Analysis of zz-sudoku-de-761453-base.sdk
Contents
Original Sudoku
level: medium
position: .1.4...5....6...82..52.193..37......9.......1......76..965.43..82...6....7...9.2. initial
Autosolve
position: .1.49.657.496..182..52.1934.371...959......41..19..763196524378824..6519573819426 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E2: 3,7 => SOL * DIS # E5: 3,7 => CTR => E5: 5,6 * PRF # E6: 5,8 => SOL * DIS # E6: 4 => CTR => E6: 5,8 * DIS # F6: 5,8 => CTR => F6: 2 * PRF # F6: 2 => SOL * PRF # F6: 2,8 => SOL * DIS # F6: 5 => CTR => F6: 2,8 * DIS # E5: 3,7 => CTR => E5: 5,6 * PRF # E2: 3,7 => SOL * DIS # E5: 3,7 => CTR => E5: 5,6 * CNT 11 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E2: 3,7 => SOL * STA E2: 3,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1.4...5....6...82..52.193..37......9.......1......76..965.43..82...6....7...9.2. | initial |
| .1.49.657.496..182..52.1934.371...959......41..19..763196524378824..6519573819426 | autosolve |
| 218493657349675182765281934637148295952367841481952763196524378824736519573819426 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A1: 2,3 C1: 2,8 A2: 3,7 A3: 6,7 B3: 6,8 F1: 3,8 E3: 7,8 A4: 4,6 B5: 5,6 C5: 2,8 A6: 2,4 B6: 5,8 E4: 4,6 F4: 2,8 D5: 3,7 G4: 2,8 G5: 2,8 D8: 3,7 E8: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 2.. / A1 = 2 => 0 pairs (*) / C1 = 2 => 0 pairs (X) C5,A6: 2.. / C5 = 2 => 0 pairs (*) / A6 = 2 => 0 pairs (X) F4,F6: 2.. / F4 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) G4,G5: 2.. / G4 = 2 => 0 pairs (*) / G5 = 2 => 0 pairs (X) F4,G4: 2.. / F4 = 2 => 0 pairs (X) / G4 = 2 => 0 pairs (_) C5,G5: 2.. / C5 = 2 => 0 pairs (*) / G5 = 2 => 0 pairs (X) A6,F6: 2.. / A6 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) A1,A6: 2.. / A1 = 2 => 0 pairs (*) / A6 = 2 => 0 pairs (X) C1,C5: 2.. / C1 = 2 => 0 pairs (X) / C5 = 2 => 0 pairs (_) A1,A2: 3.. / A1 = 3 => 0 pairs (X) / A2 = 3 => 0 pairs (_) D8,E8: 3.. / D8 = 3 => 0 pairs (X) / E8 = 3 => 18 pairs (_) A1,F1: 3.. / A1 = 3 => 0 pairs (X) / F1 = 3 => 0 pairs (_) D5,D8: 3.. / D5 = 3 => 18 pairs (_) / D8 = 3 => 0 pairs (X) A4,A6: 4.. / A4 = 4 => 0 pairs (X) / A6 = 4 => 0 pairs (_) E4,E6: 4.. / E4 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) A4,E4: 4.. / A4 = 4 => 0 pairs (X) / E4 = 4 => 0 pairs (_) A6,E6: 4.. / A6 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) E2,F2: 5.. / E2 = 5 => 22 pairs (_) / F2 = 5 => 0 pairs (*) B5,B6: 5.. / B5 = 5 => 0 pairs (*) / B6 = 5 => 0 pairs (X) A3,B3: 6.. / A3 = 6 => 0 pairs (X) / B3 = 6 => 0 pairs (_) A4,B5: 6.. / A4 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) E4,E5: 6.. / E4 = 6 => 0 pairs (X) / E5 = 6 => 0 pairs (_) A4,E4: 6.. / A4 = 6 => 0 pairs (*) / E4 = 6 => 0 pairs (X) B5,E5: 6.. / B5 = 6 => 0 pairs (X) / E5 = 6 => 0 pairs (_) A3,A4: 6.. / A3 = 6 => 0 pairs (X) / A4 = 6 => 0 pairs (_) B3,B5: 6.. / B3 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) A2,A3: 7.. / A2 = 7 => 0 pairs (X) / A3 = 7 => 0 pairs (_) D8,E8: 7.. / D8 = 7 => 18 pairs (_) / E8 = 7 => 0 pairs (X) A3,E3: 7.. / A3 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) D5,D8: 7.. / D5 = 7 => 0 pairs (X) / D8 = 7 => 18 pairs (_) F2,F5: 7.. / F2 = 7 => 0 pairs (X) / F5 = 7 => 19 pairs (_) C1,B3: 8.. / C1 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) F1,E3: 8.. / F1 = 8 => 0 pairs (X) / E3 = 8 => 0 pairs (_) C5,B6: 8.. / C5 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) G4,G5: 8.. / G4 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) C1,F1: 8.. / C1 = 8 => 0 pairs (*) / F1 = 8 => 0 pairs (X) B3,E3: 8.. / B3 = 8 => 0 pairs (X) / E3 = 8 => 0 pairs (_) F4,G4: 8.. / F4 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) C5,G5: 8.. / C5 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) B3,B6: 8.. / B3 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) C1,C5: 8.. / C1 = 8 => 0 pairs (*) / C5 = 8 => 0 pairs (X) E3,E6: 8.. / E3 = 8 => 0 pairs (*) / E6 = 8 => 0 pairs (X) * DURATION: 0:01:16.275164 START: 08:35:29.431878 END: 08:36:45.707042 2017-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,A4,A6,B3,B5,B6,C1,C5,D5,D8,E3,E4,E8,F1,F4,G4,G5) * .1.49.657.496..182..52.1934.371...959......41..19..763196524378824..6519573819426 * PAIR A2: 3,7 ROW 2 E2: 3,7,5 # reduction candidate for 3,7 E2: 3,7 => SOLVED * 218493657349675182765281934637148295952367841481952763196524378824736519573819426 E2: 5 # 22 pairs F2: 3,7,5 # reduction candidate for 3,7 F2: 3,7 # 22 pairs * PAIR B5: 5,6 ROW 5 E5: 5,6,3,7 # reduction candidate for 5,6 E5: 3,7 => CTR * .1849.657.496..182..52.1934.3716..9596...5.41.51948763196524378824..6519573819426 E5: 5,6 # 21 pairs * PAIR B6: 5,8 ROW 6 E6: 5,8,4 # reduction candidate for 5,8 E6: 5,8 => SOLVED * 218493657349675182765281934637148295952367841481952763196524378824736519573819426 E6: 4 => CTR * .1.49.657.496..182..5281934.371...959......41.81945763196524378824..6519573819426 F6: 5,8,2 # reduction candidate for 5,8 F6: 5,8 => CTR * .1.49.657.496..182..52.1934.371.28959.8...241251948763196524378824..6519573819426 F6: 2 => SOLVED * 218493657349675182765281934637148295952367841481952763196524378824736519573819426 * PAIR F4: 2,8 BLK 5 F6: 2,8,5 # reduction candidate for 2,8 F6: 2,8 => SOLVED * 218493657349675182765281934637148295952367841481952763196524378824736519573819426 F6: 5 => CTR * .1.49.657.496..182..52.1934.371.28959.8...2412519..763196524378824..6519573819426 * PAIR D5: 3,7 BLK 5 E5: 3,7,5,6 # reduction candidate for 3,7 E5: 3,7 => CTR * .1849.657.496..182..52.1934.3716..9596...5.41.51948763196524378824..6519573819426 E5: 5,6 # 21 pairs F5: 3,7,5 # reduction candidate for 3,7 F5: 3,7 # 21 pairs * PAIR