Archives

I outline an approach which may be able to determine the maximin depth of the Rubik cube R - may be able to prove the answer is 20 face turns - with a feasible amount of computer time.

Because R has 4.3*10^19 configurations, exhaustive search is not feasible.

At present at least 10000 configurations are known (including the "superflip") that require 20 face-turns (20f) to solve.

Silviu Radu has a proof at at most 27f are necessary.

So the answer is somewhere in [20, 27]. What is it?

H.Kociemba's "two phase solver" works by first getting into the H = subgroup (which is known to be possible in at most 12f because of an exhaustive search of R/H) and then solving (which is known to be possible in at most 18f because of an exhaustive search of H) thus proving an upper bound of 30f.