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Subject:

Together with Kloosterman's result for their third and fourth phase (which

together form Kociemba's second phase) the upperbound on God's algorithm

is now 37.

well, at least i had the record for a couple of days! ;-)

Below follows the set of distances for the first phase: 0: 1 1: 4 2: 74

but i don't understand how we can get 74 positions at distance 2 from

only 4 positions at distance 1. the 4 positions at distance 1 are

easy to see: they're the positions obtained from START by the turns

B, F, L and R. with only 18 different face turns, each should

extend to at most 18 positions at distance 2. am i missing something

obvious here? (the numbers do seem to add up, though.)

I conjecture that the maximal distance in phase 2 is at most 16. There is a

lower bound on it of 14.

the pattern (written in permutation notation) (FR, FL) (UFL, DFR) is

at distance 15, so that's (also) a lower bound. however, if the whole

cube is turned so that the F face becomes the U face, then the new

pattern is still in the subgroup of stage 2, but is now at distance 14.

mike