Analysis of zz-menneske-no-06913279-base.sdk
Contents
Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6913279
level: medium
position: 89.4.....4....6.....3....5..34.....8...3..7.66....89....1..5.8....2....3....6..9. initial
Autosolve
position: 89.4.....4....6.....3....5..346....8...3..7.66....893...1..5.8....2....3....6..9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G4: 1,2 => CTR => G4: 5 * DIS # H5: 1,2 => CTR => H5: 4 * DIS # H1: 1,2 => CTR => H1: 6,7 * DIS # E8: 7,9 => CTR => E8: 1,4,8 * DIS # A7: 7,9 => CTR => A7: 2,3 * CNT 5 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G4: 1,2 => CTR => G4: 5 * DIS G4: 5 # H5: 1,2 => CTR => H5: 4 * DIS G4: 5 + H5: 4 # H1: 1,2 => CTR => H1: 6,7 * DIS G4: 5 + H5: 4 + H1: 6,7 # H2: 7 => CTR => H2: 1,2 * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E8: 7,9 => CTR => E8: 1,8 * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 # F8: 7,9 => CTR => F8: 1,4 * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 # E7: 3 => CTR => E7: 7,9 * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 # D3: 7,9 => CTR => D3: 8 * PRF G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 # B2: 2,7 => SOL * STA G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 + B2: 2,7 * CNT 9 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 89.4.....4....6.....3....5..34.....8...3..7.66....89....1..5.8....2....3....6..9. | initial |
| 89.4.....4....6.....3....5..346....8...3..7.66....893...1..5.8....2....3....6..9. | autosolve |
| 892451367475936821163827459234679518589312746617548932321795684956284173748163295 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (2) H4: 1,2 D7: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,G2: 3.. / G1 = 3 => 2 pairs (_) / G2 = 3 => 16 pairs (_) A7,A9: 3.. / A7 = 3 => 2 pairs (_) / A9 = 3 => 16 pairs (_) E7,F9: 3.. / E7 = 3 => 16 pairs (_) / F9 = 3 => 2 pairs (_) E2,G2: 3.. / E2 = 3 => 2 pairs (_) / G2 = 3 => 16 pairs (_) A7,E7: 3.. / A7 = 3 => 2 pairs (_) / E7 = 3 => 16 pairs (_) A9,F9: 3.. / A9 = 3 => 16 pairs (_) / F9 = 3 => 2 pairs (_) F1,F9: 3.. / F1 = 3 => 16 pairs (_) / F9 = 3 => 2 pairs (_) G3,I3: 4.. / G3 = 4 => 4 pairs (_) / I3 = 4 => 5 pairs (_) H5,I6: 4.. / H5 = 4 => 2 pairs (_) / I6 = 4 => 0 pairs (X) E6,I6: 4.. / E6 = 4 => 2 pairs (_) / I6 = 4 => 0 pairs (X) H5,H8: 4.. / H5 = 4 => 2 pairs (_) / H8 = 4 => 0 pairs (X) G4,I6: 5.. / G4 = 5 => 2 pairs (_) / I6 = 5 => 0 pairs (X) C1,E1: 5.. / C1 = 5 => 8 pairs (_) / E1 = 5 => 3 pairs (_) D2,D6: 5.. / D2 = 5 => 6 pairs (_) / D6 = 5 => 3 pairs (_) I6,I9: 5.. / I6 = 5 => 0 pairs (X) / I9 = 5 => 2 pairs (_) C1,B3: 6.. / C1 = 6 => 0 pairs (X) / B3 = 6 => 3 pairs (_) B3,G3: 6.. / B3 = 6 => 3 pairs (_) / G3 = 6 => 0 pairs (X) B7,G7: 6.. / B7 = 6 => 0 pairs (X) / G7 = 6 => 3 pairs (_) C1,C8: 6.. / C1 = 6 => 0 pairs (X) / C8 = 6 => 3 pairs (_) H1,H8: 6.. / H1 = 6 => 3 pairs (_) / H8 = 6 => 0 pairs (X) G2,G3: 8.. / G2 = 8 => 2 pairs (_) / G3 = 8 => 15 pairs (_) B5,C5: 8.. / B5 = 8 => 2 pairs (_) / C5 = 8 => 0 pairs (X) E8,D9: 8.. / E8 = 8 => 3 pairs (_) / D9 = 8 => 0 pairs (X) I2,I3: 9.. / I2 = 9 => 2 pairs (_) / I3 = 9 => 14 pairs (_) C5,C8: 9.. / C5 = 9 => 2 pairs (_) / C8 = 9 => 0 pairs (X) * DURATION: 0:00:30.482086 START: 07:08:19.874099 END: 07:08:50.356185 2017-05-01 * CP COUNT: (25) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D7,H4) * 89.4.....4....6.....3....5..346....8...3..7.66....893...1..5.8....2....3....6..9. * PAIR H4: 1,2 BLK 6 G4: 1,2,5 # reduction candidate