True. Orientation of non-symmetric patterns is important because the first
step is to get at a situation that is also non-symmetric.
next stage: have the program account for symmetries of the pattern,
face turns that commute with the pattern, ...
'tis a shame. the english edition is very good.
The german edition is also good, but clearly older. The newer patterns you
mention are not in the german edition.
again, a shame. i think that these snake patterns are among the most
interesting things in the book.
Currently I am calculating the maximal distance in stage 1. It will take a bit of time because I have to consider 2,217,093,120 possibilities. But I think that the method I have is feasible.
how much time do you anticipate the job will take? it seems that we'd
get a much better improvement (of kloosterman's bound) by calculating
the maximal distance in stage 2. of course, this requires going through
19,508,428,800 possibilities (nearly 9 times as many). is this feasible?
also it seems that "god's algorithm" for stage 2 (i.e. face turns are
restricted to D, U, B2, F2, L2, R2) would be very similar to
god's algorithm for the "magic domino," and this similarity should
become stronger as the patterns get further away from START.
from the pruning tables used in stage 2, dik gives the following maximal
Phase 2: corners: 13 edges: 8 slice edges: 4 corners+slice: 14 edges+slice: 12
i was slightly surprised to see a difference between the figures for
"corners" and those for "corners + slice edges". but the difference
between "edges" and "edges + slice edges" is shocking. so perhaps the
two "god's algorithms" above are not TOO similar.
Based on this I expect a maximal distance [ ... ]
in phase 2 of about 16/17.
i'm pretty sure i know a pattern that requires 15 face turns. i wouldn't
be all that surprised if 15 was the maximum, although i haven't tested many