Analysis of xx-top500-301-base.sdk
Contents
Original Sudoku
level: medium
position: 5.3...2.....41...7.........64.7......8.....1.......3.....1...4.2...3.........5... initial
Autosolve
position: 513..72.482.41.53747.3521..6417.3.2538752.41.952.4137.7351.8.422.8.347511.4275..3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H3: 6,9 => SOL * DIS # H3: 8 => CTR => H3: 6,9 * PRF # D1: 6,9 => SOL * DIS # D1: 8 => CTR => D1: 6,9 * DIS # E1: 6,9 => CTR => E1: 8 * PRF # E1: 8 => SOL * PRF # H3: 6,9 => SOL * DIS # H3: 8 => CTR => H3: 6,9 * PRF # D1: 6,9 => SOL * DIS # D1: 8 => CTR => D1: 6,9 * DIS # E1: 6,9 => CTR => E1: 8 * PRF # E1: 8 => SOL * DIS # H3: 8,9 => CTR => H3: 6 * PRF # H3: 6 => SOL * PRF # E1: 8,9 => SOL * DIS # E1: 6 => CTR => E1: 8,9 * PRF # D1: 6,8 => SOL * DIS # D1: 9 => CTR => D1: 6,8 * DIS # G9: 8,9 => CTR => G9: 6 * PRF # G9: 6 => SOL * PRF # G9: 6,9 => SOL * DIS # G9: 8 => CTR => G9: 6,9 * DIS # E1: 6,9 => CTR => E1: 8 * PRF # E1: 8 => SOL * PRF # D1: 6,9 => SOL * DIS # D1: 8 => CTR => D1: 6,9 * PRF # G9: 6,9 => SOL * DIS # G9: 8 => CTR => G9: 6,9 * DIS # G9: 8,9 => CTR => G9: 6 * PRF # G9: 6 => SOL * DIS # H3: 8,9 => CTR => H3: 6 * PRF # H3: 6 => SOL * CNT 32 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H3: 6,9 => SOL * STA H3: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5.3...2.....41...7.........64.7......8.....1.......3.....1...4.2...3.........5... | initial |
| 513..72.482.41.53747.3521..6417.3.2538752.41.952.4137.7351.8.422.8.347511.4275..3 | autosolve |
| 513687294826419537479352168641793825387526419952841376735168942268934751194275683 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C2: 6,9 C3: 6,9 F2: 6,9 H1: 6,9 I3: 8,9 E4: 8,9 F5: 6,9 D6: 6,8 G4: 8,9 I5: 6,9 I6: 6,8 B8: 6,9 B9: 6,9 E7: 6,9 D8: 6,9 G7: 6,9 H9: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 6.. / C2 = 6 => 0 pairs (*) / C3 = 6 => 0 pairs (X) H1,H3: 6.. / H1 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) F5,D6: 6.. / F5 = 6 => 0 pairs (*) / D6 = 6 => 0 pairs (X) I5,I6: 6.. / I5 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) B8,B9: 6.. / B8 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) E7,D8: 6.. / E7 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) G7,G9: 6.. / G7 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) C2,F2: 6.. / C2 = 6 => 0 pairs (*) / F2 = 6 => 0 pairs (X) C3,H3: 6.. / C3 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) F5,I5: 6.. / F5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) D6,I6: 6.. / D6 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) E7,G7: 6.. / E7 = 6 => 0 pairs (*) / G7 = 6 => 0 pairs (X) B8,D8: 6.. / B8 = 6 => 0 pairs (*) / D8 = 6 => 0 pairs (X) B9,G9: 6.. / B9 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) E1,E7: 6.. / E1 = 6 => 0 pairs (X) / E7 = 6 => 0 pairs (_) F2,F5: 6.. / F2 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) D1,E1: 8.. / D1 = 8 => 0 pairs (X) / E1 = 8 => 0 pairs (_) H3,I3: 8.. / H3 = 8 => 0 pairs (X) / I3 = 8 => 0 pairs (_) E4,D6: 8.. / E4 = 8 => 0 pairs (X) / D6 = 8 => 0 pairs (_) G4,I6: 8.. / G4 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) G9,H9: 8.. / G9 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) E4,G4: 8.. / E4 = 8 => 0 pairs (X) / G4 = 8 => 0 pairs (_) D6,I6: 8.. / D6 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) D1,D6: 8.. / D1 = 8 => 0 pairs (X) / D6 = 8 => 0 pairs (_) E1,E4: 8.. / E1 = 8 => 0 pairs (*) / E4 = 8 => 0 pairs (X) G4,G9: 8.. / G4 = 8 => 0 pairs (*) / G9 = 8 => 0 pairs (X) H3,H9: 8.. / H3 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) I3,I6: 8.. / I3 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) C2,C3: 9.. / C2 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) E4,F5: 9.. / E4 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) G4,I5: 9.. / G4 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) B8,B9: 9.. / B8 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) E7,D8: 9.. / E7 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) C2,F2: 9.. / C2 = 9 => 0 pairs (X) / F2 = 9 => 0 pairs (_) E4,G4: 9.. / E4 = 9 => 0 pairs (*) / G4 = 9 => 0 pairs (X) F5,I5: 9.. / F5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) E7,G7: 9.. / E7 = 9 => 0 pairs (X) / G7 = 9 => 0 pairs (_) B8,D8: 9.. / B8 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) D1,D8: 9.. / D1 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) F2,F5: 9.. / F2 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) I3,I5: 9.. / I3 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) * DURATION: 0:01:21.235477 START: 13:14:34.043524 END: 13:15:55.279001 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,C2,C3,D6,D8,E4,E7,F2,F5,G4,G7,H1,H9,I3,I5,I6) * 513..72.482.41.53747.3521..6417.3.2538752.41.952.4137.7351.8.422.8.347511.4275..3 * PAIR C3: 6,9 ROW 3 H3: 6,9,8 # reduction candidate for 6,9 H3: 6,9 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 H3: 8 => CTR * 513..726482.4165374763521896417.39253875294169526413787351.8.422.8.347511.4275..3 * PAIR F2: 6,9 BLK 2 D1: 6,9,8 # reduction candidate for 6,9 D1: 6,9 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 D1: 8 => CTR * 5138.72.482.41.53747.3521..6417839253875294169526413787351.8.422.8.347511.4275..3 E1: 6,9,8 # reduction candidate for 6,9 E1: 6,9 => CTR * 5138.72.482.41.53747.3521..6417839253875294169526413787351.8.422.8.347511.4275..3 E1: 8 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 * PAIR H1: 6,9 BLK 3 H3: 6,9,8 # reduction candidate for 6,9 H3: 6,9 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 H3: 8 => CTR * 513..726482.4165374763521896417.39253875294169526413787351.8.422.8.347511.4275..3 * PAIR H1: 6,9 ROW 1 D1: 6,9,8 # reduction candidate for 6,9 D1: 6,9 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 D1: 8 => CTR * 5138.72.482.41.53747.3521..6417839253875294169526413787351.8.422.8.347511.4275..3 E1: 6,9,8 # reduction candidate for 6,9 E1: 6,9 => CTR * 5138.72.482.41.53747.3521..6417839253875294169526413787351.8.422.8.347511.4275..3 E1: 8 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 * PAIR I3: 8,9 BLK 3 H3: 8,9,6 # reduction candidate for 8,9 H3: 8,9 => CTR * 513..726482.4165374763521..6417.3.253875294169526413787351689422.8.347511.4275..3 H3: 6 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 * PAIR E4: 8,9 COL E E1: 8,9,6 # reduction candidate for 8,9 E1: 8,9 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 E1: 6 => CTR * 5138672948264195374793521686417.3.2538752.41.952.4137.7351.8.422.8.347511.4275..3 * PAIR D6: 6,8 COL D D1: 6,8,9 # reduction candidate for 6,8 D1: 6,8 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 D1: 9 => CTR * 5139872648294165374763521..641793.2538752.41.952.4137.7351.8.422.8.347511.4275..3 * PAIR G4: 8,9 COL G G9: 8,9,6 # reduction candidate for 8,9 G9: 8,9 => CTR * 5139.72.482.41.53747.3521..6417.3.2538752.41.952.4137.7351.86422.8634751164275..3 G9: 6 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 * PAIR B9: 6,9 ROW 9 G9: 6,9,8 # reduction candidate for 6,9 G9: 6,9 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 G9: 8 => CTR * 513..72.482.41.53747.3521..6417.3.2538752.41.952.4137.7351.86422.8634751164275893 * PAIR E7: 6,9 COL E E1: 6,9,8 # reduction candidate for 6,9 E1: 6,9 => CTR * 5138.72.482.41.53747.3521..6417839253875294169526413787351.8.422.8.347511.4275..3 E1: 8 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 * PAIR D8: 6,9 COL D D1: 6,9,8 # reduction candidate for 6,9 D1: 6,9 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 D1: 8 => CTR * 5138.72.482.41.53747.3521..6417839253875294169526413787351.8.422.8.347511.4275..3 * PAIR G7: 6,9 BLK 9 G9: 6,9,8 # reduction candidate for 6,9 G9: 6,9 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 G9: 8 => CTR * 513..72.482.41.53747.3521..6417.3.2538752.41.952.4137.7351.86422.8634751164275893 * PAIR H9: 8,9 BLK 9 G9: 8,9,6 # reduction candidate for 8,9 G9: 8,9 => CTR * 5139.72.482.41.53747.3521..6417.3.2538752.41.952.4137.7351.86422.8634751164275..3 G9: 6 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 * PAIR H9: 8,9 COL H H3: 8,9,6 # reduction candidate for 8,9 H3: 8,9 => CTR * 513..726482.4165374763521..6417.3.253875294169526413787351689422.8.347511.4275..3 H3: 6 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-301-base-pr-000.dot * REASONING * PRF # H3: 6,9 => SOL * DIS # H3: 8 => CTR => H3: 6,9 * PRF # D1: 6,9 => SOL * DIS # D1: 8 => CTR => D1: 6,9 * DIS # E1: 6,9 => CTR => E1: 8 * PRF # E1: 8 => SOL * PRF # H3: 6,9 => SOL * DIS # H3: 8 => CTR => H3: 6,9 * PRF # D1: 6,9 => SOL * DIS # D1: 8 => CTR => D1: 6,9 * DIS # E1: 6,9 => CTR => E1: 8 * PRF # E1: 8 => SOL * DIS # H3: 8,9 => CTR => H3: 6 * PRF # H3: 6 => SOL * PRF # E1: 8,9 => SOL * DIS # E1: 6 => CTR => E1: 8,9 * PRF # D1: 6,8 => SOL * DIS # D1: 9 => CTR => D1: 6,8 * DIS # G9: 8,9 => CTR => G9: 6 * PRF # G9: 6 => SOL * PRF # G9: 6,9 => SOL * DIS # G9: 8 => CTR => G9: 6,9 * DIS # E1: 6,9 => CTR => E1: 8 * PRF # E1: 8 => SOL * PRF # D1: 6,9 => SOL * DIS # D1: 8 => CTR => D1: 6,9 * PRF # G9: 6,9 => SOL * DIS # G9: 8 => CTR => G9: 6,9 * DIS # G9: 8,9 => CTR => G9: 6 * PRF # G9: 6 => SOL * DIS # H3: 8,9 => CTR => H3: 6 * PRF # H3: 6 => SOL * CNT 32 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,C2,C3,D6,D8,E4,E7,F2,F5,G4,G7,H1,H9,I3,I5,I6) * 513..72.482.41.53747.3521..6417.3.2538752.41.952.4137.7351.8.422.8.347511.4275..3 * PAIR C3: 6,9 ROW 3 H3: 6,9,8 # reduction candidate for 6,9 H3: 6,9 => SOLVED * 513687294826419537479352168641793825387526419952841376735168942268934751194275683 * DURATION: 0:00:02.117456 START: 13:16:35.755980 END: 13:16:37.873436 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-301-base-pr-001.dot * REASONING * PRF # H3: 6,9 => SOL * STA H3: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 301 solution: 513687294826419537479352168641793825387526419952841376735168942268934751194275683 info: 2582 FNBWY S8.f 33306 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 513687294826419537479352168641793825387526419952841376735168942268934751194275683 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 # H3: 6,9 => SOL * DIS # H3: 8 => CTR => H3: 6,9 * PRF # D1: 6,9 => SOL * DIS # D1: 8 => CTR => D1: 6,9 * DIS # E1: 6,9 => CTR => E1: 8 * PRF # E1: 8 => SOL * PRF # H3: 6,9 => SOL * DIS # H3: 8 => CTR => H3: 6,9 * PRF # D1: 6,9 => SOL * DIS # D1: 8 => CTR => D1: 6,9 * DIS # E1: 6,9 => CTR => E1: 8 * PRF # E1: 8 => SOL * DIS # H3: 8,9 => CTR => H3: 6 * PRF # H3: 6 => SOL * PRF # E1: 8,9 => SOL * DIS # E1: 6 => CTR => E1: 8,9 * PRF # D1: 6,8 => SOL * DIS # D1: 9 => CTR => D1: 6,8 * DIS # G9: 8,9 => CTR => G9: 6 * PRF # G9: 6 => SOL * PRF # G9: 6,9 => SOL * DIS # G9: 8 => CTR => G9: 6,9 * DIS # E1: 6,9 => CTR => E1: 8 * PRF # E1: 8 => SOL * PRF # D1: 6,9 => SOL * DIS # D1: 8 => CTR => D1: 6,9 * PRF # G9: 6,9 => SOL * DIS # G9: 8 => CTR => G9: 6,9 * DIS # G9: 8,9 => CTR => G9: 6 * PRF # G9: 6 => SOL * DIS # H3: 8,9 => CTR => H3: 6 * PRF # H3: 6 => SOL * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # H3: 6,9 => SOL * STA H3: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED