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Subject:

I'm not sure this is so interesting to all of cube-lovers; e-mail me

if you have opinions pro or con.

Jerry writes of the standard S24 x S24 model, which uses 48 bytes per

position without packing. He also has a "supplement" representation

that uses one facelet from each edge and corner, for 20 bytes. He

packs them into 13 bytes on tape.

The way I did it the last time I worked on brute force was to

pack eight twelve-bit fields:

The orientations in two twelve-bit fields (2^11 and 3^7),

The edge permutation in four twelve-bit fields,

each of three base-12 digits (12^3), and

The corner permutation in two twelve-bit fields, each of

four base-8 digits (8^4).

Unpacking the fields can be done with native arithmetic or table

lookup. In the latter case, it is better to use 12*11*10 instead of

12^3 and 8*7*6*5 instead of 8^3.

Also, postmultiplying by a fixed permutation can be done with table

lookup without unpacking. I used this feature for twelve permutations

of particular interest.

I am somewhat rusty on the implications of using this representation

in conjunction with Shamir's algorithm. I think it provides an

ordering of the permutations that enables at least an approximation to

the random access you need, then you unpack it and do a better job.

Dan Hoey

Hoey@AIC.NRL.Navy.Mil