Analysis of zz-www.sudokuoftheday.co.uk-20060623-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: ...176.2.51...48.......8......3.59......1..4.6.........5.....8..79..1....8.6..3.5 initial
Autosolve
position: ...17652.51...48.6.6...8......3659....5.1.64.6......5..56..3.8.379..1.6..8.6..3.5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 2,7 => CTR => A3: 4,9 * DIS # D5: 2,9 => CTR => D5: 7,8 * DIS # D6: 2,9 => CTR => D6: 4,7,8 * PRF # I3: 4,9 => SOL * DIS # A1: 4,9 => CTR => A1: 8 * PRF # I4: 1,7 => SOL * DIS # I6: 1,7 => CTR => I6: 2,3,8 * DIS # C4: 1,7 => CTR => C4: 4,8 * DIS # H3: 1,7 => CTR => H3: 3,9 * DIS # H9: 1,7 => CTR => H9: 9 * DIS # H9: 1,7 => CTR => H9: 9 * PRF # G3: 1,7 => SOL * CNT 12 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 2,7 => CTR => A3: 4,9 * DIS A3: 4,9 # D5: 2,9 => CTR => D5: 7,8 * DIS A3: 4,9 + D5: 7,8 # D6: 2,9 => CTR => D6: 4,7,8 * DIS A3: 4,9 + D5: 7,8 + D6: 4,7,8 # D7: 2,9 => CTR => D7: 4,7 * PRF A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 # I3: 4,9 => SOL * STA A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 + I3: 4,9 * CNT 5 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...176.2.51...48.......8......3.59......1..4.6.........5.....8..79..1....8.6..3.5 | initial |
| ...17652.51...48.6.6...8......3659....5.1.64.6......5..56..3.8.379..1.6..8.6..3.5 | autosolve |
| 843176529512934876967258134428365917795812643631749258256493781379581462184627395 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) C2: 2,7 D2: 2,9 I1: 4,9 B4: 2,4 H4: 1,7 D8: 5,8 E8: 5,8 G7: 1,7 G8: 2,4 I8: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G8,I8: 2.. / G8 = 2 => 25 pairs (_) / I8 = 2 => 0 pairs (*) B4,I4: 2.. / B4 = 2 => 0 pairs (*) / I4 = 2 => 0 pairs (X) G6,G8: 2.. / G6 = 2 => 0 pairs (*) / G8 = 2 => 0 pairs (X) B1,C1: 3.. / B1 = 3 => 0 pairs (X) / C1 = 3 => 12 pairs (_) E2,E3: 3.. / E2 = 3 => 11 pairs (_) / E3 = 3 => 10 pairs (_) H2,H3: 3.. / H2 = 3 => 10 pairs (_) / H3 = 3 => 11 pairs (_) I5,I6: 3.. / I5 = 3 => 11 pairs (_) / I6 = 3 => 13 pairs (_) E2,H2: 3.. / E2 = 3 => 11 pairs (_) / H2 = 3 => 10 pairs (_) E3,H3: 3.. / E3 = 3 => 10 pairs (_) / H3 = 3 => 11 pairs (_) B5,I5: 3.. / B5 = 3 => 13 pairs (_) / I5 = 3 => 11 pairs (_) C1,C6: 3.. / C1 = 3 => 12 pairs (_) / C6 = 3 => 0 pairs (X) D6,E6: 4.. / D6 = 4 => 10 pairs (_) / E6 = 4 => 18 pairs (_) G8,I8: 4.. / G8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) B1,B4: 4.. / B1 = 4 => 0 pairs (*) / B4 = 4 => 0 pairs (X) D6,D7: 4.. / D6 = 4 => 10 pairs (_) / D7 = 4 => 18 pairs (_) G3,G8: 4.. / G3 = 4 => 25 pairs (_) / G8 = 4 => 0 pairs (*) D3,E3: 5.. / D3 = 5 => 8 pairs (_) / E3 = 5 => 12 pairs (_) D8,E8: 5.. / D8 = 5 => 12 pairs (_) / E8 = 5 => 8 pairs (_) D3,D8: 5.. / D3 = 5 => 8 pairs (_) / D8 = 5 => 12 pairs (_) E3,E8: 5.. / E3 = 5 => 12 pairs (_) / E8 = 5 => 8 pairs (_) D7,F9: 7.. / D7 = 7 => 0 pairs (X) / F9 = 7 => 15 pairs (_) C2,H2: 7.. / C2 = 7 => 12 pairs (_) / H2 = 7 => 19 pairs (_) F9,H9: 7.. / F9 = 7 => 15 pairs (_) / H9 = 7 => 0 pairs (X) A1,C1: 8.. / A1 = 8 => 12 pairs (_) / C1 = 8 => 0 pairs (X) D8,E8: 8.. / D8 = 8 => 8 pairs (_) / E8 = 8 => 12 pairs (_) E6,E8: 8.. / E6 = 8 => 8 pairs (_) / E8 = 8 => 12 pairs (_) I7,H9: 9.. / I7 = 9 => 0 pairs (X) / H9 = 9 => 19 pairs (_) * DURATION: 0:00:31.350461 START: 00:02:50.852930 END: 00:03:22.203391 