Analysis of xx-top500-126-base.sdk
Contents
Original Sudoku
level: medium
position: 2..14.....7.....3...........8...3.....3.....7....6.1..6.5...2..1..7............8. initial
Autosolve
position: 239146758571289634864375912786.13.2..135..867.528671.36.5.382711.875.3.63.76.1.8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B8: 4,9 => CTR => B8: 2 * PRF # B8: 2 => SOL * PRF # B9: 4,9 => SOL * DIS # B9: 2 => CTR => B9: 4,9 * PRF # B8: 2,4 => SOL * DIS # B8: 9 => CTR => B8: 2,4 * PRF # B9: 2,9 => SOL * DIS # B9: 4 => CTR => B9: 2,9 * DIS # B8: 4,9 => CTR => B8: 2 * PRF # B8: 2 => SOL * CNT 10 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B8: 4,9 => CTR => B8: 2 * PRF B8: 2 => SOL * STA B8: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2..14.....7.....3...........8...3.....3.....7....6.1..6.5...2..1..7............8. | initial |
| 239146758571289634864375912786.13.2..135..867.528671.36.5.382711.875.3.63.76.1.8. | autosolve |
| 239146758571289634864375912786413529413592867952867143645938271128754396397621485 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A5: 4,9 A6: 4,9 D4: 4,9 E5: 2,9 F5: 2,4 G4: 4,5 I4: 5,9 H6: 4,9 B7: 4,9 D7: 4,9 F8: 2,4 E9: 2,9 H8: 4,9 G9: 4,5 I9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,F5: 2.. / E5 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) B8,B9: 2.. / B8 = 2 => 0 pairs (*) / B9 = 2 => 0 pairs (X) F8,E9: 2.. / F8 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) B8,F8: 2.. / B8 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) B9,E9: 2.. / B9 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) E5,E9: 2.. / E5 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) F5,F8: 2.. / F5 = 2 => 0 pairs (*) / F8 = 2 => 0 pairs (X) A5,A6: 4.. / A5 = 4 => 0 pairs (*) / A6 = 4 => 0 pairs (X) D4,F5: 4.. / D4 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) G4,H6: 4.. / G4 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) D7,F8: 4.. / D7 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) H8,G9: 4.. / H8 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) D4,G4: 4.. / D4 = 4 => 0 pairs (*) / G4 = 4 => 0 pairs (X) A5,F5: 4.. / A5 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) A6,H6: 4.. / A6 = 4 => 0 pairs (X) / H6 = 4 => 0 pairs (_) B7,D7: 4.. / B7 = 4 => 0 pairs (*) / D7 = 4 => 0 pairs (X) B9,G9: 4.. / B9 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) D4,D7: 4.. / D4 = 4 => 0 pairs (*) / D7 = 4 => 0 pairs (X) F5,F8: 4.. / F5 = 4 => 0 pairs (X) / F8 = 4 => 0 pairs (_) G4,G9: 4.. / G4 = 4 => 0 pairs (X) / G9 = 4 => 0 pairs (_) H6,H8: 4.. / H6 = 4 => 0 pairs (*) / H8 = 4 => 0 pairs (X) G4,I4: 5.. / G4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) G9,I9: 5.. / G9 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) G4,G9: 5.. / G4 = 5 => 0 pairs (*) / G9 = 5 => 0 pairs (X) I4,I9: 5.. / I4 = 5 => 0 pairs (X) / I9 = 5 => 0 pairs (_) A5,A6: 9.. / A5 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) D4,E5: 9.. / D4 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) I4,H6: 9.. / I4 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) D7,E9: 9.. / D7 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) H8,I9: 9.. / H8 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) D4,I4: 9.. / D4 = 9 => 0 pairs (X) / I4 = 9 => 0 pairs (_) A5,E5: 9.. / A5 = 9 => 0 pairs (X) / E5 = 9 => 0 pairs (_) A6,H6: 9.. / A6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) B7,D7: 9.. / B7 = 9 => 0 pairs (X) / D7 = 9 => 0 pairs (_) B8,H8: 9.. / B8 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) D4,D7: 9.. / D4 = 9 => 0 pairs (X) / D7 = 9 => 0 pairs (_) E5,E9: 9.. / E5 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) H6,H8: 9.. / H6 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) I4,I9: 9.. / I4 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) * DURATION: 0:01:05.446450 START: 07:04:26.659374 END: 07:05:32.105824 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B7,D4,D7,E5,E9,F5,F8,G4,G9,H6,H8,I4,I9) * 239146758571289634864375912786.13.2..135..867.528671.36.5.382711.875.3.63.76.1.8. * PAIR B7: 4,9 BLK 7 B8: 4,9,2 # reduction candidate for 4,9 B8: 4,9 => CTR * 239146758571289634864375912786.13.2..135..867.528671.36.5.382711.87523.6327691485 B8: 2 => SOLVED * 239146758571289634864375912786413529413592867952867143645938271128754396397621485 B9: 4,9,2 # reduction candidate for 4,9 B9: 4,9 => SOLVED * 239146758571289634864375912786413529413592867952867143645938271128754396397621485 B9: 2 => CTR * 239146758571289634864375912786.13.2..135..867.528671.36.5.382711.875.3.6327691485 * PAIR F8: 2,4 ROW 8 B8: 2,4,9 # reduction candidate for 2,4 B8: 2,4 => SOLVED * 239146758571289634864375912786413529413592867952867143645938271128754396397621485 B8: 9 => CTR * 239146758571289634864375912786.13.2..135..867.528671.36.5.382711987523463.76.1.8. * PAIR E9: 2,9 ROW 9 B9: 2,9,4 # reduction candidate for 2,9 B9: 2,9 => SOLVED * 239146758571289634864375912786413529413592867952867143645938271128754396397621485 B9: 4 => CTR * 239146758571289634864375912786.13.2..135..867.528671.36.5.382711287543963476.1.8. * PAIR H8: 4,9 ROW 8 B8: 4,9,2 # reduction candidate for 4,9 B8: 4,9 => CTR * 239146758571289634864375912786.13.2..135..867.528671.36.5.382711.87523.6327691485 B8: 2 => SOLVED * 239146758571289634864375912786413529413592867952867143645938271128754396397621485 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-126-base-pr-000.dot * REASONING * DIS # B8: 4,9 => CTR => B8: 2 * PRF # B8: 2 => SOL * PRF # B9: 4,9 => SOL * DIS # B9: 2 => CTR => B9: 4,9 * PRF # B8: 2,4 => SOL * DIS # B8: 9 => CTR => B8: 2,4 * PRF # B9: 2,9 => SOL * DIS # B9: 4 => CTR => B9: 2,9 * DIS # B8: 4,9 => CTR => B8: 2 * PRF # B8: 2 => SOL * CNT 10 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B7,D4,D7,E5,E9,F5,F8,G4,G9,H6,H8,I4,I9) * 239146758571289634864375912786.13.2..135..867.528671.36.5.382711.875.3.63.76.1.8. * PAIR B7: 4,9 BLK 7 B8: 4,9,2 # reduction candidate for 4,9 B8: 4,9 => CTR * 239146758571289634864375912786.13.2..135..867.528671.36.5.382711.87523.6327691485 B8: 2 => SOLVED * 239146758571289634864375912786413529413592867952867143645938271128754396397621485 * DURATION: 0:00:01.824918 START: 07:05:44.372005 END: 07:05:46.196923 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-126-base-pr-001.dot * REASONING * DIS # B8: 4,9 => CTR => B8: 2 * PRF B8: 2 => SOL * STA B8: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 126 solution: 239146758571289634864375912786413529413592867952867143645938271128754396397621485 info: 1808 FNWX S8.f 44689 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 239146758571289634864375912786413529413592867952867143645938271128754396397621485 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 # B8: 4,9 => CTR => B8: 2 * PRF # B8: 2 => SOL * PRF # B9: 4,9 => SOL * DIS # B9: 2 => CTR => B9: 4,9 * PRF # B8: 2,4 => SOL * DIS # B8: 9 => CTR => B8: 2,4 * PRF # B9: 2,9 => SOL * DIS # B9: 4 => CTR => B9: 2,9 * DIS # B8: 4,9 => CTR => B8: 2 * PRF # B8: 2 => SOL * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B8: 4,9 => CTR => B8: 2 * PRF B8: 2 => SOL * STA B8: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED