Analysis of zz-menneske-no-06910690-base.sdk
Contents
Original Sudoku
level: medium
position: .7......8.8..6..9....9.45....3...4.54..2....38.....9....9..6....6..5..1.7....1... initial
Autosolve
position: 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 2,3 => CTR => A2: 1,5 * PRF # A3: 2,3 => SOL * CNT 2 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 2,3 => CTR => A2: 1,5 * PRF A2: 1,5 # A3: 2,3 => SOL * STA A2: 1,5 + A3: 2,3 * CNT 2 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7......8.8..6..9....9.45....3...4.54..2....38.....9....9..6....6..5..1.7....1... | initial |
| 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1... | autosolve |
| 976532148584167392231984567613879425497215683825643971159726834362458719748391256 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (2) A8: 2,3 C8: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,I6: 1.. / G5 = 1 => 6 pairs (_) / I6 = 1 => 4 pairs (_) A7,B7: 1.. / A7 = 1 => 4 pairs (_) / B7 = 1 => 9 pairs (_) C1,C2: 4.. / C1 = 4 => 8 pairs (_) / C2 = 4 => 3 pairs (_) H1,I2: 4.. / H1 = 4 => 3 pairs (_) / I2 = 4 => 8 pairs (_) D6,E6: 4.. / D6 = 4 => 0 pairs (X) / E6 = 4 => 2 pairs (_) B7,B9: 4.. / B7 = 4 => 6 pairs (_) / B9 = 4 => 3 pairs (_) C1,H1: 4.. / C1 = 4 => 8 pairs (_) / H1 = 4 => 3 pairs (_) C2,I2: 4.. / C2 = 4 => 3 pairs (_) / I2 = 4 => 8 pairs (_) D8,I8: 4.. / D8 = 4 => 3 pairs (_) / I8 = 4 => 6 pairs (_) H7,H9: 5.. / H7 = 5 => 4 pairs (_) / H9 = 5 => 9 pairs (_) A2,A7: 5.. / A2 = 5 => 3 pairs (_) / A7 = 5 => 0 pairs (X) D4,D6: 6.. / D4 = 6 => 7 pairs (_) / D6 = 6 => 7 pairs (_) A3,A4: 6.. / A3 = 6 => 7 pairs (_) / A4 = 6 => 0 pairs (*) D2,F2: 7.. / D2 = 7 => 16 pairs (_) / F2 = 7 => 4 pairs (_) H3,I3: 7.. / H3 = 7 => 9 pairs (_) / I3 = 7 => 3 pairs (_) C5,C6: 7.. / C5 = 7 => 6 pairs (_) / C6 = 7 => 4 pairs (_) C8,C9: 8.. / C8 = 8 => 2 pairs (_) / C9 = 8 => 10 pairs (_) B4,B5: 9.. / B4 = 9 => 5 pairs (_) / B5 = 9 => 4 pairs (_) F8,E9: 9.. / F8 = 9 => 4 pairs (_) / E9 = 9 => 10 pairs (_) I8,I9: 9.. / I8 = 9 => 10 pairs (_) / I9 = 9 => 4 pairs (_) F8,I8: 9.. / F8 = 9 => 4 pairs (_) / I8 = 9 => 10 pairs (_) E9,I9: 9.. / E9 = 9 => 10 pairs (_) / I9 = 9 => 4 pairs (_) * DURATION: 0:00:26.095615 START: 06:48:44.239839 END: 06:49:10.335454 2017-05-01 * CP COUNT: (22) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C8) * 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1... * PAIR A8: 2,3 BLK 7 A7: 2,3,1,5 # reduction candidate for 2,3 A7: 2,3 # 11 pairs B7: 2,3,1,4,5 # reduction candidate for 2,3 B7: 2,3 # 7 pairs B9: 2,3,4,5 # reduction candidate for 2,3 B9: 2,3 # 6 pairs * PAIR A8: 2,3 ROW 8 F8: 2,3,7,8,9 # reduction candidate for 2,3 F8: 2,3 # 17 pairs G8: 2,3,7,8 # reduction candidate for 2,3 G8: 2,3 # 6 pairs * PAIR A8: 2,3 COL A A2: 2,3,1,5 # reduction candidate for 2,3 A2: 2,3 => CTR * 9741..6.828..6.1946319845.21.3.7.4.54.621.7838.7.4.9.1519..6.4736.457.1974..91.56 A2: 1,5 # 4 pairs A3: 2,3,1,6 # reduction candidate for 2,3 A3: 2,3 => SOLVED * 976532148584167392231984567613879425497215683825643971159726834362458719748391256 