8
$\begingroup$

Is there a rule/method to know how "random" should the cube be when solving it? in order for it to be a "valid" score?

$\endgroup$
6
$\begingroup$

The World Cube Association has regulations regarding the official scrambling algorithm used for their competitions.

An official scramble sequence must produce a random state from those that require at least 2 moves to solve.

Source: https://www.worldcubeassociation.org/regulations/#article-4-scrambling

Basically, as long as it takes at least 2 moves to solve, it's a valid scramble. All scrambles are computer-generated.

Most scrambles will require a minimum of 18 moves to solve. The number of possible permutations for a certain number of moves is given on http://www.cube20.org.

Although a 2-move scramble is in theory possible, the chance of it happening is about 243 in 43 quintillion.

I seem to recall that the standard for competition scrambles before this was 40 random turns, but I don't have a source for this.

$\endgroup$
  • $\begingroup$ An official scramble sequence must produce a random state from those that require at least 2 moves to solve. — I assume "random" means "uniformly at random". But then how does the WCA actually scramble cubes to guarantee uniformity? $\endgroup$ – JeffE May 29 '14 at 1:14
  • $\begingroup$ @JeffE They use a computer program dedicated to this purpose. The details are on the WCA page linked above. (I don't think it's specified to be uniformly random, but I expect it is. If not, probably a random series of moves, which is still pretty random.) $\endgroup$ – Kendall Frey May 29 '14 at 2:04
  • $\begingroup$ You can't ever get exactly uniform via random moves, but you can get as close as you like to uniform with enough random moves. (See Persi Diaconis' seven-shuffle theorem.) I'm a little surprised that they don't disassembled the cube, throw the pieces in a bag, reassemble the cube blindfolded, and then check whether the resulting scramble is solvable. That would be uniform. $\endgroup$ – JeffE May 29 '14 at 4:23
5
$\begingroup$

A rubik's cube cannot be more than 20 moves ([called God's number][1]) away from its initial position.

After about 16 moves, you should be random enough, since it's very hard to be in a specific 20-moves-away position.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.