Analysis of xx-top500-238-base.sdk
Contents
Original Sudoku
level: medium
position: ...8..3..4..7............2..21....5....4.........3.....6....2.7....2.4..5....1... initial
Autosolve
position: 21785.34.43.7.25.1...14372.321..7.54...41..32..423.17..635.42.7...32.4.5542.71..3 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F5: 6,9 => SOL * DIS # F6: 6,9 => CTR => F6: 5,8 * DIS # F8: 6,9 => CTR => F8: 8 * PRF # F8: 8 => SOL * DIS # C2: 6,9 => CTR => C2: 8 * DIS # E4: 6,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * DIS # I3: 6,9 => CTR => I3: 8 * DIS # I6: 8 => CTR => I6: 6,9 * DIS # E4: 6,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # F5: 6,9 => SOL * DIS # F6: 6,9 => CTR => F6: 5,8 * PRF # G4: 6,9 => SOL * DIS # G4: 8 => CTR => G4: 6,9 * DIS # A8: 8,9 => CTR => A8: 1,7 * DIS # B8: 8,9 => CTR => B8: 7 * DIS # F8: 6 => CTR => F8: 8,9 * DIS # C3: 8,9 => CTR => C3: 5,6 * DIS # C5: 8,9 => CTR => C5: 5,6 * DIS # F8: 6 => CTR => F8: 8,9 * DIS # A7: 1 => CTR => A7: 8,9 * DIS # E4: 6 => CTR => E4: 8,9 * DIS # F8: 6,9 => CTR => F8: 8 * PRF # F8: 8 => SOL * DIS # H9: 6,9 => CTR => H9: 8 * DIS # H8: 1,9 => CTR => H8: 6 * DIS # A7: 1,9 => CTR => A7: 8 * PRF # A7: 8 => SOL * CNT 29 HDP CHAINS / 51 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F5: 6,9 => SOL * STA F5: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8..3..4..7............2..21....5....4.........3.....6....2.7....2.4..5....1... | initial |
| 21785.34.43.7.25.1...14372.321..7.54...41..32..423.17..635.42.7...32.4.5542.71..3 | autosolve |
| 217859346438762591956143728321987654795416832684235179863594217179328465542671983 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) F1: 6,9 E2: 6,9 I1: 6,9 D4: 6,9 C8: 8,9 E7: 8,9 D9: 6,9 H7: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,A8: 1.. / A7 = 1 => 0 pairs (X) / A8 = 1 => 9 pairs (_) H7,H8: 1.. / H7 = 1 => 9 pairs (_) / H8 = 1 => 0 pairs (X) A7,H7: 1.. / A7 = 1 => 0 pairs (X) / H7 = 1 => 9 pairs (_) A8,H8: 1.. / A8 = 1 => 9 pairs (_) / H8 = 1 => 0 pairs (X) B3,C3: 5.. / B3 = 5 => 10 pairs (_) / C3 = 5 => 9 pairs (_) F5,F6: 5.. / F5 = 5 => 9 pairs (_) / F6 = 5 => 9 pairs (_) B6,F6: 5.. / B6 = 5 => 9 pairs (_) / F6 = 5 => 9 pairs (_) C3,C5: 5.. / C3 = 5 => 9 pairs (_) / C5 = 5 => 10 pairs (_) F1,E2: 6.. / F1 = 6 => 0 pairs (X) / E2 = 6 => 15 pairs (_) F8,D9: 6.. / F8 = 6 => 0 pairs (X) / D9 = 6 => 13 pairs (_) F1,I1: 6.. / F1 = 6 => 0 pairs (X) / I1 = 6 => 15 pairs (_) F8,H8: 6.. / F8 = 6 => 0 pairs (X) / H8 = 6 => 13 pairs (_) D4,D9: 6.. / D4 = 6 => 0 pairs (X) / D9 = 6 => 13 pairs (_) E2,E4: 6.. / E2 = 6 => 15 pairs (_) / E4 = 6 => 0 pairs (X) A5,B5: 7.. / A5 = 7 => 8 pairs (_) / B5 = 7 => 0 pairs (X) A8,B8: 7.. / A8 = 7 => 0 pairs (X) / B8 = 7 => 8 pairs (_) A5,A8: 7.. / A5 = 7 => 8 pairs (_) / A8 = 7 => 0 pairs (X) B5,B8: 7.. / B5 = 7 => 0 pairs (X) / B8 = 7 => 8 pairs (_) H2,I3: 8.. / H2 = 8 => 0 pairs (X) / I3 = 8 => 18 pairs (_) E7,F8: 8.. / E7 = 8 => 0 pairs (X) / F8 = 8 => 0 pairs (_) G9,H9: 8.. / G9 = 8 => 0 pairs (X) / H9 = 8 => 18 pairs (_) C2,H2: 8.. / C2 = 8 => 18 pairs (_) / H2 = 8 => 0 pairs (X) E4,G4: 8.. / E4 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) A7,E7: 8.. / A7 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) E4,E7: 8.. / E4 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) H2,H9: 8.. / H2 = 8 => 0 pairs (X) / H9 = 8 => 18 pairs (_) I3,I6: 8.. / I3 = 8 => 18 pairs (_) / I6 = 8 => 0 pairs (X) F1,E2: 9.. / F1 = 9 => 15 pairs (_) / E2 = 9 => 0 pairs (X) F1,I1: 9.. / F1 = 9 => 15 pairs (_) / I1 = 9 => 0 pairs (X) D4,D9: 9.. / D4 = 9 => 13 pairs (_) / D9 = 9 => 0 pairs (X) * DURATION: 0:00:47.051517 START: 10:57:14.391890 END: 10:58:01.443407 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D4,D9,E2,E7,F1,H7,I1) * 21785.34.43.7.25.1...14372.321..7.54...41..32..423.17..635.42.7...32.4.5542.71..3 * PAIR F1: 6,9 COL F F5: 6,9,5,8 # reduction candidate for 6,9 F5: 6,9 => SOLVED * 217859346438762591956143728321987654795416832684235179863594217179328465542671983 F5: 5,8 # 9 pairs F6: 6,9,5,8 # reduction candidate for 6,9 F6: 6,9 => CTR * 21785934643.762591695143728321987654...415.32.5423617.863594217179328465542671..3 F6: 5,8 # 9 pairs F8: 6,9,8 # reduction candidate for 6,9 F8: 6,9 => CTR * 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683 F8: 8 => SOLVED * 217859346438762591956143728321987654795416832684235179863594217179328465542671983 * PAIR E2: 6,9 ROW 2 C2: 6,9,8 # reduction candidate for 6,9 C2: 6,9 => CTR * 21785.34.43.7.2581...14372.321.87.54...41..32..423.178863594217179328465542671893 C2: 8 # 18 pairs H2: 6,9,8 # reduction candidate for 6,9 H2: 6,9 # 18 pairs * PAIR E2: 6,9 COL E E4: 6,9,8 # reduction candidate for 6,9 E4: 6,9 => CTR * 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683 E4: 8 => SOLVED * 217859346438762591956143728321987654795416832684235179863594217179328465542671983 * PAIR I1: 6,9 BLK 3 H2: 6,9,8 # reduction candidate for 6,9 H2: 6,9 # 18 pairs I3: 6,9,8 # reduction candidate for 6,9 I3: 6,9 => CTR * 21785.34.43.7.2581...14372.321.87.54...41..32..423.178863594217179328465542671893 I3: 8 # 18 pairs * PAIR I1: 6,9 COL I I6: 6,9,8 # reduction candidate for 6,9 I6: 8 => CTR * 21785.34.43.7.2581...14372.321.87.54...41..32..423.178863594217179328465542671893 I6: 6,9 # 18 pairs * PAIR D4: 6,9 BLK 5 E4: 6,9,8 # reduction candidate for 6,9 E4: 6,9 => CTR * 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683 E4: 8 => SOLVED * 217859346438762591956143728321987654795416832684235179863594217179328465542671983 F5: 6,9,5,8 # reduction candidate for 6,9 F5: 6,9 => SOLVED * 217859346438762591956143728321987654795416832684235179863594217179328465542671983 F5: 5,8 # 9 pairs F6: 6,9,5,8 # reduction candidate for 6,9 F6: 6,9 => CTR * 21785934643.762591695143728321987654...415.32.5423617.863594217179328465542671..3 F6: 5,8 # 9 pairs * PAIR D4: 6,9 ROW 4 G4: 6,9,8 # reduction candidate for 6,9 G4: 6,9 => SOLVED * 