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But I have not the time right now to check. I am busy trying to prove

that 20 is minimal for superfliptwist. I have already found that there

is no 19 turn solution with 16 turns in phase 1. That took about 48

hours (distributed over 6 machines). Now I am doing the same for 17

turns in phase 1; which wil obviously take much longer. (And yes, I

took the precaution of allowing as the first turn only F, F2, R, R2,

U, U2 in phase 1. When I go to 19 turns in phase 1, I can skip 18,

I need only F, F2, R and R2, I think.)

in fact, you can eliminate the possibility of starting with F2, R2 or U2,

since these each commute with superfliptwist, and may be done in stage 2.

in other words, if F2 sequence = superfliptwist, then also

sequence F2 = superfliptwist.

also, you need not consider 19 turns in stage 1. by symmetry, you may

suppose the last face turned is U, which is done in stage 2.

if you use the fact that U and D commute, L and R commute and F and B

commute, then the number of sequences of length n in stage 1 grows

exponentially, with ratio approximately 13.35. if the runtime is

proportional to the number of sequences tested in stage 1, (which

may or may not be the case) that would mean testing 18 turns deep

would take approximately 178.18 times as long. (eliminating the

possibility of starting with F2, R2 or U2 would cut that in half.)

here's something you may have already considered. if your prune tables

in stage 1 consider only pairs (flip, twist), (flip, location) and

(twist, location), some search paths may be pruned 8 turns early.

(each of these pairs had positions 9 twists from start.) at the

expense of a lot more memory, you can do some pruning 11 turns early,

by storing tables for triples (flip, twist, location). you'd probably

have to store these tables in very compressed form, and divide out by

symmetries of the cube that preserve the U-D axis. it may turn out

that the overhead of processing this compressed information does not

adequately compensate for the improved foresight, but it's worth

considering.

it would be excellent if you could show that 20 face turns is minimal

for superfliptwist! even finding a shorter solution would be great!

mike