~~~ From:

Subject:

mark.longridge@canrem.com (Mark Longridge) writes:

Certain states, such as the 12-flip, require quite a few moves, in

fact more moves than possible to search using brute force even when

using high-order computers. The best results using the Kociemba

algorithm need 28 q turns or 20 q+h turns for the 12-flip.

I found Mark's post generally interesting and thought provoking.

Without detracting from his ideas I would like to comment on the

paragraph above.

If a certain state (such as the 12 flip) is known to be reachable

in no more than 20 moves, then isn't that state within reach of

a brute force search? Start one brute force at the initial state,

one at the final state, expand the position trees one move at a time

until the trees touch. A state 20 moves from start will require a

tree (well, two trees) 10 moves deep, which is about 10 billion states.

That seems achievable in a reasonable time on fast computers of today.

Doesn't it?

regards,

Tim Rentsch