Analysis of zz-menneske-no-06899619-base.sdk
Contents
Original Sudoku
level: medium
position: ...8.1..55......2...69..........6.873...8....1.....4.......96...3.4....2.596.7... initial
Autosolve
position: ...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E1: 3,7 => SOL * DIS # E2: 3,7 => CTR => E2: 4,6 * DIS # E3: 3,7 => CTR => E3: 2,4,5 * DIS # C2: 3,7 => CTR => C2: 1,4,8 * PRF # G2: 3,7 => SOL * DIS # D6: 3,7 => CTR => D6: 2,5 * DIS # E1: 3,4 => CTR => E1: 2,6,7 * DIS # E2: 3,4 => CTR => E2: 6,7 * DIS # E3: 3,4 => CTR => E3: 2,5,7 * DIS # F3: 3,4 => CTR => F3: 2,5 * DIS # C2: 3,4 => CTR => C2: 1,7,8 * DIS # I2: 3,4 => CTR => I2: 1,6,8,9 * DIS # C7: 1,7 => CTR => C7: 2,4,8 * PRF # C2: 1,7 => SOL * PRF # D7: 1,5 => SOL * DIS # D7: 2,3 => CTR => D7: 1,5 * DIS # E7: 1,5 => CTR => E7: 2,3 * DIS # E4: 1,5 => CTR => E4: 2,3,4,9 * DIS # H8: 5,7 => CTR => H8: 9 * CNT 19 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E1: 3,7 => SOL * STA E1: 3,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8.1..55......2...69..........6.873...8....1.....4.......96...3.4....2.596.7... | initial |
| ...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7... | autosolve |
| 243871965591364728786952143925146387364785219178293456812539674637418592459627831 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) D2: 3,7 F2: 3,4 C8: 1,7 E8: 1,5 H7: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C8,E8: 1.. / C8 = 1 => 0 pairs (X) / E8 = 1 => 0 pairs (_) G4,G5: 2.. / G4 = 2 => 0 pairs (X) / G5 = 2 => 6 pairs (_) A9,E9: 2.. / A9 = 2 => 8 pairs (_) / E9 = 2 => 0 pairs (*) C1,C2: 3.. / C1 = 3 => 6 pairs (_) / C2 = 3 => 0 pairs (X) E4,F5: 4.. / E4 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 0 pairs (*) / F3 = 5 => 0 pairs (X) E1,E2: 6.. / E1 = 6 => 0 pairs (X) / E2 = 6 => 5 pairs (_) H1,I2: 6.. / H1 = 6 => 5 pairs (_) / I2 = 6 => 0 pairs (X) B5,B6: 6.. / B5 = 6 => 7 pairs (_) / B6 = 6 => 8 pairs (_) E1,H1: 6.. / E1 = 6 => 0 pairs (X) / H1 = 6 => 5 pairs (_) E2,I2: 6.. / E2 = 6 => 5 pairs (_) / I2 = 6 => 0 pairs (X) B6,C6: 8.. / B6 = 8 => 0 pairs (X) / C6 = 8 => 5 pairs (_) E4,E6: 9.. / E4 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) G8,H8: 9.. / G8 = 9 => 0 pairs (X) / H8 = 9 => 6 pairs (_) A1,A4: 9.. / A1 = 9 => 7 pairs (_) / A4 = 9 => 0 pairs (*) * DURATION: 0:00:21.102467 START: 06:32:27.618982 END: 06:32:48.721449 2017-05-01 * CP COUNT: (15) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D2,E8,F2,H7) * ...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7... * PAIR D2: 3,7 BLK 2 E1: 3,7,2,4,6 # reduction candidate for 3,7 E1: 3,7 => SOLVED * 243871965591364728786952143925146387364785219178293456812539674637418592459627831 E1: 2,4,6 # 5 pairs E2: 3,7,4,6 # reduction candidate for 3,7 E2: 3,7 => CTR * ..3861..55....4.26..69.........46.873...8....1...934.......96..63.4.8..2.596.7... E2: 4,6 # 6 pairs E3: 3,7,2,4,5 # reduction candidate for 3,7 E3: 3,7 => CTR * ...821.655...64.2...69.5.......46.873...82...1...9345......96..63.4.8..2.596.7... E3: 2,4,5 # 5 pairs * PAIR D2: 3,7 ROW 2 C2: 3,7,1,4,8 # reduction candidate for 3,7 C2: 3,7 => CTR * ...8.1.655.7364.2...69.........463873...8.2..1...934567....96..63.4.8..2.596.7... C2: 1,4,8 # 6 pairs G2: 3,7,1,8,9 # reduction candidate for 3,7 G2: 3,7 => SOLVED * 243871965591364728786952143925146387364785219178293456812539674637418592459627831 G2: 1,8,9 # 5 pairs * PAIR D2: 3,7 COL D D6: 3,7,2,5 # reduction candidate for 3,7 D6: 3,7 => CTR * ...8.1..55......2...69........1.638737.5842..1.....4.......967.637418592.596.7... D6: 2,5 # 6 pairs * PAIR F2: 3,4 BLK 2 E1: 3,4,2,6,7 # reduction candidate for 3,4 E1: 3,4 => CTR * 9238417655..763.2...69.....245.96.873.7.842..1.8.7.4....2..96..631458972.59627... E1: 2,6,7 # 5 pairs E2: 3,4,6,7 # reduction candidate for 3,4 E2: 3,4 => CTR * 9238617455..7439264769.....245.96.873.7.842..1.8.7.4..7.4..96..63.4.8592.596.7..4 E2: 6,7 # 6 pairs E3: 3,4,2,5,7 # reduction candidate for 3,4 E3: 3,4 => CTR * ...821.655..76..2..269.5.......96.873...84...1...724.....2.96..63.4.8..22596.7... E3: 2,5,7 # 5 pairs F3: 3,4,2,5 # reduction candidate for 3,4 F3: 3,4 => CTR * ...821.655...6..2...695........46.873...8....1.....4.....5.967.637418..2.596.7... F3: 2,5 # 6 pairs * PAIR F2: 3,4 ROW 2 C2: 3,4,1,7,8 # reduction candidate for 3,4 C2: 3,4 => CTR * 9238417655.4763.2...69.....245.96.873.7.842..1.8.7.4....2..96..631458972.59627... C2: 1,7,8 # 6 pairs I2: 3,4,1,6,8,9 # reduction candidate for 3,4 I2: 3,4 => CTR * ..38.1965598763124.169.5.7.9....6.87367.84.1.1...7.4.......96..631458792.596.7... I2: 1,6,8,9 # 5 pairs * PAIR C8: 1,7 BLK 7 B7: 1,7,2,4,8 # reduction candidate for 1,7 B7: 1,7 # 6 pairs C7: 1,7,2,4,8 # reduction candidate for 1,7 C7: 1,7 => CTR * ...8.1..55..3.4.2...69..........6.873...8....1.8.9.4.......96..63.4.8..2.596.7... C7: 2,4,8 # 5 pairs * PAIR C8: 1,7 COL C C2: 1,7,3,4,8 # reduction candidate for 1,7 C2: 1,7 => SOLVED * 243871965591364728786952143925146387364785219178293456812539674637418592459627831 C2: 3,4,8 # 5 pairs * PAIR E8: 1,5 BLK 8 D7: 1,5,2,3 # reduction candidate for 1,5 D7: 1,5 => SOLVED * 243871965591364728786952143925146387364785219178293456812539674637418592459627831 D7: 2,3 => CTR * ..38.1..55......2...69.5........6.873...8....1.....4.....2.96..63.4.8..22596.7... E7: 1,5,2,3 # reduction candidate for 1,5 E7: 1,5 => CTR * ..38.1..55......2...69.5........6.873...8....1.....4.....2.96.363.4.8..2259637... E7: 2,3 # 6 pairs * PAIR E8: 1,5 COL E E4: 1,5,2,3,4,9 # reduction candidate for 1,5 E4: 1,5 => CTR * ..38.1..55..7.3.2...69..........6.873...84...1...9.4.......96..63.4.8..2.596.7... E4: 2,3,4,9 # 5 pairs * PAIR H7: 5,7 BLK 9 G8: 5,7,9 # reduction candidate for 5,7 G8: 5,7 # 6 pairs H8: 5,7,9 # reduction candidate for 5,7 H8: 5,7 => CTR * ..38.17.55..7.3.2...69..........6.873...84...1...9.4.......96..63.4.89.2.596.7... H8: 9 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06899619-base-pr-000.dot * REASONING * PRF # E1: 3,7 => SOL * DIS # E2: 3,7 => CTR => E2: 4,6 * DIS # E3: 3,7 => CTR => E3: 2,4,5 * DIS # C2: 3,7 => CTR => C2: 1,4,8 * PRF # G2: 3,7 => SOL * DIS # D6: 3,7 => CTR => D6: 2,5 * DIS # E1: 3,4 => CTR => E1: 2,6,7 * DIS # E2: 3,4 => CTR => E2: 6,7 * DIS # E3: 3,4 => CTR => E3: 2,5,7 * DIS # F3: 3,4 => CTR => F3: 2,5 * DIS # C2: 3,4 => CTR => C2: 1,7,8 * DIS # I2: 3,4 => CTR => I2: 1,6,8,9 * DIS # C7: 1,7 => CTR => C7: 2,4,8 * PRF # C2: 1,7 => SOL * PRF # D7: 1,5 => SOL * DIS # D7: 2,3 => CTR => D7: 1,5 * DIS # E7: 1,5 => CTR => E7: 2,3 * DIS # E4: 1,5 => CTR => E4: 2,3,4,9 * DIS # H8: 5,7 => CTR => H8: 9 * CNT 19 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D2,E8,F2,H7) * ...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7... * PAIR D2: 3,7 BLK 2 E1: 3,7,2,4,6 # reduction candidate for 3,7 E1: 3,7 => SOLVED * 243871965591364728786952143925146387364785219178293456812539674637418592459627831 * DURATION: 0:00:02.586193 START: 06:33:14.620912 END: 06:33:17.207105 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06899619-base-pr-001.dot * REASONING * PRF # E1: 3,7 => SOL * STA E1: 3,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6899619 umulig * PAIR REDUCTION .. * ROUND 1: ...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7... D2: 3,7 E1: 2,3,4,6,7 # reduction candidate for 3,7 E1: 3,7 => SOLVED * 243871965591364728786952143925146387364785219178293456812539674637418592459627831 * SOLVED! |:step:| 00 -------------------------------------------------- C2 = 1,7 => SOL |:step:| 01 --------------------------------------------------
Solution
position: 243871965591364728786952143925146387364785219178293456812539674637418592459627831 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 # E1: 3,7 => SOL * INC # E1: 2,4,6 => UNS * DIS # E2: 3,7 => CTR => E2: 4,6 * INC # E2: 4,6 => UNS * DIS # E3: 3,7 => CTR => E3: 2,4,5 * INC # E3: 2,4,5 => UNS * DIS # C2: 3,7 => CTR => C2: 1,4,8 * INC # C2: 1,4,8 => UNS * PRF # G2: 3,7 => SOL * INC # G2: 1,8,9 => UNS * DIS # D6: 3,7 => CTR => D6: 2,5 * INC # D6: 2,5 => UNS * DIS # E1: 3,4 => CTR => E1: 2,6,7 * INC # E1: 2,6,7 => UNS * DIS # E2: 3,4 => CTR => E2: 6,7 * INC # E2: 6,7 => UNS * DIS # E3: 3,4 => CTR => E3: 2,5,7 * INC # E3: 2,5,7 => UNS * DIS # F3: 3,4 => CTR => F3: 2,5 * INC # F3: 2,5 => UNS * DIS # C2: 3,4 => CTR => C2: 1,7,8 * INC # C2: 1,7,8 => UNS * DIS # I2: 3,4 => CTR => I2: 1,6,8,9 * INC # I2: 1,6,8,9 => UNS * INC # B7: 1,7 => UNS * DIS # C7: 1,7 => CTR => C7: 2,4,8 * INC # C7: 2,4,8 => UNS * PRF # C2: 1,7 => SOL * INC # C2: 3,4,8 => UNS * PRF # D7: 1,5 => SOL * DIS # D7: 2,3 => CTR => D7: 1,5 * DIS # E7: 1,5 => CTR => E7: 2,3 * INC # E7: 2,3 => UNS * DIS # E4: 1,5 => CTR => E4: 2,3,4,9 * INC # E4: 2,3,4,9 => UNS * INC # G8: 5,7 => UNS * DIS # H8: 5,7 => CTR => H8: 9 * INC # H8: 9 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # E1: 3,7 => SOL * STA E1: 3,7 * CNT 1 HDP CHAINS / 1 HYP OPENED