Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 exptools 1/6/84; site ihnet.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!ihnp4!ihnet!eklhad
From: eklhad@ihnet.UUCP (K. A. Dahlke)
Newsgroups: net.math,net.puzzle
Subject: solve the 2x2x2 Rubix cube,  minimum path to start
Message-ID: <141@ihnet.UUCP>
Date: Fri, 27-Jul-84 10:30:52 EDT
Article-I.D.: ihnet.141
Posted: Fri Jul 27 10:30:52 1984
Date-Received: Sat, 28-Jul-84 10:12:54 EDT
Organization: AT&T Bell Labs, Naperville, IL
Lines: 35

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