From cube-lovers-errors@mc.lcs.mit.edu Fri Jul 10 12:57:34 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id MAA06279; Fri, 10 Jul 1998 12:57:33 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Fri Jul 10 08:48:35 1998 Date: Fri, 10 Jul 1998 08:48:05 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Ten Face Moves from Start To: cube-lovers@ai.mit.edu Message-Id: Face Moves Patterns Positions Branching Positions/ from Factor Patterns Start 0 1 1 1.0 1 2 18 18 9.0 2 9 243 13.5 27.0 3 75 3240 13.333 43.2 4 934 43239 13.345 46.294 5 12077 574908 13.296 47.604 6 159131 7618438 13.252 47.875 7 2101575 100803036 13.231 47.965 8 27762103 1332343288 13.217 47.991 9 366611212 17596479795 13.207 47.998 10 4838564147 232248063316 13.199 47.999 This run took about three weeks on a Pentium 300. The next level from Start is going to be difficult. With the current algorithm and hardware, it would take about thirty to forty weeks. In addition, the memory requirements will go up considerably. Currently, I store only the positions up to five moves from Start in memory. To calculate the next level, I will have to store the positions up to six moves from Start. I still suggest (see "How Big is Big?" in the archives) that the problem can be calculated all the way to the bitter end, eventually. The Cube problem simply is not as big as, for example, Chess or Go. As a possible strategy, if we could add one level per decade, we could probably calculate the problem all the way to the end within about 100 years. Moore's Law (the power of computers doubles about every eighteen months) suggests that such a schedule might be possible. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990