Analysis of zz-menneske-no-06913681-base.sdk
Contents
Original Sudoku
level: medium
position: .95.........16.....3.8....1.41.....5..29..4.....3...7.2..5...4.....86.........89. initial
Autosolve
position: 195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H8: 3,5 => CTR => H8: 1,2 * DIS # H8: 2,5 => CTR => H8: 1,3 * PRF # F4: 8 => SOL * DIS # E3: 2,7 => CTR => E3: 4,5,9 * PRF # B7: 1,7 => SOL * DIS # B9: 1,7 => CTR => B9: 5,6 * DIS # G8: 1,7 => CTR => G8: 2,3,5 * CNT 7 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H8: 3,5 => CTR => H8: 1,2 * DIS H8: 1,2 # F2: 4,7,9 => CTR => F2: 3,5 * DIS H8: 1,2 + F2: 3,5 # E3: 2,5 => CTR => E3: 4,7,9 * DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 # F3: 2,5 => CTR => F3: 4,7,9 * DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 # F4: 2,7 => CTR => F4: 8 * PRF H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8 => SOL * STA H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8 * CNT 6 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .95.........16.....3.8....1.41.....5..29..4.....3...7.2..5...4.....86.........89. | initial |
| 195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89. | autosolve |
| 195732684824165739637849251341678925782951463569324178218597346973486512456213897 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) H2: 3,5 H3: 2,5 E4: 2,7 B8: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,G6: 1.. / H5 = 1 => 0 pairs (X) / G6 = 1 => 0 pairs (_) H5,H8: 1.. / H5 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) A4,A5: 3.. / A4 = 3 => 0 pairs (*) / A5 = 3 => 0 pairs (X) I1,I2: 4.. / I1 = 4 => 0 pairs (*) / I2 = 4 => 0 pairs (X) E6,F6: 4.. / E6 = 4 => 4 pairs (_) / F6 = 4 => 4 pairs (_) A9,B9: 5.. / A9 = 5 => 4 pairs (_) / B9 = 5 => 5 pairs (_) G8,H8: 5.. / G8 = 5 => 4 pairs (_) / H8 = 5 => 0 pairs (X) A3,C3: 6.. / A3 = 6 => 5 pairs (_) / C3 = 6 => 6 pairs (_) H1,H5: 6.. / H1 = 6 => 0 pairs (X) / H5 = 6 => 0 pairs (_) A2,C2: 8.. / A2 = 8 => 5 pairs (_) / C2 = 8 => 7 pairs (_) H1,I1: 8.. / H1 = 8 => 0 pairs (*) / I1 = 8 => 0 pairs (X) B7,C7: 8.. / B7 = 8 => 5 pairs (_) / C7 = 8 => 6 pairs (_) A8,C8: 9.. / A8 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) E7,F7: 9.. / E7 = 9 => 4 pairs (_) / F7 = 9 => 4 pairs (_) A4,G4: 9.. / A4 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) C6,C8: 9.. / C6 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) E3,E7: 9.. / E3 = 9 => 4 pairs (_) / E7 = 9 => 4 pairs (_) I2,I6: 9.. / I2 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) * DURATION: 0:00:25.044800 START: 07:11:21.238432 END: 07:11:46.283232 2017-05-01 * CP COUNT: (18) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E4,H2,H3) * 195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89. * PAIR H2: 3,5 BLK 3 G2: 3,5,7,9 # reduction candidate for 3,5 G2: 3,5 # 8 pairs G2: 7,9 # 5 pairs * PAIR H2: 3,5 ROW 2 F2: 3,5,4,7,9 # reduction candidate for 3,5 F2: 4,7,9 # 7 pairs F2: 3,5 # 6 pairs * PAIR H2: 3,5 COL H H8: 3,5,1,2 # reduction candidate for 3,5 H8: 3,5 => CTR * 195....68.2.16...4.3.8...219416..385372958416...3..2792..5..64..19.86.........89. H8: 1,2 # 5 pairs * PAIR H3: 2,5 BLK 3 G3: 2,5,7,9 # reduction candidate for 2,5 G3: 2,5 # 12 pairs G3: 7,9 # 5 pairs * PAIR H3: 2,5 ROW 3 E3: 2,5,4,7,9 # reduction candidate for 2,5 E3: 2,5 # 6 pairs F3: 2,5,4,7,9 # reduction candidate for 2,5 F3: 2,5 # 6 pairs * PAIR H3: 2,5 COL H H8: 2,5,1,3 # reduction candidate for 2,5 H8: 2,5 => CTR * 195....68.2.16..34.3.8....19416..385372958416...3..2792..5..64..19.86..3......892 H8: 1,3 # 6 pairs * PAIR E4: 2,7 BLK 5 F4: 2,7,8 # reduction candidate for 2,7 F4: 8 => SOLVED * 195732684824165739637849251341678925782951463569324178218597346973486512456213897 F4: 2,7 # 8 pairs * PAIR E4: 2,7 COL E E1: 2,7,3,4 # reduction candidate for 2,7 E1: 2,7 # 6 pairs E3: 2,7,4,5,9 # reduction candidate for 2,7 E3: 2,7 => CTR * 195.......2.16...4.3.8....19416....537295.416...3..2792..59..4..19.86.........89. E3: 4,5,9 # 4 pairs E9: 2,7,1,3,4 # reduction candidate for 2,7 E9: 2,7 # 9 pairs * PAIR B8: 1,7 BLK 7 B7: 1,7,6,8 # reduction candidate for 1,7 B7: 1,7 => SOLVED * 195732684824165739637849251341678925782951463569324178218597346973486512456213897 B7: 6,8 # 5 pairs B9: 1,7,5,6 # reduction candidate for 1,7 B9: 1,7 => CTR * 195...68482.165739.378..251341678925782951463.593..178268519347973486512514...89. B9: 5,6 # 5 pairs * PAIR B8: 1,7 ROW 8 G8: 1,7,2,3,5 # reduction candidate for 1,7 G8: 1,7 => CTR * 195...768.2.16..34.3.8...219416..385372958416...3..2792..5..647.19.86.53......892 G8: 2,3,5 # 4 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06913681-base-pr-000.dot * REASONING * DIS # H8: 3,5 => CTR => H8: 1,2 * DIS # H8: 2,5 => CTR => H8: 1,3 * PRF # F4: 8 => SOL * DIS # E3: 2,7 => CTR => E3: 4,5,9 * PRF # B7: 1,7 => SOL * DIS # B9: 1,7 => CTR => B9: 5,6 * DIS # G8: 1,7 => CTR => G8: 2,3,5 * CNT 7 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E4,H2,H3) * 195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89. * PAIR H2: 3,5 BLK 3 G2: 3,5,7,9 # reduction candidate for 3,5 G2: 3,5 # 8 pairs G2: 7,9 # 5 pairs * PAIR H2: 3,5 ROW 2 F2: 3,5,4,7,9 # reduction candidate for 3,5 F2: 4,7,9 # 7 pairs F2: 3,5 # 6 pairs * PAIR H2: 3,5 COL H H8: 3,5,1,2 # reduction candidate for 3,5 H8: 3,5 => CTR * 195....68.2.16...4.3.8...219416..385372958416...3..2792..5..64..19.86.........89. * PAIR RESTART * PAIR H2: 3,5 ROW 2 F2: 3,5,4,7,9 # reduction candidate for 3,5 F2: 4,7,9 => CTR * 195.......2.16.35..3.8..921941678235..29..4.....3..1792..5...4..79.86513......892 * PAIR RESTART * PAIR H3: 2,5 ROW 3 E3: 2,5,4,7,9 # reduction candidate for 2,5 E3: 2,5 => CTR * 195.....2.2.16.9.4.3.82975194167...53729..41....3...792..59..4..19.86523......89. F3: 2,5,4,7,9 # reduction candidate for 2,5 F3: 2,5 => CTR * 195.....2.2.16.9.4.3.8927519416....537295.41....3...792..5.9.4..19.86523......89. * PAIR RESTART * PAIR E4: 2,7 BLK 5 F4: 2,7,8 # reduction candidate for 2,7 F4: 2,7 => CTR * 195....68.2.165.3..3.8..251.416...85..29..4.....3...722..5...4.....8652.......89. F4: 8 => SOLVED * 195732684824165739637849251341678925782951463569324178218597346973486512456213897 * DURATION: 0:00:10.912017 START: 07:12:04.661430 END: 07:12:15.573447 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06913681-base-pr-001.dot * REASONING * DIS # H8: 3,5 => CTR => H8: 1,2 * DIS H8: 1,2 # F2: 4,7,9 => CTR => F2: 3,5 * DIS H8: 1,2 + F2: 3,5 # E3: 2,5 => CTR => E3: 4,7,9 * DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 # F3: 2,5 => CTR => F3: 4,7,9 * DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 # F4: 2,7 => CTR => F4: 8 * PRF H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8 => SOL * STA H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8 * CNT 6 HDP CHAINS / 10 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6913681 umulig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89. H2: 3,5 G2: 3,5,7,9 # reduction candidate for 3,5 F2: 3,4,5,7,9 # reduction candidate for 3,5 H8: 1,2,3,5 # reduction candidate for 3,5 H8: 3,5 => CTR * 195....68.2.16...4.3.8...219416..385372958416...3..2792..5..64..19.86.........89. H3: 2,5 E3: 2,4,5,7,9 # reduction candidate for 2,5 F3: 2,4,5,7,9 # reduction candidate for 2,5 E4: 2,7 F4: 2,7,8 # reduction candidate for 2,7 F4: 8 => SOLVED * 195732684824165739637849251341678925782951463569324178218597346973486512456213897 * SOLVED!
Solution
position: 195732684824165739637849251341678925782951463569324178218597346973486512456213897 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 # G2: 3,5 => UNS * INC # G2: 7,9 => UNS * INC # F2: 3,5 => UNS * INC # F2: 4,7,9 => UNS * DIS # H8: 3,5 => CTR => H8: 1,2 * INC # H8: 1,2 => UNS * INC # G3: 2,5 => UNS * INC # G3: 7,9 => UNS * INC # E3: 2,5 => UNS * INC # F3: 2,5 => UNS * DIS # H8: 2,5 => CTR => H8: 1,3 * INC # H8: 1,3 => UNS * INC # F4: 2,7 => UNS * PRF # F4: 8 => SOL * INC # E1: 2,7 => UNS * DIS # E3: 2,7 => CTR => E3: 4,5,9 * INC # E3: 4,5,9 => UNS * INC # E9: 2,7 => UNS * PRF # B7: 1,7 => SOL * INC # B7: 6,8 => UNS * DIS # B9: 1,7 => CTR => B9: 5,6 * INC # B9: 5,6 => UNS * DIS # G8: 1,7 => CTR => G8: 2,3,5 * INC # G8: 2,3,5 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 3,5 => UNS * INC # G2: 7,9 => UNS * INC # F2: 3,5 => UNS * INC # F2: 4,7,9 => UNS * DIS # H8: 3,5 => CTR => H8: 1,2 * INC H8: 1,2 # F2: 3,5 => UNS * DIS H8: 1,2 # F2: 4,7,9 => CTR => F2: 3,5 * DIS H8: 1,2 + F2: 3,5 # E3: 2,5 => CTR => E3: 4,7,9 * DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 # F3: 2,5 => CTR => F3: 4,7,9 * DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 # F4: 2,7 => CTR => F4: 8 * PRF H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8 => SOL * STA H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8 * CNT 11 HDP CHAINS / 10 HYP OPENED