Analysis of zz-www.sudokuoftheday.co.uk-20060607-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: ....8...1..5.9.7......1739.4....1.....2......37..4...8.2....54...34..6..5.4.36... initial
Autosolve
position: ..7.8...1..5.9.78.....1739.4....1.....2......37..4...8.2..7.5437.34..6..5.4.368.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 6,8 => CTR => A3: 2 * DIS # B3: 6,8 => CTR => B3: 4 * PRF # C4: 6,8 => SOL * DIS # C4: 9 => CTR => C4: 6,8 * DIS # C7: 6,8 => CTR => C7: 1,9 * DIS # I3: 2,4 => CTR => I3: 5,6 * DIS # A5: 1,6 => CTR => A5: 8,9 * DIS # C7: 1,6 => CTR => C7: 8,9 * PRF # C7: 8,9 => SOL * DIS # E4: 5,6 => CTR => E4: 2 * PRF # E4: 2 => SOL * PRF # H5: 5,6 => SOL * DIS # I5: 5,6 => CTR => I5: 4,7 * DIS # A7: 1,9 => CTR => A7: 6,8 * DIS # B8: 1,9 => CTR => B8: 8 * DIS # D9: 2 => CTR => D9: 1,9 * PRF # B5: 1,9 => SOL * DIS # D7: 8,9 => CTR => D7: 1 * PRF # D7: 1 => SOL * DIS # F8: 8,9 => CTR => F8: 2,5 * DIS # A7: 8,9 => CTR => A7: 1,6 * PRF # C7: 8,9 => SOL * DIS # C7: 1,6 => CTR => C7: 8,9 * DIS # F8: 8,9 => CTR => F8: 2,5 * DIS # E4: 6 => CTR => E4: 2,5 * PRF # F8: 2,9 => SOL * CNT 26 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 6,8 => CTR => A3: 2 * DIS A3: 2 # B3: 6,8 => CTR => B3: 4 * PRF A3: 2 + B3: 4 # I2: 6 => SOL * STA A3: 2 + B3: 4 + I2: 6 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....8...1..5.9.7......1739.4....1.....2......37..4...8.2....54...34..6..5.4.36... | initial |
| ..7.8...1..5.9.78.....1739.4....1.....2......37..4...8.2..7.5437.34..6..5.4.368.. | autosolve |
| 967385421135294786248617395456821937892763154371549268629178543783452619514936872 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C3: 6,8 G1: 2,4 C6: 1,6 E5: 5,6 F5: 3,8 G4: 2,9 G6: 1,2 B9: 1,9 F7: 8,9 E8: 2,5 H8: 1,2 I8: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,B2: 1.. / A2 = 1 => 12 pairs (_) / B2 = 1 => 0 pairs (X) G5,G6: 1.. / G5 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) D7,D9: 1.. / D7 = 1 => 0 pairs (*) / D9 = 1 => 0 pairs (X) H8,H9: 1.. / H8 = 1 => 13 pairs (_) / H9 = 1 => 0 pairs (X) C6,G6: 1.. / C6 = 1 => 0 pairs (*) / G6 = 1 => 0 pairs (X) B8,H8: 1.. / B8 = 1 => 0 pairs (X) / H8 = 1 => 13 pairs (_) C6,C7: 1.. / C6 = 1 => 0 pairs (*) / C7 = 1 => 0 pairs (X) E4,E8: 2.. / E4 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) B1,B2: 3.. / B1 = 3 => 12 pairs (_) / B2 = 3 => 14 pairs (_) H4,H5: 3.. / H4 = 3 => 13 pairs (_) / H5 = 3 => 0 pairs (X) D4,H4: 3.. / D4 = 3 => 