Analysis of xx-top500-246-base.sdk
Contents
Original Sudoku
level: medium
position: 1...7..4.....385.............8...6.2...9...1..3........2....3..9..1.............8 initial
Autosolve
position: 153279846.9..385218.2.1.937.183..6922..98..13.39.21.85.218..3.998.1.32.43...921.8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 4,6 => CTR => D3: 5 * DIS # B5: 4,6 => CTR => B5: 7 * DIS # D3: 4,6 => CTR => D3: 5 * DIS # D6: 7 => CTR => D6: 4,6 * DIS # F4: 4,5 => CTR => F4: 7 * PRF # F5: 4,5 => SOL * DIS # A4: 7 => CTR => A4: 4,5 * DIS # C5: 4,7 => CTR => C5: 5,6 * DIS # F5: 4,7 => CTR => F5: 5,6 * PRF # A6: 4,7 => SOL * DIS # E7: 4 => CTR => E7: 5,6 * CNT 11 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 4,6 => CTR => D3: 5 * DIS D3: 5 # B5: 4,6 => CTR => B5: 7 * PRF D3: 5 + B5: 7 # C2: 7 => SOL * STA D3: 5 + B5: 7 + C2: 7 * CNT 3 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1...7..4.....385.............8...6.2...9...1..3........2....3..9..1.............8 | initial |
| 153279846.9..385218.2.1.937.183..6922..98..13.39.21.85.218..3.998.1.32.43...921.8 | autosolve |
| 153279846697438521842516937518347692276985413439621785721854369985163274364792158 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) B3: 4,6 D2: 4,6 E4: 4,5 G5: 4,7 G6: 4,7 E8: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,G6: 4.. / G5 = 4 => 14 pairs (_) / G6 = 4 => 0 pairs (X) E4,E7: 4.. / E4 = 4 => 12 pairs (_) / E7 = 4 => 0 pairs (X) D3,F3: 5.. / D3 = 5 => 8 pairs (_) / F3 = 5 => 0 pairs (X) A4,C5: 5.. / A4 = 5 => 0 pairs (*) / C5 = 5 => 0 pairs (X) C5,F5: 5.. / C5 = 5 => 12 pairs (_) / F5 = 5 => 0 pairs (*) A4,A7: 5.. / A4 = 5 => 0 pairs (*) / A7 = 5 => 0 pairs (X) D3,D9: 5.. / D3 = 5 => 8 pairs (_) / D9 = 5 => 0 pairs (X) F5,D6: 6.. / F5 = 6 => 16 pairs (_) / D6 = 6 => 0 pairs (*) E7,E8: 6.. / E7 = 6 => 13 pairs (_) / E8 = 6 => 8 pairs (_) A6,D6: 6.. / A6 = 6 => 16 pairs (_) / D6 = 6 => 0 pairs (*) F3,F5: 6.. / F3 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) A2,C2: 7.. / A2 = 7 => 16 pairs (_) / C2 = 7 => 10 pairs (_) G5,G6: 7.. / G5 = 7 => 0 pairs (X) / G6 = 7 => 14 pairs (_) F7,D9: 7.. / F7 = 7 => 0 pairs (X) / D9 = 7 => 14 pairs (_) A4,F4: 7.. / A4 = 7 => 0 pairs (X) / F4 = 7 => 14 pairs (_) C8,H8: 7.. / C8 = 7 => 16 pairs (_) / H8 = 7 => 9 pairs (_) B5,B9: 7.. / B5 = 7 => 14 pairs (_) / B9 = 7 => 0 pairs (X) D6,D9: 7.. / D6 = 7 => 0 pairs (X) / D9 = 7 => 14 pairs (_) * DURATION: 0:00:31.172884 START: 11:12:07.963884 END: 11:12:39.136768 2017-05-04 * CP COUNT: (18) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,D2,E4,E8,G5,G6) * 153279846.9..385218.2.1.937.183..6922..98..13.39.21.85.218..3.998.1.32.43...921.8 * PAIR B3: 4,6 BLK 1 A2: 4,6,7 # reduction candidate for 4,6 A2: 4,6 # 10 pairs C2: 4,6,7 # reduction candidate for 4,6 C2: 4,6 # 16 pairs * PAIR B3: 