Date: Wed, 20 May 92 03:00:27 +0200
From: Dik T. Winter <Dik.Winter@cwi.nl >
Subject: Re: assorted results

My program was able to improve
"stripes", but i reoriented the pattern first. perhaps this is why
True. Orientation of non-symmetric patterns is important because the first
step is to get at a situation that is also non-symmetric.

'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. (I may note that Christoph Bandelow
is still selling puzzles. The 5x5x5 amongst others.)

```R3 L2 F1 R1 U1 L3 F3 B1 U1 B3 U3 L3 U3  (12 + 1)
D1 R1 F3 R1 L1 F2 R2 D3 L2 F2 L1 F3  (12 + 0)
```

this last one was very nice, since it was completely solved in stage 1!
Yup. But the last but one will not improve and is optimal, and in fact solved
with stage 1 (but you did not find it because you limited your search 12 deep).

I'm trying to think of the best way to do this.
unfortunately, the temptation is NOT to think, but to feed every
imaginable pattern into the program. :-)
How true. I stopped feeding new patterns. 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. My conjecture was that the maximal distance was 11 or 12.
That was wrong. It is at least 12 (the superfliptwist needs 12 moves in
phase 1). My current conjecture is 12. Work is in progress, the first
1,082,565 configurations give the following picture (i.e. all configurations
without flip):
Moves Number
0 1
1 2
2 17
3 134
4 1065
5 8214
6 54919
7 269388
8 562427
9 183730
10 2668
The pattern is similar to what was found with the 2x2x2 cube. The majority
of configurations requires 2 less than the maximum. But apparently flips are
harder to deal with than the rest of phase 1, so I am waiting for more results.
Note that 12 would improve Kloostermans 42 moves to 37.

dik
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland
dik@cwi.nl