0 pairs (X) / H4 = 3 => 13 pairs (_) F1,F2: 4.. / F1 = 4 => 0 pairs (X) / F2 = 4 => 13 pairs (_) G5,I5: 4.. / G5 = 4 => 0 pairs (X) / I5 = 4 => 14 pairs (_) B3,I3: 4.. / B3 = 4 => 12 pairs (_) / I3 = 4 => 0 pairs (X) G1,G5: 4.. / G1 = 4 => 14 pairs (_) / G5 = 4 => 0 pairs (X) H1,I3: 5.. / H1 = 5 => 0 pairs (X) / I3 = 5 => 14 pairs (_) B4,B5: 5.. / B4 = 5 => 13 pairs (_) / B5 = 5 => 17 pairs (_) E8,F8: 5.. / E8 = 5 => 0 pairs (*) / F8 = 5 => 0 pairs (X) D3,I3: 5.. / D3 = 5 => 0 pairs (X) / I3 = 5 => 14 pairs (_) E4,E5: 6.. / E4 = 6 => 0 pairs (X) / E5 = 6 => 12 pairs (_) A7,C7: 6.. / A7 = 6 => 15 pairs (_) / C7 = 6 => 0 pairs (X) C6,H6: 6.. / C6 = 6 => 0 pairs (X) / H6 = 6 => 0 pairs (_) D4,D5: 7.. / D4 = 7 => 13 pairs (_) / D5 = 7 => 13 pairs (_) H9,I9: 7.. / H9 = 7 => 15 pairs (_) / I9 = 7 => 18 pairs (_) B8,F8: 8.. / B8 = 8 => 13 pairs (_) / F8 = 8 => 0 pairs (X) A1,B1: 9.. / A1 = 9 => 12 pairs (_) / B1 = 9 => 0 pairs (X) D6,F6: 9.. / D6 = 9 => 15 pairs (_) / F6 = 9 => 18 pairs (_) G4,G5: 9.. / G4 = 9 => 0 pairs (*) / G5 = 9 => 0 pairs (X) I8,I9: 9.. / I8 = 9 => 13 pairs (_) / I9 = 9 => 0 pairs (X) C4,C7: 9.. / C4 = 9 => 0 pairs (X) / C7 = 9 => 0 pairs (_) * DURATION: 0:00:32.024987 START: 23:41:19.765466 END: 23:41:51.790453 2019-04-30 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C3,C6,E5,E8,F5,F7,G1,G4,G6,H8,I8) * ..7.8...1..5.9.78.....1739.4....1.....2......37..4...8.2..7.5437.34..6..5.4.368.. * PAIR C3: 6,8 BLK 1 A3: 6,8,2 # reduction candidate for 6,8 A3: 6,8 => CTR * 2976834.1..5.94786.4..1739.4...219..9.2.6.1.4371.4.268.29.7854378345.61.514.368.. A3: 2 # 15 pairs B3: 6,8,4 # reduction candidate for 6,8 B3: 6,8 => CTR * 9.7.8.251..5.9.786...5173944.9..1.....2...4..37..4.1.8.21.7.5437.34..61.5941368.. B3: 4 # 12 pairs * PAIR C3: 6,8 COL C C4: 6,8,9 # reduction candidate for 6,8 C4: 6,8 => SOLVED * 967385421135294786248617395456821937892763154371549268629178543783452619514936872 C4: 9 => CTR * 9.758.4.1..5.9478.248617395459861237812753964376.4.158621978543783425619594136872 C7: 6,8,1,9 # reduction candidate for 6,8 C7: 6,8 => CTR * ..7.8...1..5.9.78.....1739.4.9..12....2...9.4371.4...8.2..7.5437.34..6..5.4.368.. C7: 1,9 # 17 pairs * PAIR G1: 2,4 BLK 3 I2: 2,4,6 # reduction candidate for 2,4 I2: 2,4 # 15 pairs I3: 2,4,5,6 # reduction candidate for 2,4 I3: 2,4 => CTR * ..768..51..5.9.786...51739.4...219....2.6....37.945..8.29.78543783459612514236879 I3: 5,6 # 13 pairs * PAIR G1: 2,4 ROW 1 F1: 2,4,3,5 # reduction