217859346438762591956143728321987654795416832684235179863594217179328465542671983 G4: 8 => CTR * 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683 * PAIR C8: 8,9 BLK 7 A7: 8,9,1 # reduction candidate for 8,9 A7: 8,9 # 9 pairs A8: 8,9,1,7 # reduction candidate for 8,9 A8: 8,9 => CTR * 21785.34.43.7.25.1...14372.3216978547..41.932..423.176163584297.7.326415542971..3 A8: 1,7 # 9 pairs B8: 8,9,7 # reduction candidate for 8,9 B8: 8,9 => CTR * 217859346439762581...143729321697854.7.41..32..423.17.1635842977..326415542971..3 B8: 7 # 8 pairs * PAIR C8: 8,9 ROW 8 F8: 8,9,6 # reduction candidate for 8,9 F8: 6 => CTR * 21785934643.7625.1...14372.321697854...41..32..423.17..635842.7...3264.5542971..3 F8: 8,9 # 13 pairs * PAIR C8: 8,9 COL C C2: 8,9,6 # reduction candidate for 8,9 C2: 8,9 # 12 pairs C3: 8,9,5,6 # reduction candidate for 8,9 C3: 8,9 => CTR * 21785.34.436792581.5.143726321.67854..5418632684235179.635.42.7...32.4.5542.71..3 C3: 5,6 # 9 pairs C5: 8,9,5,6 # reduction candidate for 8,9 C5: 8,9 => CTR * 21785.34.436792581..5143726321.67854...41.6326.423.179.635.42.7...32.4.5542.71..3 C5: 5,6 # 9 pairs * PAIR E7: 8,9 BLK 8 F8: 8,9,6 # reduction candidate for 8,9 F8: 6 => CTR * 21785934643.7625.1...14372.321697854...41..32..423.17..635842.7...3264.5542971..3 F8: 8,9 # 13 pairs * PAIR E7: 8,9 ROW 7 A7: 8,9,1 # reduction candidate for 8,9 A7: 1 => CTR * 21785.34.43.7.25.1...14372.321697854...41.932..423.176163584297...326415542971..3 A7: 8,9 # 9 pairs * PAIR E7: 8,9 COL E E4: 8,9,6 # reduction candidate for 8,9 E4: 6 => CTR * 217856349438792561...143728321967854...41.632..423.17..635842.7...32.4.5542671983 E4: 8,9 # 15 pairs * PAIR D9: 6,9 BLK 8 F8: 6,9,8 # reduction candidate for 6,9 F8: 6,9 => CTR * 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683 F8: 8 => SOLVED * 217859346438762591956143728321987654795416832684235179863594217179328465542671983 * PAIR D9: 6,9 ROW 9 G9: 6,9,8 # reduction candidate for 6,9 G9: 6,9 # 18 pairs H9: 6,9,8 # reduction candidate for 6,9 H9: 6,9 => CTR * 21785.34.43.7.2581...14372.321.87.54...41..32..423.178863594217179328465542671893 H9: 8 # 18 pairs * PAIR H7: 1,9 BLK 9 H8: 1,9,6 # reduction candidate for 1,9 H8: 1,9 => CTR * 21785934643.7625.1...14372.321697854...41..32..423.17..635.42.7...3264.5542971..3 H8: 6 # 13 pairs * PAIR H7: 1,9 ROW 7 A7: 1,9,8 # reduction candidate for 1,9 A7: 1,9 => CTR * 2178593464387.25.1...143728321..7854...41..32..423.17..635842.7..9326415542971683 A7: 8 => SOLVED * 217859346438762591956143728321987654795416832684235179863594217179328465542671983 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-238-base-pr-000.dot * REASONING * PRF # F5: 6,9 => SOL * DIS # F6: 6,9 => CTR => F6: 5,8 * DIS # F8: 6,9 => CTR => F8: 8 * PRF # F8: 8 => SOL * DIS # C2: 6,9 => CTR => C2: 8 * DIS # E4: 6,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * DIS # I3: 6,9 => CTR => I3: 8 * DIS # I6: 8 => CTR => I6: 6,9 * DIS # E4: 6,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # F5: 6,9 => SOL * DIS # F6: 6,9 => CTR => F6: 5,8 * PRF # G4: 6,9 => SOL * DIS # G4: 8 => CTR => G4: 6,9 * DIS # A8: 8,9 => CTR => A8: 1,7 * DIS # B8: 8,9 => CTR => B8: 7 * DIS # F8: 6 => CTR => F8: 8,9 * DIS # C3: 8,9 => CTR => C3: 5,6 * DIS # C5: 8,9 => CTR => C5: 5,6 * DIS # F8: 6 => CTR => F8: 8,9 * DIS # A7: 1 => CTR => A7: 8,9 * DIS # E4: 6 => CTR => E4: 8,9 * DIS # F8: 6,9 => CTR => F8: 8 * PRF # F8: 8 => SOL * DIS # H9: 6,9 => CTR => H9: 8 * DIS # H8: 1,9 => CTR => H8: 6 * DIS # A7: 1,9 => CTR => A7: 8 * PRF # A7: 8 => SOL * CNT 29 HDP CHAINS / 51 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D4,D9,E2,E7,F1,H7,I1) * 21785.34.43.7.25.1...14372.321..7.54...41..32..423.17..635.42.7...32.4.5542.71..3 * PAIR F1: 6,9 COL F F5: 6,9,5,8 # reduction candidate for 6,9 F5: 6,9 => SOLVED * 217859346438762591956143728321987654795416832684235179863594217179328465542671983 * DURATION: 0:00:02.131210 START: 10:58:48.961396 END: 10:58:51.092606 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-238-base-pr-001.dot * REASONING * PRF # F5: 6,9 => SOL * STA F5: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 238 solution: 217859346438762591956143728321987654795416832684235179863594217179328465542671983 info: 2069 FNBWXY S8.f 12156 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 217859346438762591956143728321987654795416832684235179863594217179328465542671983 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 # F5: 6,9 => SOL * INC # F5: 5,8 => UNS * DIS # F6: 6,9 => CTR => F6: 5,8 * INC # F6: 5,8 => UNS * DIS # F8: 6,9 => CTR => F8: 8 * PRF # F8: 8 => SOL * DIS # C2: 6,9 => CTR => C2: 8 * INC # C2: 8 => UNS * INC # H2: 6,9 => UNS * DIS # E4: 6,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * INC # H2: 6,9 => UNS * DIS # I3: 6,9 => CTR => I3: 8 * INC # I3: 8 => UNS * INC # I6: 6,9 => UNS * DIS # I6: 8 => CTR => I6: 6,9 * DIS # E4: 6,9 => CTR => E4: 8 * PRF # E4: 8 => SOL * PRF # F5: 6,9 => SOL * INC # F5: 5,8 => UNS * DIS # F6: 6,9 => CTR => F6: 5,8 * INC # F6: 5,8 => UNS * PRF # G4: 6,9 => SOL * DIS # G4: 8 => CTR => G4: 6,9 * INC # A7: 8,9 => UNS * DIS # A8: 8,9 => CTR => A8: 1,7 * INC # A8: 1,7 => UNS * DIS # B8: 8,9 => CTR => B8: 7 * INC # B8: 7 => UNS * INC # F8: 8,9 => UNS * DIS # F8: 6 => CTR => F8: 8,9 * INC # C2: 8,9 => UNS * DIS # C3: 8,9 => CTR => C3: 5,6 * INC # C3: 5,6 => UNS * DIS # C5: 8,9 => CTR => C5: 5,6 * INC # C5: 5,6 => UNS * INC # F8: 8,9 => UNS * DIS # F8: 6 => CTR => F8: 8,9 * INC # A7: 8,9 => UNS * DIS # A7: 1 => CTR => A7: 8,9 * INC # E4: 8,9 => UNS * DIS # E4: 6 => CTR => E4: 8,9 * DIS # F8: 6,9 => CTR => F8: 8 * PRF # F8: 8 => SOL * INC # G9: 6,9 => UNS * DIS # H9: 6,9 => CTR => H9: 8 * INC # H9: 8 => UNS * DIS # H8: 1,9 => CTR => H8: 6 * INC # H8: 6 => UNS * DIS # A7: 1,9 => CTR => A7: 8 * PRF # A7: 8 => SOL * CNT 51 HDP CHAINS / 51 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F5: 6,9 => SOL * STA F5: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED