Analysis of zz-www.sudokuoftheday.co.uk-20060606-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: 7.68......8..1.64.13.2...5.2...51.3...5.....9....7......978.........2..362....... initial
Autosolve
position: 7.68..3...82.1.6471342679582...51.3...5.2...9..3.7....3.978.........2..362..3.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 4 => CTR => F1: 5,9 * DIS # F2: 5,9 => CTR => F2: 3 * PRF # F1: 4,9 => SOL * DIS # F1: 5 => CTR => F1: 4,9 * PRF # H6: 1,2 => SOL * DIS # G4: 4 => CTR => G4: 7,8 * DIS # C8: 7,8 => CTR => C8: 1 * PRF # A6: 4,8 => SOL * DIS # A6: 9 => CTR => A6: 4,8 * DIS # G5: 4,8 => CTR => G5: 1,7 * DIS # A8: 4,8 => CTR => A8: 5 * PRF # A8: 5 => SOL * PRF # I6: 4,6 => SOL * PRF # D4: 4,6 => SOL * PRF # A8: 4,5 => SOL * DIS # A8: 8 => CTR => A8: 4,5 * DIS # B8: 4,5 => CTR => B8: 7 * PRF # B8: 7 => SOL * PRF # F7: 4,5 => SOL * DIS # F7: 6 => CTR => F7: 4,5 * DIS # G7: 4,5 => CTR => G7: 1,2 * DIS # I7: 4,5 => CTR => I7: 1,2,6 * DIS # D8: 4,9 => CTR => D8: 1,5,6 * DIS # D9: 4,9 => CTR => D9: 1,5 * DIS # G7: 4,5 => CTR => G7: 1,2 * DIS # I7: 4,5 => CTR => I7: 1,2,6 * PRF # G8: 4,5 => SOL * DIS # G9: 4,5 => CTR => G9: 7,8 * DIS # D9: 4,5 => CTR => D9: 1,9 * CNT 29 HDP CHAINS / 59 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 4 => CTR => F1: 5,9 * DIS F1: 5,9 # F2: 5,9 => CTR => F2: 3 * PRF F1: 5,9 + F2: 3 # H6: 1,2 => SOL * STA F1: 5,9 + F2: 3 + H6: 1,2 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7.68......8..1.64.13.2...5.2...51.3...5.....9....7......978.........2..362....... | initial |
| 7.68..3...82.1.6471342679582...51.3...5.2...9..3.7....3.978.........2..362..3.... | autosolve |
| 756849312982513647134267958297451836465328179813976524349785261571692483628134795 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) B1: 5,9 A2: 5,9 E1: 4,9 H1: 1,2 I1: 1,2 C4: 7,8 A5: 4,8 I4: 4,6 B7: 4,5 E8: 4,9 I9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,I1: 1.. / H1 = 1 => 10 pairs (_) / I1 = 1 => 12 pairs (_) B5,B6: 1.. / B5 = 1 => 0 pairs (X) / B6 = 1 => 11 pairs (_) C8,C9: 1.. / C8 = 1 => 12 pairs (_) / C9 = 1 => 0 pairs (X) D8,D9: 1.. / D8 = 1 => 0 pairs (X) / D9 = 1 => 12 pairs (_) C8,D8: 1.. / C8 = 1 => 12 pairs (_) / D8 = 1 => 0 pairs (X) C9,D9: 1.. / C9 = 1 => 0 pairs (X) / D9 = 1 => 12 pairs (_) H1,I1: 2.. / H1 = 2 => 12 pairs (_) / I1 = 2 => 10 pairs (_) G6,G7: 2.. / G6 = 2 => 17 pairs (_) / G7 = 2 => 12 pairs (_) D2,F2: 3.. / D2 = 3 => 0 pairs (X) / F2 = 3 => 12 pairs (_) D5,F5: 3.. / D5 = 3 => 12 pairs (_) / F5 = 3 => 0 pairs (X) D2,D5: 3.. / D2 = 3 => 0 pairs (X) / D5 = 3 => 12 pairs (_) F2,F5: 3.. / F2 = 3 => 12 pairs (_) / F5 = 3 => 0 pairs (X) E1,F1: 4.. / E1 = 4 => 13 pairs (_) / F1 = 4 => 0 pairs (X) E1,E8: 4.. / E1 = 4 => 13 pairs (_) / E8 = 4 => 0 pairs (X) B1,A2: 5.. / B1 = 5 => 0 pairs (*) / A2 = 5 => 0 pairs (X) G6,I6: 5.. / G6 = 5 => 12 pairs (_) / I6 = 5 => 15 pairs (_) B1,F1: 5.. / B1 = 5 => 0 pairs (*) / F1 = 5 => 0 pairs (X) A2,A8: 5.. / A2 = 5 => 0 pairs (X) / A8 = 5 => 0 pairs (_) F7,D8: 6.. / F7 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) D8,H8: 6.. / D8 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) F5,F6: 8.. / F5 = 8 => 14 pairs (_) / F6 = 8 => 0 pairs (X) C4,G4: 8.. / C4 = 8 => 0 pairs (X) / G4 = 8 => 0 pairs (_) B1,A2: 9.. / B1 = 9 => 0 pairs (X) / A2 = 9 => 0 pairs (_) H8,H9: 9.. / H8 = 9 => 0 pairs (X) / H9 = 9 => 14 pairs (_) B4,D4: 9.. / B4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) A2,A6: 9.. / A2 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) E1,E8: 9.. / E1 = 9 => 0 pairs (X) / E8 = 9 => 13 pairs (_) * DURATION: 0:00:28.435706 START: 23:40:00.297995 END: 23:40:28.733701 2019-04-30 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B1,B7,C4,E1,E8,H1,I1,I4,I9) * 7.68..3...82.1.6471342679582...51.3...5.2...9..3.7....3.978.........2..362..3.... * PAIR B1: 5,9 ROW 1 F1: 5,9,4 # reduction candidate for 5,9 F1: 4 => CTR * 7568943..982.1.6471342679582...51.3...5.2...9..3.7....34978....57..428.3628.3.... F1: 5,9 # 13 pairs * PAIR A2: 5,9 ROW 2 D2: 5,9,3 # reduction candidate for 5,9 D2: 5,9 # 12 pairs F2: 5,9,3 # reduction candidate for 5,9 F2: 5,9 => CTR * 7.68..3...8231.6471342679582...51.3...5.23..9..3.78...3.9786........2.6362..3..9. F2: 3 # 12 pairs * PAIR E1: 4,9 BLK 2 F1: 4,9,5 # reduction candidate for 4,9 F1: 4,9 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 F1: 5 => CTR * 7968453..582.196471342679582..951.3...5.23..99.3.785..359786214...592.6362.134.95 * PAIR H1: 1,2 COL H H6: 1,2,6,8 # reduction candidate for 1,2 H6: 1,2 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 H6: 6,8 # 14 pairs H7: 1,2,6 # reduction candidate for 1,2 H7: 1,2 # 16 pairs * PAIR I1: 1,2 COL I I6: 1,2,4,5,6 # reduction candidate for 1,2 I6: 1,2 # 11 pairs I7: 1,2,4,5,6 # reduction candidate for 1,2 I7: 1,2 # 12 pairs * PAIR C4: 7,8 ROW 4 G4: 7,8,4 # reduction candidate for 7,8 G4: 4 => CTR * 7968453..5823196471342679582789514364.5623..99634785..35978621484.59276362..34.95 G4: 7,8 # 12 pairs * PAIR C4: 7,8 COL C C8: 7,8,1 # reduction candidate for 7,8 C8: 7,8 => CTR * 7.68..3...82.1.6471342679582...51.3...5.2...9..3.7....3.978.......1.2.63621.3..9. C8: 