From reid@math.berkeley.edu Tue May 19 13:25:44 1992 Return-Path: Received: from math.berkeley.edu by life.ai.mit.edu (4.1/AI-4.10) id AA14775; Tue, 19 May 92 13:25:44 EDT Received: from asparagus.berkeley.edu.berkeley.edu by math.berkeley.edu (4.1/1.33(math)) id AA25455; Tue, 19 May 92 10:25:38 PDT Date: Tue, 19 May 92 10:25:38 PDT From: reid@math.berkeley.edu (michael reid) Message-Id: <9205191725.AA25455@math.berkeley.edu> To: cube-lovers@ai.mit.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