A3: 1,6 # 3 pairs * PAIR C8: 2,8 BLK 7 C9: 2,8,5 # reduction candidate for 2,8 C9: 2,8 # 7 pairs C9: 5 # 3 pairs * PAIR C8: 2,8 ROW 8 F8: 2,8,3,7,9 # reduction candidate for 2,8 F8: 2,8 # 13 pairs G8: 2,8,3,7 # reduction candidate for 2,8 G8: 2,8 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06910690-base-pr-000.dot * REASONING * DIS # A2: 2,3 => CTR => A2: 1,5 * PRF # A3: 2,3 => SOL * CNT 2 HDP CHAINS / 13 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C8) * 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1... * PAIR A8: 2,3 BLK 7 A7: 2,3,1,5 # reduction candidate for 2,3 A7: 2,3 # 11 pairs B7: 2,3,1,4,5 # reduction candidate for 2,3 B7: 2,3 # 7 pairs B9: 2,3,4,5 # reduction candidate for 2,3 B9: 2,3 # 6 pairs * PAIR A8: 2,3 ROW 8 F8: 2,3,7,8,9 # reduction candidate for 2,3 F8: 2,3 # 17 pairs G8: 2,3,7,8 # reduction candidate for 2,3 G8: 2,3 # 6 pairs * PAIR A8: 2,3 COL A A2: 2,3,1,5 # reduction candidate for 2,3 A2: 2,3 => CTR * 9741..6.828..6.1946319845.21.3.7.4.54.621.7838.7.4.9.1519..6.4736.457.1974..91.56 A3: 2,3,1,6 # reduction candidate for 2,3 A3: 2,3 => SOLVED * 976532148584167392231984567613879425497215683825643971159726834362458719748391256 * DURATION: 0:00:07.641991 START: 06:49:20.961498 END: 06:49:28.603489 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06910690-base-pr-001.dot * REASONING * DIS # A2: 2,3 => CTR => A2: 1,5 * PRF A2: 1,5 # A3: 2,3 => SOL * STA A2: 1,5 + A3: 2,3 * CNT 2 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6910690 umulig * PAIR REDUCTION .. * ROUND 1: 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1... A8: 2,3 A7: 1,2,3,5 # reduction candidate for 2,3 B7: 1,2,3,4,5 # reduction candidate for 2,3 B9: 2,3,4,5 # reduction candidate for 2,3 F8: 2,3,7,8,9 # reduction candidate for 2,3 G8: 2,3,7,8 # reduction candidate for 2,3 A2: 1,2,3,5 # reduction candidate for 2,3 A2: 2,3 => CTR * 9741..6.828..6.1946319845.21.3.7.4.54.621.7838.7.4.9.1519..6.4736.457.1974..91.56 A3: 1,2,3,6 # reduction candidate for 2,3 A3: 2,3 => SOLVED * 976532148584167392231984567613879425497215683825643971159726834362458719748391256 * SOLVED! |:step:| 00 -------------------------------------------------- C1 = 6 => SOL |:step:| 01 --------------------------------------------------
Solution
position: 976532148584167392231984567613879425497215683825643971159726834362458719748391256 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 # A7: 2,3 => UNS * INC # B7: 2,3 => UNS * INC # B9: 2,3 => UNS * INC # F8: 2,3 => UNS * INC # G8: 2,3 => UNS * DIS # A2: 2,3 => CTR => A2: 1,5 * INC # A2: 1,5 => UNS * PRF # A3: 2,3 => SOL * INC # A3: 1,6 => UNS * INC # C9: 2,8 => UNS * INC # C9: 5 => UNS * INC # F8: 2,8 => UNS * INC # G8: 2,8 => UNS * CNT 13 HDP CHAINS / 13 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A7: 2,3 => UNS * INC # B7: 2,3 => UNS * INC # B9: 2,3 => UNS * INC # F8: 2,3 => UNS * INC # G8: 2,3 => UNS * DIS # A2: 2,3 => CTR => A2: 1,5 * PRF A2: 1,5 # A3: 2,3 => SOL * STA A2: 1,5 + A3: 2,3 * CNT 7 HDP CHAINS / 7 HYP OPENED