Analysis of xx-top95-082-base.sdk
Contents
Original Sudoku
level: medium
position: ..........5724...98....947...9..3...5..9..12...3.1.9...6....25....56.....7......6 initial
Autosolve
position: ..........5724...98....947...9..3...5..9..123..3.1.9...6....25....56.....75.....6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B4: 4,8 => CTR => B4: 1,2 * DIS # B6: 4,8 => CTR => B6: 2 * DIS # F5: 4,8 => CTR => F5: 6,7 * DIS # F5: 7,8 => CTR => F5: 4,6 * CNT 4 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B4: 4,8 => CTR => B4: 1,2 * DIS B4: 1,2 # B6: 4,8 => CTR => B6: 2 * DIS B4: 1,2 + B6: 2 # C5: 6 => CTR => C5: 4,8 * PRF B4: 1,2 + B6: 2 + C5: 4,8 # B8: 9 => SOL * STA B4: 1,2 + B6: 2 + C5: 4,8 + B8: 9 * CNT 4 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..........5724...98....947...9..3...5..9..12...3.1.9...6....25....56.....7......6 | initial |
| ..........5724...98....947...9..3...5..9..123..3.1.9...6....25....56.....75.....6 | autosolve |
| 946731582157248639832659471719423865584976123623815947461397258398562714275184396 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) E3: 3,5 B5: 4,8 E4: 2,5 E5: 7,8 F6: 2,5 G9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,B4: 1.. / A4 = 1 => 0 pairs (X) / B4 = 1 => 7 pairs (_) I1,I3: 2.. / I1 = 2 => 7 pairs (_) / I3 = 2 => 6 pairs (_) E4,F6: 2.. / E4 = 2 => 4 pairs (_) / F6 = 2 => 0 pairs (X) E4,E9: 2.. / E4 = 2 => 4 pairs (_) / E9 = 2 => 0 pairs (X) E4,F6: 5.. / E4 = 5 => 0 pairs (X) / F6 = 5 => 4 pairs (_) E3,I3: 5.. / E3 = 5 => 4 pairs (_) / I3 = 5 => 0 pairs (X) F6,I6: 5.. / F6 = 5 => 4 pairs (_) / I6 = 5 => 0 pairs (X) F1,F6: 5.. / F1 = 5 => 0 pairs (X) / F6 = 5 => 4 pairs (_) G1,G4: 5.. / G1 = 5 => 4 pairs (_) / G4 = 5 => 6 pairs (_) C3,D3: 6.. / C3 = 6 => 0 pairs (X) / D3 = 6 => 22 pairs (_) C5,F5: 6.. / C5 = 6 => 0 pairs (X) / F5 = 6 => 19 pairs (_) A4,A6: 7.. / A4 = 7 => 5 pairs (_) / A6 = 7 => 6 pairs (_) E5,F5: 7.. / E5 = 7 => 5 pairs (_) / F5 = 7 => 0 pairs (X) A6,I6: 7.. / A6 = 7 => 6 pairs (_) / I6 = 7 => 5 pairs (_) D1,D7: 7.. / D1 = 7 => 6 pairs (_) / D7 = 7 => 8 pairs (_) G4,G8: 7.. / G4 = 7 => 11 pairs (_) / G8 = 7 => 6 pairs (_) A1,B1: 9.. / A1 = 9 => 8 pairs (_) / B1 = 9 => 6 pairs (_) E7,E9: 9.. / E7 = 9 => 6 pairs (_) / E9 = 9 => 4 pairs (_) H8,H9: 9.. / H8 = 9 => 6 pairs (_) / H9 = 9 => 6 pairs (_) A7,E7: 9.. / A7 = 9 => 4 pairs (_) / E7 = 9 => 6 pairs (_) B1,B8: 9.. / B1 = 9 => 6 pairs (_) / B8 = 9 => 8 pairs (_) * DURATION: 0:00:23.353043 START: 00:50:14.756468 END: 00:50:38.109511 2017-05-04 * CP COUNT: (21) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,E3,E4,E5,F6,G9) * ..........5724...98....947...9..3...5..9..123..3.1.9...6....25....56.....75.....6 * PAIR E3: 3,5 BLK 2 E1: 3,5,7,8 # reduction candidate for 3,5 E1: 7,8 # 8 pairs E1: 3,5 # 7 pairs * PAIR B5: 4,8 BLK 4 B4: 4,8,1,2 # reduction candidate for 4,8 B4: 4,8 => CTR * ..........5724...98..6.947.1.9.23...5.69..123723.1596..6....25....56.....75.....6 B4: 1,2 # 7 pairs C5: 4,8,6 # reduction candidate for 4,8 C5: 4,8 # 19 pairs B6: 4,8,2 # reduction candidate for 4,8 B6: 4,8 => CTR * ..........5724...98..6.947...9..3...5.69..123..3.1.96..6....25....56.....75.....6 B6: 2 # 5 pairs * PAIR B5: 4,8 ROW 5 F5: 4,8,6,7 # reduction candidate for 4,8 F5: 4,8 => CTR * ..........5724...98..6.947...9..3...5.697.123..3.1.96..6....25....56.....75.....6 F5: 6,7 # 8 pairs * PAIR B5: 4,8 COL B B8: 4,8,1,2,3,9 # reduction candidate for 4,8 B8: 4,8 # 8 pairs B8: 1,2,3,9 # 7 pairs * PAIR E5: 7,8 BLK 5 F5: 7,8,4,6 # reduction candidate for 7,8 F5: 7,8 => CTR * ..........5724...98..6.947...9..3...5469..123..3.1.96..6....25....56.....75.....6 F5: 4,6 # 7 pairs * PAIR E5: 7,8 COL E E1: 7,8,3,5 # reduction candidate for 7,8 E1: 7,8 # 8 pairs E7: 7,8,3,9 # reduction candidate for 7,8 E7: 7,8 # 7 pairs * PAIR G9: 3,8 BLK 9 G8: 3,8,7 # reduction candidate for 3,8 G8: 3,8 # 11 pairs H8: 3,8,1,4,9 # reduction candidate for 3,8 H8: 3,8 # 10 pairs H9: 3,8,1,4,9 # reduction candidate for 3,8 H9: 3,8 # 12 pairs * PAIR G9: 3,8 ROW 9 D9: 3,8,1,4 # reduction candidate for 3,8 D9: 3,8 # 8 pairs E9: 3,8,2,9 # reduction candidate for 3,8 E9: 3,8 # 6 pairs * PAIR G9: 3,8 COL G G1: 3,8,5,6 # reduction candidate for 3,8 G1: 3,8 # 9 pairs G2: 3,8,6 # reduction candidate for 3,8 G2: 3,8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-082-base-pr-000.dot * REASONING * DIS # B4: 4,8 => CTR => B4: 1,2 * DIS # B6: 4,8 => CTR => B6: 2 * DIS # F5: 4,8 => CTR => F5: 6,7 * DIS # F5: 7,8 => CTR => F5: 4,6 * CNT 4 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,E3,E4,E5,F6,G9) * ..........5724...98....947...9..3...5..9..123..3.1.9...6....25....56.....75.....6 * PAIR E3: 3,5 BLK 2 E1: 3,5,7,8 # reduction candidate for 3,5 E1: 7,8 # 8 pairs E1: 3,5 # 7 pairs * PAIR B5: 4,8 BLK 4 B4: 4,8,1,2 # reduction candidate for 4,8 B4: 4,8 => CTR * ..........5724...98..6.947.1.9.23...5.69..123723.1596..6....25....56.....75.....6 C5: 4,8,6 # reduction candidate for 4,8 C5: 4,8 # 19 pairs B6: 4,8,2 # reduction candidate for 4,8 B6: 4,8 => CTR * ..........5724...98..6.947...9..3...5.69..123..3.1.96..6....25....56.....75.....6 * RESTART * PAIR B5: 4,8 BLK 4 C5: 4,8,6 # reduction candidate for 4,8 C5: 6 => CTR * ..........5724...983.65947..19823...586974123.23.159...6....25....56.....75.....6 * PAIR B5: 4,8 COL B B8: 4,8,9 # reduction candidate for 4,8 B8: 9 => SOLVED * 946731582157248639832659471719423865584976123623815947461397258398562714275184396 * DURATION: 0:00:08.585383 START: 00:50:52.297213 END: 00:51:00.882596 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-082-base-pr-001.dot * REASONING * DIS # B4: 4,8 => CTR => B4: 1,2 * DIS B4: 1,2 # B6: 4,8 => CTR => B6: 2 * DIS B4: 1,2 + B6: 2 # C5: 6 => CTR => C5: 4,8 * PRF B4: 1,2 + B6: 2 + C5: 4,8 # B8: 9 => SOL * STA B4: 1,2 + B6: 2 + C5: 4,8 + B8: 9 * CNT 4 HDP CHAINS / 9 HYP OPENED
Header Info
Top 95 Sudokus 082 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 946731582157248639832659471719423865584976123623815947461397258398562714275184396 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 # E1: 3,5 => UNS * INC # E1: 7,8 => UNS * DIS # B4: 4,8 => CTR => B4: 1,2 * INC # B4: 1,2 => UNS * INC # C5: 4,8 => UNS * DIS # B6: 4,8 => CTR => B6: 2 * INC # B6: 2 => UNS * DIS # F5: 4,8 => CTR => F5: 6,7 * INC # F5: 6,7 => UNS * INC # B8: 4,8 => UNS * INC # B8: 1,2,3,9 => UNS * DIS # F5: 7,8 => CTR => F5: 4,6 * INC # F5: 4,6 => UNS * INC # E1: 7,8 => UNS * INC # E7: 7,8 => UNS * INC # G8: 3,8 => UNS * INC # H8: 3,8 => UNS * INC # H9: 3,8 => UNS * INC # D9: 3,8 => UNS * INC # E9: 3,8 => UNS * INC # G1: 3,8 => UNS * INC # G2: 3,8 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 3,5 => UNS * INC # E1: 7,8 => UNS * DIS # B4: 4,8 => CTR => B4: 1,2 * INC B4: 1,2 # C5: 4,8 => UNS * DIS B4: 1,2 # B6: 4,8 => CTR => B6: 2 * INC B4: 1,2 + B6: 2 # C5: 4,8 => UNS * DIS B4: 1,2 + B6: 2 # C5: 6 => CTR => C5: 4,8 * INC B4: 1,2 + B6: 2 + C5: 4,8 # B8: 4,8 => UNS * PRF B4: 1,2 + B6: 2 + C5: 4,8 # B8: 9 => SOL * STA B4: 1,2 + B6: 2 + C5: 4,8 + B8: 9 * CNT 9 HDP CHAINS / 9 HYP OPENED