorize several sextillion different positions?

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    $\begingroup$ There're are actually competitions where solvers try and use as few moves as possible. I believe the world record is 21 or 22 (w/o computers of course). Thus I doubt there is any way known. If there was, it would have been a lot easier to prove that 20 moves was the max (it was proven with computers checking each position). $\endgroup$ – Trevor Norton Jan 5 '16 at 18:53
  • $\begingroup$ worldcubeassociation.org/results/e.php?i=333fm Turns out the record is 19, but that was only done once. $\endgroup$ – Trevor Norton Jan 5 '16 at 18:56

Simple answer is that there is no known algorithm that can solve the Rubiks Cube in 20 moves maximum for an arbitrary starting position. Nevertheless, it is known that all positions are solvable in 20 moves, thus some algorithm must exist. Whether or not this algorithm requires less work than memorizing all the possible moves is currently somewhat open. (not comoletely.... We have used patterns and some group theory to reduce the number of solutions we needed to check to prove the number 20.) If we ever do find a simpler algorithm the proof will be much easier!

  • $\begingroup$ Ofcourse there is an algorithm, it's called bruteforce... Cube explorer is an implementation of this algorithm (and others) $\endgroup$ – Jens Renders Apr 19 '16 at 0:09
  • $\begingroup$ @JensRenders first of all, please don't necropost. Secondly, the OP asked for an algorithm without computers, and no human can brute force a rubiks cube in any reasonable amount of time... Probably not in the entirety of a humans lifetime, hence my answer. As is pointed out above, the world record for a human without computers is above 20, a thus no one has a good algorithm for HUMANS to use $\endgroup$ – Brevan Ellefsen Apr 19 '16 at 0:14
  • $\begingroup$ First of all, commenting to point out that an answer contains an incorrect statement is never wrong, second, this is an unanswered question so any comment should be welcome. Third, just the fact the OP asks for a human algorithm doesn't make you're abselutely false statement any more correct. You litteraly say the oposite of what is true. You should be more precise $\endgroup$ – Jens Renders Apr 19 '16 at 0:19

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