4,6 ROW 3 D3: 4,6,5 # reduction candidate for 4,6 D3: 4,6 => CTR * 153279846.9..385218.2.1593771835469224598671363972148552184736998716325436.592178 D3: 5 # 8 pairs F3: 4,6,5 # reduction candidate for 4,6 F3: 4,6 # 8 pairs * PAIR B3: 4,6 COL B B5: 4,6,7 # reduction candidate for 4,6 B5: 4,6 => CTR * 153279846.9..385218.2.1.9377183..6922.59867136397214855218473699861.327437..921.8 B5: 7 # 14 pairs B9: 4,6,7 # reduction candidate for 4,6 B9: 4,6 # 14 pairs * PAIR D2: 4,6 BLK 2 D3: 4,6,5 # reduction candidate for 4,6 D3: 4,6 => CTR * 153279846.9..385218.2.1593771835469224598671363972148552184736998716325436.592178 D3: 5 # 8 pairs F3: 4,6,5 # reduction candidate for 4,6 F3: 4,6 # 8 pairs * PAIR D2: 4,6 ROW 2 A2: 4,6,7 # reduction candidate for 4,6 A2: 4,6 # 10 pairs C2: 4,6,7 # reduction candidate for 4,6 C2: 4,6 # 16 pairs * PAIR D2: 4,6 COL D D6: 4,6,7 # reduction candidate for 4,6 D6: 7 => CTR * 153279846.9..385218.2.1.9377183..69224598671363972148552184736998.16325437..921.8 D6: 4,6 # 14 pairs * PAIR E4: 4,5 BLK 5 F4: 4,5,7 # reduction candidate for 4,5 F4: 4,5 => CTR * 153279846.9..385218.2.1.9377183..6922.598..13.39.21.855218..3.998.1.32.4374592168 F4: 7 # 14 pairs F5: 4,5,6,7 # reduction candidate for 4,5 F5: 4,5 => SOLVED * 153279846697438521842516937518347692276985413439621785721854369985163274364792158 F5: 6,7 # 13 pairs * PAIR E4: 4,5 ROW 4 A4: 4,5,7 # reduction candidate for 4,5 A4: 7 => CTR * 153279846.9..385218.2.1.9377183..6922.598..13.39.21.855218..3.998.1.32.4374592168 A4: 4,5 # 14 pairs * PAIR E4: 4,5 COL E E7: 4,5,6 # reduction candidate for 4,5 E7: 6 # 13 pairs E7: 4,5 # 8 pairs * PAIR G5: 4,7 ROW 5 B5: 4,7,6 # reduction candidate for 4,7 B5: 4,7 # 9 pairs C5: 4,7,5,6 # reduction candidate for 4,7 C5: 4,7 => CTR * 153279846.9..385218.2.1.9375183476922..985.13.39621.85.218.43.998.1.32.43..7921.8 C5: 5,6 # 7 pairs F5: 4,7,5,6 # reduction candidate for 4,7 F5: 4,7 => CTR * 153279846.9..385218.2.16937.183..6922.598..13.39621.855218..3.998.1.32.43..792158 F5: 5,6 # 7 pairs * PAIR G6: 4,7 ROW 6 A6: 4,7,6 # reduction candidate for 4,7 A6: 4,7 => SOLVED * 153279846697438521842516937518347692276985413439621785721854369985163274364792158 A6: 6 # 16 pairs D6: 4,7,6 # reduction candidate for 4,7 D6: 4,7 # 16 pairs * PAIR E8: 5,6 BLK 8 E7: 5,6,4 # reduction candidate for 5,6 E7: 4 => CTR * 15327984679..385218.2.1593741835.6922.598..13.39.21.855218473699871632543..592178 E7: 5,6 # 12 pairs * PAIR E8: 5,6 ROW 8 C8: 5,6,7 # reduction candidate for 5,6 C8: 5,6 # 9 pairs H8: 5,6,7 # reduction candidate for 5,6 H8: 5,6 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-246-base-pr-000.dot * REASONING * DIS # D3: 4,6 => CTR => D3: 5 * DIS # B5: 4,6 => CTR => B5: 7 * DIS # D3: 4,6 => CTR => D3: 5 * DIS # D6: 7 => CTR => D6: 4,6 * DIS # F4: 4,5 => CTR => F4: 7 * PRF # F5: 4,5 => SOL * DIS # A4: 7 => CTR => A4: 4,5 * DIS # C5: 4,7 => CTR => C5: 5,6 * DIS # F5: 4,7 => CTR => F5: 5,6 * PRF # A6: 4,7 => SOL * DIS # E7: 4 => CTR => E7: 5,6 * CNT 11 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,D2,E4,E8,G5,G6) * 153279846.9..385218.2.1.937.183..6922..98..13.39.21.85.218..3.998.1.32.43...921.8 * PAIR B3: 4,6 BLK 1 A2: 4,6,7 # reduction candidate for 4,6 A2: 4,6 # 10 pairs C2: 4,6,7 # reduction candidate for 4,6 C2: 4,6 # 16 pairs * PAIR B3: 4,6 ROW 3 D3: 4,6,5 # reduction candidate for 4,6 D3: 4,6 => CTR * 153279846.9..385218.2.1593771835469224598671363972148552184736998716325436.592178 * RESTART * PAIR B3: 4,6 COL B B5: 4,6,7 # reduction candidate for 4,6 B5: 4,6 => CTR * 153279846.9.638521862514937.1834.69224.9867136397214854218.73.998.1.327437.4921.8 * RESTART * PAIR RESTART * PAIR B3: 4,6 BLK 1 C2: 4,6,7 # reduction candidate for 4,6 C2: 7 => SOLVED * 153279846697438521842516937518347692276985413439621785721854369985163274364792158 * DURATION: 0:00:07.140607 START: 11:13:12.307314 END: 11:13:19.447921 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-246-base-pr-001.dot * REASONING * DIS # D3: 4,6 => CTR => D3: 5 * DIS D3: 5 # B5: 4,6 => CTR => B5: 7 * PRF D3: 5 + B5: 7 # C2: 7 => SOL * STA D3: 5 + B5: 7 + C2: 7 * CNT 3 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 246 solution: 153279846697438521842516937518347692276985413439621785721854369985163274364792158 info: 2071 FNBWXY S8.f 25384 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 153279846697438521842516937518347692276985413439621785721854369985163274364792158 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 # A2: 4,6 => UNS * INC # C2: 4,6 => UNS * DIS # D3: 4,6 => CTR => D3: 5 * INC # D3: 5 => UNS * INC # F3: 4,6 => UNS * DIS # B5: 4,6 => CTR => B5: 7 * INC # B5: 7 => UNS * INC # B9: 4,6 => UNS * DIS # D3: 4,6 => CTR => D3: 5 * INC # D3: 5 => UNS * INC # F3: 4,6 => UNS * INC # A2: 4,6 => UNS * INC # C2: 4,6 => UNS * INC # D6: 4,6 => UNS * DIS # D6: 7 => CTR => D6: 4,6 * DIS # F4: 4,5 => CTR => F4: 7 * INC # F4: 7 => UNS * PRF # F5: 4,5 => SOL * INC # F5: 6,7 => UNS * INC # A4: 4,5 => UNS * DIS # A4: 7 => CTR => A4: 4,5 * INC # E7: 4,5 => UNS * INC # E7: 6 => UNS * INC # B5: 4,7 => UNS * DIS # C5: 4,7 => CTR => C5: 5,6 * INC # C5: 5,6 => UNS * DIS # F5: 4,7 => CTR => F5: 5,6 * INC # F5: 5,6 => UNS * PRF # A6: 4,7 => SOL * INC # A6: 6 => UNS * INC # D6: 4,7 => UNS * INC # E7: 5,6 => UNS * DIS # E7: 4 => CTR => E7: 5,6 * INC # C8: 5,6 => UNS * INC # H8: 5,6 => UNS * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 4,6 => UNS * INC # C2: 4,6 => UNS * DIS # D3: 4,6 => CTR => D3: 5 * DIS D3: 5 # B5: 4,6 => CTR => B5: 7 * INC D3: 5 + B5: 7 # C2: 4,6 => UNS * PRF D3: 5 + B5: 7 # C2: 7 => SOL * STA D3: 5 + B5: 7 + C2: 7 * CNT 6 HDP CHAINS / 6 HYP OPENED