From mreid@ptc.com Fri Jan 20 15:46:17 1995 Return-Path: Received: from ptc.com (poster.ptc.com) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA12414; Fri, 20 Jan 95 15:46:17 EST Received: from ducie.ptc.com by ptc.com (5.0/SMI-SVR4-NN) id AA19444; Fri, 20 Jan 95 15:44:52 EST Received: by ducie.ptc.com (1.38.193.4/sendmail.28-May-87) id AA10072; Fri, 20 Jan 1995 15:58:08 -0500 Date: Fri, 20 Jan 1995 15:58:08 -0500 From: mreid@ptc.com (michael reid) Message-Id: <9501202058.AA10072@ducie.ptc.com> To: cube-lovers@ai.mit.edu Subject: superflip in quarter turn metric Content-Length: 3456 i've finished searching for superflip in 20q , and no solutions were found. thus superflip requires at least 22q , which gives a new lower bound for the diameter of the cube group in the quarter turn metric. total cpu spent on the search was 29 cpu hours. based on this, i would make a rough estimate of 2.5 to 3 months cpu time for an exhaustive search through depth 22q. this time i collected some statistics the way dik did. this should be helpful for troubleshooting. it's not foolproof, but it's a reasonable start. i will rerun the face turn search and collect the same data along the way. mike statistics follow: depth in number of times solutions stage 1 stage 2 is reached found superflip R1 L1 U1: 9q 64 33q, 31q, 29q 10q 272 11q 3728 27q 12q 26440 13q 164664 25q 14q 911112 15q 5516208 superflip R1 L1 U3: 9q 64 31q, 29q, 27q 10q 272 11q 3728 12q 26440 13q 164664 14q 911112 25q 15q 5516208 superflip R1 L1 F1: 9q 288 31q, 29q, 27q 10q 2192 11q 13496 12q 65280 13q 352056 25q, 23q 14q 1810744 15q 9753608 superflip R1 L1 F3: 9q 288 31q, 29q, 27q 10q 2192 11q 13496 12q 65280 25q 13q 352056 14q 1810744 15q 9753608 superflip R1 L3 U1: 9q 64 33q, 31q, 29q, 27q 10q 272 11q 3728 12q 26440 25q 13q 164664 14q 911112 23q 15q 5516208 superflip R1 L3 F1: 9q 288 33q, 31q, 29q 10q 2192 27q 11q 13496 25q 12q 65280 13q 352056 14q 1810744 15q 9753608 superflip R1 U1: 10q 6 32q 11q 106 28q 12q 4216 26q 13q 30318 14q 212208 15q 1414882 16q 9807890 superflip R1 U3: 10q 6 32q 11q 106 30q, 28q 12q 4216 26q 13q 30318 14q 212208 24q 15q 1414882 16q 9807890 superflip R1 F1: 10q 78 32q, 30q, 28q 11q 352 12q 5338 26q, 24q 13q 35996 14q 241230 15q 1549382 16q 10531798 17q 71358512 superflip R1 F3: 10q 78 28q 11q 352 12q 5338 26q, 24q 13q 35996 14q 241230 15q 1549382 16q 10531798 17q 71358512