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A lower bound on the number of twists can be derived as follows: There are

4.3*10^19 distinct reachable arrangments of the cube. Suppose the moves are

restricted to the (more than sufficient) set RLFBUD. Then there are at most six

independent choices at each step and the number of reachable places is bounded

by 6^n. That gives

6^25 < 4.3*10^19 < 6^26,

or 26 moves as the (probably unachievable) minimum. If all single-hand-motion

twists, R RR RRR L LL .... DDD are allowed, there are 18 choices, giving

18^15 < 4.3*10^19 < 18^16,

or 16 moves as a minimum. This isn't very interesting since Singmaster has

examples 18 twists away. If the orientation of the center squares is also

considered, then the combinatoric is 8.8*10^22, and the minima are, respectively,

30 and 19.