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On 12/17/94 at 22:46:08 txr@alumni.caltech.edu said: >In mlist.cube-lovers you write:

For each cube position, we only need to store the depth, assuming

we have some way to index to the proper cell in a data structure

containing the depth for each cube position. As long as the depth

does not exceed 31, then 5 bits will suffice for each cell.I think depth modulo 3 is enough, since depth of adjacent positions

will differ by at most one -- just move in the direction of depth

getting less. So we could get by with 2 bits per cell.regards,

Tim Rentsch

You are certainly correct. And as Dan Hoey pointed out to me via

private E-mail once upon a time, for Q turns you can get it down

to only one bit by storing (depth modulo 4)/2 because you can infer

the state of the low order bit from the parity of cube position.

(Parity of the cube position equals the parity of the depth for Q turns,

but not for Q+H turns.)

But I tend to think that certain kinds of interesting analyses

of a data base for the entire God's Algorithm

would be greatly assisted by storing the entire depth.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU