From hoey@aic.nrl.navy.mil Tue May 12 11:03:38 1992 Return-Path: Received: from Sun0.AIC.NRL.Navy.Mil by life.ai.mit.edu (4.1/AI-4.10) id AA05297; Tue, 12 May 92 11:03:38 EDT Received: by Sun0.AIC.NRL.Navy.Mil (4.1/SMI-4.0) id AA04073; Tue, 12 May 92 11:03:34 EDT Date: Tue, 12 May 92 11:03:34 EDT From: hoey@aic.nrl.navy.mil (Dan Hoey) Message-Id: <9205121503.AA04073@Sun0.AIC.NRL.Navy.Mil> To: Cube-Lovers@life.ai.mit.edu Cc: Dik.Winter@cwi.nl, reid@math.berkeley.edu (michael reid) Subject: Diameter of the 2^3 cube and the 3^3 corners I sent the results of a quarter-turn analysis of these puzzles to Cube-Lovers in several messages during August, 1984. I modified a program written by Karl Dahlke to get these results. I counted both positions and local maxima at every distance up to the diameter of 14 quarter-turns. In case you don't have the archives handy, here are the results: Quarter 2^3 Puzzle Corners of 3^3 Puzzle Turns Positions Local Maxima Positions Local Maxima ____________________________________________________________ 0 1 0 1 0 1 6 0 12 0 _____2___________27________0______________114___________0___ 3 120 0 924 0 4 534 0 6539 0 _____5_________2256________0____________39528___________0___ 6 8969 0 199926 114 7 33058 16 806136 600 _____8_______114149_______53__________2761740_______17916___ 9 360508 260 8656152 10200 10 930588 1460 22334112 35040 ____11______1350852____34088_________32420448______818112___ 12 782536 402260 18780864 9654240 13 90280 88636 2166720 2127264 ____14__________276______276_____________6624________6624___ The first column agrees with Dik Winter's findings. As Michael Reid surmised, the diameters of the two groups are the same. My hazy recollection is that the 2^3 program ran for a few minutes on a Vax 750, while the corners program took a couple of hours. Dan Hoey Hoey@AIC.NRL.Navy.Mil