Analysis of xx-top500-081-base.sdk
Contents
Original Sudoku
level: medium
position: .......8473..........1.......8.5.......2..4...4......72......6......41......37... initial
Autosolve
position: .217.3.8473.845.2148.1.237.17845..3...327841..4231.8.72.4.817633.7.241.881..37.4. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 6,9 => CTR => C3: 5 * DIS # C9: 5 => CTR => C9: 6,9 * DIS # G1: 6,9 => CTR => G1: 5 * DIS # C3: 6,9 => CTR => C3: 5 * DIS # G1: 6,9 => CTR => G1: 5 * PRF # A6: 5 => SOL * DIS # I5: 6 => CTR => I5: 5,9 * DIS # A6: 6 => CTR => A6: 5,9 * PRF # B8: 5,9 => SOL * PRF # B5: 6 => SOL * PRF # D9: 5,9 => SOL * PRF # B8: 5,9 => SOL * CNT 12 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 6,9 => CTR => C3: 5 * PRF C3: 5 # G4: 2 => SOL * STA C3: 5 + G4: 2 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......8473..........1.......8.5.......2..4...4......72......6......41......37... | initial |
| .217.3.8473.845.2148.1.237.17845..3...327841..4231.8.72.4.817633.7.241.881..37.4. | autosolve |
| 621793584739845621485162379178459236963278415542316897254981763397624158816537942 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) C2: 6,9 E1: 6,9 E3: 6,9 G2: 6,9 F4: 6,9 F6: 6,9 H6: 5,9 B7: 5,9 D7: 5,9 H8: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,I4: 2.. / G4 = 2 => 13 pairs (_) / I4 = 2 => 16 pairs (_) G9,I9: 2.. / G9 = 2 => 16 pairs (_) / I9 = 2 => 13 pairs (_) G4,G9: 2.. / G4 = 2 => 13 pairs (_) / G9 = 2 => 16 pairs (_) I4,I9: 2.. / I4 = 2 => 16 pairs (_) / I9 = 2 => 13 pairs (_) A1,C3: 5.. / A1 = 5 => 0 pairs (X) / C3 = 5 => 15 pairs (_) G1,I3: 5.. / G1 = 5 => 15 pairs (_) / I3 = 5 => 0 pairs (X) I5,H6: 5.. / I5 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) A1,G1: 5.. / A1 = 5 => 0 pairs (X) / G1 = 5 => 15 pairs (_) C3,I3: 5.. / C3 = 5 => 15 pairs (_) / I3 = 5 => 0 pairs (X) A6,H6: 5.. / A6 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) B7,D7: 5.. / B7 = 5 => 16 pairs (_) / D7 = 5 => 14 pairs (_) C3,C9: 5.. / C3 = 5 => 15 pairs (_) / C9 = 5 => 0 pairs (X) G1,G9: 5.. / G1 = 5 => 15 pairs (_) / G9 = 5 => 0 pairs (X) H6,H8: 5.. / H6 = 5 => 18 pairs (_) / H8 = 5 => 0 pairs (*) E1,E3: 6.. / E1 = 6 => 17 pairs (_) / E3 = 6 => 15 pairs (_) F4,F6: 6.. / F4 = 6 => 0 pairs (X) / F6 = 6 => 12 pairs (_) B8,C9: 6.. / B8 = 6 => 14 pairs (_) / C9 = 6 => 0 pairs (*) D8,D9: 6.. / D8 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) C2,G2: 6.. / C2 = 6 => 17 pairs (_) / G2 = 6 => 15 pairs (_) A6,F6: 6.. / A6 = 6 => 0 pairs (X) / F6 = 6 => 12 pairs (_) B8,D8: 6.. / B8 = 6 => 14 pairs (_) / D8 = 6 => 0 pairs (*) C9,D9: 6.. / C9 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) B5,B8: 6.. / B5 = 6 => 0 pairs (*) / B8 = 6 => 0 pairs (X) E1,E3: 9.. / E1 = 9 => 15 pairs (_) / E3 = 9 => 17 pairs (_) F4,F6: 9.. / F4 = 9 => 12 pairs (_) / F6 = 9 => 0 pairs (X) C2,G2: 9.. / C2 = 9 => 15 pairs (_) / G2 = 9 => 17 pairs (_) B7,D7: 9.. / B7 = 9 => 14 pairs (_) / D7 = 9 => 16 pairs (_) H6,H8: 9.. / H6 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) * DURATION: 0:00:45.258512 START: 05:33:57.507176 END: 05:34:42.765688 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C2,D7,E1,E3,F4,F6,G2,H6,H8) * .217.3.8473.845.2148.1.237.17845..3...327841..4231.8.72.4.817633.7.241.881..37.4. * PAIR C2: 6,9 BLK 1 A1: 6,9,5 # reduction candidate for 6,9 A1: 6,9 # 15 pairs C3: 6,9,5 # reduction candidate for 6,9 C3: 6,9 => CTR * 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4. C3: 5 # 15 pairs * PAIR C2: 6,9 COL C C9: 6,9,5 # reduction candidate for 6,9 C9: 5 => CTR * 5217.3.8473.845.2148.1.237517845..3..5327841..4231.857294581763367.241.8815637.4. C9: 6,9 # 15 pairs * PAIR E1: 6,9 ROW 1 A1: 6,9,5 # reduction candidate for 6,9 A1: 6,9 # 15 pairs G1: 6,9,5 # reduction candidate for 6,9 G1: 6,9 => CTR * 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4. G1: 5 # 15 pairs * PAIR E3: 6,9 ROW 3 C3: 6,9,5 # reduction candidate for 6,9 C3: 6,9 => CTR * 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4. C3: 5 # 15 pairs I3: 6,9,5 # reduction candidate for 6,9 I3: 6,9 # 15 pairs * PAIR G2: 6,9 BLK 3 G1: 6,9,5 # reduction candidate for 6,9 G1: 6,9 => CTR * 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4. G1: 5 # 15 pairs I3: 6,9,5 # reduction candidate for 6,9 I3: 6,9 # 15 pairs * PAIR G2: 6,9 COL G G4: 6,9,2 # reduction candidate for 6,9 G4: 6,9 # 16 pairs G4: 2 # 13 pairs * PAIR F4: 6,9 ROW 4 G4: 6,9,2 # reduction candidate for 6,9 G4: 6,9 # 16 pairs I4: 6,9,2 # reduction candidate for 6,9 I4: 6,9 # 13 pairs * PAIR F6: 6,9 ROW 6 A6: 6,9,5 # reduction candidate for 6,9 A6: 5 => SOLVED * 621793584739845621485162379178459236963278415542316897254981763397624158816537942 A6: 6,9 # 18 pairs * PAIR H6: 5,9 BLK 6 I5: 5,9,6 # reduction candidate for 5,9 I5: 6 => CTR * 92176358473.845.2148.1.237.178456.3...3278416642319857254981763367524198819637.4. I5: 5,9 # 12 pairs * PAIR H6: 5,9 ROW 6 A6: 5,9,6 # reduction candidate for 5,9 A6: 6 => CTR * 92176358473.845.2148.1.237.178456.3...3278416642319857254981763367524198819637.4. A6: 5,9 # 12 pairs * PAIR B7: 5,9 BLK 7 B8: 5,9,6 # reduction candidate for 5,9 B8: 5,9 => SOLVED * 621793584739845621485162379178459236963278415542316897254981763397624158816537942 B8: 6 # 14 pairs C9: 5,9,6 # reduction candidate for 5,9 C9: 5,9 # 14 pairs * PAIR B7: 5,9 COL B B5: 5,9,6 # reduction candidate for 5,9 B5: 6 => SOLVED * 621793584739845621485162379178459236963278415542316897254981763397624158816537942 B5: 5,9 # 14 pairs * PAIR D7: 5,9 BLK 8 D8: 5,9,6 # reduction candidate for 5,9 D8: 5,9 # 14 pairs D9: 5,9,6 # reduction candidate for 5,9 D9: 5,9 => SOLVED * 621793584739845621485162379178459236963278415542316897254981763397624158816537942 D9: 6 # 14 pairs * PAIR H8: 5,9 BLK 9 G9: 5,9,2 # reduction candidate for 5,9 G9: 5,9 # 13 pairs I9: 5,9,2 # reduction candidate for 5,9 I9: 5,9 # 16 pairs * PAIR H8: 5,9 ROW 8 B8: 5,9,6 # reduction candidate for 5,9 B8: 5,9 => SOLVED * 621793584739845621485162379178459236963278415542316897254981763397624158816537942 B8: 6 # 14 pairs D8: 5,9,6 # reduction candidate for 5,9 D8: 5,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-081-base-pr-000.dot * REASONING * DIS # C3: 6,9 => CTR => C3: 5 * DIS # C9: 5 => CTR => C9: 6,9 * DIS # G1: 6,9 => CTR => G1: 5 * DIS # C3: 6,9 => CTR => C3: 5 * DIS # G1: 6,9 => CTR => G1: 5 * PRF # A6: 5 => SOL * DIS # I5: 6 => CTR => I5: 5,9 * DIS # A6: 6 => CTR => A6: 5,9 * PRF # B8: 5,9 => SOL * PRF # B5: 6 => SOL * PRF # D9: 5,9 => SOL * PRF # B8: 5,9 => SOL * CNT 12 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C2,D7,E1,E3,F4,F6,G2,H6,H8) * .217.3.8473.845.2148.1.237.17845..3...327841..4231.8.72.4.817633.7.241.881..37.4. * PAIR C2: 6,9 BLK 1 A1: 6,9,5 # reduction candidate for 6,9 A1: 6,9 # 15 pairs C3: 6,9,5 # reduction candidate for 6,9 C3: 6,9 => CTR * 5217.3.8473.845.2148.1.237517845..3..5327841..4231.8572945817633679241.881..37.4. * RESTART * PAIR G2: 6,9 COL G G4: 6,9,2 # reduction candidate for 6,9 G4: 2 => SOLVED * 621793584739845621485162379178459236963278415542316897254981763397624158816537942 * DURATION: 0:00:04.801220 START: 05:35:18.078699 END: 05:35:22.879919 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-081-base-pr-001.dot * REASONING * DIS # C3: 6,9 => CTR => C3: 5 * PRF C3: 5 # G4: 2 => SOL * STA C3: 5 + G4: 2 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 081 solution: 621793584739845621485162379178459236963278415542316897254981763397624158816537942 info: 1550 FNWX S8.f 46908 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 621793584739845621485162379178459236963278415542316897254981763397624158816537942 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 # A1: 6,9 => UNS * DIS # C3: 6,9 => CTR => C3: 5 * INC # C3: 5 => UNS * INC # C9: 6,9 => UNS * DIS # C9: 5 => CTR => C9: 6,9 * INC # A1: 6,9 => UNS * DIS # G1: 6,9 => CTR => G1: 5 * INC # G1: 5 => UNS * DIS # C3: 6,9 => CTR => C3: 5 * INC # C3: 5 => UNS * INC # I3: 6,9 => UNS * DIS # G1: 6,9 => CTR => G1: 5 * INC # G1: 5 => UNS * INC # I3: 6,9 => UNS * INC # G4: 6,9 => UNS * INC # G4: 2 => UNS * INC # G4: 6,9 => UNS * INC # I4: 6,9 => UNS * INC # A6: 6,9 => UNS * PRF # A6: 5 => SOL * INC # I5: 5,9 => UNS * DIS # I5: 6 => CTR => I5: 5,9 * INC # A6: 5,9 => UNS * DIS # A6: 6 => CTR => A6: 5,9 * PRF # B8: 5,9 => SOL * INC # B8: 6 => UNS * INC # C9: 5,9 => UNS * INC # B5: 5,9 => UNS * PRF # B5: 6 => SOL * INC # D8: 5,9 => UNS * PRF # D9: 5,9 => SOL * INC # D9: 6 => UNS * INC # G9: 5,9 => UNS * INC # I9: 5,9 => UNS * PRF # B8: 5,9 => SOL * INC # B8: 6 => UNS * INC # D8: 5,9 => UNS * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 6,9 => UNS * DIS # C3: 6,9 => CTR => C3: 5 * INC C3: 5 # G4: 6,9 => UNS * PRF C3: 5 # G4: 2 => SOL * STA C3: 5 + G4: 2 * CNT 4 HDP CHAINS / 4 HYP OPENED