Analysis of xx-top500-136-base.sdk
Contents
Original Sudoku
level: medium
position: ...12....6.....9.....3.......1....3.....8.6...4...9........75.13..4............2. initial
Autosolve
position: .3912.4..6128749534.839.1.2.61.42.3929..83614.436192.598623754132.4.1.9.1.49.832. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A4: 5,7 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # H1: 7,8 => SOL * DIS # H1: 6 => CTR => H1: 7,8 * DIS # I8: 7,8 => CTR => I8: 6 * PRF # I8: 6 => SOL * PRF # H1: 6,7 => SOL * DIS # H1: 8 => CTR => H1: 6,7 * DIS # A4: 5,7 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # A4: 7,8 => SOL * DIS # A4: 5 => CTR => A4: 7,8 * DIS # A4: 5,7 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # A4: 7,8 => SOL * DIS # A4: 5 => CTR => A4: 7,8 * PRF # H1: 7,8 => SOL * DIS # H1: 6 => CTR => H1: 7,8 * DIS # I8: 7,8 => CTR => I8: 6 * PRF # I8: 6 => SOL * PRF # I8: 6,7 => SOL * DIS # I8: 8 => CTR => I8: 6,7 * CNT 22 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 # A4: 5,7 => CTR => A4: 8 * PRF A4: 8 => SOL * STA A4: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...12....6.....9.....3.......1....3.....8.6...4...9........75.13..4............2. | initial |
| .3912.4..6128749534.839.1.2.61.42.3929..83614.436192.598623754132.4.1.9.1.49.832. | autosolve |
| 539126478612874953478395162861542739295783614743619285986237541327451896154968327 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 5,7 B3: 5,7 F1: 5,6 F3: 5,6 I1: 7,8 H3: 6,7 C5: 5,7 A6: 7,8 D4: 5,7 D5: 5,7 G4: 7,8 H6: 7,8 C8: 5,7 B9: 5,7 E8: 5,6 E9: 5,6 G8: 7,8 I9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B3: 5.. / A1 = 5 => 0 pairs (*) / B3 = 5 => 0 pairs (X) F1,F3: 5.. / F1 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) A4,C5: 5.. / A4 = 5 => 0 pairs (X) / C5 = 5 => 0 pairs (_) D4,D5: 5.. / D4 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) C8,B9: 5.. / C8 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) E8,E9: 5.. / E8 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) A1,F1: 5.. / A1 = 5 => 0 pairs (*) / F1 = 5 => 0 pairs (X) B3,F3: 5.. / B3 = 5 => 0 pairs (X) / F3 = 5 => 0 pairs (_) A4,D4: 5.. / A4 = 5 => 0 pairs (X) / D4 = 5 => 0 pairs (_) C5,D5: 5.. / C5 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) C8,E8: 5.. / C8 = 5 => 0 pairs (X) / E8 = 5 => 0 pairs (_) B9,E9: 5.. / B9 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) A1,A4: 5.. / A1 = 5 => 0 pairs (*) / A4 = 5 => 0 pairs (X) B3,B9: 5.. / B3 = 5 => 0 pairs (X) / B9 = 5 => 0 pairs (_) C5,C8: 5.. / C5 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) F1,F3: 6.. / F1 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) H1,H3: 6.. / H1 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) E8,E9: 6.. / E8 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) I8,I9: 6.. / I8 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) F1,H1: 6.. / F1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) F3,H3: 6.. / F3 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) E8,I8: 6.. / E8 = 6 => 0 pairs (X) / I8 = 6 => 0 pairs (_) E9,I9: 6.. / E9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) A1,B3: 7.. / A1 = 7 => 0 pairs (X) / B3 = 7 => 0 pairs (_) D4,D5: 7.. / D4 = 7 => 0 pairs (X) / D5 = 7 => 0 pairs (_) G4,H6: 7.. / G4 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) C8,B9: 7.. / C8 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) B3,H3: 7.. / B3 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) C5,D5: 7.. / C5 = 7 => 0 pairs (X) / D5 = 7 => 0 pairs (_) A6,H6: 7.. / A6 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) B9,I9: 7.. / B9 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) B3,B9: 7.. / B3 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) C5,C8: 7.. / C5 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) G4,G8: 7.. / G4 = 7 => 0 pairs (*) / G8 = 7 => 0 pairs (X) H1,I1: 8.. / H1 = 8 => 0 pairs (X) / I1 = 8 => 0 pairs (_) A4,A6: 8.. / A4 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) G4,H6: 8.. / G4 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) G8,I8: 8.. / G8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) A4,G4: 8.. / A4 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) A6,H6: 8.. / A6 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) G4,G8: 8.. / G4 = 8 => 0 pairs (X) / G8 = 8 => 0 pairs (_) H1,H6: 8.. / H1 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) I1,I8: 8.. / I1 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) * DURATION: 0:01:13.361604 START: 07:23:21.746365 END: 07:24:35.107969 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B3,B9,C5,C8,D4,D5,E8,E9,F1,F3,G4,G8,H3,H6,I1,I9) * .3912.4..6128749534.839.1.2.61.42.3929..83614.436192.598623754132.4.1.9.1.49.832. * PAIR A1: 5,7 COL A A4: 5,7,8 # reduction candidate for 5,7 A4: 5,7 => CTR * .3912.4..6128749534.839.1.2.61.4283929..8361484361927598623754132.4.1798174958326 A4: 8 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 * PAIR I1: 7,8 BLK 3 H1: 7,8,6 # reduction candidate for 7,8 H1: 7,8 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 H1: 6 => CTR * .3912.4686128749534.8396172.61.4273929.7836147436192859862375413274518961549.832. * PAIR I1: 7,8 COL I I8: 7,8,6 # reduction candidate for 7,8 I8: 7,8 => CTR * .3912.4..612874953458396172561742.3929..83614.436192.598623754132.461.9.1.4958326 I8: 6 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 * PAIR H3: 6,7 BLK 3 H1: 6,7,8 # reduction candidate for 6,7 H1: 6,7 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 H1: 8 => CTR * .39126487612874953478395162.61.4283929..836148436192759862375413274.1.9.1.49.832. * PAIR C5: 5,7 BLK 4 A4: 5,7,8 # reduction candidate for 5,7 A4: 5,7 => CTR * .3912.4..6128749534.839.1.2.61.4283929..8361484361927598623754132.4.1798174958326 A4: 8 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 * PAIR A6: 7,8 BLK 4 A4: 7,8,5 # reduction candidate for 7,8 A4: 7,8 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 A4: 5 => CTR * .3912.4..6128749534.839.1.25617428392975836148436192759862375413254617981749.832. * PAIR D4: 5,7 ROW 4 A4: 5,7,8 # reduction candidate for 5,7 A4: 5,7 => CTR * .3912.4..6128749534.839.1.2.61.4283929..8361484361927598623754132.4.1798174958326 A4: 8 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 * PAIR G4: 7,8 ROW 4 A4: 7,8,5 # reduction candidate for 7,8 A4: 7,8 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 A4: 5 => CTR * .3912.4..6128749534.839.1.25617428392975836148436192759862375413254617981749.832. * PAIR H6: 7,8 COL H H1: 7,8,6 # reduction candidate for 7,8 H1: 7,8 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 H1: 6 => CTR * .3912.4686128749534.8396172.61.4273929.7836147436192859862375413274518961549.832. * PAIR G8: 7,8 BLK 9 I8: 7,8,6 # reduction candidate for 7,8 I8: 7,8 => CTR * .3912.4..612874953458396172561742.3929..83614.436192.598623754132.461.9.1.4958326 I8: 6 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 * PAIR I9: 6,7 BLK 9 I8: 6,7,8 # reduction candidate for 6,7 I8: 6,7 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 I8: 8 => CTR * .3912.4876128749534.839.1.2.61.42.3929..83614.436192.598623754132.461.981.4958326 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-136-base-pr-000.dot * REASONING * DIS # A4: 5,7 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # H1: 7,8 => SOL * DIS # H1: 6 => CTR => H1: 7,8 * DIS # I8: 7,8 => CTR => I8: 6 * PRF # I8: 6 => SOL * PRF # H1: 6,7 => SOL * DIS # H1: 8 => CTR => H1: 6,7 * DIS # A4: 5,7 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # A4: 7,8 => SOL * DIS # A4: 5 => CTR => A4: 7,8 * DIS # A4: 5,7 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # A4: 7,8 => SOL * DIS # A4: 5 => CTR => A4: 7,8 * PRF # H1: 7,8 => SOL * DIS # H1: 6 => CTR => H1: 7,8 * DIS # I8: 7,8 => CTR => I8: 6 * PRF # I8: 6 => SOL * PRF # I8: 6,7 => SOL * DIS # I8: 8 => CTR => I8: 6,7 * CNT 22 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B3,B9,C5,C8,D4,D5,E8,E9,F1,F3,G4,G8,H3,H6,I1,I9) * .3912.4..6128749534.839.1.2.61.42.3929..83614.436192.598623754132.4.1.9.1.49.832. * PAIR A1: 5,7 COL A A4: 5,7,8 # reduction candidate for 5,7 A4: 5,7 => CTR * .3912.4..6128749534.839.1.2.61.4283929..8361484361927598623754132.4.1798174958326 A4: 8 => SOLVED * 539126478612874953478395162861542739295783614743619285986237541327451896154968327 * DURATION: 0:00:02.916924 START: 07:25:01.697243 END: 07:25:04.614167 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-136-base-pr-001.dot * REASONING * DIS # A4: 5,7 => CTR => A4: 8 * PRF A4: 8 => SOL * STA A4: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 136 solution: 539126478612874953478395162861542739295783614743619285986237541327451896154968327 info: 1812 FNBWX S8.f 40956 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 539126478612874953478395162861542739295783614743619285986237541327451896154968327 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:
* DIS # A4: 5,7 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # H1: 7,8 => SOL * DIS # H1: 6 => CTR => H1: 7,8 * DIS # I8: 7,8 => CTR => I8: 6 * PRF # I8: 6 => SOL * PRF # H1: 6,7 => SOL * DIS # H1: 8 => CTR => H1: 6,7 * DIS # A4: 5,7 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # A4: 7,8 => SOL * DIS # A4: 5 => CTR => A4: 7,8 * DIS # A4: 5,7 => CTR => A4: 8 * PRF # A4: 8 => SOL * PRF # A4: 7,8 => SOL * DIS # A4: 5 => CTR => A4: 7,8 * PRF # H1: 7,8 => SOL * DIS # H1: 6 => CTR => H1: 7,8 * DIS # I8: 7,8 => CTR => I8: 6 * PRF # I8: 6 => SOL * PRF # I8: 6,7 => SOL * DIS # I8: 8 => CTR => I8: 6,7 * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A4: 5,7 => CTR => A4: 8 * PRF A4: 8 => SOL * STA A4: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED