Analysis of zz-www.sudokuoftheday.co.uk-20190407-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
level: medium
position: ...1...3...4.7...8812..4..5....35....9.78.1..........6..........28..75..1..9....3 initial
Autosolve
position: ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.2.3286.75..1..9.2863 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A6: 5,7 => SOL * DIS # B9: 5,7 => CTR => B9: 4 * PRF # G4: 7,9 => SOL * DIS # G4: 4 => CTR => G4: 7,9 * DIS # A6: 4,5 => CTR => A6: 2,7 * PRF # A6: 5,7 => SOL * PRF # H6: 4 => SOL * PRF # A4: 2,4 => SOL * DIS # A4: 7 => CTR => A4: 2,4 * PRF # A6: 5,7 => SOL * PRF # G4: 7,9 => SOL * DIS # G4: 4 => CTR => G4: 7,9 * PRF # H6: 4,5 => SOL * DIS # H6: 7 => CTR => H6: 4,5 * DIS # B9: 7 => CTR => B9: 4,5 * DIS # E7: 4,5 => CTR => E7: 1 * PRF # E7: 1 => SOL * DIS # B9: 5,7 => CTR => B9: 4 * DIS # E7: 5 => CTR => E7: 1,4 * DIS # E7: 4,5 => CTR => E7: 1 * PRF # E7: 1 => SOL * DIS # B9: 7 => CTR => B9: 4,5 * PRF # G4: 4,7 => SOL * DIS # G4: 9 => CTR => G4: 4,7 * CNT 24 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:
* PRF # A6: 5,7 => SOL * STA A6: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...1...3...4.7...8812..4..5....35....9.78.1..........6..........28..75..1..9....3 | initial |
| ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.2.3286.75..1..9.2863 | autosolve |
| 579128634634579218812364975261435789493786152785291346956813427328647591147952863 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 5,7 B1: 5,7 G3: 7,9 H3: 7,9 A5: 4,5 C6: 5,7 D4: 2,4 D6: 2,4 I4: 7,9 H5: 4,5 B7: 4,5 C9: 5,7 E8: 1,4 E9: 4,5 G7: 4,7 I7: 1,7 H8: 4,9 I8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E7,E8: 1.. / E7 = 1 => 0 pairs (*) / E8 = 1 => 0 pairs (X) I7,I8: 1.. / I7 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) E7,I7: 1.. / E7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) E8,I8: 1.. / E8 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) A4,A6: 2.. / A4 = 2 => 0 pairs (*) / A6 = 2 => 0 pairs (X) D4,D6: 2.. / D4 = 2 => 18 pairs (_) / D6 = 2 => 0 pairs (*) A4,D4: 2.. / A4 = 2 => 0 pairs (*) / D4 = 2 => 0 pairs (X) A6,D6: 2.. / A6 = 2 => 18 pairs (_) / D6 = 2 => 0 pairs (*) D4,D6: 4.. / D4 = 4 => 0 pairs (*) / D6 = 4 => 0 pairs (X) B7,B9: 4.. / B7 = 4 => 0 pairs (X) / B9 = 4 => 14 pairs (_) G7,H8: 4.. / G7 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) A5,H5: 4.. / A5 = 4 => 18 pairs (_) / H5 = 4 => 0 pairs (X) E8,H8: 4.. / E8 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) B9,E9: 4.. / B9 = 4 => 14 pairs (_) / E9 = 4 => 0 pairs (X) G4,G7: 4.. / G4 = 4 => 0 pairs (X) / G7 = 4 => 0 pairs (_) A1,B1: 5.. / A1 = 5 => 16 pairs (_) / B1 = 5 => 0 pairs (X) H5,H6: 5.. / H5 = 5 => 18 pairs (_) / H6 = 5 => 0 pairs (X) E7,E9: 5.. / E7 = 5 => 0 pairs (X) / E9 = 5 => 14 pairs (_) A5,H5: 5.. / A5 = 5 => 0 pairs (X) / H5 = 5 => 18 pairs (_) B7,E7: 5.. / B7 = 5 => 14 pairs (_) / E7 = 5 => 0 pairs (X) C6,C9: 5.. / C6 = 5 => 16 pairs (_) / C9 = 5 => 0 pairs (X) A1,B1: 7.. / A1 = 7 => 0 pairs (X) / B1 = 7 => 16 pairs (_) G3,H3: 7.. / G3 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) B9,C9: 7.. / B9 = 7 => 0 pairs (X) / C9 = 7 => 16 pairs (_) G7,I7: 7.. / G7 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) B1,B9: 7.. / B1 = 7 => 16 pairs (_) / B9 = 7 => 0 pairs (X) C6,C9: 7.. / C6 = 7 => 0 pairs (X) / C9 = 7 => 16 pairs (_) H3,H6: 7.. / H3 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) I4,I7: 7.. / I4 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) G3,H3: 9.. / G3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) G4,I4: 9.. / G4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) H8,I8: 9.. / H8 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) G3,G4: 9.. / G3 = 9 => 0 pairs (*) / G4 = 9 => 0 pairs (X) H3,H8: 9.. / H3 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) I4,I8: 9.. / I4 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) * DURATION: 0:00:41.025591 START: 05:07:45.165849 END: 05:08:26.191440 2019-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B1,B7,C6,C9,D4,D6,E8,E9,G3,G7,H3,H5,H8,I4,I7,I8) * ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.2.3286.75..1..9.2863 * PAIR A1: 5,7 COL A A6: 5,7,2,4 # reduction candidate for 5,7 A6: 5,7 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 A6: 2,4 # 20 pairs * PAIR B1: 5,7 COL B B9: 5,7,4 # reduction candidate for 5,7 B9: 5,7 => CTR * ..9128634634579218812364..5.61.35.8..937861.2.8..913.69468537213286175491..942863 B9: 4 # 14 pairs * PAIR G3: 7,9 COL G G4: 7,9,4 # reduction candidate for 7,9 G4: 7,9 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 G4: 4 => CTR * ..9128634634579218812364975.61.3548..937861.2.8..913.69.68.3.2.3286.75..1..9.2863 * PAIR A5: 4,5 BLK 4 A6: 4,5,2,7 # reduction candidate for 4,5 A6: 4,5 => CTR * ..9128634634579218812364..5261435.8..937861.2.872913.69.68.34273286475911..9.2863 A6: 2,7 # 19 pairs * PAIR C6: 5,7 BLK 4 A6: 5,7,2,4 # reduction candidate for 5,7 A6: 5,7 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 A6: 2,4 # 20 pairs * PAIR C6: 5,7 ROW 6 H6: 5,7,4 # reduction candidate for 5,7 H6: 4 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 H6: 5,7 # 20 pairs * PAIR D4: 2,4 ROW 4 A4: 2,4,7 # reduction candidate for 2,4 A4: 2,4 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 A4: 7 => CTR * ..9128634634579218812364..5761235489493786152.8..913.69.68.3.2.3286.75..1..9.2863 * PAIR D6: 2,4 ROW 6 A6: 2,4,5,7 # reduction candidate for 2,4 A6: 5,7 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 A6: 2,4 # 20 pairs * PAIR I4: 7,9 BLK 6 G4: 7,9,4 # reduction candidate for 7,9 G4: 7,9 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 G4: 4 => CTR * ..9128634634579218812364975.61.3548..937861.2.8..913.69.68.3.2.3286.75..1..9.2863 * PAIR H5: 4,5 BLK 6 H6: 4,5,7 # reduction candidate for 4,5 H6: 4,5 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 H6: 7 => CTR * ..9128634634579218812364..5.61.35.8..93786152.8..913769.68.3.273286.754.1..9.2863 * PAIR B7: 4,5 BLK 7 B9: 4,5,7 # reduction candidate for 4,5 B9: 7 => CTR * ..9128634634579218812364..5.61.35.8..937861.2.8..913.6946853721328617549175942863 B9: 4,5 # 16 pairs * PAIR B7: 4,5 ROW 7 E7: 4,5,1 # reduction candidate for 4,5 E7: 4,5 => CTR * ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.213286175491..9.2863 E7: 1 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 * PAIR C9: 5,7 BLK 7 B9: 5,7,4 # reduction candidate for 5,7 B9: 5,7 => CTR * ..9128634634579218812364..5.61.35.8..937861.2.8..913.69468537213286175491..942863 B9: 4 # 14 pairs * PAIR E8: 1,4 BLK 8 E7: 1,4,5 # reduction