From cube-lovers-errors@mc.lcs.mit.edu Sat Jan 22 14:53:38 2000 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA01807 for ; Sat, 22 Jan 2000 14:53:37 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <20000110161852.11773.qmail@web118.yahoomail.com> Date: Mon, 10 Jan 2000 08:18:52 -0800 (PST) From: Jaap Scherphuis Reply-To: jaap@org2.com Subject: Re: Square-1 tables of move sequences To: Cube-Lovers@ai.mit.edu Dear Cube-Lovers, Here are my latest and probably final Square-One results. I have finalised my square-1 solving program, and it can now be downloaded from my website. I managed to speed it up so much that it can do an exhaustive depth 9 search in a few hours on a fast pc. It has thus confirmed that all the sequences below of length <=10 are minimal (though there might be other sequences that are easier to perform). The only sequences that are more than 10 long are A13 and C5, and these are 11 and 12 moves respectively. I have no plans as yet to do longer searches on these two. Here are the move tables. I will quote them in full, even though many are the same as in my previous post. A. Sequences involving only edges, and where some of them change layer: 1. Swap DF-UF, DR-UR, DB-UB, DL-UL: (0,5)/(1,1)/(-4,2)/(1,1)/(2,3) 2. Swap DF-UF, DB-UB: (0,5)/(1,1)/(-1,6) 3. Swap DF-UB, DB-UF: (0,-1)/(1,1)/(-1,0) 4. Swap DR-UR, DB-UB: (0,2)/(0,3)/(1,1)/(-1,-4)/(0,-2) 5. Swap DR-UB, DB-UR: (0,2)/(0,3)/(1,-5)/(-1,5)/(0,3)/(0,-2) 6. Swap DB-UB, DR-UF: /(-3,0)/(0,5)/(6,1)/(0,3)/(-5,0)/(-1,6) 7. Swap DB-UF, DR-UB: (1,0)/(0,5)/(6,3)/(0,5)/(-5,0)/(-3,6)/(6,0) 8. Swap DR-UF, UR-UB: (1,0)/(-4,5)/(0,-3)/(1,1)/(-1,2)/(4,-5)/(-1,0) 9. Swap DR-UR, UF-UB: (1,3)/(0,3)/(0,3)/(-1,2)/(1,4)/(0,3)/(-1,0) 10. Swap DR-UB, UF-UR: (4,3)/(3,0)/(-4,5)/(1,1)/(-3,0)/(0,-3)/(2,3) 11. Cycle UF->UR->DR: (1,3)/(0,5)/(0,3)/(6,1)/(0,5)/(3,6)/(6,-3) 12. Cycle UF->UB->DR: (0,5)/(0,1)/(6,3)/(5,0)/(-5,0)/(0,3)/(-1,0)/(0,1) 13. Swap UF-DF: (4,5)/(3,0)/(0,1)/(10,2)/(0,4)/(0,4)/(10,2)/(0,1)/(3,0)/(3,5)/(7,4)/(11,0) B. Sequences involving only edges of both layers where they do not change layer: 1. Swap UF-UB, UR-UL, DF-DB, DR-DL: (1,0)/(-3,3)/(2,2)/(3,3)/(-2,4)/(5,0) 2. Swap UF-UL, UR-UB, DF-DL, DR-DB: (0,2)/(-3,0)/(1,1)/(-4,2)/(1,1)/(5,-4)/(0,-2) 3. Swap UF-UB, DF-DB: (1,0)/(-1,5)/(1,-5)/(-1,6) 4. Swap UR-UB, DR-DB: (0,2)/(0,-3)/(1,1)/(-1,2)/(0,-2) 5. Swap UF-UB, DR-DB: (0,2)/(1,0)/(0,3)/(6,1)/(0,5)/(-3,0)/(5,6)/(6,-2) 6. Swap UF-UB, UL-UR, DF-DB: /(3,3)/(1,2)/(2,-4)/(-2,4)/(2,4)/(3,3)/(3,0)/(3,3)/(3,0) C. Sequences involving only edges of the top layer: 1. Swap UF-UB, UR-UL: /(3,-3)/(3,-3)/(6,-2)/(3,-3)/(3,-3)/(2,0) 2. Swap UF-UL, UR-UB: /(3,3)/(1,4)/(5,5)/(-3,0)/(3,3)/ 3. Cycle UF->UB->UR: (1,0)/(-1,2)/(-5,1)/(0,3)/(-3,0)/(5,2)/(-5,4)/(-4,0) 4. Swap UF-UB: /(3,3)/(3,2)/(-4,2)/(-2,4)/(-2,0)/(-4,2)/(-5,1)/(3,0)/(3,3)/(0,-3) 5. Swap UF-UR: (3,0)/(3,0)/(1,2)/(10,3)/(10,3)/(10,5)/(4,0)/(0,1)/(3,5)/(9,0)/(2,3)/(10,4)/(5,3) 6. Cycle UF->UR->UB->UL: /(3,3)/(1,0)/(2,2)/(0,2)/(4,4)/(2,0)/(2,2)/(-1,0)/(-3,-3)/(0,3) D. Sequences involving only corners, and where some of them change layer: 1. Swap UFR-DFR, UBR-DBR, UBL-DBL, UFL-DFL: (4,0)/(2,2)/(-3,3)/(-2,-2)/(-1,-3) 2. Swap UFL-DFL, UBR-DBR: (4,0)/(2,2)/(6,-2) 3. Swap UFL-DBR, UBR-DFL: (-2,0)/(2,2)/(0,-2) 4. Swap UFL-DFL, UFR-DFR: (6,5)/(-3,0)/(4,4)/(2,5)/(0,1) 5. Swap UFL-DFR, UFR-DFL: (1,0)/(3,0)/(-4,2)/(-2,4)/(0,3)/(5,6) 6. Swap UFL-DFL, UBR-DFR: /(3,0)/(6,2)/(4,0)/(-3,0)/(6,-2)/(-4,0) 7. Swap UFL-DFR, UBR-DFL: (6,0)/(3,0)/(6,2)/(4,0)/(-3,0)/(6,-2)/(2,0) 8. Swap UFR-UBR, UFL-DFR: (4,3)/(0,3)/(3,0)/(2,5)/(-5,4)/(3,0)/(5,3) 9. Swap UFL-UBR, UFR-DFR: (0,5)/(0,3)/(0,3)/(-2,1)/(2,5)/(0,3)/(0,-2) 10. Swap UFL-UFR, UBR-DFR: (-2,0)/(0,3)/(6,3)/(2,2)/(-2,1)/(-3,0)/(-4,6) 11. Cycle UFL->UFR->DFR: (1,3)/(-4,0)/(6,3)/(0,4)/(-4,0)/(3,0)/(-3,3) 12. Cycle UFL->UBR->DFR: (-5,0)/(3,0)/(5,2)/(-5,4)/(0,3)/(-1,2)/(-2,4)/(-4,6) 13. Swap UFR-DFR: /(3,0)/(1,2)/(-2,0)/(2,1)/(6,3)/(1,0)/(-2,2)/(0,1)/(3,3)/ E. Sequences involving only edges of both layers where they do not change layer: 1. Swap UFR-UBL, UFL-UBR, DFR-DBL, DFL-DBR: (1,0)/(-1,5)/(3,3)/(1,1)/(-3,3)/(5,0) 2. Swap UFR-UFL, UBL-UBR, DFR-DFL, DBL-DBR: (0,5)/(0,3)/(4,4)/(-3,3)/(2,2)/(0,-3)/(6,1) 3. Swap UFL-UBR, DFL-DBR: (0,5)/(-2,4)/(2,-4)/(0,1) 4. Swap UFL-UFR, DFL-DFR: (1,0)/(-3,0)/(2,2)/(1,-2)/(-1,0) 5. Swap UFL-UBR, DFL-DFR: (-2,0)/(0,2)/(0,3)/(-4,0)/(4,0)/(6,3)/(-2,0)/(2,6) 6. Swap UFL-UBR, UFR-UBL, DFL-DBR: /(3,3)/(-3,4)/(-2,4)/(-4,2)/(-4,3)/(3,3)/ F. Sequences involving only edges of the top layer: 1. Swap UFL-UBR, UFR-UBL: /(-3,3)/(-3,3)/(0,1)/(-3,3)/(-3,3)/(-1,6) 2. Swap UFL-UFR, UBR-UBL: /(3,3)/(-3,0)/(4,4)/(2,5)/(3,3)/ 3. Cycle UFL->UBR->UFR: (-5,0)/(-4,5)/(4,1)/(-3,0)/(0,3)/(-4,2)/(-2,1)/(2,0) 4. Swap UFL-UBR: /(3,3)/(-5,0)/(4,4)/(2,0)/(4,4)/(-2,5)/(3,3)/(0,5)/(-2,-2)/(5,0) 5. Swap UFL-UFR: /(3,3)/(1,4)/(0,4)/(10,4)/(8,2)/(2,0)/(10,4)/(4,1)/(3,3)/ 6. Cycle UFL->UBL->UBR->UFR: /(3,3)/(-5,0)/(4,4)/(2,0)/(4,4)/(-2,5)/(3,3)/(0,5)/(-2,-2)/(5,0) Jaap Scherphuis Copyright January 2000 -------------------------- Jaap's Puzzle Site: http://www.org2.com/jaap/puzzles Psion Organiser II homepage: http://www.org2.com