eklhad@ihnet.UUCP (K. A. Dahlke) (07/27/84)
After solving the Rubix cube 4 years ago, I turned my attention to more interesting (and more difficult) questions. How can one find the minimum path solution for an arbitrary position? How far away is the farthest positions? Is there one position diametrically opposed to start, or does it fan out into billions? I thought about these questions periodically, and even did a little work on them during grad school. Recently, I have started playing again, and have made some progress. I have a computer program (C/unix) which solves the 2x2x2 cube in a minimum number of moves. The 2 cube is not as common as the 3 cube, but it is commercially available. If you only have a 3 cube (standard), just ignore the sides and centers, and use the corners. This effectively simulates a 2 cube. I will submit the program to net.sources soon. I hope to continue playing with the cube(s). Thanks to ATT-BL for the use of their computing facilities. Unfortunately, my program cannot be expanded to handle the 3 cube. Nobody has that much memory/CPU time. I will have to come up with something better. Here is the move-position table for the 2 cube (byproduct of my program). A move is defined as a quarter-turn on any face. moves from start: 0 1 2 3 4 5 number of positions: 1 6 27 120 534 2256 moves from start: 6 7 8 9 10 11 number of positions: 8969 33058 114149 360508 930588 1350852 moves from start: 12 13 14 number of positions: 782536 90280 276 Feel free to contact me with any ideas about this subject. -- Karl Dahlke ihnp4!ihnet!eklhad
ljdickey@watmath.UUCP (Lee Dickey) (08/10/84)
The 4x4x4 cube seems to be rather common, and lends itself well as a model for the 2x2x2, because you can make moves that slide only along a center plane. This has a visual advantage over ignoring the middle sections of a 3x3x3.