   Date: Sun, 24 May 92 06:10:21 -0700 (PDT)   From: michael reid <reid@math.berkeley.edu >   Subject: Re: New upper bound on God's algorithm for Rubik's cube

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     