1 # 12 pairs C9: 7,8,1 # reduction candidate for 7,8 C9: 7,8 # 12 pairs * PAIR A5: 4,8 BLK 4 A6: 4,8,9 # reduction candidate for 4,8 A6: 4,8 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 A6: 9 => CTR * 7968453..5823196471342679582..951.3...5.23..99.3.785..359786214...592.6362.134.95 * PAIR A5: 4,8 ROW 5 F5: 4,8,3,6 # reduction candidate for 4,8 F5: 4,8 # 14 pairs G5: 4,8,1,7 # reduction candidate for 4,8 G5: 4,8 => CTR * 7.68..3...825136471342679582...51.36.15326.79.63.78..53.978..6.5.16.278362.13...4 G5: 1,7 # 12 pairs * PAIR A5: 4,8 COL A A8: 4,8,5 # reduction candidate for 4,8 A8: 4,8 => CTR * 7968453..5823196471342679582..951.3...5.23..99.3.785..359786214...592.6362.134.95 A8: 5 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 * PAIR I4: 4,6 BLK 6 I6: 4,6,1,2,5 # reduction candidate for 4,6 I6: 4,6 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 I6: 1,2,5 # 11 pairs * PAIR I4: 4,6 ROW 4 B4: 4,6,7,9 # reduction candidate for 4,6 B4: 4,6 # 15 pairs D4: 4,6,9 # reduction candidate for 4,6 D4: 4,6 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 D4: 9 # 13 pairs * PAIR I4: 4,6 COL I I7: 4,6,1,2,5 # reduction candidate for 4,6 I7: 4,6 # 15 pairs I7: 1,2,5 # 11 pairs * PAIR B7: 4,5 BLK 7 A8: 4,5,8 # reduction candidate for 4,5 A8: 4,5 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 A8: 8 => CTR * 7968453..5823196471342679582.8951.3.4.5623..99.34785..35978621484.59276362..34.95 B8: 4,5,7 # reduction candidate for 4,5 B8: 4,5 => CTR * 7968453..5823196471342679582.8951.3.4.5623..99.34785..35978621484.59276362..34.95 B8: 7 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 * PAIR B7: 4,5 ROW 7 F7: 4,5,6 # reduction candidate for 4,5 F7: 4,5 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 F7: 6 => CTR * 7.68..3...82.1.6471342679582.8.514364.5.28179913674.8.3.9786...8....2.6362..35894 G7: 4,5,1,2 # reduction candidate for 4,5 G7: 4,5 => CTR * 7.68..3...82.1.6471342679582.8.51436465328179913.7.2853497865..85...2763627135894 G7: 1,2 # 12 pairs I7: 4,5,1,2,6 # reduction candidate for 4,5 I7: 4,5 => CTR * 796845321582.196471342679582789514364.5.2.179913.7.5823.978621.8.1..276362713.89. I7: 1,2,6 # 11 pairs * PAIR E8: 4,9 BLK 8 D8: 4,9,1,5,6 # reduction candidate for 4,9 D8: 4,9 => CTR * 7568..3..9825136471342679582...51.36..532..79..367..8.349786...571..2863628135.94 D8: 1,5,6 # 11 pairs D9: 4,9,1,5 # reduction candidate for 4,9 D9: 4,9 => CTR * 7.68..3...82.1.6471342679582...51.3...5.2...9..3.7....3.978.......1.2.63621.3..9. D9: 1,5 # 12 pairs F9: 4,9,5 # reduction candidate for 4,9 F9: 4,9 # 14 pairs * PAIR I9: 4,5 BLK 9 G7: 4,5,1,2 # reduction candidate for 4,5 G7: 4,5 => CTR * 7.68..3...82.1.6471342679582.8.51436465328179913.7.2853497865..85...2763627135894 G7: 1,2 # 12 pairs I7: 4,5,1,2,6 # reduction candidate for 4,5 I7: 4,5 => CTR * 796845321582.196471342679582789514364.5.2.179913.7.5823.978621.8.1..276362713.89. I7: 1,2,6 # 11 pairs G8: 4,5,7,8 # reduction candidate for 4,5 G8: 4,5 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 G8: 7,8 # 12 pairs G9: 4,5,7,8 # reduction candidate for 4,5 G9: 4,5 => CTR * 7.68943..9825136471342679582...51.3...532...9..3.7....349785...571642893628139... G9: 7,8 # 12 pairs * PAIR I9: 4,5 ROW 9 D9: 4,5,1,9 # reduction candidate for 4,5 D9: 4,5 => CTR * 7.68..3...82.1.6471342679582...51.3...5.2...9..3.7....3.978.......1.2.63621.3..9. D9: 1,9 # 12 pairs F9: 4,5,9 # reduction candidate for 4,5 F9: 4,5 # 14 pairs * PAIR I9: 4,5 COL I I6: 4,5,1,2,6 # reduction candidate for 4,5 I6: 4,5 # 16 pairs I6: 1,2,6 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060606-absurd-base-pr-000.dot * REASONING * DIS # F1: 4 => CTR => F1: 5,9 * DIS # F2: 5,9 => CTR => F2: 3 * PRF # F1: 4,9 => SOL * DIS # F1: 5 => CTR => F1: 4,9 * PRF # H6: 1,2 => SOL * DIS # G4: 4 => CTR => G4: 7,8 * DIS # C8: 7,8 => CTR => C8: 1 * PRF # A6: 4,8 => SOL * DIS # A6: 9 => CTR => A6: 4,8 * DIS # G5: 4,8 => CTR => G5: 1,7 * DIS # A8: 4,8 => CTR => A8: 5 * PRF # A8: 5 => SOL * PRF # I6: 4,6 => SOL * PRF # D4: 4,6 => SOL * PRF # A8: 4,5 => SOL * DIS # A8: 8 => CTR => A8: 4,5 * DIS # B8: 4,5 => CTR => B8: 7 * PRF # B8: 7 => SOL * PRF # F7: 4,5 => SOL * DIS # F7: 6 => CTR => F7: 4,5 * DIS # G7: 4,5 => CTR => G7: 1,2 * DIS # I7: 4,5 => CTR => I7: 1,2,6 * DIS # D8: 4,9 => CTR => D8: 1,5,6 * DIS # D9: 4,9 => CTR => D9: 1,5 * DIS # G7: 4,5 => CTR => G7: 1,2 * DIS # I7: 4,5 => CTR => I7: 1,2,6 * PRF # G8: 4,5 => SOL * DIS # G9: 4,5 => CTR => G9: 7,8 * DIS # D9: 4,5 => CTR => D9: 1,9 * CNT 29 HDP CHAINS / 59 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B1,B7,C4,E1,E8,H1,I1,I4,I9) * 7.68..3...82.1.6471342679582...51.3...5.2...9..3.7....3.978.........2..362..3.... * PAIR B1: 5,9 ROW 1 F1: 5,9,4 # reduction candidate for 5,9 F1: 4 => CTR * 7568943..982.1.6471342679582...51.3...5.2...9..3.7....34978....57..428.3628.3.... * PAIR RESTART * PAIR A2: 5,9 ROW 2 D2: 5,9,3 # reduction candidate for 5,9 D2: 5,9 # 14 pairs F2: 5,9,3 # reduction candidate for 5,9 F2: 5,9 => CTR * 7.684.3...8231.6471342679582...51.3...5.23..9..3.78...3.9786.....1592.6362.134.95 * RESTART * PAIR