Date: Tue, 19 May 92 10:25:38 -0700 (PDT)
From: michael reid <reid@math.berkeley.edu >
~~~ Subject: assorted results
``` > stripes: (18) F3 U1 F2 U3 R1 B2 R3 U1 F2 L2 U3 L1 B2 L3 U1 L2 U3 F1.
> python: (15) R1 U3 F3 B1 L1 F2 L3 F1 B3 U3 R3 L1 F2 U2 L3.
I could not improve the first but what do you think of:
(12+ 2=14): U2 B3 D3 L1 F1 B3 U3 F1 U3 D1 R3 B1 D1 F2
```

i mentioned these because i was particularly proud of them, especially
since they were constructed by hand. my program was able to improve
"stripes", but i reoriented the pattern first. perhaps this is why
i had better success. stripes (17 face / 20 quarter):
R1 U1 D1 R2 F1 U3 D1 F3 B1 U3 R3 L3 B1 L2 U1 D3 B2 (14 + 3)
so if you have any efficient pattern maneuvers that you're especially
proud of, let's see if they can't be improved.

```I did some more and found fast algorithms.  The most amazing one was for
the configuration with two 2x2x2 cubes embedded in the cube:
( 9+ 6=15): U1 L2 D1 R1 B3 R1 B3 R1 B3 D3 L2 U1 R2 F2 U2
```
```this can also be done in 18 quarter turns:
L1 F1 L1 D3 B1 D1 L2 F2 D3 F3 R1 U3 R3 F2 D1  (13 + 2)
also "cube within cube within cube"  17 face / 22 quarter turns:
L3 D1 R3 B3 D1 L2 D2 L3 D3 L1 U1 D2 R3 U3 B2 R2 D3  (13 + 4)
"twisted rings"  16 face / 18 quarter turns:
B1 R1 B3 R2 U3 F3 L1 U1 R1 D1 L1 U3 B3 L1 U1 L2  (14 + 2)
"twisted cube edges"  14 face / 14 quarter turns:
D1 L3 B1 R1 D3 R3 D1 B3 L1 B1 R3 B3 R1 D3  (13 + 1)
```

Leider haben wir nur die Deutschen Ausgabe. There are apparently
differences between the German and the English edition. The English
edition is later and has probably improved sequences (he has promised
also improved sequences for the second German edition, but I do not
think it ever came out).

```'tis a shame.  the english edition is very good.  i've never seen the
german.  in the english edition he gives several "open snakes".
here's what my program has to say about them.
"rattlesnake"  14 face / 18 quarter turns:
F3 D3 L1 D3 L2 F1 B2 U1 L3 U3 R3 B2 R1 L2  (13 + 1)
"black mamba"  14 face / 14 quarter turns:
L1 U1 R1 F3 R3 L1 U1 L3 U3 D1 B1 D3 L3 U3  (13 + 1)
"green mamba"  13 face / 14 quarter turns:
R3 L2 F1 R1 U1 L3 F3 B1 U1 B3 U3 L3 U3  (12 + 1)
"boa"  12 face / 16 quarter turns:
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!

Also done, I do not look for ties.

i am currently looking for ties, but will soon stop. this is mainly to
catch (by eye) maneuvers that are short quarter turn-wise. i realize
this is stupid for at least two reasons: 1: the program may well be
passing up sequences which are shorter in quarter turns; 2: a slightly
different version of the program will specifically look for the shortest
sequence in quarter turns. 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. :-)

still need to do some polishing ...

mike