candidate for 1,4 E7: 5 => CTR * ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.6853.213286175491..942863 E7: 1,4 # 14 pairs * PAIR E9: 4,5 BLK 8 E7: 4,5,1 # reduction candidate for 4,5 E7: 4,5 => CTR * ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.213286175491..9.2863 E7: 1 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 * PAIR E9: 4,5 ROW 9 B9: 4,5,7 # reduction candidate for 4,5 B9: 7 => CTR * ..9128634634579218812364..5.61.35.8..937861.2.8..913.6946853721328617549175942863 B9: 4,5 # 16 pairs * PAIR G7: 4,7 COL G G4: 4,7,9 # reduction candidate for 4,7 G4: 4,7 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 G4: 9 => CTR * ..9128634634579218812364..5.61.35987.937861.2.8..913.69.68.3.2.3286.75..1..9.2863 * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190407-absurd-base-pr-000.dot * REASONING * PRF # A6: 5,7 => SOL * DIS # B9: 5,7 => CTR => B9: 4 * PRF # G4: 7,9 => SOL * DIS # G4: 4 => CTR => G4: 7,9 * DIS # A6: 4,5 => CTR => A6: 2,7 * PRF # A6: 5,7 => SOL * PRF # H6: 4 => SOL * PRF # A4: 2,4 => SOL * DIS # A4: 7 => CTR => A4: 2,4 * PRF # A6: 5,7 => SOL * PRF # G4: 7,9 => SOL * DIS # G4: 4 => CTR => G4: 7,9 * PRF # H6: 4,5 => SOL * DIS # H6: 7 => CTR => H6: 4,5 * DIS # B9: 7 => CTR => B9: 4,5 * DIS # E7: 4,5 => CTR => E7: 1 * PRF # E7: 1 => SOL * DIS # B9: 5,7 => CTR => B9: 4 * DIS # E7: 5 => CTR => E7: 1,4 * DIS # E7: 4,5 => CTR => E7: 1 * PRF # E7: 1 => SOL * DIS # B9: 7 => CTR => B9: 4,5 * PRF # G4: 4,7 => SOL * DIS # G4: 9 => CTR => G4: 4,7 * CNT 24 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B1,B7,C6,C9,D4,D6,E8,E9,G3,G7,H3,H5,H8,I4,I7,I8) * ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.2.3286.75..1..9.2863 * PAIR A1: 5,7 COL A A6: 5,7,2,4 # reduction candidate for 5,7 A6: 5,7 => SOLVED * 579128634634579218812364975261435789493786152785291346956813427328647591147952863 * DURATION: 0:00:01.370291 START: 05:08:51.355830 END: 05:08:52.726121 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190407-absurd-base-pr-001.dot * REASONING * PRF # A6: 5,7 => SOL * STA A6: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190407, absurd
Solution
position: 579128634634579218812364975261435789493786152785291346956813427328647591147952863 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:
* PRF # A6: 5,7 => SOL * INC # A6: 2,4 => UNS * DIS # B9: 5,7 => CTR => B9: 4 * INC # B9: 4 => UNS * PRF # G4: 7,9 => SOL * DIS # G4: 4 => CTR => G4: 7,9 * DIS # A6: 4,5 => CTR => A6: 2,7 * INC # A6: 2,7 => UNS * PRF # A6: 5,7 => SOL * INC # A6: 2,4 => UNS * INC # H6: 5,7 => UNS * PRF # H6: 4 => SOL * PRF # A4: 2,4 => SOL * DIS # A4: 7 => CTR => A4: 2,4 * INC # A6: 2,4 => UNS * PRF # A6: 5,7 => SOL * PRF # G4: 7,9 => SOL * DIS # G4: 4 => CTR => G4: 7,9 * PRF # H6: 4,5 => SOL * DIS # H6: 7 => CTR => H6: 4,5 * INC # B9: 4,5 => UNS * DIS # B9: 7 => CTR => B9: 4,5 * DIS # E7: 4,5 => CTR => E7: 1 * PRF # E7: 1 => SOL * DIS # B9: 5,7 => CTR => B9: 4 * INC # B9: 4 => UNS * INC # E7: 1,4 => UNS * DIS # E7: 5 => CTR => E7: 1,4 * DIS # E7: 4,5 => CTR => E7: 1 * PRF # E7: 1 => SOL * INC # B9: 4,5 => UNS * DIS # B9: 7 => CTR => B9: 4,5 * PRF # G4: 4,7 => SOL * DIS # G4: 9 => CTR => G4: 4,7 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A6: 5,7 => SOL * STA A6: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED