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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.

however, i've recently had some new thoughts about this which

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