From:

Subject:

My program was able to improve

"stripes", but i reoriented the pattern first. perhaps this is why

i had better success.

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