candidate for 2,4 F1: 3,5 # 18 pairs F1: 2,4 # 16 pairs * PAIR C6: 1,6 BLK 4 A5: 1,6,8,9 # reduction candidate for 1,6 A5: 1,6 => CTR * 9.7.8...11.5.9.78.2.8.1739.4.9..12....2......37..4...8.2..7.5437.34..6..5.4.368.. A5: 8,9 # 13 pairs B5: 1,6,5,8,9 # reduction candidate for 1,6 B5: 1,6 # 16 pairs * PAIR C6: 1,6 COL C C7: 1,6,8,9 # reduction candidate for 1,6 C7: 1,6 => CTR * 9.758.4.1..5.9478.248617395459861237812753964376.4.158621978543783425619594136872 C7: 8,9 => SOLVED * 967385421135294786248617395456821937892763154371549268629178543783452619514936872 * PAIR E5: 5,6 BLK 5 E4: 5,6,2 # reduction candidate for 5,6 E4: 5,6 => CTR * 9.758...1..5.9.78.....173954.98.1237812753964376.4.158621978543783425619594136872 E4: 2 => SOLVED * 967385421135294786248617395456821937892763154371549268629178543783452619514936872 * PAIR E5: 5,6 ROW 5 B5: 5,6,1,8,9 # reduction candidate for 5,6 B5: 5,6 # 18 pairs H5: 5,6,3,7 # reduction candidate for 5,6 H5: 5,6 => SOLVED * 967385421135294786248617395456821937892763154371549268629178543783452619514936872 H5: 3,7 # 13 pairs I5: 5,6,4,7 # reduction candidate for 5,6 I5: 5,6 => CTR * 9.7.8.2.1..5.9.78.....1739.4.9..1.....2...4..37..4.1.8.21.7.5437.34..61.5941368.. I5: 4,7 # 13 pairs * PAIR F5: 3,8 BLK 5 D4: 3,8,7 # reduction candidate for 3,8 D4: 3,8 # 13 pairs D5: 3,8,7 # reduction candidate for 3,8 D5: 3,8 # 13 pairs * PAIR B9: 1,9 BLK 7 A7: 1,9,6,8 # reduction candidate for 1,9 A7: 1,9 => CTR * ..7.8...1..5.9.78...8.1739.4.98.12378.27.39.4371.4...8.26.7.5437834..61.5.4.368.. A7: 6,8 # 13 pairs C7: 1,9,6,8 # reduction candidate for 1,9 C7: 1,9 # 17 pairs B8: 1,9,8 # reduction candidate for 1,9 B8: 1,9 => CTR * ..7.8...1..5.9.78.....1739.4.9.21.....2..3...37..4...8.2..795437.34586..5.42368.. B8: 8 # 13 pairs * PAIR B9: 1,9 ROW 9 D9: 1,9,2 # reduction candidate for 1,9 D9: 2 => CTR * ..7.8.4211.5.9.78.....1739.4...219....2.6....371945268.29178543783459612514236879 D9: 1,9 # 15 pairs * PAIR B9: 1,9 COL B B5: 1,9,5,6,8 # reduction candidate for 1,9 B5: 1,9 => SOLVED * 967385421135294786248617395456821937892763154371549268629178543783452619514936872 B5: 5,6,8 # 15 pairs * PAIR F7: 8,9 BLK 8 D7: 8,9,1 # reduction candidate for 8,9 D7: 8,9 => CTR * 9.7582461..5.9478..48.1739.4.98.12378127.39.4376.4.158621978543783425619594136872 D7: 1 => SOLVED * 967385421135294786248617395456821937892763154371549268629178543783452619514936872 F8: 8,9,2,5 # reduction candidate for 8,9 F8: 8,9 => CTR * ..7.8...11.5.9278.2.8.1739.4.6821937892763154371945268629178543783459612514236879 F8: 2,5 # 15 pairs * PAIR F7: 8,9 ROW 7 A7: 8,9,1,6 # reduction candidate for 8,9 A7: 8,9 => CTR * ..7.8...1..5.9.78...8.1739.4.9..12....2...9.4371.4...8.2617.5437.34..6..5.4.368.. A7: 1,6 # 13 pairs C7: 8,9,1,6 # reduction candidate for 8,9 C7: 8,9 => SOLVED * 967385421135294786248617395456821937892763154371549268629178543783452619514936872 C7: 1,6 => CTR * 9.758.4.1..5.9478.248617395459861237812753964376.4.158621978543783425619594136872 * PAIR E8: 2,5 BLK 8 F8: 2,5,8,9 # reduction candidate for 2,5 F8: 8,9 => CTR * ..7.8...11.5.9278.2.8.1739.4.6821937892763154371945268629178543783459612514236879 F8: 2,5 # 15 pairs * PAIR E8: 2,5 COL E E4: 2,5,6 # reduction candidate for 2,5 E4: 6 => CTR * 9.758...1..5.9.78..48617395459861237812753964376.4.158621978543783425619594136872 E4: 2,5 # 12 pairs * PAIR H8: 1,2 BLK 9 H9: 1,2,7 # reduction candidate for 1,2 H9: 1,2 # 18 pairs H9: 7 # 15 pairs * PAIR I8: 2,9 BLK 9 I9: 2,9,7 # reduction candidate for 2,9 I9: 7 # 18 pairs I9: 2,9 # 15 pairs * PAIR I8: 2,9 ROW 8 F8: 2,9,5,8 # reduction candidate for 2,9 F8: 2,9 => SOLVED * 967385421135294786248617395456821937892763154371549268629178543783452619514936872 F8: 5,8 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060607-absurd-base-pr-000.dot * REASONING * DIS # A3: 6,8 => CTR => A3: 2 * DIS # B3: 6,8 => CTR => B3: 4 * PRF # C4: 6,8 => SOL * DIS # C4: 9 => CTR => C4: 6,8 * DIS # C7: 6,8 => CTR => C7: 1,9 * DIS # I3: 2,4 => CTR => I3: 5,6 * DIS # A5: 1,6 => CTR => A5: 8,9 * DIS # C7: 1,6 => CTR => C7: 8,9 * PRF # C7: 8,9 => SOL * DIS # E4: 5,6 => CTR => E4: 2 * PRF # E4: 2 => SOL * PRF # H5: 5,6 => SOL * DIS # I5: 5,6 => CTR => I5: 4,7 * DIS # A7: 1,9 => CTR => A7: 6,8 * DIS # B8: 1,9 => CTR => B8: 8 * DIS # D9: 2 => CTR => D9: 1,9 * PRF # B5: 1,9 => SOL * DIS # D7: 8,9 => CTR => D7: 1 * PRF # D7: 1 => SOL * DIS # F8: 8,9 => CTR => F8: 2,5 * DIS # A7: 8,9 => CTR => A7: 1,6 * PRF # C7: 8,9 => SOL * DIS # C7: 1,6 => CTR => C7: 8,9 * DIS # F8: 8,9 => CTR => F8: 2,5 * DIS # E4: 6 => CTR => E4: 2,5 * PRF # F8: 2,9 => SOL * CNT 26 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C3,C6,E5,E8,F5,F7,G1,G4,G6,H8,I8) * ..7.8...1..5.9.78.....1739.4....1.....2......37..4...8.2..7.5437.34..6..5.4.368.. * PAIR C3: 6,8 BLK 1 A3: 6,8,2 # reduction candidate for 6,8 A3: 6,8 => CTR * 2976834.1..5.94786.4..1739.4...219..9.2.6.1.4371.4.268.29.7854378345.61.514.368.. B3: 6,8,4 # reduction candidate for 6,8 B3: 6,8 => CTR * 9.7.8.251..5.9.7862..5173944.9..1.....2...4..37..4.1.8.21.7.5437.34..61.5941368.. * PAIR G1: 2,4 BLK 3 I2: 2,4,6 # reduction candidate for 2,4 I2: 6 => SOLVED * 967385421135294786248617395456821937892763154371549268629178543783452619514936872 * DURATION: 0:00:03.865210 START: 23:42:27.780060 END: 23:42:31.645270 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060607-absurd-base-pr-001.dot * REASONING * DIS # A3: 6,8 => CTR => A3: 2 * DIS A3: 2 # B3: 6,8 => CTR => B3: 4 * PRF A3: 2 + B3: 4 # I2: 6 => SOL * STA A3: 2 + B3: 4 + I2: 6 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060607, absurd
Solution
position: 967385421135294786248617395456821937892763154371549268629178543783452619514936872 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 # A3: 6,8 => CTR => A3: 2 * INC # A3: 2 => UNS * DIS # B3: 6,8 => CTR => B3: 4 * INC # B3: 4 => UNS * PRF # C4: 6,8 => SOL * DIS # C4: 9 => CTR => C4: 6,8 * DIS # C7: 6,8 => CTR => C7: 1,9 * INC # C7: 1,9 => UNS * INC # I2: 2,4 => UNS * DIS # I3: 2,4 => CTR => I3: 5,6 * INC # I3: 5,6 => UNS * INC # F1: 2,4 => UNS * INC # F1: 3,5 => UNS * DIS # A5: 1,6 => CTR => A5: 8,9 * INC # A5: 8,9 => UNS * INC # B5: 1,6 => UNS * DIS # C7: 1,6 => CTR => C7: 8,9 * PRF # C7: 8,9 => SOL * DIS # E4: 5,6 => CTR => E4: 2 * PRF # E4: 2 => SOL * INC # B5: 5,6 => UNS * PRF # H5: 5,6 => SOL * INC # H5: 3,7 => UNS * DIS # I5: 5,6 => CTR => I5: 4,7 * INC # I5: 4,7 => UNS * INC # D4: 3,8 => UNS * INC # D5: 3,8 => UNS * DIS # A7: 1,9 => CTR => A7: 6,8 * INC # A7: 6,8 => UNS * INC # C7: 1,9 => UNS * DIS # B8: 1,9 => CTR => B8: 8 * INC # B8: 8 => UNS * INC # D9: 1,9 => UNS * DIS # D9: 2 => CTR => D9: 1,9 * PRF # B5: 1,9 => SOL * INC # B5: 5,6,8 => UNS * DIS # D7: 8,9 => CTR => D7: 1 * PRF # D7: 1 => SOL * DIS # F8: 8,9 => CTR => F8: 2,5 * INC # F8: 2,5 => UNS * DIS # A7: 8,9 => CTR => A7: 1,6 * INC # A7: 1,6 => UNS * PRF # C7: 8,9 => SOL * DIS # C7: 1,6 => CTR => C7: 8,9 * INC # F8: 2,5 => UNS * DIS # F8: 8,9 => CTR => F8: 2,5 * INC # E4: 2,5 => UNS * DIS # E4: 6 => CTR => E4: 2,5 * INC # H9: 1,2 => UNS * INC # H9: 7 => UNS * INC # I9: 2,9 => UNS * INC # I9: 7 => UNS * PRF # F8: 2,9 => SOL * INC # F8: 5,8 => UNS * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 6,8 => CTR => A3: 2 * DIS A3: 2 # B3: 6,8 => CTR => B3: 4 * INC A3: 2 + B3: 4 # I2: 2,4 => UNS * PRF A3: 2 + B3: 4 # I2: 6 => SOL * STA A3: 2 + B3: 4 + I2: 6 * CNT 4 HDP CHAINS / 4 HYP OPENED