Analysis of zz-sudoku-de-620657-base.sdk
Contents
Original Sudoku
level: medium
position: 8..5.....79..8......3...17..4.9.8..66..1.5..31..6.7.2..68...9......6..37.....4..5 initial
Autosolve
position: 8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 3 => CTR => F1: 1,2 * DIS # D2: 2,4 => CTR => D2: 3 * PRF # D2: 3 => SOL * DIS # I1: 2,4 => CTR => I1: 9 * PRF # I1: 9 => SOL * DIS # D2: 2,4 => CTR => D2: 3 * PRF # D2: 3 => SOL * PRF # G5: 7,8 => SOL * DIS # G5: 4 => CTR => G5: 7,8 * DIS # I1: 2 => CTR => I1: 4,9 * DIS # C2: 1,4 => CTR => C2: 6 * PRF # C5: 2,7 => SOL * DIS # C5: 9 => CTR => C5: 2,7 * DIS # D9: 8 => CTR => D9: 2,3 * DIS # F2: 2,3 => CTR => F2: 1 * PRF # D9: 2,8 => SOL * DIS # D9: 3 => CTR => D9: 2,8 * DIS # G9: 2,8 => CTR => G9: 6 * PRF # G9: 6 => SOL * DIS # G9: 2 => CTR => G9: 6,8 * CNT 20 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 3 => CTR => F1: 1,2 * PRF F1: 1,2 # G5: 7,8 => SOL * STA F1: 1,2 + G5: 7,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8..5.....79..8......3...17..4.9.8..66..1.5..31..6.7.2..68...9......6..37.....4..5 | initial |
| 8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5 | autosolve |
| 814572369796381452523496178345928716672145893189637524268753941451869237937214685 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (27) B1: 1,2 A3: 4,5 B3: 2,5 D3: 2,4 H1: 6,9 I2: 2,4 A4: 2,3 C4: 5,7 B5: 7,8 B6: 3,8 C6: 5,9 E4: 2,3 E5: 2,4 E6: 3,4 G4: 5,7 H5: 8,9 I6: 4,9 A7: 2,3 A8: 4,5 B8: 1,5 C8: 1,4 B9: 3,7 C9: 2,7 F7: 2,3 D8: 2,8 G8: 2,8 H9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F2: 1.. / F1 = 1 => 0 pairs (X) / F2 = 1 => 29 pairs (_) B8,C8: 1.. / B8 = 1 => 0 pairs (X) / C8 = 1 => 24 pairs (_) C2,F2: 1.. / C2 = 1 => 0 pairs (X) / F2 = 1 => 29 pairs (_) B1,B8: 1.. / B1 = 1 => 24 pairs (_) / B8 = 1 => 0 pairs (X) B1,B3: 2.. / B1 = 2 => 0 pairs (X) / B3 = 2 => 24 pairs (_) I1,I2: 2.. / I1 = 2 => 0 pairs (X) / I2 = 2 => 29 pairs (_) A4,C5: 2.. / A4 = 2 => 0 pairs (X) / C5 = 2 => 0 pairs (_) E4,E5: 2.. / E4 = 2 => 0 pairs (*) / E5 = 2 => 0 pairs (X) A7,C9: 2.. / A7 = 2 => 0 pairs (*) / C9 = 2 => 0 pairs (X) G8,G9: 2.. / G8 = 2 => 27 pairs (_) / G9 = 2 => 0 pairs (X) B3,D3: 2.. / B3 = 2 => 24 pairs (_) / D3 = 2 => 0 pairs (X) A4,E4: 2.. / A4 = 2 => 0 pairs (X) / E4 = 2 => 0 pairs (_) C5,E5: 2.. / C5 = 2 => 0 pairs (*) / E5 = 2 => 0 pairs (X) A7,F7: 2.. / A7 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) D8,G8: 2.. / D8 = 2 => 0 pairs (X) / G8 = 2 => 27 pairs (_) A4,A7: 2.. / A4 = 2 => 0 pairs (X) / A7 = 2 => 0 pairs (_) C5,C9: 2.. / C5 = 2 => 0 pairs (*) / C9 = 2 => 0 pairs (X) G1,G2: 3.. / G1 = 3 => 32 pairs (_) / G2 = 3 => 0 pairs (X) A4,B6: 3.. / A4 = 3 => 0 pairs (*) / B6 = 3 => 0 pairs (X) E4,E6: 3.. / E4 = 3 => 0 pairs (X) / E6 = 3 => 0 pairs (_) A7,B9: 3.. / A7 = 3 => 0 pairs (X) / B9 = 3 => 0 pairs (_) F7,D9: 3.. / F7 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) F1,G1: 3.. / F1 = 3 => 0 pairs (X) / G1 = 3 => 32 pairs (_) A4,E4: 3.. / A4 = 3 => 0 pairs (*) / E4 = 3 => 0 pairs (X) B6,E6: 3.. / B6 = 3 => 0 pairs (X) / E6 = 3 => 0 pairs (_) A7,F7: 3.. / A7 = 3 => 0 pairs (X) / F7 = 3 => 0 pairs (_) B9,D9: 3.. / B9 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) A4,A7: 3.. / A4 = 3 => 0 pairs (*) / A7 = 3 => 0 pairs (X) B6,B9: 3.. / B6 = 3 => 0 pairs (X) / B9 = 3 => 0 pairs (_) D2,D9: 3.. / D2 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) D2,D3: 4.. / D2 = 4 => 0 pairs (X) / D3 = 4 => 24 pairs (_) E5,E6: 4.. / E5 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) A8,C8: 4.. / A8 = 4 => 24 pairs (_) / C8 = 4 => 0 pairs (X) A3,D3: 4.. / A3 = 4 => 0 pairs (X) / D3 = 4 => 24 pairs (_) E5,G5: 4.. / E5 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) A3,A8: 4.. / A3 = 4 => 0 pairs (X) / A8 = 4 => 24 pairs (_) A3,B3: 5.. / A3 = 5 => 24 pairs (_) / B3 = 5 => 0 pairs (X) C4,C6: 5.. / C4 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) G4,G6: 5.. / G4 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) A8,B8: 5.. / A8 = 5 => 0 pairs (X) / B8 = 5 => 24 pairs (_) C4,G4: 5.. / C4 = 5 => 0 pairs (*) / G4 = 5 => 0 pairs (X) C6,G6: 5.. / C6 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) A3,A8: 5.. / A3 = 5 => 24 pairs (_) / A8 = 5 => 0 pairs (X) B3,B8: 5.. / B3 = 5 => 0 pairs (X) / B8 = 5 => 24 pairs (_) C1,C2: 6.. / C1 = 6 => 0 pairs (X) / C2 = 6 => 30 pairs (_) G9,H9: 6.. / G9 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) C2,G2: 6.. / C2 = 6 => 30 pairs (_) / G2 = 6 => 0 pairs (X) H1,H9: 6.. / H1 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) G4,G5: 7.. / G4 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) B9,C9: 7.. / B9 = 7 => 0 pairs (X) / C9 = 7 => 0 pairs (_) C4,G4: 7.. / C4 = 7 => 0 pairs (X) / G4 = 7 => 0 pairs (_) B5,B9: 7.. / B5 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) B5,B6: 8.. / B5 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) D8,D9: 8.. / D8 = 8 => 27 pairs (_) / D9 = 8 => 0 pairs (X) B6,G6: 8.. / B6 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) D8,G8: 8.. / D8 = 8 => 27 pairs (_) / G8 = 8 => 0 pairs (X) H5,H9: 8.. / H5 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) H1,I1: 9.. / H1 = 9 => 0 pairs (X) / I1 = 9 => 0 pairs (_) C5,C6: 9.. / C5 = 9 => 0 pairs (X) / C6 = 9 => 0 pairs (_) H5,I6: 9.. / H5 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) C5,H5: 9.. / C5 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) C6,I6: 9.. / C6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) H1,H5: 9.. / H1 = 9 => 0 pairs (X) / H5 = 9 => 0 pairs (_) I1,I6: 9.. / I1 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) * DURATION: 0:01:52.576056 START: 07:20:18.546856 END: 07:22:11.122912 2017-05-01 * CP COUNT: (64) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,A8,B1,B3,B5,B6,B8,B9,C4,C6,C8,C9,D3,D8,E4,E5,E6,F7,G4,G8,H1,H5,H9,I2,I6) * 8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5 * PAIR B1: 1,2 ROW 1 F1: 1,2,3 # reduction candidate for 1,2 F1: 3 => CTR * 8..573...796.8135...3.9617824.938.1668.1254931..6.7.2.368752941...869237972314..5 F1: 1,2 # 32 pairs * PAIR D3: 2,4 BLK 2 D2: 2,4,3 # reduction candidate for 2,4 D2: 2,4 => CTR * 8..57....79..8..5...3.96178.4.9.8.166..1.5..313.647829.6875.941....69.379..314..5 D2: 3 => SOLVED * 814572369796381452523496178345928716672145893189637524268753941451869237937214685 * PAIR I2: 2,4 BLK 3 I1: 2,4,9 # reduction candidate for 2,4 I1: 2,4 => CTR * 8..57..9.79..8..5...3.96178.4.9.8.166.91254831856.7.2..6875.941....69.379...14..5 I1: 9 => SOLVED * 814572369796381452523496178345928716672145893189637524268753941451869237937214685 * PAIR I2: 2,4 ROW 2 D2: 2,4,3 # reduction candidate for 2,4 D2: 2,4 => CTR * 8..57....79..8..5...3.96178.4.9.8.166..1.5..313.647829.6875.941....69.379..314..5 D2: 3 => SOLVED * 814572369796381452523496178345928716672145893189637524268753941451869237937214685 * PAIR B5: 7,8 ROW 5 G5: 7,8,4 # reduction candidate for 7,8 G5: 7,8 => SOLVED * 814572369796381452523496178345928716672145893189637524268753941451869237937214685 G5: 4 => CTR * 8..57....79..8..5...3.96178.4.9.87166..1.54.31..647529.6875.941....69.379...14..5 * PAIR I6: 4,9 COL I I1: 4,9,2 # reduction candidate for 4,9 I1: 2 => CTR * 8..57..9279..8..54.23496178.4.9.8.166.91254831856.7.2..6875.941....69.379...14..5 I1: 4,9 # 29 pairs * PAIR C8: 1,4 COL C C1: 1,4,6 # reduction candidate for 1,4 C1: 1,4 # 30 pairs C2: 1,4,6 # reduction candidate for 1,4 C2: 1,4 => CTR * 8.657..9.79..8.65...3.96178.4.9.8.166.91254831856.7.2..6875.941....69.379...14..5 C2: 6 # 30 pairs * PAIR C9: 2,7 COL C C5: 2,7,9 # reduction candidate for 2,7 C5: 2,7 => SOLVED * 814572369796381452523496178345928716672145893189637524268753941451869237937214685 C5: 9 => CTR * 8..57....79..8..5...3.9617824.938.166.91254831..6.7.2..6875.941....69.379...14..5 * PAIR F7: 2,3 BLK 8 D9: 2,3,8 # reduction candidate for 2,3 D9: 8 => CTR * 81.57239479438..5...3496178.4.9.8.166..1.5..31..6.7.2..68753941451269837937814265 D9: 2,3 # 27 pairs * PAIR F7: 2,3 COL F F1: 2,3,1 # reduction candidate for 2,3 F1: 2,3 # 29 pairs F2: 2,3,1 # reduction candidate for 2,3 F2: 2,3 => CTR * 826571394791483652453296178.4.9.8.166.91254831856.7.2..6875.941.14.69.379...14.65 F2: 1 # 29 pairs * PAIR D8: 2,8 BLK 8 D9: 2,8,3 # reduction candidate for 2,8 D9: 2,8 => SOLVED * 814572369796381452523496178345928716672145893189637524268753941451869237937214685 D9: 3 => CTR * 8..57....79..8..5...3.9617824.938.166..1254.313.647829.6875.941...8692379.2314..5 * PAIR G8: 2,8 BLK 9 G9: 2,8,6 # reduction candidate for 2,8 G9: 2,8 => CTR * 8..57..9.79..8..5...3.96178.4.9.8.166.91254831856.7.2..6875.941....69.379...14.65 G9: 6 => SOLVED * 814572369796381452523496178345928716672145893189637524268753941451869237937214685 * PAIR H9: 6,8 BLK 9 G9: 6,8,2 # reduction candidate for 6,8 G9: 2 => CTR * 8..57..9.79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14265 G9: 6,8 # 27 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-620657-base-pr-000.dot * REASONING * DIS # F1: 3 => CTR => F1: 1,2 * DIS # D2: 2,4 => CTR => D2: 3 * PRF # D2: 3 => SOL * DIS # I1: 2,4 => CTR => I1: 9 * PRF # I1: 9 => SOL * DIS # D2: 2,4 => CTR => D2: 3 * PRF # D2: 3 => SOL * PRF # G5: 7,8 => SOL * DIS # G5: 4 => CTR => G5: 7,8 * DIS # I1: 2 => CTR => I1: 4,9 * DIS # C2: 1,4 => CTR => C2: 6 * PRF # C5: 2,7 => SOL * DIS # C5: 9 => CTR => C5: 2,7 * DIS # D9: 8 => CTR => D9: 2,3 * DIS # F2: 2,3 => CTR => F2: 1 * PRF # D9: 2,8 => SOL * DIS # D9: 3 => CTR => D9: 2,8 * DIS # G9: 2,8 => CTR => G9: 6 * PRF # G9: 6 => SOL * DIS # G9: 2 => CTR => G9: 6,8 * CNT 20 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,A8,B1,B3,B5,B6,B8,B9,C4,C6,C8,C9,D3,D8,E4,E5,E6,F7,G4,G8,H1,H5,H9,I2,I6) * 8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5 * PAIR B1: 1,2 ROW 1 F1: 1,2,3 # reduction candidate for 1,2 F1: 3 => CTR * 8..573...796.8135...3.9617824.938.1668.1254931..6.7.2.368752941...869237972314..5 * PAIR RESTART * PAIR B5: 7,8 ROW 5 G5: 7,8,4 # reduction candidate for 7,8 G5: 7,8 => SOLVED * 814572369796381452523496178345928716672145893189637524268753941451869237937214685 * DURATION: 0:00:04.638167 START: 07:22:40.791678 END: 07:22:45.429845 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-620657-base-pr-001.dot * REASONING * DIS # F1: 3 => CTR => F1: 1,2 * PRF F1: 1,2 # G5: 7,8 => SOL * STA F1: 1,2 + G5: 7,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokus.de/620657.html sehr schwierig level: medium * PAIR REDUCTION .. * ROUND 1: 8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5 B1: 1,2 F1: 1,2,3 # reduction candidate for 1,2 F1: 3 => CTR * 8..573...796.8135...3.9617824.938.1668.1254931..6.7.2.368752941...869237972314..5 A3: 4,5 B3: 2,5 D3: 2,4 H1: 6,9 A4: 2,3 C4: 5,7 B5: 7,8 G5: 4,7,8 # reduction candidate for 7,8 G5: 7,8 => SOLVED * 814572369796381452523496178345928716672145893189637524268753941451869237937214685 * SOLVED! -------------------------------------------------- * AUTO .. E1 = 7 # set value F3 = 6 # set value I3 = 8 # set value H4 = 1 # set value H7: 4 # naked single E7 = 5 # set value H7 = 4 # set value I7 = 1 # set value E3: 9.. # hidden single D7: 7.. # hidden single E9: 1.. # hidden single H2: 5.. # hidden single H2 = 5 # set value E3 = 9 # set value D7 = 7 # set value E9 = 1 # set value F8: 9.. # hidden single F8 = 9 # set value A9: 9.. # hidden single A9 = 9 # set value Q9: 2.. = G8,G9: 2.. => G1,G2 != 2 A8,B8,C8: 1,4,5.. => A8,B8,C8 != 2 # hidden triple B5,B6,B9: 3,7,8.. => B5,B6,B9 != 2,5 # hidden triple C1,C2,C8: 6,1,4.. => C1,C2,C8 != 2,5 # hidden triple Q4,Q7: 2.. => A3 != 2 Q1,Q7: 5.. => A4 != 5 C4,G4: 5,7.. => C4 != 2 # hidden pair * UNSOLVED! |:step:| 00 -------------------------------------------------- pair quad D8: 2,8 G8: 2,8 D9: 2,3,8 G9: 2,6,8 * FORCE VALUE:: D9 = 3 D9 = 3 # set value => CTR * FORCE VALUE:: G9 = 6 G9 = 6 # set value * SOLVED! |:step:| 01 --------------------------------------------------
Solution
position: 814572369796381452523496178345928716672145893189637524268753941451869237937214685 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: 1,2 => UNS * DIS # F1: 3 => CTR => F1: 1,2 * DIS # D2: 2,4 => CTR => D2: 3 * PRF # D2: 3 => SOL * DIS # I1: 2,4 => CTR => I1: 9 * PRF # I1: 9 => SOL * DIS # D2: 2,4 => CTR => D2: 3 * PRF # D2: 3 => SOL * PRF # G5: 7,8 => SOL * DIS # G5: 4 => CTR => G5: 7,8 * INC # I1: 4,9 => UNS * DIS # I1: 2 => CTR => I1: 4,9 * INC # C1: 1,4 => UNS * DIS # C2: 1,4 => CTR => C2: 6 * INC # C2: 6 => UNS * PRF # C5: 2,7 => SOL * DIS # C5: 9 => CTR => C5: 2,7 * INC # D9: 2,3 => UNS * DIS # D9: 8 => CTR => D9: 2,3 * INC # F1: 2,3 => UNS * DIS # F2: 2,3 => CTR => F2: 1 * INC # F2: 1 => UNS * PRF # D9: 2,8 => SOL * DIS # D9: 3 => CTR => D9: 2,8 * DIS # G9: 2,8 => CTR => G9: 6 * PRF # G9: 6 => SOL * INC # G9: 6,8 => UNS * DIS # G9: 2 => CTR => G9: 6,8 * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 1,2 => UNS * DIS # F1: 3 => CTR => F1: 1,2 * PRF F1: 1,2 # G5: 7,8 => SOL * STA F1: 1,2 + G5: 7,8 * CNT 3 HDP CHAINS / 3 HYP OPENED