RESTART * PAIR H1: 1,2 COL H H6: 1,2,6,8 # reduction candidate for 1,2 H6: 1,2 => SOLVED * 756849312982513647134267958297451836465328179813976524349785261571692483628134795 * DURATION: 0:00:04.428283 START: 23:41:06.622611 END: 23:41:11.050894 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060606-absurd-base-pr-001.dot * REASONING * DIS # F1: 4 => CTR => F1: 5,9 * DIS F1: 5,9 # F2: 5,9 => CTR => F2: 3 * PRF F1: 5,9 + F2: 3 # H6: 1,2 => SOL * STA F1: 5,9 + F2: 3 + H6: 1,2 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060606, absurd
Solution
position: 756849312982513647134267958297451836465328179813976524349785261571692483628134795 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:
* INC # F1: 5,9 => UNS * DIS # F1: 4 => CTR => F1: 5,9 * INC # D2: 5,9 => UNS * DIS # F2: 5,9 => CTR => F2: 3 * INC # F2: 3 => UNS * PRF # F1: 4,9 => SOL * DIS # F1: 5 => CTR => F1: 4,9 * PRF # H6: 1,2 => SOL * INC # H6: 6,8 => UNS * INC # H7: 1,2 => UNS * INC # I6: 1,2 => UNS * INC # I7: 1,2 => UNS * INC # G4: 7,8 => UNS * DIS # G4: 4 => CTR => G4: 7,8 * DIS # C8: 7,8 => CTR => C8: 1 * INC # C8: 1 => UNS * INC # C9: 7,8 => UNS * PRF # A6: 4,8 => SOL * DIS # A6: 9 => CTR => A6: 4,8 * INC # F5: 4,8 => UNS * DIS # G5: 4,8 => CTR => G5: 1,7 * INC # G5: 1,7 => UNS * DIS # A8: 4,8 => CTR => A8: 5 * PRF # A8: 5 => SOL * PRF # I6: 4,6 => SOL * INC # I6: 1,2,5 => UNS * INC # B4: 4,6 => UNS * PRF # D4: 4,6 => SOL * INC # D4: 9 => UNS * INC # I7: 4,6 => UNS * INC # I7: 1,2,5 => UNS * PRF # A8: 4,5 => SOL * DIS # A8: 8 => CTR => A8: 4,5 * DIS # B8: 4,5 => CTR => B8: 7 * PRF # B8: 7 => SOL * PRF # F7: 4,5 => SOL * DIS # F7: 6 => CTR => F7: 4,5 * DIS # G7: 4,5 => CTR => G7: 1,2 * INC # G7: 1,2 => UNS * DIS # I7: 4,5 => CTR => I7: 1,2,6 * INC # I7: 1,2,6 => UNS * DIS # D8: 4,9 => CTR => D8: 1,5,6 * INC # D8: 1,5,6 => UNS * DIS # D9: 4,9 => CTR => D9: 1,5 * INC # D9: 1,5 => UNS * INC # F9: 4,9 => UNS * DIS # G7: 4,5 => CTR => G7: 1,2 * INC # G7: 1,2 => UNS * DIS # I7: 4,5 => CTR => I7: 1,2,6 * INC # I7: 1,2,6 => UNS * PRF # G8: 4,5 => SOL * INC # G8: 7,8 => UNS * DIS # G9: 4,5 => CTR => G9: 7,8 * INC # G9: 7,8 => UNS * DIS # D9: 4,5 => CTR => D9: 1,9 * INC # D9: 1,9 => UNS * INC # F9: 4,5 => UNS * INC # I6: 4,5 => UNS * INC # I6: 1,2,6 => UNS * CNT 59 HDP CHAINS / 59 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 5,9 => UNS * DIS # F1: 4 => CTR => F1: 5,9 * INC F1: 5,9 # D2: 5,9 => UNS * DIS F1: 5,9 # F2: 5,9 => CTR => F2: 3 * PRF F1: 5,9 + F2: 3 # H6: 1,2 => SOL * STA F1: 5,9 + F2: 3 + H6: 1,2 * CNT 5 HDP CHAINS / 5 HYP OPENED