   Date: Thu, 12 Jan 95 19:47:42 -0500   From: michael reid <mreid@ptc.com >   Subject: superflip

i've also done some searching for short maneuvers for superflip,
although not to the extent that dik has. i was never really
satisfied with my efforts to exploit its symmetry and centrality.
look promising.

consider two cases:

case 1:
suppose that there is a minimal sequence for superflip which
contains a half-turn. then, by applying R' U2 to superflip,
we've moved 3q (or 2f ) closer to start.

case 2:
otherwise, every minimal sequence contains only 90 degree turns.
then either R' U' gets us 2q (or 2f ) closer to start,
or R' U gets us 2q (or 2f ) closer to start. (and probably
both do.)

it would be nice to reduce this latter case to only one of R' U'
or R' U . can anyone do this?

this was how i found the 24q sequence for superflip. i figured
that case 1 was fairly likely, so i tested the position

superflip R' U2

```kociemba's algorithm found in succession  11 + 22 = 33q,
11 + 20 = 31q,  12 + 17 = 29q,  13 + 14 = 27q,  13 + 12 = 25q,
which gives superflip in  28q.  there was no improvement for quite
some time until depth 17 in stage 1 when it found  17 + 6 = 23q.
it searched for several days more and finished depth 17 and depth 18
in stage 1.  i was about to give up when i saw that it found
19 + 2 = 21q,  to give superflip in  24q.
```

here's a nice (and quite surprising application) of the above
use of symmetry and centrality:

when searching for superflip in the face turn metric, it's
sufficient to search through depth 17 in stage 1!

suppose we have a 19f sequence for superflip. then, by considering
parity, some turn must be a half-turn. now we may suppose (as above)
that the last two face turns are U R2 , which is in stage 2!

mike     