Analysis of xx-top500-386-base.sdk
Contents
Original Sudoku
level: medium
position: ....2..5.6.....3..8.............1..6..4.5....9.......8.7.6.8.........24....9..... initial
Autosolve
position: ....2..5.6.....3..8.............1..6..4.5...39.......8279648135......249...9.2..7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 1,4 => CTR => B1: 3,9 * DIS # H5: 1,7 => CTR => H5: 2,9 * DIS # H5: 7,9 => CTR => H5: 1,2 * DIS # F5: 6 => CTR => F5: 7,9 * DIS # G1: 7,9 => CTR => G1: 6,8 * DIS # A9: 1,3 => CTR => A9: 4,5 * DIS # A1: 1,3 => CTR => A1: 4,7 * DIS # B5: 1,2 => CTR => B5: 6,8 * DIS # A9: 1,3 => CTR => A9: 4,5 * PRF # E3: 1,3 => SOL * DIS # G1: 7,9 => CTR => G1: 6,8 * CNT 11 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 1,4 => CTR => B1: 3,9 * DIS B1: 3,9 # H5: 1,7 => CTR => H5: 2,9 * DIS B1: 3,9 + H5: 2,9 # H4: 2 => CTR => H4: 7,9 * DIS B1: 3,9 + H5: 2,9 + H4: 7,9 # F5: 6 => CTR => F5: 7,9 * PRF B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # F2: 4,5 => SOL * STA B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 + F2: 4,5 * CNT 5 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....2..5.6.....3..8.............1..6..4.5....9.......8.7.6.8.........24....9..... | initial |
| ....2..5.6.....3..8.............1..6..4.5...39.......8279648135......249...9.2..7 | autosolve |
| 791326854652784391843519762538291476164857923927463518279648135386175249415932687 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) I1: 1,4 A5: 1,7 G4: 4,5 G5: 7,9 G6: 4,5 A8: 1,3 B8: 6,8 C8: 6,8 E9: 1,3 G9: 6,8 H9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H5,H6: 1.. / H5 = 1 => 0 pairs (X) / H6 = 1 => 11 pairs (_) I2,I3: 2.. / I2 = 2 => 12 pairs (_) / I3 = 2 => 12 pairs (_) G4,G6: 4.. / G4 = 4 => 9 pairs (_) / G6 = 4 => 14 pairs (_) A9,B9: 4.. / A9 = 4 => 9 pairs (_) / B9 = 4 => 14 pairs (_) D4,G4: 4.. / D4 = 4 => 14 pairs (_) / G4 = 4 => 9 pairs (_) A1,A9: 4.. / A1 = 4 => 14 pairs (_) / A9 = 4 => 9 pairs (_) G4,G6: 5.. / G4 = 5 => 14 pairs (_) / G6 = 5 => 9 pairs (_) D8,F8: 5.. / D8 = 5 => 12 pairs (_) / F8 = 5 => 11 pairs (_) A4,A9: 5.. / A4 = 5 => 9 pairs (_) / A9 = 5 => 16 pairs (_) B8,C8: 6.. / B8 = 6 => 0 pairs (X) / C8 = 6 => 16 pairs (_) G9,H9: 6.. / G9 = 6 => 16 pairs (_) / H9 = 6 => 0 pairs (X) F1,G1: 6.. / F1 = 6 => 16 pairs (_) / G1 = 6 => 0 pairs (X) B5,F5: 6.. / B5 = 6 => 16 pairs (_) / F5 = 6 => 0 pairs (X) C6,C8: 6.. / C6 = 6 => 0 pairs (X) / C8 = 6 => 16 pairs (_) E3,E6: 6.. / E3 = 6 => 0 pairs (X) / E6 = 6 => 16 pairs (_) H3,H9: 6.. / H3 = 6 => 16 pairs (_) / H9 = 6 => 0 pairs (X) G1,H2: 8.. / G1 = 8 => 16 pairs (_) / H2 = 8 => 0 pairs (X) B8,C8: 8.. / B8 = 8 => 16 pairs (_) / C8 = 8 => 0 pairs (X) G9,H9: 8.. / G9 = 8 => 0 pairs (X) / H9 = 8 => 16 pairs (_) D1,G1: 8.. / D1 = 8 => 0 pairs (X) / G1 = 8 => 16 pairs (_) B5,D5: 8.. / B5 = 8 => 0 pairs (X) / D5 = 8 => 16 pairs (_) C4,C8: 8.. / C4 = 8 => 16 pairs (_) / C8 = 8 => 0 pairs (X) E2,E4: 8.. / E2 = 8 => 16 pairs (_) / E4 = 8 => 0 pairs (X) G1,G9: 8.. / G1 = 8 => 16 pairs (_) / G9 = 8 => 0 pairs (X) H2,H9: 8.. / H2 = 8 => 0 pairs (X) / H9 = 8 => 16 pairs (_) E4,F5: 9.. / E4 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) E4,H4: 9.. / E4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) * DURATION: 0:00:50.848643 START: 16:02:02.201552 END: 16:02:53.050195 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B8,C8,E9,G4,G5,G6,G9,H9,I1) * ....2..5.6.....3..8.............1..6..4.5...39.......8279648135......249...9.2..7 * PAIR I1: 1,4 BLK 3 I2: 1,4,2 # reduction candidate for 1,4 I2: 1,4 # 12 pairs I3: 1,4,2 # reduction candidate for 1,4 I3: 1,4 # 12 pairs * PAIR I1: 1,4 ROW 1 A1: 1,4,3,7 # reduction candidate for 1,4 A1: 1,4 # 14 pairs B1: 1,4,3,9 # reduction candidate for 1,4 B1: 1,4 => CTR * ...82..5.6.....38.8............81.96.84.5...39.......8279648135......249...9.2..7 B1: 3,9 # 12 pairs D1: 1,4,3,7,8 # reduction candidate for 1,4 D1: 1,4 # 16 pairs * PAIR A5: 1,7 BLK 4 C6: 1,7,2,3,5,6 # reduction candidate for 1,7 C6: 1,7 # 16 pairs C6: 2,3,5,6 # 11 pairs * PAIR A5: 1,7 ROW 5 H5: 1,7,2,9 # reduction candidate for 1,7 H5: 1,7 => CTR * ....2.65.6...8.3..8...6.79.....91..6..4.569.39.......8279648135......249...9.2..7 H5: 2,9 # 12 pairs * PAIR A5: 1,7 COL A A1: 1,7,3,4 # reduction candidate for 1,7 A1: 1,7 # 13 pairs A1: 3,4 # 12 pairs * PAIR G5: 7,9 BLK 6 H4: 7,9,2 # reduction candidate for 7,9 H4: 7,9 # 14 pairs H5: 7,9,1,2 # reduction candidate for 7,9 H5: 7,9 => CTR * ....2685.6...8.3..8......6...8.91.26.64.5...39...6..18279648135..6...249...9.2687 H5: 1,2 # 12 pairs * PAIR G5: 7,9 ROW 5 F5: 7,9,6 # reduction candidate for 7,9 F5: 6 => CTR * ....2.65.6...8.3..8...6........91..6..4.56..39.......8279648135......249...9.28.7 F5: 7,9 # 16 pairs * PAIR G5: 7,9 COL G G1: 7,9,6,8 # reduction candidate for 7,9 G1: 7,9 => CTR * ...826.5.6.....38.8............81.96..4.5...39.......8279648135......249...9.2..7 G1: 6,8 # 13 pairs G3: 7,9,6 # reduction candidate for 7,9 G3: 7,9 # 13 pairs * PAIR A8: 1,3 BLK 7 A9: 1,3,4,5 # reduction candidate for 1,3 A9: 1,3 => CTR * 4...2.6516...8.3..8...6.79.5...914.67.4.569.39.....5.8279648135......249.459.2..7 A9: 4,5 # 12 pairs B9: 1,3,4,5 # reduction candidate for 1,3 B9: 1,3 # 11 pairs C9: 1,3,5 # reduction candidate for 1,3 C9: 1,3 # 14 pairs * PAIR A8: 1,3 ROW 8 D8: 1,3,5,7 # reduction candidate for 1,3 D8: 1,3 # 13 pairs E8: 1,3,7 # reduction candidate for 1,3 E8: 1,3 # 15 pairs * PAIR A8: 1,3 COL A A1: 1,3,4,7 # reduction candidate for 1,3 A1: 1,3 => CTR * ....2.65.6...8.3..8...6.79.5...914.67.4.569.39.....5.8279648135......2494..9.2..7 A1: 4,7 # 12 pairs * PAIR B8: 6,8 COL B B5: 6,8,1,2 # reduction candidate for 6,8 B5: 1,2 => CTR * ....2..5.6.....3..8.............1..6..4856..39.......8279648135......249...9.2..7 B5: 6,8 # 12 pairs * PAIR E9: 1,3 BLK 8 D8: 1,3,5,7 # reduction candidate for 1,3 D8: 1,3 # 13 pairs E8: 1,3,7 # reduction candidate for 1,3 E8: 1,3 # 15 pairs * PAIR E9: 1,3 ROW 9 A9: 1,3,4,5 # reduction candidate for 1,3 A9: 1,3 => CTR * 4...2.6516...8.3..8...6.79.5...914.67.4.569.39.....5.8279648135......249.459.2..7 A9: 4,5 # 12 pairs B9: 1,3,4,5 # reduction candidate for 1,3 B9: 1,3 # 11 pairs C9: 1,3,5 # reduction candidate for 1,3 C9: 1,3 # 14 pairs * PAIR E9: 1,3 COL E E3: 1,3,6,7,9 # reduction candidate for 1,3 E3: 1,3 => SOLVED * 791326854652784391843519762538291476164857923927463518279648135386175249415932687 E3: 6,7,9 # 11 pairs * PAIR G9: 6,8 COL G G1: 6,8,7,9 # reduction candidate for 6,8 G1: 7,9 => CTR * ...826.5.6.....38.8............81.96..4.5...39.......8279648135......249...9.2..7 G1: 6,8 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-386-base-pr-000.dot * REASONING * DIS # B1: 1,4 => CTR => B1: 3,9 * DIS # H5: 1,7 => CTR => H5: 2,9 * DIS # H5: 7,9 => CTR => H5: 1,2 * DIS # F5: 6 => CTR => F5: 7,9 * DIS # G1: 7,9 => CTR => G1: 6,8 * DIS # A9: 1,3 => CTR => A9: 4,5 * DIS # A1: 1,3 => CTR => A1: 4,7 * DIS # B5: 1,2 => CTR => B5: 6,8 * DIS # A9: 1,3 => CTR => A9: 4,5 * PRF # E3: 1,3 => SOL * DIS # G1: 7,9 => CTR => G1: 6,8 * CNT 11 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B8,C8,E9,G4,G5,G6,G9,H9,I1) * ....2..5.6.....3..8.............1..6..4.5...39.......8279648135......249...9.2..7 * PAIR I1: 1,4 BLK 3 I2: 1,4,2 # reduction candidate for 1,4 I2: 1,4 # 12 pairs I3: 1,4,2 # reduction candidate for 1,4 I3: 1,4 # 12 pairs * PAIR I1: 1,4 ROW 1 A1: 1,4,3,7 # reduction candidate for 1,4 A1: 1,4 # 14 pairs B1: 1,4,3,9 # reduction candidate for 1,4 B1: 1,4 => CTR * ...82..5.6.....38.8............81.96.84.5...39.......8279648135......249...9.2..7 D1: 1,4,3,7,8 # reduction candidate for 1,4 D1: 1,4 # 16 pairs * PAIR RESTART * PAIR I1: 1,4 BLK 3 I2: 1,4,2 # reduction candidate for 1,4 I2: 1,4 # 13 pairs I3: 1,4,2 # reduction candidate for 1,4 I3: 1,4 # 13 pairs * PAIR I1: 1,4 ROW 1 A1: 1,4,3,7 # reduction candidate for 1,4 A1: 1,4 # 14 pairs D1: 1,4,3,7,8 # reduction candidate for 1,4 D1: 1,4 # 16 pairs * PAIR A5: 1,7 BLK 4 C6: 1,7,2,3,5,6 # reduction candidate for 1,7 C6: 1,7 # 16 pairs C6: 2,3,5,6 # 12 pairs * PAIR A5: 1,7 ROW 5 H5: 1,7,2,9 # reduction candidate for 1,7 H5: 1,7 => CTR * ....2.65.6...8.3..8...6.79.....91..6..4.569.39.......8279648135......249...9.2..7 * PAIR A5: 1,7 COL A A1: 1,7,3,4 # reduction candidate for 1,7 A1: 3,4 # 16 pairs A1: 1,7 # 15 pairs * PAIR RESTART * PAIR A5: 1,7 COL A A1: 1,7,3,4 # reduction candidate for 1,7 A1: 3,4 # 16 pairs A1: 1,7 # 15 pairs * PAIR G5: 7,9 BLK 6 H4: 7,9,2 # reduction candidate for 7,9 H4: 2 => CTR * ....2..5.6...8.37.8......6.....91.261.4.567939......182796481353.....249...932687 * PAIR G5: 7,9 ROW 5 F5: 7,9,6 # reduction candidate for 7,9 F5: 6 => CTR * ....2.65.6...8.39.8............91.76..4.569239......18279648135......249...9.2..7 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B4,B6,B9,C1,C9,D4,E4,E8,F5,F6,F8,G3,G5,H2,H4,I1) * 79..2685.6...8.3..8......6.5.8..14.616485..239.7.6.518279648135386...2494..932687 * PAIR C1: 1,3 BLK 1 C3: 1,3,2,5 # reduction candidate for 1,3 C3: 1,3 # 18 pairs C3: 2,5 # 17 pairs * PAIR C1: 1,3 ROW 1 D1: 1,3,4 # reduction candidate for 1,3 D1: 1,3 # 18 pairs D1: 4 # 16 pairs * PAIR I1: 1,4 BLK 3 I2: 1,4,2 # reduction candidate for 1,4 I2: 1,4 # 17 pairs I3: 1,4,2 # reduction candidate for 1,4 I3: 1,4 # 18 pairs * PAIR I1: 1,4 ROW 1 D1: 1,4,3 # reduction candidate for 1,4 D1: 1,4 # 16 pairs D1: 3 # 11 pairs * PAIR H2: 7,9 ROW 2 F2: 7,9,4,5 # reduction candidate for 7,9 F2: 4,5 => SOLVED * 791326854652784391843519762538291476164857923927463518279648135386175249415932687 * DURATION: 0:00:37.824545 START: 16:03:31.337813 END: 16:04:09.162358 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-386-base-pr-001.dot * REASONING * DIS # B1: 1,4 => CTR => B1: 3,9 * DIS B1: 3,9 # H5: 1,7 => CTR => H5: 2,9 * DIS B1: 3,9 + H5: 2,9 # H4: 2 => CTR => H4: 7,9 * DIS B1: 3,9 + H5: 2,9 + H4: 7,9 # F5: 6 => CTR => F5: 7,9 * PRF B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # F2: 4,5 => SOL * STA B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 + F2: 4,5 * CNT 5 HDP CHAINS / 30 HYP OPENED
Header Info
Top 500 Minimum 17 386 solution: 791326854652784391843519762538291476164857923927463518279648135386175249415932687 info: 34914 FNBTHXYK S8.f 46770 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 791326854652784391843519762538291476164857923927463518279648135386175249415932687 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 # I2: 1,4 => UNS * INC # I3: 1,4 => UNS * INC # A1: 1,4 => UNS * DIS # B1: 1,4 => CTR => B1: 3,9 * INC # B1: 3,9 => UNS * INC # D1: 1,4 => UNS * INC # C6: 1,7 => UNS * INC # C6: 2,3,5,6 => UNS * DIS # H5: 1,7 => CTR => H5: 2,9 * INC # H5: 2,9 => UNS * INC # A1: 1,7 => UNS * INC # A1: 3,4 => UNS * INC # H4: 7,9 => UNS * DIS # H5: 7,9 => CTR => H5: 1,2 * INC # H5: 1,2 => UNS * INC # F5: 7,9 => UNS * DIS # F5: 6 => CTR => F5: 7,9 * DIS # G1: 7,9 => CTR => G1: 6,8 * INC # G1: 6,8 => UNS * INC # G3: 7,9 => UNS * DIS # A9: 1,3 => CTR => A9: 4,5 * INC # A9: 4,5 => UNS * INC # B9: 1,3 => UNS * INC # C9: 1,3 => UNS * INC # D8: 1,3 => UNS * INC # E8: 1,3 => UNS * DIS # A1: 1,3 => CTR => A1: 4,7 * INC # A1: 4,7 => UNS * INC # B5: 6,8 => UNS * DIS # B5: 1,2 => CTR => B5: 6,8 * INC # D8: 1,3 => UNS * INC # E8: 1,3 => UNS * DIS # A9: 1,3 => CTR => A9: 4,5 * INC # A9: 4,5 => UNS * INC # B9: 1,3 => UNS * INC # C9: 1,3 => UNS * PRF # E3: 1,3 => SOL * INC # E3: 6,7,9 => UNS * INC # G1: 6,8 => UNS * DIS # G1: 7,9 => CTR => G1: 6,8 * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I2: 1,4 => UNS * INC # I3: 1,4 => UNS * INC # A1: 1,4 => UNS * DIS # B1: 1,4 => CTR => B1: 3,9 * INC B1: 3,9 # D1: 1,4 => UNS * INC B1: 3,9 # I2: 1,4 => UNS * INC B1: 3,9 # I3: 1,4 => UNS * INC B1: 3,9 # A1: 1,4 => UNS * INC B1: 3,9 # D1: 1,4 => UNS * INC B1: 3,9 # C6: 1,7 => UNS * INC B1: 3,9 # C6: 2,3,5,6 => UNS * DIS B1: 3,9 # H5: 1,7 => CTR => H5: 2,9 * INC B1: 3,9 + H5: 2,9 # A1: 1,7 => UNS * INC B1: 3,9 + H5: 2,9 # A1: 3,4 => UNS * INC B1: 3,9 + H5: 2,9 # A1: 1,7 => UNS * INC B1: 3,9 + H5: 2,9 # A1: 3,4 => UNS * INC B1: 3,9 + H5: 2,9 # H4: 7,9 => UNS * DIS B1: 3,9 + H5: 2,9 # H4: 2 => CTR => H4: 7,9 * INC B1: 3,9 + H5: 2,9 + H4: 7,9 # F5: 7,9 => UNS * DIS B1: 3,9 + H5: 2,9 + H4: 7,9 # F5: 6 => CTR => F5: 7,9 * INC B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # C3: 1,3 => UNS * INC B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # C3: 2,5 => UNS * INC B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # D1: 1,3 => UNS * INC B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # D1: 4 => UNS * INC B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # I2: 1,4 => UNS * INC B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # I3: 1,4 => UNS * INC B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # D1: 1,4 => UNS * INC B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # D1: 3 => UNS * INC B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # F2: 7,9 => UNS * PRF B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 # F2: 4,5 => SOL * STA B1: 3,9 + H5: 2,9 + H4: 7,9 + F5: 7,9 + F2: 4,5 * CNT 30 HDP CHAINS / 30 HYP OPENED