for 1,2 G4: 1,2 => CTR * 8954..36.4.75368191638...5.7346591285893..7466127489353.197568.9.6284573..8163.9. G4: 5 # 2 pairs H5: 1,2,4 # reduction candidate for 1,2 H5: 1,2 => CTR * 89745.36.4...3687..63...45..346..5.8..93..7.66....8934321945687956287143748163295 H5: 4 # 2 pairs I6: 1,2,4,5 # reduction candidate for 1,2 I6: 1,2 # 3 pairs * PAIR H4: 1,2 ROW 4 A4: 1,2,5,7,9 # reduction candidate for 1,2 A4: 1,2 # 6 pairs E4: 1,2,5,7,9 # reduction candidate for 1,2 E4: 1,2 # 5 pairs F4: 1,2,7,9 # reduction candidate for 1,2 F4: 1,2 # 5 pairs * PAIR H4: 1,2 COL H H1: 1,2,6,7 # reduction candidate for 1,2 H1: 1,2 => CTR * 8964573..4...36879..3...654.3467.5.8...3..7466..54893.361.9548....2...63....6..95 H1: 6,7 # 3 pairs H2: 1,2,7 # reduction candidate for 1,2 H2: 1,2 # 5 pairs * PAIR D7: 7,9 BLK 8 E7: 7,9,3,4 # reduction candidate for 7,9 E7: 7,9 # 6 pairs E8: 7,9,1,4,8 # reduction candidate for 7,9 E8: 7,9 => CTR * 89645....4....6.....3...654.346....8...3..7466..54893..61.3548....2....3...86..9. E8: 1,4,8 # 2 pairs F8: 7,9,1,4 # reduction candidate for 7,9 F8: 7,9 # 5 pairs * PAIR D7: 7,9 ROW 7 A7: 7,9,2,3 # reduction candidate for 7,9 A7: 7,9 => CTR * 89.4.3.6741.8.6329.63...854.346....8.893..7466..548931.41.35682..628...3328.6..95 A7: 2,3 # 3 pairs * PAIR D7: 7,9 COL D D2: 7,9,1,5,8 # reduction candidate for 7,9 D2: 7,9 # 8 pairs D3: 7,9,1,8 # reduction candidate for 7,9 D3: 7,9 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06913279-base-pr-000.dot * REASONING * DIS # G4: 1,2 => CTR => G4: 5 * DIS # H5: 1,2 => CTR => H5: 4 * DIS # H1: 1,2 => CTR => H1: 6,7 * DIS # E8: 7,9 => CTR => E8: 1,4,8 * DIS # A7: 7,9 => CTR => A7: 2,3 * CNT 5 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D7,H4) * 89.4.....4....6.....3....5..346....8...3..7.66....893...1..5.8....2....3....6..9. * PAIR H4: 1,2 BLK 6 G4: 1,2,5 # reduction candidate for 1,2 G4: 1,2 => CTR * 8954..36.4.75368191638...5.7346591285893..7466127489353.197568.9.6284573..8163.9. H5: 1,2,4 # reduction candidate for 1,2 H5: 1,2 => CTR * 89745.36.4...3687..63...45..346..5.8..93..7.66....8934321945687956287143748163295 * RESTART * PAIR H4: 1,2 ROW 4 A4: 1,2,7,9 # reduction candidate for 1,2 A4: 1,2 # 8 pairs E4: 1,2,7,9 # reduction candidate for 1,2 E4: 1,2 # 6 pairs F4: 1,2,7,9 # reduction candidate for 1,2 F4: 1,2 # 6 pairs * PAIR H4: 1,2 COL H H1: 1,2,6,7 # reduction candidate for 1,2 H1: 1,2 => CTR * 8964573..4...36879..3...654.3467.5.8...3..7466..54893..61..5487...2..163....6.295 H2: 1,2,7 # reduction candidate for 1,2 H2: 1,2 # 6 pairs * RESTART * PAIR H4: 1,2 COL H H2: 1,2,7 # reduction candidate for 1,2 H2: 7 => CTR * 89.4.31624..8.6379.637..8547346..5285.93..7466...489312419356879562874133.8164295 * PAIR RESTART * PAIR H4: 1,2 ROW 4 A4: 1,2,7,9 # reduction candidate for 1,2 A4: 1,2 # 11 pairs E4: 1,2,7,9 # reduction candidate for 1,2 E4: 1,2 # 9 pairs F4: 1,2,7,9 # reduction candidate for 1,2 F4: 1,2 # 9 pairs * PAIR D7: 7,9 BLK 8 E7: 7,9,3 # reduction candidate for 7,9 E7: 7,9 # 19 pairs E8: 7,9,1,8 # reduction candidate for 7,9 E8: 7,9 => CTR * 8964532714....6.....3....5..346..5.8...3..7466...4893...1..5.8....2....3...86..95 F8: 7,9,1,4 # reduction candidate for 7,9 F8: 7,9 => CTR * 89.4.32674....6319163...854.346..528..93..7466..14893...1.3568...62..4733...64195 * RESTART * PAIR D7: 7,9 BLK 8 E7: 7,9,3 # reduction candidate for 7,9 E7: 3 => CTR * 89.4.32674....63191637..854.34671528.1.3..7466...4893...193568...62...733...6..95 * PAIR D7: 7,9 COL D D2: 7,9,8 # reduction candidate for 7,9 D2: 7,9 # 19 pairs D3: 7,9,8 # reduction candidate for 7,9 D3: 7,9 => CTR * 89.4...674..8.6.19163.2.8542346..5.85893..7466..54893.341..5682956284173..8163495 * RESTART * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,A9,B7,C1,C6,D2,D7,E3,E4,E5,E7,F4,F5,G3,G9,H2,H4,I6,I7) * 89.45.36.4.5.368...638...5..346..5.85893..7466..54893.3.1..568.956284173..8163.95 * PAIR C1: 2,7 BLK 1 B2: 2,7,1 # reduction candidate for 2,7 B2: 2,7 => SOLVED * 892451367475936821163827459234679518589312746617548932321795684956284173748163295 * DURATION: 0:00:19.035519 START: 07:09:01.943432 END: 07:09:20.978951 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06913279-base-pr-001.dot * REASONING * DIS # G4: 1,2 => CTR => G4: 5 * DIS G4: 5 # H5: 1,2 => CTR => H5: 4 * DIS G4: 5 + H5: 4 # H1: 1,2 => CTR => H1: 6,7 * DIS G4: 5 + H5: 4 + H1: 6,7 # H2: 7 => CTR => H2: 1,2 * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E8: 7,9 => CTR => E8: 1,8 * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 # F8: 7,9 => CTR => F8: 1,4 * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 # E7: 3 => CTR => E7: 7,9 * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 # D3: 7,9 => CTR => D3: 8 * PRF G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 # B2: 2,7 => SOL * STA G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 + B2: 2,7 * CNT 9 HDP CHAINS / 20 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6913279 umulig
Solution
position: 892451367475936821163827459234679518589312746617548932321795684956284173748163295 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 # G4: 1,2 => CTR => G4: 5 * INC # G4: 5 => UNS * DIS # H5: 1,2 => CTR => H5: 4 * INC # H5: 4 => UNS * INC # I6: 1,2 => UNS * INC # A4: 1,2 => UNS * INC # E4: 1,2 => UNS * INC # F4: 1,2 => UNS * DIS # H1: 1,2 => CTR => H1: 6,7 * INC # H1: 6,7 => UNS * INC # H2: 1,2 => UNS * INC # E7: 7,9 => UNS * DIS # E8: 7,9 => CTR => E8: 1,4,8 * INC # E8: 1,4,8 => UNS * INC # F8: 7,9 => UNS * DIS # A7: 7,9 => CTR => A7: 2,3 * INC # A7: 2,3 => UNS * INC # D2: 7,9 => UNS * INC # D3: 7,9 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G4: 1,2 => CTR => G4: 5 * DIS G4: 5 # H5: 1,2 => CTR => H5: 4 * INC G4: 5 + H5: 4 # A4: 1,2 => UNS * INC G4: 5 + H5: 4 # E4: 1,2 => UNS * INC G4: 5 + H5: 4 # F4: 1,2 => UNS * DIS G4: 5 + H5: 4 # H1: 1,2 => CTR => H1: 6,7 * INC G4: 5 + H5: 4 + H1: 6,7 # H2: 1,2 => UNS * INC G4: 5 + H5: 4 + H1: 6,7 # H2: 1,2 => UNS * DIS G4: 5 + H5: 4 + H1: 6,7 # H2: 7 => CTR => H2: 1,2 * INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # A4: 1,2 => UNS * INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E4: 1,2 => UNS * INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # F4: 1,2 => UNS * INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E7: 7,9 => UNS * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E8: 7,9 => CTR => E8: 1,8 * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 # F8: 7,9 => CTR => F8: 1,4 * INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 # E7: 7,9 => UNS * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 # E7: 3 => CTR => E7: 7,9 * INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 # D2: 7,9 => UNS * DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 # D3: 7,9 => CTR => D3: 8 * PRF G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 # B2: 2,7 => SOL * STA G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 + B2: 2,7 * CNT 20 HDP CHAINS / 20 HYP OPENED