Analysis of xx-top500-024-base.sdk
Contents
Original Sudoku
level: medium
position: 7..5....83......6.....2....67.3........4..2........1...42.1...........73......... initial
Autosolve
position: 7165349283251..7644..6273516713.2.4..534.12..2.4...13..427136..16.2...73.37....12 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F9: 8,9 => SOL * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * PRF # F9: 8,9 => SOL * PRF # A9: 5,8 => SOL * DIS # A9: 9 => CTR => A9: 5,8 * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * PRF # F8: 5 => SOL * PRF # G8: 8 => SOL * PRF # F9: 8,9 => SOL * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * CNT 13 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F9: 8,9 => SOL * STA F9: 8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7..5....83......6.....2....67.3........4..2........1...42.1...........73......... | initial |
| 7165349283251..7644..6273516713.2.4..534.12..2.4...13..427136..16.2...73.37....12 | autosolve |
| 716534928325198764498627351671382549953471286284956137842713695169245873537869412 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) B3: 8,9 C3: 8,9 E2: 8,9 F2: 8,9 A5: 8,9 B6: 8,9 E4: 8,9 E5: 6,7 D6: 8,9 F6: 5,6 G4: 5,8 I4: 5,9 H5: 8,9 I5: 6,7 I6: 6,7 A7: 5,8 C8: 8,9 E8: 4,5 D9: 8,9 H7: 8,9 I7: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E8,E9: 4.. / E8 = 4 => 22 pairs (_) / E9 = 4 => 22 pairs (_) G8,G9: 4.. / G8 = 4 => 22 pairs (_) / G9 = 4 => 22 pairs (_) E8,G8: 4.. / E8 = 4 => 22 pairs (_) / G8 = 4 => 22 pairs (_) E9,G9: 4.. / E9 = 4 => 22 pairs (_) / G9 = 4 => 22 pairs (_) E6,F6: 5.. / E6 = 5 => 17 pairs (_) / F6 = 5 => 24 pairs (_) G4,I4: 5.. / G4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) A7,A9: 5.. / A7 = 5 => 0 pairs (X) / A9 = 5 => 0 pairs (_) A7,I7: 5.. / A7 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) I4,I7: 5.. / I4 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) I5,I6: 6.. / I5 = 6 => 19 pairs (_) / I6 = 6 => 20 pairs (_) E9,F9: 6.. / E9 = 6 => 17 pairs (_) / F9 = 6 => 24 pairs (_) E5,I5: 6.. / E5 = 6 => 20 pairs (_) / I5 = 6 => 19 pairs (_) F6,F9: 6.. / F6 = 6 => 17 pairs (_) / F9 = 6 => 24 pairs (_) E5,E6: 7.. / E5 = 7 => 19 pairs (_) / E6 = 7 => 20 pairs (_) I5,I6: 7.. / I5 = 7 => 20 pairs (_) / I6 = 7 => 19 pairs (_) E5,I5: 7.. / E5 = 7 => 19 pairs (_) / I5 = 7 => 20 pairs (_) E6,I6: 7.. / E6 = 7 => 20 pairs (_) / I6 = 7 => 19 pairs (_) B3,C3: 8.. / B3 = 8 => 0 pairs (X) / C3 = 8 => 0 pairs (_) E2,F2: 8.. / E2 = 8 => 0 pairs (X) / F2 = 8 => 0 pairs (_) A5,B6: 8.. / A5 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) E4,D6: 8.. / E4 = 8 => 0 pairs (*) / D6 = 8 => 0 pairs (X) G4,H5: 8.. / G4 = 8 => 0 pairs (X) / H5 = 8 => 0 pairs (_) E4,G4: 8.. / E4 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) A5,H5: 8.. / A5 = 8 => 0 pairs (X) / H5 = 8 => 0 pairs (_) B6,D6: 8.. / B6 = 8 => 0 pairs (*) / D6 = 8 => 0 pairs (X) A7,H7: 8.. / A7 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) B3,B6: 8.. / B3 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) C3,C8: 8.. / C3 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) D6,D9: 8.. / D6 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) E2,E4: 8.. / E2 = 8 => 0 pairs (X) / E4 = 8 => 0 pairs (_) H5,H7: 8.. / H5 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) B3,C3: 9.. / B3 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) E2,F2: 9.. / E2 = 9 => 0 pairs (*) / F2 = 9 => 0 pairs (X) A5,B6: 9.. / A5 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) E4,D6: 9.. / E4 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) I4,H5: 9.. / I4 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) C8,A9: 9.. / C8 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) H7,I7: 9.. / H7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) E4,I4: 9.. / E4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) A5,H5: 9.. / A5 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) B6,D6: 9.. / B6 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) C8,F8: 9.. / C8 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) A5,A9: 9.. / A5 = 9 => 0 pairs (*) / A9 = 9 => 0 pairs (X) B3,B6: 9.. / B3 = 9 => 0 pairs (*) / B6 = 9 => 0 pairs (X) C3,C8: 9.. / C3 = 9 => 0 pairs (X) / C8 = 9 => 0 pairs (_) D6,D9: 9.. / D6 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) E2,E4: 9.. / E2 = 9 => 0 pairs (*) / E4 = 9 => 0 pairs (X) H5,H7: 9.. / H5 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) I4,I7: 9.. / I4 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) * DURATION: 0:01:50.502692 START: 03:24:24.304535 END: 03:26:14.807227 2017-05-04 * CP COUNT: (49) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B3,B6,C3,C8,D6,D9,E2,E4,E5,E8,F2,F6,G4,H5,H7,I4,I5,I6,I7) * 7165349283251..7644..6273516713.2.4..534.12..2.4...13..427136..16.2...73.37....12 * PAIR F2: 8,9 COL F F8: 8,9,5 # reduction candidate for 8,9 F8: 8,9 # 24 pairs F9: 8,9,5,6 # reduction candidate for 8,9 F9: 8,9 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 F9: 5,6 # 24 pairs * PAIR A5: 8,9 COL A A9: 8,9,5 # reduction candidate for 8,9 A9: 8,9 => CTR * 7165349283251..7644..6273516713928458534.129.2948..13.5427136891682.9.73.37....12 A9: 5 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 * PAIR E5: 6,7 BLK 5 E6: 6,7,5 # reduction candidate for 6,7 E6: 6,7 # 24 pairs E6: 5 # 17 pairs * PAIR F6: 5,6 BLK 5 E6: 5,6,7 # reduction candidate for 5,6 E6: 7 # 20 pairs E6: 5,6 # 19 pairs * PAIR F6: 5,6 COL F F9: 5,6,8,9 # reduction candidate for 5,6 F9: 8,9 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 F9: 5,6 # 24 pairs * PAIR G4: 5,8 COL G G8: 5,8,4 # reduction candidate for 5,8 G8: 5,8 # 22 pairs G9: 5,8,4 # reduction candidate for 5,8 G9: 5,8 # 22 pairs * PAIR I6: 6,7 ROW 6 E6: 6,7,5 # reduction candidate for 6,7 E6: 6,7 # 24 pairs E6: 5 # 17 pairs * PAIR A7: 5,8 BLK 7 A9: 5,8,9 # reduction candidate for 5,8 A9: 5,8 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 A9: 9 => CTR * 7165349283251..7644..6273516713.2.4..534.12..2.4...13.5427136891682.9.739378...12 * PAIR C8: 8,9 BLK 7 A9: 8,9,5 # reduction candidate for 8,9 A9: 8,9 => CTR * 7165349283251..7644..6273516713928458534.129.2948..13.5427136891682.9.73.37....12 A9: 5 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 * PAIR C8: 8,9 ROW 8 F8: 8,9,5 # reduction candidate for 8,9 F8: 5 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 F8: 8,9 # 24 pairs * PAIR E8: 4,5 BLK 8 E9: 4,5,6 # reduction candidate for 4,5 E9: 4,5 # 24 pairs E9: 6 # 17 pairs * PAIR E8: 4,5 ROW 8 G8: 4,5,8 # reduction candidate for 4,5 G8: 8 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 G8: 4,5 # 24 pairs * PAIR D9: 8,9 BLK 8 F8: 8,9,5 # reduction candidate for 8,9 F8: 8,9 # 24 pairs F9: 8,9,5,6 # reduction candidate for 8,9 F9: 8,9 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 F9: 5,6 # 24 pairs * PAIR D9: 8,9 ROW 9 A9: 8,9,5 # reduction candidate for 8,9 A9: 8,9 => CTR * 7165349283251..7644..6273516713928458534.129.2948..13.5427136891682.9.73.37....12 A9: 5 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-024-base-pr-000.dot * REASONING * PRF # F9: 8,9 => SOL * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * PRF # F9: 8,9 => SOL * PRF # A9: 5,8 => SOL * DIS # A9: 9 => CTR => A9: 5,8 * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * PRF # F8: 5 => SOL * PRF # G8: 8 => SOL * PRF # F9: 8,9 => SOL * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * CNT 13 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A7,B3,B6,C3,C8,D6,D9,E2,E4,E5,E8,F2,F6,G4,H5,H7,I4,I5,I6,I7) * 7165349283251..7644..6273516713.2.4..534.12..2.4...13..427136..16.2...73.37....12 * PAIR F2: 8,9 COL F F8: 8,9,5 # reduction candidate for 8,9 F8: 8,9 # 24 pairs F9: 8,9,5,6 # reduction candidate for 8,9 F9: 8,9 => SOLVED * 716534928325198764498627351671382549953471286284956137842713695169245873537869412 * DURATION: 0:00:03.758607 START: 03:26:58.108536 END: 03:27:01.867143 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-024-base-pr-001.dot * REASONING * PRF # F9: 8,9 => SOL * STA F9: 8,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 024 solution: 716534928325198764498627351671382549953471286284956137842713695169245873537869412 info: 1321 FNBTHWX S8.f 37008 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 716534928325198764498627351671382549953471286284956137842713695169245873537869412 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 # F8: 8,9 => UNS * PRF # F9: 8,9 => SOL * INC # F9: 5,6 => UNS * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * INC # E6: 6,7 => UNS * INC # E6: 5 => UNS * INC # E6: 5,6 => UNS * INC # E6: 7 => UNS * INC # F9: 5,6 => UNS * PRF # F9: 8,9 => SOL * INC # G8: 5,8 => UNS * INC # G9: 5,8 => UNS * INC # E6: 6,7 => UNS * INC # E6: 5 => UNS * PRF # A9: 5,8 => SOL * DIS # A9: 9 => CTR => A9: 5,8 * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * INC # F8: 8,9 => UNS * PRF # F8: 5 => SOL * INC # E9: 4,5 => UNS * INC # E9: 6 => UNS * INC # G8: 4,5 => UNS * PRF # G8: 8 => SOL * INC # F8: 8,9 => UNS * PRF # F9: 8,9 => SOL * INC # F9: 5,6 => UNS * DIS # A9: 8,9 => CTR => A9: 5 * PRF # A9: 5 => SOL * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F8: 8,9 => UNS * PRF # F9: 8,9 => SOL * STA F9: 8,9 * CNT 2 HDP CHAINS / 2 HYP OPENED