Analysis of zz-www.sudokuoftheday.co.uk-20060706-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006
level: medium
position: .2...5.1..3...2.69...83......86.7.2..9..5....3..92....7......86..9..6....5......4 initial
Autosolve
position: 92..6531883...2.69...839...5.86.7923.9..5....3..92....7...9..86.89..6.3..5..8..94 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 4,7 => CTR => C2: 5 * DIS # C3: 6,7 => CTR => C3: 1,4,5 * DIS # D2: 4,7 => CTR => D2: 1 * DIS # D5: 1,4 => CTR => D5: 3 * PRF # C7: 1,4 => SOL * DIS # D7: 1,4 => CTR => D7: 2,3,5 * DIS # D7: 1,3 => CTR => D7: 2,4,5 * DIS # D9: 1,3 => CTR => D9: 2,7 * DIS # F5: 1,3 => CTR => F5: 4,8 * CNT 9 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C2: 4,7 => CTR => C2: 5 * DIS C2: 5 # C3: 6,7 => CTR => C3: 1,4 * DIS C2: 5 + C3: 1,4 # D2: 4,7 => CTR => D2: 1 * DIS C2: 5 + C3: 1,4 + D2: 1 # E8: 7 => CTR => E8: 1,4 * PRF C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # C7: 1,4 => SOL * STA C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 + C7: 1,4 * CNT 5 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2...5.1..3...2.69...83......86.7.2..9..5....3..92....7......86..9..6....5......4 | initial |
| 92..6531883...2.69...839...5.86.7923.9..5....3..92....7...9..86.89..6.3..5..8..94 | autosolve |
| 927465318835172469461839572548617923192358647376924851714593286289746135653281794 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C1: 4,7 B3: 6,7 D1: 4,7 H3: 5,7 B4: 1,4 B6: 6,7 E4: 1,4 G5: 6,8 H5: 4,7 I5: 1,7 G6: 6,8 B7: 1,4 F9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,C3: 1.. / A3 = 1 => 15 pairs (_) / C3 = 1 => 15 pairs (_) D2,E2: 1.. / D2 = 1 => 15 pairs (_) / E2 = 1 => 0 pairs (X) I5,I6: 1.. / I5 = 1 => 14 pairs (_) / I6 = 1 => 15 pairs (_) B4,E4: 1.. / B4 = 1 => 0 pairs (X) / E4 = 1 => 18 pairs (_) B4,B7: 1.. / B4 = 1 => 0 pairs (X) / B7 = 1 => 18 pairs (_) G3,I3: 2.. / G3 = 2 => 23 pairs (_) / I3 = 2 => 14 pairs (_) A5,C5: 2.. / A5 = 2 => 17 pairs (_) / C5 = 2 => 17 pairs (_) I3,I8: 2.. / I3 = 2 => 14 pairs (_) / I8 = 2 => 23 pairs (_) D5,F5: 3.. / D5 = 3 => 13 pairs (_) / F5 = 3 => 0 pairs (X) C7,C9: 3.. / C7 = 3 => 16 pairs (_) / C9 = 3 => 18 pairs (_) G2,G3: 4.. / G2 = 4 => 16 pairs (_) / G3 = 4 => 16 pairs (_) H5,H6: 4.. / H5 = 4 => 14 pairs (_) / H6 = 4 => 15 pairs (_) C1,D1: 4.. / C1 = 4 => 0 pairs (X) / D1 = 4 => 17 pairs (_) B4,E4: 4.. / B4 = 4 => 18 pairs (_) / E4 = 4 => 0 pairs (X) B4,B7: 4.. / B4 = 4 => 18 pairs (_) / B7 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 14 pairs (_) / C3 = 5 => 0 pairs (X) H6,I6: 5.. / H6 = 5 => 15 pairs (_) / I6 = 5 => 16 pairs (_) D7,D8: 5.. / D7 = 5 => 14 pairs (_) / D8 = 5 => 15 pairs (_) C2,G2: 5.. / C2 = 5 => 14 pairs (_) / G2 = 5 => 0 pairs (X) D7,G7: 5.. / D7 = 5 => 14 pairs (_) / G7 = 5 => 15 pairs (_) H3,H6: 5.. / H3 = 5 => 16 pairs (_) / H6 = 5 => 15 pairs (_) G5,G6: 6.. / G5 = 6 => 12 pairs (_) / G6 = 6 => 16 pairs (_) A9,C9: 6.. / A9 = 6 => 14 pairs (_) / C9 = 6 => 19 pairs (_) B3,B6: 6.. / B3 = 6 => 14 pairs (_) / B6 = 6 => 0 pairs (X) C1,D1: 7.. / C1 = 7 => 17 pairs (_) / D1 = 7 => 0 pairs (X) D9,G9: 7.. / D9 = 7 => 18 pairs (_) / G9 = 7 => 16 pairs (_) B3,B6: 7.. / B3 = 7 => 0 pairs (X) / B6 = 7 => 14 pairs (_) E2,E8: 7.. / E2 = 7 => 17 pairs (_) / E8 = 7 => 17 pairs (_) F5,F6: 8.. / F5 = 8 => 12 pairs (_) / F6 = 8 => 16 pairs (_) G5,G6: 8.. / G5 = 8 => 16 pairs (_) / G6 = 8 => 12 pairs (_) F5,G5: 8.. / F5 = 8 => 12 pairs (_) / G5 = 8 => 16 pairs (_) F6,G6: 8.. / F6 = 8 => 16 pairs (_) / G6 = 8 => 12 pairs (_) * DURATION: 0:00:37.475730 START: 00:25:38.411722 END: 00:26:15.887452 2019-05-01 * CP COUNT: (32) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B6,B7,C1,D1,E4,F9,G5,G6,H3,H5,I5) * 92..6531883...2.69...839...5.86.7923.9..5....3..92....7...9..86.89..6.3..5..8..94 * PAIR C1: 4,7 BLK 1 C2: 4,7,5 # reduction candidate for 4,7 C2: 4,7 => CTR * 92..6531883...2569165839472548617923.9135864737692485171.593286489..6.35.5..8..94 C2: 5 # 14 pairs C3: 4,7,1,5,6 # reduction candidate for 4,7 C3: 4,7 # 18 pairs * PAIR C1: 4,7 COL C C5: 4,7,1,2,6 # reduction candidate for 4,7 C5: 4,7 # 20 pairs C6: 4,7,1,6 # reduction candidate for 4,7 C6: 4,7 # 18 pairs * PAIR B3: 6,7 BLK 1 C3: 6,7,1,4,5 # reduction candidate for 6,7 C3: 6,7 => CTR * 924765318835..27691..8394525.86.7923.9..5....3..92...57...9..86.89.76.3..5..8..94 C3: 1,4,5 # 13 pairs * PAIR D1: 4,7 BLK 2 D2: 4,7,1 # reduction candidate for 4,7 D2: 4,7 => CTR * 92..6531883..12.69...839...518647923.9..5....3..92....74..9..86.89476.3..5..8.794 D2: 1 # 15 pairs E2: 4,7,1 # reduction candidate for 4,7 E2: 4,7 # 15 pairs * PAIR D1: 4,7 COL D D8: 4,7,1,2,5 # reduction candidate for 4,7 D8: 4,7 # 20 pairs D8: 1,2,5 # 13 pairs * PAIR H3: 5,7 BLK 3 G2: 5,7,4 # reduction candidate for 5,7 G2: 5,7 # 16 pairs G3: 5,7,2,4 # reduction candidate for 5,7 G3: 5,7 # 18 pairs I3: 5,7,2 # reduction candidate for 5,7 I3: 5,7 # 23 pairs * PAIR H3: 5,7 ROW 3 C3: 5,7,1,4,6 # reduction candidate for 5,7 C3: 5,7 # 19 pairs C3: 1,4,6 # 14 pairs * PAIR H3: 5,7 COL H H6: 5,7,4 # reduction candidate for 5,7 H6: 4 # 15 pairs H6: 5,7 # 14 pairs * PAIR B4: 1,4 BLK 4 A5: 1,4,2,6 # reduction candidate for 1,4 A5: 1,4 # 18 pairs C5: 1,4,2,6,7 # reduction candidate for 1,4 C5: 1,4 # 20 pairs C6: 1,4,6,7 # reduction candidate for 1,4 C6: 1,4 # 15 pairs * PAIR B6: 6,7 BLK 4 C5: 6,7,1,2,4 # reduction candidate for 6,7 C5: 6,7 # 19 pairs C6: 6,7,1,4 # reduction candidate for 6,7 C6: 6,7 # 15 pairs * PAIR E4: 1,4 BLK 5 D5: 1,4,3 # reduction candidate for 1,4 D5: 1,4 => CTR * 924765318837142569.6.839...548617923.9.45387137192864571..94.86489.76132.5..81794 D5: 3 # 13 pairs F5: 1,4,3,8 # reduction candidate for 1,4 F5: 1,4 # 17 pairs F6: 1,4,8 # reduction candidate for 1,4 F6: 1,4 # 12 pairs * PAIR E4: 1,4 COL E E2: 1,4,7 # reduction candidate for 1,4 E2: 1,4 # 17 pairs E8: 1,4,7 # reduction candidate for 1,4 E8: 1,4 # 17 pairs * PAIR H5: 4,7 BLK 6 H6: 4,7,5 # reduction candidate for 4,7 H6: 4,7 # 16 pairs H6: 5 # 15 pairs * PAIR H5: 4,7 ROW 5 C5: 4,7,1,2,6 # reduction candidate for 4,7 C5: 4,7 # 20 pairs C5: 1,2,6 # 15 pairs * PAIR I5: 1,7 BLK 6 I6: 1,7,5 # reduction candidate for 1,7 I6: 5 # 16 pairs I6: 1,7 # 15 pairs * PAIR I5: 1,7 ROW 5 C5: 1,7,2,4,6 # reduction candidate for 1,7 C5: 1,7 # 17 pairs C5: 2,4,6 # 15 pairs * PAIR B7: 1,4 BLK 7 C7: 1,4,2,3 # reduction candidate for 1,4 C7: 1,4 => SOLVED * 927465318835172469461839572548617923192358647376924851714593286289746135653281794 C7: 2,3 # 14 pairs A8: 1,4,2 # reduction candidate for 1,4 A8: 1,4 # 16 pairs * PAIR B7: 1,4 ROW 7 D7: 1,4,2,3,5 # reduction candidate for 1,4 D7: 1,4 => CTR * 92..65318835..2469...8392..5.86.7923.9.35....3..92....7.2.93586.89576132.53281794 D7: 2,3,5 # 13 pairs F7: 1,4,3 # reduction candidate for 1,4 F7: 1,4 # 16 pairs * PAIR F9: 1,3 BLK 8 D7: 1,3,2,4,5 # reduction candidate for 1,3 D7: 1,3 => CTR * 92.465318835712469...8392..51864792329.1538.73..9286.1742.9.586.89576132.53281794 D7: 2,4,5 # 13 pairs F7: 1,3,4 # reduction candidate for 1,3 F7: 1,3 # 20 pairs D9: 1,3,2,7 # reduction candidate for 1,3 D9: 1,3 => CTR * 92..6531883...2.6916.839...548617923.9.453871371928645713.94586489576132.5.381794 D9: 2,7 # 14 pairs * PAIR F9: 1,3 ROW 9 C9: 1,3,2,6 # reduction candidate for 1,3 C9: 2,6 # 17 pairs C9: 1,3 # 17 pairs * PAIR F9: 1,3 COL F F5: 1,3,4,8 # reduction candidate for 1,3 F5: 1,3 => CTR * 924765318837142569.6.839...548617923.9.45387137192864571..94.86489.76.32.5..81794 F5: 4,8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060706-absurd-base-pr-000.dot * REASONING * DIS # C2: 4,7 => CTR => C2: 5 * DIS # C3: 6,7 => CTR => C3: 1,4,5 * DIS # D2: 4,7 => CTR => D2: 1 * DIS # D5: 1,4 => CTR => D5: 3 * PRF # C7: 1,4 => SOL * DIS # D7: 1,4 => CTR => D7: 2,3,5 * DIS # D7: 1,3 => CTR => D7: 2,4,5 * DIS # D9: 1,3 => CTR => D9: 2,7 * DIS # F5: 1,3 => CTR => F5: 4,8 * CNT 9 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B6,B7,C1,D1,E4,F9,G5,G6,H3,H5,I5) * 92..6531883...2.69...839...5.86.7923.9..5....3..92....7...9..86.89..6.3..5..8..94 * PAIR C1: 4,7 BLK 1 C2: 4,7,5 # reduction candidate for 4,7 C2: 4,7 => CTR * 92..6531883...2569165839472548617923.9135864737692485171.593286489..6.35.5..8..94 C3: 4,7,1,6 # reduction candidate for 4,7 C3: 4,7 # 18 pairs * RESTART * PAIR C1: 4,7 BLK 1 C3: 4,7,1,6 # reduction candidate for 4,7 C3: 4,7 # 18 pairs C3: 1,6 # 15 pairs * PAIR C1: 4,7 COL C C5: 4,7,1,2,6 # reduction candidate for 4,7 C5: 4,7 # 20 pairs C6: 4,7,1,6 # reduction candidate for 4,7 C6: 4,7 # 18 pairs * PAIR B3: 6,7 BLK 1 C3: 6,7,1,4 # reduction candidate for 6,7 C3: 6,7 => CTR * 924765318835..27691..8394525.86.7923.9..5....3..92...57...9..86.89.76.3..5..8..94 * PAIR D1: 4,7 BLK 2 D2: 4,7,1 # reduction candidate for 4,7 D2: 4,7 => CTR * 92..65318835.12.69...839...518647923.9..5....3..92....74..9..86.89476.3..5..8.794 * RESTART * PAIR D1: 4,7 COL D D8: 4,7,2,5 # reduction candidate for 4,7 D8: 4,7 # 18 pairs D8: 2,5 # 18 pairs * PAIR H3: 5,7 BLK 3 G3: 5,7,2,4 # reduction candidate for 5,7 G3: 5,7 # 18 pairs I3: 5,7,2 # reduction candidate for 5,7 I3: 5,7 # 25 pairs * PAIR H3: 5,7 COL H H6: 5,7,4 # reduction candidate for 5,7 H6: 5,7 # 18 pairs H6: 4 # 17 pairs * PAIR B4: 1,4 BLK 4 A5: 1,4,2,6 # reduction candidate for 1,4 A5: 1,4 # 22 pairs C5: 1,4,2,6,7 # reduction candidate for 1,4 C5: 1,4 # 19 pairs C6: 1,4,6,7 # reduction candidate for 1,4 C6: 1,4 # 19 pairs * PAIR B6: 6,7 BLK 4 C5: 6,7,1,2,4 # reduction candidate for 6,7 C5: 6,7 # 19 pairs C6: 6,7,1,4 # reduction candidate for 6,7 C6: 6,7 # 19 pairs * PAIR E4: 1,4 BLK 5 F5: 1,4,3,8 # reduction candidate for 1,4 F5: 1,4 # 19 pairs F6: 1,4,8 # reduction candidate for 1,4 F6: 1,4 # 16 pairs * PAIR E4: 1,4 COL E E8: 1,4,7 # reduction candidate for 1,4 E8: 7 => CTR * 92..653188351.2.69...839...5.8617923.9..5....3..92....71..9..86.89.7613..5..81794 * PAIR RESTART * PAIR E4: 1,4 BLK 5 F5: 1,4,8 # reduction candidate for 1,4 F5: 1,4 # 19 pairs F6: 1,4,8 # reduction candidate for 1,4 F6: 1,4 # 15 pairs * PAIR B7: 1,4 BLK 7 C7: 1,4,2,3 # reduction candidate for 1,4 C7: 1,4 => SOLVED * 927465318835172469461839572548617923192358647376924851714593286289746135653281794 * DURATION: 0:00:20.152878 START: 00:26:50.507567 END: 00:27:10.660445 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060706-absurd-base-pr-001.dot * REASONING * DIS # C2: 4,7 => CTR => C2: 5 * DIS C2: 5 # C3: 6,7 => CTR => C3: 1,4 * DIS C2: 5 + C3: 1,4 # D2: 4,7 => CTR => D2: 1 * DIS C2: 5 + C3: 1,4 + D2: 1 # E8: 7 => CTR => E8: 1,4 * PRF C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # C7: 1,4 => SOL * STA C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 + C7: 1,4 * CNT 5 HDP CHAINS / 26 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060706, absurd
Solution
position: 927465318835172469461839572548617923192358647376924851714593286289746135653281794 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # C2: 4,7 => CTR => C2: 5 * INC # C2: 5 => UNS * INC # C3: 4,7 => UNS * INC # C5: 4,7 => UNS * INC # C6: 4,7 => UNS * DIS # C3: 6,7 => CTR => C3: 1,4,5 * INC # C3: 1,4,5 => UNS * DIS # D2: 4,7 => CTR => D2: 1 * INC # D2: 1 => UNS * INC # E2: 4,7 => UNS * INC # D8: 4,7 => UNS * INC # D8: 1,2,5 => UNS * INC # G2: 5,7 => UNS * INC # G3: 5,7 => UNS * INC # I3: 5,7 => UNS * INC # C3: 5,7 => UNS * INC # C3: 1,4,6 => UNS * INC # H6: 5,7 => UNS * INC # H6: 4 => UNS * INC # A5: 1,4 => UNS * INC # C5: 1,4 => UNS * INC # C6: 1,4 => UNS * INC # C5: 6,7 => UNS * INC # C6: 6,7 => UNS * DIS # D5: 1,4 => CTR => D5: 3 * INC # D5: 3 => UNS * INC # F5: 1,4 => UNS * INC # F6: 1,4 => UNS * INC # E2: 1,4 => UNS * INC # E8: 1,4 => UNS * INC # H6: 4,7 => UNS * INC # H6: 5 => UNS * INC # C5: 4,7 => UNS * INC # C5: 1,2,6 => UNS * INC # I6: 1,7 => UNS * INC # I6: 5 => UNS * INC # C5: 1,7 => UNS * INC # C5: 2,4,6 => UNS * PRF # C7: 1,4 => SOL * INC # C7: 2,3 => UNS * INC # A8: 1,4 => UNS * DIS # D7: 1,4 => CTR => D7: 2,3,5 * INC # D7: 2,3,5 => UNS * INC # F7: 1,4 => UNS * DIS # D7: 1,3 => CTR => D7: 2,4,5 * INC # D7: 2,4,5 => UNS * INC # F7: 1,3 => UNS * DIS # D9: 1,3 => CTR => D9: 2,7 * INC # D9: 2,7 => UNS * INC # C9: 1,3 => UNS * INC # C9: 2,6 => UNS * DIS # F5: 1,3 => CTR => F5: 4,8 * INC # F5: 4,8 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 4,7 => CTR => C2: 5 * INC C2: 5 # C3: 4,7 => UNS * INC C2: 5 # C3: 4,7 => UNS * INC C2: 5 # C3: 1,6 => UNS * INC C2: 5 # C5: 4,7 => UNS * INC C2: 5 # C6: 4,7 => UNS * DIS C2: 5 # C3: 6,7 => CTR => C3: 1,4 * DIS C2: 5 + C3: 1,4 # D2: 4,7 => CTR => D2: 1 * INC C2: 5 + C3: 1,4 + D2: 1 # D8: 4,7 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # D8: 2,5 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # G3: 5,7 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # I3: 5,7 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # H6: 5,7 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # H6: 4 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # A5: 1,4 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # C5: 1,4 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # C6: 1,4 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # C5: 6,7 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # C6: 6,7 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # F5: 1,4 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # F6: 1,4 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 # E8: 1,4 => UNS * DIS C2: 5 + C3: 1,4 + D2: 1 # E8: 7 => CTR => E8: 1,4 * INC C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # F5: 1,4 => UNS * INC C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # F6: 1,4 => UNS * PRF C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # C7: 1,4 => SOL * STA C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 + C7: 1,4 * CNT 26 HDP CHAINS / 26 HYP OPENED