From dik@cwi.nl Mon Oct 31 18:14:47 1994 Return-Path: Received: from charon.cwi.nl by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA20716; Mon, 31 Oct 94 18:14:47 EST Received: from boring.cwi.nl by charon.cwi.nl with SMTP id ; Tue, 1 Nov 1994 00:14:46 +0100 Received: by boring.cwi.nl id AA06573 (5.65b/3.8/CWI-Amsterdam); Tue, 1 Nov 1994 00:14:45 +0100 Date: Tue, 1 Nov 1994 00:14:45 +0100 From: Dik.Winter@cwi.nl Message-Id: <9410312314.AA06573=dik@boring.cwi.nl> To: Cube-Lovers@ai.mit.edu Subject: Re: Speed Cubing Path Lengths > I have received several private E-mail messages indicating that > the algorithms used by speed cubists solve the cube in 50 or > 60 moves. On the one hand, that seems astonishingly good to me, > being fairly close to the solutions from early Thistlethwaite > programs. On the other hand, it is roughly double (depending, I > suppose on whether H-turns are counted or not) what is probably > the true God's Algorithm. Hence, it doesn't tell us much about > God's Algorithm except that the speed cubists are very, very > good. The best current algorithm has a proven upperbound of 37 turns (q and h). God's Algorithm is probably much shorter. In fact the program that implements Kociemba's algorithms has not yet found a configuration (out of many thousands random configurations tested) that could not be solved in 20 turns or less. If we look at distributions for similar puzzles it is expected that more than one in three configurations requires the maximum number of turns minus 1 or 2. So I expect God's Algorithm to be at most 22 turns. Still a long way to go. dik