Analysis of zz-sudoku-de-691604-base.sdk
Contents
Original Sudoku
level: medium
position: ....2.4...9...7.383...9......3..6.819.......341.5..6......8...514.2...7...6.1.... initial
Autosolve
position: 6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 2,5 => SOL * DIS # C2: 1,4 => CTR => C2: 2,5 * PRF # A4: 7 => SOL * DIS # D3: 4 => CTR => D3: 1,8 * PRF # F5: 1,8 => SOL * DIS # F5: 2 => CTR => F5: 1,8 * PRF # D3: 1,4 => SOL * DIS # D3: 8 => CTR => D3: 1,4 * DIS # C2: 1,4 => CTR => C2: 2,5 * PRF # C2: 2,5 => SOL * DIS # G3: 1,2 => CTR => G3: 7 * PRF # G3: 7 => SOL * PRF # C2: 1,2 => SOL * PRF # G3: 2,7 => SOL * DIS # G3: 1 => CTR => G3: 2,7 * PRF # A4: 2,7 => SOL * DIS # A4: 5 => CTR => A4: 2,7 * DIS # C6: 2,7 => CTR => C6: 8 * PRF # C6: 8 => SOL * DIS # G4: 2,7 => CTR => G4: 5 * PRF # G4: 5 => SOL * PRF # F5: 1,8 => SOL * DIS # F5: 2 => CTR => F5: 1,8 * DIS # D3: 4 => CTR => D3: 1,8 * DIS # F5: 2,8 => CTR => F5: 1 * PRF # F5: 1 => SOL * PRF # C6: 2,8 => SOL * DIS # C6: 7 => CTR => C6: 2,8 * PRF # G4: 2,5 => SOL * DIS # G4: 7 => CTR => G4: 2,5 * PRF # C5: 2,5 => SOL * DIS # C5: 8 => CTR => C5: 2,5 * DIS # G4: 2,7 => CTR => G4: 5 * PRF # G4: 5 => SOL * DIS # C6: 2,7 => CTR => C6: 8 * PRF # C6: 8 => SOL * PRF # A4: 2,7 => SOL * DIS # A4: 5 => CTR => A4: 2,7 * DIS # C6: 2,7 => CTR => C6: 8 * PRF # C6: 8 => SOL * CNT 40 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 2,5 => SOL * STA C2: 2,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....2.4...9...7.383...9......3..6.819.......341.5..6......8...514.2...7...6.1.... | initial |
| 6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324 | autosolve |
| 671328459592467138384195762723946581965871243418532697237684915149253876856719324 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B1: 7,8 C1: 1,7 A2: 2,5 B3: 2,8 F1: 1,8 D2: 1,4 G2: 1,2 I3: 2,7 B4: 2,7 D5: 1,8 F6: 2,8 G5: 2,5 I6: 2,7 A7: 2,7 C7: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,G3: 1.. / G2 = 1 => 0 pairs (*) / G3 = 1 => 0 pairs (X) D5,F5: 1.. / D5 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) C1,F1: 1.. / C1 = 1 => 0 pairs (*) / F1 = 1 => 0 pairs (X) F1,F5: 1.. / F1 = 1 => 0 pairs (X) / F5 = 1 => 0 pairs (_) F5,F6: 2.. / F5 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) A7,C7: 2.. / A7 = 2 => 0 pairs (*) / C7 = 2 => 0 pairs (X) B3,B4: 2.. / B3 = 2 => 0 pairs (X) / B4 = 2 => 0 pairs (_) I3,I6: 2.. / I3 = 2 => 0 pairs (*) / I6 = 2 => 0 pairs (X) C2,C3: 4.. / C2 = 4 => 0 pairs (X) / C3 = 4 => 15 pairs (_) D2,D3: 4.. / D2 = 4 => 15 pairs (_) / D3 = 4 => 0 pairs (X) C2,D2: 4.. / C2 = 4 => 0 pairs (X) / D2 = 4 => 15 pairs (_) C3,D3: 4.. / C3 = 4 => 15 pairs (_) / D3 = 4 => 0 pairs (X) A2,C2: 5.. / A2 = 5 => 0 pairs (*) / C2 = 5 => 0 pairs (X) A4,C5: 5.. / A4 = 5 => 0 pairs (X) / C5 = 5 => 0 pairs (_) G4,G5: 5.. / G4 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) A4,G4: 5.. / A4 = 5 => 0 pairs (X) / G4 = 5 => 0 pairs (_) C5,G5: 5.. / C5 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) A2,A4: 5.. / A2 = 5 => 0 pairs (*) / A4 = 5 => 0 pairs (X) C2,C5: 5.. / C2 = 5 => 0 pairs (X) / C5 = 5 => 0 pairs (_) B1,C1: 7.. / B1 = 7 => 0 pairs (*) / C1 = 7 => 0 pairs (X) G3,I3: 7.. / G3 = 7 => 0 pairs (*) / I3 = 7 => 0 pairs (X) G4,I6: 7.. / G4 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) A7,C7: 7.. / A7 = 7 => 18 pairs (_) / C7 = 7 => 0 pairs (*) C6,I6: 7.. / C6 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) A4,A7: 7.. / A4 = 7 => 0 pairs (*) / A7 = 7 => 0 pairs (X) B1,B4: 7.. / B1 = 7 => 0 pairs (*) / B4 = 7 => 0 pairs (X) G3,G4: 7.. / G3 = 7 => 0 pairs (*) / G4 = 7 => 0 pairs (X) I3,I6: 7.. / I3 = 7 => 0 pairs (X) / I6 = 7 => 0 pairs (_) B1,B3: 8.. / B1 = 8 => 0 pairs (X) / B3 = 8 => 0 pairs (_) F1,D3: 8.. / F1 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) C5,C6: 8.. / C5 = 8 => 0 pairs (X) / C6 = 8 => 0 pairs (_) B1,F1: 8.. / B1 = 8 => 0 pairs (X) / F1 = 8 => 0 pairs (_) B3,D3: 8.. / B3 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) C6,F6: 8.. / C6 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) D3,D5: 8.. / D3 = 8 => 0 pairs (X) / D5 = 8 => 0 pairs (_) * DURATION: 0:01:04.812383 START: 07:51:02.736415 END: 07:52:07.548798 2017-05-01 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B1,B3,B4,C1,C7,D2,D5,F1,F6,G2,G5,I3,I6) * 6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324 * PAIR A2: 2,5 BLK 1 C2: 2,5,1,4 # reduction candidate for 2,5 C2: 2,5 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 C2: 1,4 => CTR * 6..32.45959..672383...95167..3946.8196..7..4341.53.69..3.684915149253876856719324 * PAIR A2: 2,5 COL A A4: 2,5,7 # reduction candidate for 2,5 A4: 7 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 A4: 2,5 # 18 pairs * PAIR F1: 1,8 BLK 2 D3: 1,8,4 # reduction candidate for 1,8 D3: 4 => CTR * 6..328459.9.167238382495167.23946.8196..7..4341.53.69..3.684915149253876856719324 D3: 1,8 # 15 pairs * PAIR F1: 1,8 COL F F5: 1,8,2 # reduction candidate for 1,8 F5: 1,8 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 F5: 2 => CTR * 6..321459.9.467.383.4895167..394678196817254341753.69..3.684915149253876856719324 * PAIR D2: 1,4 BLK 2 D3: 1,4,8 # reduction candidate for 1,4 D3: 1,4 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 D3: 8 => CTR * 6..32.459.9.467.383.4895167..394678196.17.54341753.69..3.684915149253876856719324 * PAIR D2: 1,4 ROW 2 C2: 1,4,2,5 # reduction candidate for 1,4 C2: 1,4 => CTR * 6..32.45959..672383...95167..3946.8196..7..4341.53.69..3.684915149253876856719324 C2: 2,5 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * PAIR G2: 1,2 BLK 3 G3: 1,2,7 # reduction candidate for 1,2 G3: 1,2 => CTR * 6..32.459.9..67.383...95.67..394678196..7.543417538692732684915149253876856719324 G3: 7 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * PAIR G2: 1,2 ROW 2 C2: 1,2,4,5 # reduction candidate for 1,2 C2: 1,2 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 C2: 4,5 # 16 pairs * PAIR I3: 2,7 BLK 3 G3: 2,7,1 # reduction candidate for 2,7 G3: 2,7 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 G3: 1 => CTR * 6..32.459.9..67.383...95167..394678196..7.543417538692732684915149253876856719324 * PAIR B4: 2,7 BLK 4 A4: 2,7,5 # reduction candidate for 2,7 A4: 2,7 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 A4: 5 => CTR * 6..32.459295467138384195.6.523946781968.7.54341.53.69.732684915149253876856719324 C6: 2,7,8 # reduction candidate for 2,7 C6: 2,7 => CTR * 687321459.9546713832..95.6...3946.8196817254341.53869..3.684915149253876856719324 C6: 8 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * PAIR B4: 2,7 ROW 4 G4: 2,7,5 # reduction candidate for 2,7 G4: 2,7 => CTR * 6..32.459295467138384195.6.523946781968.7.54341.53.69.732684915149253876856719324 G4: 5 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * PAIR D5: 1,8 BLK 5 F5: 1,8,2 # reduction candidate for 1,8 F5: 1,8 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 F5: 2 => CTR * 6..321459.9.467.383.4895167..394678196817254341753.69..3.684915149253876856719324 * PAIR D5: 1,8 COL D D3: 1,8,4 # reduction candidate for 1,8 D3: 4 => CTR * 6..328459.9.167238382495167.23946.8196..7..4341.53.69..3.684915149253876856719324 D3: 1,8 # 15 pairs * PAIR F6: 2,8 BLK 5 F5: 2,8,1 # reduction candidate for 2,8 F5: 2,8 => CTR * 6..321459.9.467.383.4895167..394678196.17.54341753.69..3.684915149253876856719324 F5: 1 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * PAIR F6: 2,8 ROW 6 C6: 2,8,7 # reduction candidate for 2,8 C6: 2,8 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 C6: 7 => CTR * 6..32.459.9..67.383...95.6...3946.81968172543417538692732684915149253876856719324 * PAIR G5: 2,5 BLK 6 G4: 2,5,7 # reduction candidate for 2,5 G4: 2,5 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 G4: 7 => CTR * 6..32.459.9..67.383...95.6.523946781968172543417538692732684915149253876856719324 * PAIR G5: 2,5 ROW 5 C5: 2,5,8 # reduction candidate for 2,5 C5: 2,5 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 C5: 8 => CTR * 6..32.459.954671383.4195.6.5.3946.81968.7..4341.53.69..3.684915149253876856719324 * PAIR I6: 2,7 BLK 6 G4: 2,7,5 # reduction candidate for 2,7 G4: 2,7 => CTR * 6..32.459295467138384195.6.523946781968.7.54341.53.69.732684915149253876856719324 G4: 5 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * PAIR I6: 2,7 ROW 6 C6: 2,7,8 # reduction candidate for 2,7 C6: 2,7 => CTR * 687321459.9546713832..95.6...3946.8196817254341.53869..3.684915149253876856719324 C6: 8 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * PAIR A7: 2,7 COL A A4: 2,7,5 # reduction candidate for 2,7 A4: 2,7 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 A4: 5 => CTR * 6..32.459295467138384195.6.523946781968.7.54341.53.69.732684915149253876856719324 * PAIR C7: 2,7 COL C C6: 2,7,8 # reduction candidate for 2,7 C6: 2,7 => CTR * 687321459.9546713832..95.6...3946.8196817254341.53869..3.684915149253876856719324 C6: 8 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-691604-base-pr-000.dot * REASONING * PRF # C2: 2,5 => SOL * DIS # C2: 1,4 => CTR => C2: 2,5 * PRF # A4: 7 => SOL * DIS # D3: 4 => CTR => D3: 1,8 * PRF # F5: 1,8 => SOL * DIS # F5: 2 => CTR => F5: 1,8 * PRF # D3: 1,4 => SOL * DIS # D3: 8 => CTR => D3: 1,4 * DIS # C2: 1,4 => CTR => C2: 2,5 * PRF # C2: 2,5 => SOL * DIS # G3: 1,2 => CTR => G3: 7 * PRF # G3: 7 => SOL * PRF # C2: 1,2 => SOL * PRF # G3: 2,7 => SOL * DIS # G3: 1 => CTR => G3: 2,7 * PRF # A4: 2,7 => SOL * DIS # A4: 5 => CTR => A4: 2,7 * DIS # C6: 2,7 => CTR => C6: 8 * PRF # C6: 8 => SOL * DIS # G4: 2,7 => CTR => G4: 5 * PRF # G4: 5 => SOL * PRF # F5: 1,8 => SOL * DIS # F5: 2 => CTR => F5: 1,8 * DIS # D3: 4 => CTR => D3: 1,8 * DIS # F5: 2,8 => CTR => F5: 1 * PRF # F5: 1 => SOL * PRF # C6: 2,8 => SOL * DIS # C6: 7 => CTR => C6: 2,8 * PRF # G4: 2,5 => SOL * DIS # G4: 7 => CTR => G4: 2,5 * PRF # C5: 2,5 => SOL * DIS # C5: 8 => CTR => C5: 2,5 * DIS # G4: 2,7 => CTR => G4: 5 * PRF # G4: 5 => SOL * DIS # C6: 2,7 => CTR => C6: 8 * PRF # C6: 8 => SOL * PRF # A4: 2,7 => SOL * DIS # A4: 5 => CTR => A4: 2,7 * DIS # C6: 2,7 => CTR => C6: 8 * PRF # C6: 8 => SOL * CNT 40 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B1,B3,B4,C1,C7,D2,D5,F1,F6,G2,G5,I3,I6) * 6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324 * PAIR A2: 2,5 BLK 1 C2: 2,5,1,4 # reduction candidate for 2,5 C2: 2,5 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * DURATION: 0:00:02.169026 START: 07:53:02.941107 END: 07:53:05.110133 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-691604-base-pr-001.dot * REASONING * PRF # C2: 2,5 => SOL * STA C2: 2,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/691604.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324 B1: 7,8 C1: 1,7 A2: 2,5 C2: 1,2,4,5 # reduction candidate for 2,5 C2: 2,5 => SOLVED * 671328459592467138384195762723946581965871243418532697237684915149253876856719324 * SOLVED! --------------------------------------------------
Solution
position: 671328459592467138384195762723946581965871243418532697237684915149253876856719324 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 # C2: 2,5 => SOL * DIS # C2: 1,4 => CTR => C2: 2,5 * INC # A4: 2,5 => UNS * PRF # A4: 7 => SOL * INC # D3: 1,8 => UNS * DIS # D3: 4 => CTR => D3: 1,8 * PRF # F5: 1,8 => SOL * DIS # F5: 2 => CTR => F5: 1,8 * PRF # D3: 1,4 => SOL * DIS # D3: 8 => CTR => D3: 1,4 * DIS # C2: 1,4 => CTR => C2: 2,5 * PRF # C2: 2,5 => SOL * DIS # G3: 1,2 => CTR => G3: 7 * PRF # G3: 7 => SOL * PRF # C2: 1,2 => SOL * INC # C2: 4,5 => UNS * PRF # G3: 2,7 => SOL * DIS # G3: 1 => CTR => G3: 2,7 * PRF # A4: 2,7 => SOL * DIS # A4: 5 => CTR => A4: 2,7 * DIS # C6: 2,7 => CTR => C6: 8 * PRF # C6: 8 => SOL * DIS # G4: 2,7 => CTR => G4: 5 * PRF # G4: 5 => SOL * PRF # F5: 1,8 => SOL * DIS # F5: 2 => CTR => F5: 1,8 * INC # D3: 1,8 => UNS * DIS # D3: 4 => CTR => D3: 1,8 * DIS # F5: 2,8 => CTR => F5: 1 * PRF # F5: 1 => SOL * PRF # C6: 2,8 => SOL * DIS # C6: 7 => CTR => C6: 2,8 * PRF # G4: 2,5 => SOL * DIS # G4: 7 => CTR => G4: 2,5 * PRF # C5: 2,5 => SOL * DIS # C5: 8 => CTR => C5: 2,5 * DIS # G4: 2,7 => CTR => G4: 5 * PRF # G4: 5 => SOL * DIS # C6: 2,7 => CTR => C6: 8 * PRF # C6: 8 => SOL * PRF # A4: 2,7 => SOL * DIS # A4: 5 => CTR => A4: 2,7 * DIS # C6: 2,7 => CTR => C6: 8 * PRF # C6: 8 => SOL * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 2,5 => SOL * STA C2: 2,5 * CNT 1 HDP CHAINS / 1 HYP OPENED