E8: 3,7 COL E E2: 3,7,5 # reduction candidate for 3,7 E2: 3,7 => SOLVED * 218493657349675182765281934637148295952367841481952763196524378824736519573819426 E2: 5 # 22 pairs E5: 3,7,5,6 # reduction candidate for 3,7 E5: 3,7 => CTR * .1849.657.496..182..52.1934.3716..9596...5.41.51948763196524378824..6519573819426 E5: 5,6 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-761453-base-pr-000.dot * REASONING * PRF # E2: 3,7 => SOL * DIS # E5: 3,7 => CTR => E5: 5,6 * PRF # E6: 5,8 => SOL * DIS # E6: 4 => CTR => E6: 5,8 * DIS # F6: 5,8 => CTR => F6: 2 * PRF # F6: 2 => SOL * PRF # F6: 2,8 => SOL * DIS # F6: 5 => CTR => F6: 2,8 * DIS # E5: 3,7 => CTR => E5: 5,6 * PRF # E2: 3,7 => SOL * DIS # E5: 3,7 => CTR => E5: 5,6 * CNT 11 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A3,A4,A6,B3,B5,B6,C1,C5,D5,D8,E3,E4,E8,F1,F4,G4,G5) * .1.49.657.496..182..52.1934.371...959......41..19..763196524378824..6519573819426 * PAIR A2: 3,7 ROW 2 E2: 3,7,5 # reduction candidate for 3,7 E2: 3,7 => SOLVED * 218493657349675182765281934637148295952367841481952763196524378824736519573819426 * DURATION: 0:00:02.090480 START: 08:37:07.030597 END: 08:37:09.121077 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-761453-base-pr-001.dot * REASONING * PRF # E2: 3,7 => SOL * STA E2: 3,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/761453.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: .1.49.657.496..182..52.1934.371...959......41..19..763196524378824..6519573819426 A1: 2,3 C1: 2,8 A2: 3,7 E2: 3,5,7 # reduction candidate for 3,7 E2: 3,7 => SOLVED * 218493657349675182765281934637148295952367841481952763196524378824736519573819426 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- highlight 7 pair quad D5: 3,7 D8: 3,7 E8: 3,7 E5: 3,5,6,7 => E5 != 3,7 * DISABLE VALUE:: E5 != 7 * DISABLE VALUE:: E5 != 3 * AUTO .. D5,F5: 3,7.. => F5 != 5 # hidden pair * UNSOLVED! |:step:| 01 -------------------------------------------------- A2: 3,7 E2: 3,5,7 F2: 3,5,7 => E2 = 5 or F2 = 5 E2 = 5 => E5 = 6 & E6 = 4,8 & B5 = 5 => B6 = 8 => E6 = 4 => E4 = 6 => CTR => E2 != 5 => F2 = 5
Solution
position: 218493657349675182765281934637148295952367841481952763196524378824736519573819426 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 # E2: 3,7 => SOL * INC # E2: 5 => UNS * INC # F2: 3,7 => UNS * INC # E5: 5,6 => UNS * DIS # E5: 3,7 => CTR => E5: 5,6 * PRF # E6: 5,8 => SOL * DIS # E6: 4 => CTR => E6: 5,8 * DIS # F6: 5,8 => CTR => F6: 2 * PRF # F6: 2 => SOL * PRF # F6: 2,8 => SOL * DIS # F6: 5 => CTR => F6: 2,8 * DIS # E5: 3,7 => CTR => E5: 5,6 * INC # E5: 5,6 => UNS * INC # F5: 3,7 => UNS * PRF # E2: 3,7 => SOL * INC # E2: 5 => UNS * DIS # E5: 3,7 => CTR => E5: 5,6 * INC # E5: 5,6 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # E2: 3,7 => SOL * STA E2: 3,7 * CNT 1 HDP CHAINS / 1 HYP OPENED