2019-05-01 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C2,D2,D8,E8,G7,G8,H4,I1,I8) * ...17652.51...48.6.6...8......3659....5.1.64.6......5..56..3.8.379..1.6..8.6..3.5 * PAIR C2: 2,7 BLK 1 A3: 2,7,4,9 # reduction candidate for 2,7 A3: 2,7 => CTR * ...17652451...48.6.64..8....4.3659.2..5.1.64.6......5..56..3.8.379..1.6..8.6..3.5 A3: 4,9 # 13 pairs C3: 2,7,4 # reduction candidate for 2,7 C3: 2,7 # 13 pairs * PAIR D2: 2,9 BLK 2 E2: 2,9,3 # reduction candidate for 2,9 E2: 2,9 # 10 pairs D3: 2,9,5 # reduction candidate for 2,9 D3: 2,9 # 12 pairs E3: 2,9,3,5 # reduction candidate for 2,9 E3: 2,9 # 10 pairs * PAIR D2: 2,9 COL D D5: 2,9,7,8 # reduction candidate for 2,9 D5: 2,9 => CTR * ...176524517..48.6.6.5.87.1.4.365912..5.1.64.6......5..567.3189379851.6..8.6..375 D5: 7,8 # 11 pairs D6: 2,9,4,7,8 # reduction candidate for 2,9 D6: 2,9 => CTR * ...17652.51...48.6.6...8......3659....5.1.64.6...4..5..564.3.8.379.81.6..8.6.73.5 D6: 4,7,8 # 10 pairs D7: 2,9,4,7 # reduction candidate for 2,9 D7: 2,9 # 13 pairs * PAIR I1: 4,9 BLK 3 I3: 4,9,1,7 # reduction candidate for 4,9 I3: 4,9 => SOLVED * 843176529512934876967258134428365917795812643631749258256493781379581462184627395 I3: 1,7 # 11 pairs * PAIR I1: 4,9 ROW 1 A1: 4,9,8 # reduction candidate for 4,9 A1: 4,9 => CTR * 43817652951...48.696..58431841365972..5.1.6436.3....58.56..3.8.379.81264.8.6..3.5 A1: 8 # 12 pairs B1: 4,9,3 # reduction candidate for 4,9 B1: 4,9 # 12 pairs * PAIR H4: 1,7 BLK 6 I4: 1,7,2,8 # reduction candidate for 1,7 I4: 1,7 => SOLVED * 843176529512934876967258134428365917795812643631749258256493781379581462184627395 I4: 2,8 # 11 pairs G6: 1,7,2 # reduction candidate for 1,7 G6: 1,7 # 25 pairs I6: 1,7,2,3,8 # reduction candidate for 1,7 I6: 1,7 => CTR * 84317652951...48.696..587.4.2.3659.8.95.1.643638...251.56..3.87379.81462.8.6.7395 I6: 2,3,8 # 10 pairs * PAIR H4: 1,7 ROW 4 A4: 1,7,4,8 # reduction candidate for 1,7 A4: 1,7 # 13 pairs C4: 1,7,4,8 # reduction candidate for 1,7 C4: 1,7 => CTR * 9.8176524517234896.6.958137..136597.7.581.64.6..74..5.156423789379581.6..8.697315 C4: 4,8 # 11 pairs * PAIR H4: 1,7 COL H H3: 1,7,3,9 # reduction candidate for 1,7 H3: 1,7 => CTR * ..317652.517..4836.6.538.7.7.83659129.5712648621489753.56..3187379851.6.18.6.7395 H3: 3,9 # 11 pairs H9: 1,7,9 # reduction candidate for 1,7 H9: 1,7 => CTR * ...17652451...48.6.6...8....4.3659.2..5.1.64.6......5..56..3.89379..1.6..8.6..3.5 H9: 9 # 19 pairs * PAIR G7: 1,7 BLK 9 I7: 1,7,9 # reduction candidate for 1,7 I7: 1,7 # 19 pairs H9: 1,7,9 # reduction candidate for 1,7 H9: 1,7 => CTR * ...17652451...48.6.6...8....4.3659.2..5.1.64.6......5..56..3.89379..1.6..8.6..3.5 H9: 9 # 19 pairs * PAIR G7: 1,7 COL G G3: 1,7,4 # reduction candidate for 1,7 G3: 1,7 => SOLVED * 843176529512934876967258134428365917795812643631749258256493781379581462184627395 G3: 4 # 25 pairs G6: 1,7,2 # reduction candidate for 1,7 G6: 1,7 # 25 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060623-absurd-base-pr-000.dot * REASONING * DIS # A3: 2,7 => CTR => A3: 4,9 * DIS # D5: 2,9 => CTR => D5: 7,8 * DIS # D6: 2,9 => CTR => D6: 4,7,8 * PRF # I3: 4,9 => SOL * DIS # A1: 4,9 => CTR => A1: 8 * PRF # I4: 1,7 => SOL * DIS # I6: 1,7 => CTR => I6: 2,3,8 * DIS # C4: 1,7 => CTR => C4: 4,8 * DIS # H3: 1,7 => CTR => H3: 3,9 * DIS # H9: 1,7 => CTR => H9: 9 * DIS # H9: 1,7 => CTR => H9: 9 * PRF # G3: 1,7 => SOL * CNT 12 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C2,D2,D8,E8,G7,G8,H4,I1,I8) * ...17652.51...48.6.6...8......3659....5.1.64.6......5..56..3.8.379..1.6..8.6..3.5 * PAIR C2: 2,7 BLK 1 A3: 2,7,4,9 # reduction candidate for 2,7 A3: 2,7 => CTR * ...17652451...48.6.64..8....4.3659.2..5.1.64.6......5..56..3.8.379..1.6..8.6..3.5 * RESTART * PAIR D2: 2,9 BLK 2 E2: 2,9,3 # reduction candidate for 2,9 E2: 2,9 # 11 pairs D3: 2,9,5 # reduction candidate for 2,9 D3: 2,9 # 15 pairs E3: 2,9,3,5 # reduction candidate for 2,9 E3: 2,9 # 14 pairs * PAIR D2: 2,9 COL D D5: 2,9,7,8 # reduction candidate for 2,9 D5: 2,9 => CTR * ...176524517..48.64625.87.1.4.365912..5.1.64.6......5..567.3189379851.6..8.6..375 D6: 2,9,4,7,8 # reduction candidate for 2,9 D6: 2,9 => CTR * ...17652.51...48.6.6...8......3659....5.1.64.6...4..5..564.3.8.379.81.6..8.6.73.5 D7: 2,9,4,7 # reduction candidate for 2,9 D7: 2,9 => CTR * ..317652.51.294836.62538.7.7483659129.5712648621489753256943187379851.6.184627395 * RESTART * PAIR RESTART * PAIR I1: 4,9 BLK 3 I3: 4,9,1,7 # reduction candidate for 4,9 I3: 4,9 => SOLVED * 843176529512934876967258134428365917795812643631749258256493781379581462184627395 * DURATION: 0:00:07.163437 START: 00:03:44.802585 END: 00:03:51.966022 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060623-absurd-base-pr-001.dot * REASONING * DIS # A3: 2,7 => CTR => A3: 4,9 * DIS A3: 4,9 # D5: 2,9 => CTR => D5: 7,8 * DIS A3: 4,9 + D5: 7,8 # D6: 2,9 => CTR => D6: 4,7,8 * DIS A3: 4,9 + D5: 7,8 + D6: 4,7,8 # D7: 2,9 => CTR => D7: 4,7 * PRF A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 # I3: 4,9 => SOL * STA A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 + I3: 4,9 * CNT 5 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060623, absurd
Solution
position: 843176529512934876967258134428365917795812643631749258256493781379581462184627395 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: 2,7 => CTR => A3: 4,9 * INC # A3: 4,9 => UNS * INC # C3: 2,7 => UNS * INC # E2: 2,9 => UNS * INC # D3: 2,9 => UNS * INC # E3: 2,9 => UNS * DIS # D5: 2,9 => CTR => D5: 7,8 * INC # D5: 7,8 => UNS * DIS # D6: 2,9 => CTR => D6: 4,7,8 * INC # D6: 4,7,8 => UNS * INC # D7: 2,9 => UNS * PRF # I3: 4,9 => SOL * INC # I3: 1,7 => UNS * DIS # A1: 4,9 => CTR => A1: 8 * INC # A1: 8 => UNS * INC # B1: 4,9 => UNS * PRF # I4: 1,7 => SOL * INC # I4: 2,8 => UNS * INC # G6: 1,7 => UNS * DIS # I6: 1,7 => CTR => I6: 2,3,8 * INC # I6: 2,3,8 => UNS * INC # A4: 1,7 => UNS * DIS # C4: 1,7 => CTR => C4: 4,8 * INC # C4: 4,8 => UNS * DIS # H3: 1,7 => CTR => H3: 3,9 * INC # H3: 3,9 => UNS * DIS # H9: 1,7 => CTR => H9: 9 * INC # H9: 9 => UNS * INC # I7: 1,7 => UNS * DIS # H9: 1,7 => CTR => H9: 9 * INC # H9: 9 => UNS * PRF # G3: 1,7 => SOL * INC # G3: 4 => UNS * INC # G6: 1,7 => UNS * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 2,7 => CTR => A3: 4,9 * INC A3: 4,9 # E2: 2,9 => UNS * INC A3: 4,9 # D3: 2,9 => UNS * INC A3: 4,9 # E3: 2,9 => UNS * DIS A3: 4,9 # D5: 2,9 => CTR => D5: 7,8 * DIS A3: 4,9 + D5: 7,8 # D6: 2,9 => CTR => D6: 4,7,8 * DIS A3: 4,9 + D5: 7,8 + D6: 4,7,8 # D7: 2,9 => CTR => D7: 4,7 * PRF A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 # I3: 4,9 => SOL * STA A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 + I3: 4,9 * CNT 8 HDP CHAINS / 8 HYP OPENED