Analysis of zz-sudoku-de-635431-base.sdk
Contents
Original Sudoku
level: medium
position: .6.....9.5.7.4.2.6..46.15...5.....8....3.6....7.....3...64.28..3.1.7.9.2.8.....4. initial
Autosolve
position: 168...394537849216924631578.53....8..193.6.2..721...3.796412853341578962285963.4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 4,6 => CTR => A6: 8 * PRF # A6: 8 => SOL * PRF # G4: 4,6 => SOL * DIS # G4: 1 => CTR => G4: 4,6 * DIS # A6: 6 => CTR => A6: 4,8 * PRF # E6: 5,8 => SOL * DIS # E6: 9 => CTR => E6: 5,8 * PRF # G4: 4,6 => SOL * DIS # G4: 1 => CTR => G4: 4,6 * DIS # A6: 4,6 => CTR => A6: 8 * PRF # A6: 8 => SOL * PRF # E6: 5,9 => SOL * DIS # E6: 8 => CTR => E6: 5,9 * CNT 13 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 4,6 => CTR => A6: 8 * PRF A6: 8 => SOL * STA A6: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.....9.5.7.4.2.6..46.15...5.....8....3.6....7.....3...64.28..3.1.7.9.2.8.....4. | initial |
| 168...394537849216924631578.53....8..193.6.2..721...3.796412853341578962285963.4. | autosolve |
| 168725394537849216924631578653297481419386725872154639796412853341578962285963147 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) D1: 2,7 E1: 2,5 F1: 5,7 A4: 4,6 A5: 4,8 D4: 2,7 E4: 2,9 F4: 4,7 E5: 5,8 F6: 4,5 I4: 1,9 G5: 4,7 I5: 5,7 G6: 4,6 I6: 5,9 G9: 1,7 I9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,I4: 1.. / G4 = 1 => 0 pairs (X) / I4 = 1 => 0 pairs (_) G9,I9: 1.. / G9 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) G4,G9: 1.. / G4 = 1 => 0 pairs (X) / G9 = 1 => 0 pairs (_) I4,I9: 1.. / I4 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) D1,E1: 2.. / D1 = 2 => 0 pairs (X) / E1 = 2 => 0 pairs (_) D4,E4: 2.. / D4 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) D1,D4: 2.. / D1 = 2 => 0 pairs (X) / D4 = 2 => 0 pairs (_) E1,E4: 2.. / E1 = 2 => 0 pairs (*) / E4 = 2 => 0 pairs (X) F4,F6: 4.. / F4 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) A5,G5: 4.. / A5 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) E1,F1: 5.. / E1 = 5 => 0 pairs (X) / F1 = 5 => 0 pairs (_) I5,I6: 5.. / I5 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) E5,I5: 5.. / E5 = 5 => 0 pairs (X) / I5 = 5 => 0 pairs (_) F1,F6: 5.. / F1 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) A4,A6: 6.. / A4 = 6 => 17 pairs (_) / A6 = 6 => 0 pairs (X) G4,G6: 6.. / G4 = 6 => 0 pairs (X) / G6 = 6 => 17 pairs (_) A4,G4: 6.. / A4 = 6 => 17 pairs (_) / G4 = 6 => 0 pairs (X) A6,G6: 6.. / A6 = 6 => 0 pairs (X) / G6 = 6 => 17 pairs (_) D1,F1: 7.. / D1 = 7 => 0 pairs (*) / F1 = 7 => 0 pairs (X) D4,F4: 7.. / D4 = 7 => 0 pairs (X) / F4 = 7 => 0 pairs (_) G5,I5: 7.. / G5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) G9,I9: 7.. / G9 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) D1,D4: 7.. / D1 = 7 => 0 pairs (*) / D4 = 7 => 0 pairs (X) F1,F4: 7.. / F1 = 7 => 0 pairs (X) / F4 = 7 => 0 pairs (_) G5,G9: 7.. / G5 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) I5,I9: 7.. / I5 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) A5,A6: 8.. / A5 = 8 => 0 pairs (X) / A6 = 8 => 0 pairs (_) E5,E6: 8.. / E5 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) A5,E5: 8.. / A5 = 8 => 0 pairs (X) / E5 = 8 => 0 pairs (_) A6,E6: 8.. / A6 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) E4,E6: 9.. / E4 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) I4,I6: 9.. / I4 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) E4,I4: 9.. / E4 = 9 => 0 pairs (*) / I4 = 9 => 0 pairs (X) E6,I6: 9.. / E6 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) * DURATION: 0:00:58.114843 START: 07:27:12.790399 END: 07:28:10.905242 2017-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,D1,D4,E1,E4,E5,F1,F4,F6,G5,G6,G9,I4,I5,I6,I9) * 168...394537849216924631578.53....8..193.6.2..721...3.796412853341578962285963.4. * PAIR A4: 4,6 BLK 4 A6: 4,6,8 # reduction candidate for 4,6 A6: 4,6 => CTR * 168...394537849216924631578.53....8.819356427.72184.3.796412853341578962285963.4. A6: 8 => SOLVED * 168725394537849216924631578653297481419386725872154639796412853341578962285963147 * PAIR A4: 4,6 ROW 4 G4: 4,6,1 # reduction candidate for 4,6 G4: 4,6 => SOLVED * 168725394537849216924631578653297481419386725872154639796412853341578962285963147 G4: 1 => CTR * 168...394537849216924631578653..4189.193.6.2..72195.3.796412853341578962285963.4. * PAIR A5: 4,8 BLK 4 A6: 4,8,6 # reduction candidate for 4,8 A6: 6 => CTR * 168...394537849216924631578.53....8.8193564276721...3.796412853341578962285963.4. A6: 4,8 # 17 pairs * PAIR E5: 5,8 BLK 5 E6: 5,8,9 # reduction candidate for 5,8 E6: 5,8 => SOLVED * 168725394537849216924631578653297481419386725872154639796412853341578962285963147 E6: 9 => CTR * 168...394537849216924631578.53....8..19386.2587219..3.796412853341578962285963.4. * PAIR G6: 4,6 BLK 6 G4: 4,6,1 # reduction candidate for 4,6 G4: 4,6 => SOLVED * 168725394537849216924631578653297481419386725872154639796412853341578962285963147 G4: 1 => CTR * 168...394537849216924631578653..4189.193.6.2..72195.3.796412853341578962285963.4. * PAIR G6: 4,6 ROW 6 A6: 4,6,8 # reduction candidate for 4,6 A6: 4,6 => CTR * 168...394537849216924631578.53....8.819356427.72184.3.796412853341578962285963.4. A6: 8 => SOLVED * 168725394537849216924631578653297481419386725872154639796412853341578962285963147 * PAIR I6: 5,9 ROW 6 E6: 5,9,8 # reduction candidate for 5,9 E6: 5,9 => SOLVED * 168725394537849216924631578653297481419386725872154639796412853341578962285963147 E6: 8 => CTR * 168...394537849216924631578.53.9..81.193.6.2..7218..39796412853341578962285963147 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-635431-base-pr-000.dot * REASONING * DIS # A6: 4,6 => CTR => A6: 8 * PRF # A6: 8 => SOL * PRF # G4: 4,6 => SOL * DIS # G4: 1 => CTR => G4: 4,6 * DIS # A6: 6 => CTR => A6: 4,8 * PRF # E6: 5,8 => SOL * DIS # E6: 9 => CTR => E6: 5,8 * PRF # G4: 4,6 => SOL * DIS # G4: 1 => CTR => G4: 4,6 * DIS # A6: 4,6 => CTR => A6: 8 * PRF # A6: 8 => SOL * PRF # E6: 5,9 => SOL * DIS # E6: 8 => CTR => E6: 5,9 * CNT 13 HDP CHAINS / 14 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,D1,D4,E1,E4,E5,F1,F4,F6,G5,G6,G9,I4,I5,I6,I9) * 168...394537849216924631578.53....8..193.6.2..721...3.796412853341578962285963.4. * PAIR A4: 4,6 BLK 4 A6: 4,6,8 # reduction candidate for 4,6 A6: 4,6 => CTR * 168...394537849216924631578.53....8.819356427.72184.3.796412853341578962285963.4. A6: 8 => SOLVED * 168725394537849216924631578653297481419386725872154639796412853341578962285963147 * DURATION: 0:00:02.960571 START: 07:28:27.448858 END: 07:28:30.409429 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-635431-base-pr-001.dot * REASONING * DIS # A6: 4,6 => CTR => A6: 8 * PRF A6: 8 => SOL * STA A6: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/635431.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 168...394537849216924631578.53....8..193.6.2..721...3.796412853341578962285963.4. D1: 2,7 E1: 2,5 F1: 5,7 A4: 4,6 A6: 4,6,8 # reduction candidate for 4,6 A6: 4,6 => CTR * 168...394537849216924631578.53....8.819356427.72184.3.796412853341578962285963.4. A6: 8 => SOLVED * 168725394537849216924631578653297481419386725872154639796412853341578962285963147 * SOLVED! -------------------------------------------------- * AUTO .. Q5: 7.. = D4,F4: 7.. => G4,I4 != 7 * UNSOLVED! A5 = 8 => E6 = 8 & E5,A6 != 8 => E5 = 5 A6,G6 = 4,6 => F6 = 5 E5,F6 = 5 => CTR => A5 != 8 # forcing chain * SOLVED
Solution
position: 168725394537849216924631578653297481419386725872154639796412853341578962285963147 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 # A6: 4,6 => CTR => A6: 8 * PRF # A6: 8 => SOL * PRF # G4: 4,6 => SOL * DIS # G4: 1 => CTR => G4: 4,6 * INC # A6: 4,8 => UNS * DIS # A6: 6 => CTR => A6: 4,8 * PRF # E6: 5,8 => SOL * DIS # E6: 9 => CTR => E6: 5,8 * PRF # G4: 4,6 => SOL * DIS # G4: 1 => CTR => G4: 4,6 * DIS # A6: 4,6 => CTR => A6: 8 * PRF # A6: 8 => SOL * PRF # E6: 5,9 => SOL * DIS # E6: 8 => CTR => E6: 5,9 * CNT 14 HDP CHAINS / 14 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A6: 4,6 => CTR => A6: 8 * PRF A6: 8 => SOL * STA A6: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED