Analysis of xx-top500-350-base.sdk
Contents
Original Sudoku
level: medium
position: 69...2..........31...........314....2.....6.....3........71..4.86....5........... initial
Autosolve
position: 691.324.....6.493143.971.6.9.314672.214..7693..63291.43.971..4686.49351.14.26.3.9 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B2: 5,7 => SOL * DIS # B2: 2 => CTR => B2: 5,7 * DIS # C2: 5,8 => CTR => C2: 2 * PRF # C2: 2 => SOL * PRF # I3: 5,8 => SOL * DIS # I3: 2 => CTR => I3: 5,8 * PRF # H1: 5,8 => SOL * DIS # H1: 7 => CTR => H1: 5,8 * DIS # I1: 5,8 => CTR => I1: 7 * PRF # I1: 7 => SOL * DIS # C2: 5,8 => CTR => C2: 2 * PRF # C2: 2 => SOL * DIS # I3: 2,8 => CTR => I3: 5 * PRF # I3: 5 => SOL * PRF # B6: 5,8 => SOL * DIS # B6: 7 => CTR => B6: 5,8 * DIS # B6: 5,7 => CTR => B6: 8 * PRF # B6: 8 => SOL * DIS # I1: 5,8 => CTR => I1: 7 * PRF # I1: 7 => SOL * PRF # I3: 5,8 => SOL * DIS # I3: 2 => CTR => I3: 5,8 * PRF # B6: 5,8 => SOL * DIS # B6: 7 => CTR => B6: 5,8 * PRF # H1: 5,8 => SOL * DIS # H1: 7 => CTR => H1: 5,8 * DIS # B2: 2,5 => CTR => B2: 7 * PRF # B2: 7 => SOL * PRF # H1: 7,8 => SOL * DIS # H1: 5 => CTR => H1: 7,8 * CNT 30 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 # B2: 5,7 => SOL * STA B2: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 69...2..........31...........314....2.....6.....3........71..4.86....5........... | initial |
| 691.324.....6.493143.971.6.9.314672.214..7693..63291.43.971..4686.49351.14.26.3.9 | autosolve |
| 691532487572684931438971265953146728214857693786329154329715846867493512145268379 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A2: 5,7 C3: 5,8 D1: 5,8 E2: 5,8 G3: 2,8 B4: 5,8 A6: 5,7 D5: 5,8 E5: 5,8 I4: 5,8 H6: 5,8 B7: 2,5 C8: 2,7 C9: 5,7 F7: 5,8 F9: 5,8 G7: 2,8 I8: 2,7 H9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 2.. / B2 = 2 => 0 pairs (X) / C2 = 2 => 0 pairs (_) G3,I3: 2.. / G3 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) B7,C8: 2.. / B7 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) G7,I8: 2.. / G7 = 2 => 0 pairs (X) / I8 = 2 => 0 pairs (_) B7,G7: 2.. / B7 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) C8,I8: 2.. / C8 = 2 => 0 pairs (X) / I8 = 2 => 0 pairs (_) B2,B7: 2.. / B2 = 2 => 0 pairs (X) / B7 = 2 => 0 pairs (_) C2,C8: 2.. / C2 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) G3,G7: 2.. / G3 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) I3,I8: 2.. / I3 = 2 => 0 pairs (X) / I8 = 2 => 0 pairs (_) D1,E2: 5.. / D1 = 5 => 0 pairs (*) / E2 = 5 => 0 pairs (X) D5,E5: 5.. / D5 = 5 => 0 pairs (X) / E5 = 5 => 0 pairs (_) I4,H6: 5.. / I4 = 5 => 0 pairs (X) / H6 = 5 => 0 pairs (_) B7,C9: 5.. / B7 = 5 => 0 pairs (X) / C9 = 5 => 0 pairs (_) F7,F9: 5.. / F7 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) C3,I3: 5.. / C3 = 5 => 0 pairs (X) / I3 = 5 => 0 pairs (_) B4,I4: 5.. / B4 = 5 => 0 pairs (*) / I4 = 5 => 0 pairs (X) B7,F7: 5.. / B7 = 5 => 0 pairs (X) / F7 = 5 => 0 pairs (_) C9,F9: 5.. / C9 = 5 => 0 pairs (*) / F9 = 5 => 0 pairs (X) A2,A6: 5.. / A2 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) D1,D5: 5.. / D1 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) E2,E5: 5.. / E2 = 5 => 0 pairs (X) / E5 = 5 => 0 pairs (_) H1,H6: 5.. / H1 = 5 => 0 pairs (X) / H6 = 5 => 0 pairs (_) A2,B2: 7.. / A2 = 7 => 0 pairs (X) / B2 = 7 => 0 pairs (_) H1,I1: 7.. / H1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) A6,B6: 7.. / A6 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) C8,C9: 7.. / C8 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) I8,H9: 7.. / I8 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) C8,I8: 7.. / C8 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) C9,H9: 7.. / C9 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) A2,A6: 7.. / A2 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) B2,B6: 7.. / B2 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) H1,H9: 7.. / H1 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) I1,I8: 7.. / I1 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) C2,C3: 8.. / C2 = 8 => 0 pairs (X) / C3 = 8 => 0 pairs (_) D1,E2: 8.. / D1 = 8 => 0 pairs (X) / E2 = 8 => 0 pairs (_) B4,B6: 8.. / B4 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) D5,E5: 8.. / D5 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) I4,H6: 8.. / I4 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) F7,F9: 8.. / F7 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) G7,H9: 8.. / G7 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) C2,E2: 8.. / C2 = 8 => 0 pairs (X) / E2 = 8 => 0 pairs (_) B4,I4: 8.. / B4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) B6,H6: 8.. / B6 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) F7,G7: 8.. / F7 = 8 => 0 pairs (X) / G7 = 8 => 0 pairs (_) F9,H9: 8.. / F9 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) D1,D5: 8.. / D1 = 8 => 0 pairs (X) / D5 = 8 => 0 pairs (_) E2,E5: 8.. / E2 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) G3,G7: 8.. / G3 = 8 => 0 pairs (X) / G7 = 8 => 0 pairs (_) * DURATION: 0:01:39.166938 START: 14:42:00.109950 END: 14:43:39.276888 2017-05-04 * CP COUNT: (49) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B4,B7,C3,C8,C9,D1,D5,E2,E5,F7,F9,G3,G7,H6,H9,I4,I8) * 691.324.....6.493143.971.6.9.314672.214..7693..63291.43.971..4686.49351.14.26.3.9 * PAIR A2: 5,7 BLK 1 B2: 5,7,2 # reduction candidate for 5,7 B2: 5,7 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 B2: 2 => CTR * 691.324..72.6.493143.971.6.9.314672.214..769357632918435971..4686.49351.14.26.3.9 * PAIR C3: 5,8 BLK 1 C2: 5,8,2 # reduction candidate for 5,8 C2: 5,8 => CTR * 691.324...2.6.493143.971.6.9.314672.214..7693.7632918435971..4686.49351.14.26.3.9 C2: 2 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 * PAIR C3: 5,8 ROW 3 I3: 5,8,2 # reduction candidate for 5,8 I3: 5,8 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 I3: 2 => CTR * 691.324.....6.49314359718629.3146728214..76935.63291.43.971..4686.49351.14.26.3.9 * PAIR D1: 5,8 ROW 1 H1: 5,8,7 # reduction candidate for 5,8 H1: 5,8 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 H1: 7 => CTR * 691.3247.5726.493143.971.6.9.314672.214..7693..63291543.971..4686.493517147265389 I1: 5,8,7 # reduction candidate for 5,8 I1: 5,8 => CTR * 691.3247.5726.493143.971.6.9.314672.214..7693..63291543.971..4686.493517147265389 I1: 7 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 * PAIR E2: 5,8 ROW 2 C2: 5,8,2 # reduction candidate for 5,8 C2: 5,8 => CTR * 691.324...2.6.493143.971.6.9.314672.214..7693.7632918435971..4686.49351.14.26.3.9 C2: 2 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 * PAIR G3: 2,8 BLK 3 I3: 2,8,5 # reduction candidate for 2,8 I3: 2,8 => CTR * 691.324.....6.4931435971.6.9.314672.214..7693576329184359718.4686.49351.14.26.3.9 I3: 5 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 * PAIR B4: 5,8 BLK 4 B6: 5,8,7 # reduction candidate for 5,8 B6: 5,8 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 B6: 7 => CTR * 691.324577.26.493143.971.6.983146725214..76935763291843.971.84686.49351214.268379 * PAIR A6: 5,7 BLK 4 B6: 5,7,8 # reduction candidate for 5,7 B6: 5,7 => CTR * 691.32457..26.493143.971.6.983146725214..7693..63291843.971.84686.49351214.268379 B6: 8 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 * PAIR I4: 5,8 COL I I1: 5,8,7 # reduction candidate for 5,8 I1: 5,8 => CTR * 691.3247.5726.493143.971.6.9.314672.214..7693..63291543.971..4686.493517147265389 I1: 7 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 I3: 5,8,2 # reduction candidate for 5,8 I3: 5,8 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 I3: 2 => CTR * 691.324.....6.49314359718629.3146728214..76935.63291.43.971..4686.49351.14.26.3.9 * PAIR H6: 5,8 ROW 6 B6: 5,8,7 # reduction candidate for 5,8 B6: 5,8 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 B6: 7 => CTR * 691.324577.26.493143.971.6.983146725214..76935763291843.971.84686.49351214.268379 * PAIR H6: 5,8 COL H H1: 5,8,7 # reduction candidate for 5,8 H1: 5,8 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 H1: 7 => CTR * 691.3247.5726.493143.971.6.9.314672.214..7693..63291543.971..4686.493517147265389 * PAIR B7: 2,5 COL B B2: 2,5,7 # reduction candidate for 2,5 B2: 2,5 => CTR * 691.324577.26.493143.971.6.9.314672.214..76935763291843.971.84686.49351214.268379 B2: 7 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 * PAIR H9: 7,8 COL H H1: 7,8,5 # reduction candidate for 7,8 H1: 7,8 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 H1: 5 => CTR * 691.32457...654931435971.6.9.3146725214587693576329184359718.4686.49351.14.26.3.9 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-350-base-pr-000.dot * REASONING * PRF # B2: 5,7 => SOL * DIS # B2: 2 => CTR => B2: 5,7 * DIS # C2: 5,8 => CTR => C2: 2 * PRF # C2: 2 => SOL * PRF # I3: 5,8 => SOL * DIS # I3: 2 => CTR => I3: 5,8 * PRF # H1: 5,8 => SOL * DIS # H1: 7 => CTR => H1: 5,8 * DIS # I1: 5,8 => CTR => I1: 7 * PRF # I1: 7 => SOL * DIS # C2: 5,8 => CTR => C2: 2 * PRF # C2: 2 => SOL * DIS # I3: 2,8 => CTR => I3: 5 * PRF # I3: 5 => SOL * PRF # B6: 5,8 => SOL * DIS # B6: 7 => CTR => B6: 5,8 * DIS # B6: 5,7 => CTR => B6: 8 * PRF # B6: 8 => SOL * DIS # I1: 5,8 => CTR => I1: 7 * PRF # I1: 7 => SOL * PRF # I3: 5,8 => SOL * DIS # I3: 2 => CTR => I3: 5,8 * PRF # B6: 5,8 => SOL * DIS # B6: 7 => CTR => B6: 5,8 * PRF # H1: 5,8 => SOL * DIS # H1: 7 => CTR => H1: 5,8 * DIS # B2: 2,5 => CTR => B2: 7 * PRF # B2: 7 => SOL * PRF # H1: 7,8 => SOL * DIS # H1: 5 => CTR => H1: 7,8 * CNT 30 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,B4,B7,C3,C8,C9,D1,D5,E2,E5,F7,F9,G3,G7,H6,H9,I4,I8) * 691.324.....6.493143.971.6.9.314672.214..7693..63291.43.971..4686.49351.14.26.3.9 * PAIR A2: 5,7 BLK 1 B2: 5,7,2 # reduction candidate for 5,7 B2: 5,7 => SOLVED * 691532487572684931438971265953146728214857693786329154329715846867493512145268379 * DURATION: 0:00:02.179395 START: 14:44:19.605936 END: 14:44:21.785331 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-350-base-pr-001.dot * REASONING * PRF # B2: 5,7 => SOL * STA B2: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 350 solution: 691532487572684931438971265953146728214857693786329154329715846867493512145268379 info: 4882 FNBWY S8.f 36162 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 691532487572684931438971265953146728214857693786329154329715846867493512145268379 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:
* PRF # B2: 5,7 => SOL * DIS # B2: 2 => CTR => B2: 5,7 * DIS # C2: 5,8 => CTR => C2: 2 * PRF # C2: 2 => SOL * PRF # I3: 5,8 => SOL * DIS # I3: 2 => CTR => I3: 5,8 * PRF # H1: 5,8 => SOL * DIS # H1: 7 => CTR => H1: 5,8 * DIS # I1: 5,8 => CTR => I1: 7 * PRF # I1: 7 => SOL * DIS # C2: 5,8 => CTR => C2: 2 * PRF # C2: 2 => SOL * DIS # I3: 2,8 => CTR => I3: 5 * PRF # I3: 5 => SOL * PRF # B6: 5,8 => SOL * DIS # B6: 7 => CTR => B6: 5,8 * DIS # B6: 5,7 => CTR => B6: 8 * PRF # B6: 8 => SOL * DIS # I1: 5,8 => CTR => I1: 7 * PRF # I1: 7 => SOL * PRF # I3: 5,8 => SOL * DIS # I3: 2 => CTR => I3: 5,8 * PRF # B6: 5,8 => SOL * DIS # B6: 7 => CTR => B6: 5,8 * PRF # H1: 5,8 => SOL * DIS # H1: 7 => CTR => H1: 5,8 * DIS # B2: 2,5 => CTR => B2: 7 * PRF # B2: 7 => SOL * PRF # H1: 7,8 => SOL * DIS # H1: 5 => CTR => H1: 7,8 * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B2: 5,7 => SOL * STA B2: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED