Analysis of xx-top500-009-base.sdk
Contents
Original Sudoku
level: medium
position: .31.....5...8...2..........2.....1..7..4............83....319..64...........5.... initial
Autosolve
position: .31...8.55..893421...1.5.3.25.3..14.7.341.5..1.45...838..6319546459..31.319.54..8 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E1: 2,7 => SOL * DIS # F1: 2,7 => CTR => F1: 6 * PRF # I3: 6,7 => SOL * PRF # E3: 4 => SOL * DIS # G6: 6,7 => CTR => G6: 2 * PRF # G6: 2 => SOL * PRF # G9: 6,7 => SOL * DIS # G9: 2 => CTR => G9: 6,7 * DIS # B5: 9 => CTR => B5: 6,8 * DIS # F4: 6,8 => CTR => F4: 7,9 * DIS # B5: 6,9 => CTR => B5: 8 * DIS # I4: 6,9 => CTR => I4: 7 * PRF # I4: 7 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 2 => CTR => I5: 6,9 * DIS # B5: 6,9 => CTR => B5: 8 * DIS # F5: 6,9 => CTR => F5: 2,8 * PRF # H1: 6,9 => SOL * DIS # H1: 7 => CTR => H1: 6,9 * DIS # G9: 2,7 => CTR => G9: 6 * PRF # G9: 6 => SOL * DIS # G9: 2,7 => CTR => G9: 6 * PRF # G9: 6 => SOL * PRF # G9: 6,7 => SOL * DIS # G9: 2 => CTR => G9: 6,7 * PRF # H1: 9 => SOL * CNT 26 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E1: 2,7 => SOL * STA E1: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .31.....5...8...2..........2.....1..7..4............83....319..64...........5.... | initial |
| .31...8.55..893421...1.5.3.25.3..14.7.341.5..1.45...838..6319546459..31.319.54..8 | autosolve |
| 431726895567893421928145736256389147783412569194567283872631954645978312319254678 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 4,9 B2: 6,7 C2: 6,7 A3: 4,9 B3: 2,8 C3: 2,8 D1: 2,7 G3: 6,7 C4: 6,8 B6: 6,9 H5: 6,9 B7: 2,7 C7: 2,7 D9: 2,7 I8: 2,7 H9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 2.. / B3 = 2 => 10 pairs (_) / C3 = 2 => 0 pairs (X) I5,G6: 2.. / I5 = 2 => 0 pairs (X) / G6 = 2 => 0 pairs (_) B7,C7: 2.. / B7 = 2 => 0 pairs (X) / C7 = 2 => 10 pairs (_) I8,G9: 2.. / I8 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) F5,I5: 2.. / F5 = 2 => 0 pairs (*) / I5 = 2 => 0 pairs (X) D9,G9: 2.. / D9 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) B3,B7: 2.. / B3 = 2 => 10 pairs (_) / B7 = 2 => 0 pairs (X) C3,C7: 2.. / C3 = 2 => 0 pairs (X) / C7 = 2 => 10 pairs (_) D1,D9: 2.. / D1 = 2 => 0 pairs (X) / D9 = 2 => 0 pairs (_) G6,G9: 2.. / G6 = 2 => 0 pairs (*) / G9 = 2 => 0 pairs (X) I5,I8: 2.. / I5 = 2 => 0 pairs (X) / I8 = 2 => 0 pairs (_) A1,A3: 4.. / A1 = 4 => 0 pairs (*) / A3 = 4 => 0 pairs (X) E1,E3: 4.. / E1 = 4 => 20 pairs (_) / E3 = 4 => 0 pairs (*) A1,E1: 4.. / A1 = 4 => 0 pairs (*) / E1 = 4 => 0 pairs (X) A3,E3: 4.. / A3 = 4 => 20 pairs (_) / E3 = 4 => 0 pairs (*) B2,C2: 6.. / B2 = 6 => 10 pairs (_) / C2 = 6 => 0 pairs (X) G9,H9: 6.. / G9 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) C2,C4: 6.. / C2 = 6 => 0 pairs (X) / C4 = 6 => 10 pairs (_) B2,C2: 7.. / B2 = 7 => 0 pairs (X) / C2 = 7 => 10 pairs (_) I4,G6: 7.. / I4 = 7 => 0 pairs (*) / G6 = 7 => 0 pairs (X) B7,C7: 7.. / B7 = 7 => 10 pairs (_) / C7 = 7 => 0 pairs (X) B2,B7: 7.. / B2 = 7 => 0 pairs (X) / B7 = 7 => 10 pairs (_) C2,C7: 7.. / C2 = 7 => 10 pairs (_) / C7 = 7 => 0 pairs (X) D1,D9: 7.. / D1 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) H1,H9: 7.. / H1 = 7 => 0 pairs (X) / H9 = 7 => 0 pairs (_) B3,C3: 8.. / B3 = 8 => 0 pairs (X) / C3 = 8 => 10 pairs (_) C4,B5: 8.. / C4 = 8 => 0 pairs (X) / B5 = 8 => 10 pairs (_) E8,F8: 8.. / E8 = 8 => 18 pairs (_) / F8 = 8 => 11 pairs (_) B5,F5: 8.. / B5 = 8 => 10 pairs (_) / F5 = 8 => 0 pairs (X) B3,B5: 8.. / B3 = 8 => 0 pairs (X) / B5 = 8 => 10 pairs (_) C3,C4: 8.. / C3 = 8 => 10 pairs (_) / C4 = 8 => 0 pairs (X) E4,E8: 8.. / E4 = 8 => 11 pairs (_) / E8 = 8 => 18 pairs (_) A1,A3: 9.. / A1 = 9 => 20 pairs (_) / A3 = 9 => 0 pairs (*) H1,I3: 9.. / H1 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) B5,B6: 9.. / B5 = 9 => 0 pairs (X) / B6 = 9 => 16 pairs (_) A1,H1: 9.. / A1 = 9 => 20 pairs (_) / H1 = 9 => 0 pairs (*) A3,I3: 9.. / A3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) F4,I4: 9.. / F4 = 9 => 17 pairs (_) / I4 = 9 => 0 pairs (X) B6,F6: 9.. / B6 = 9 => 16 pairs (_) / F6 = 9 => 0 pairs (X) H1,H5: 9.. / H1 = 9 => 0 pairs (*) / H5 = 9 => 0 pairs (X) * DURATION: 0:01:10.979536 START: 02:54:06.809298 END: 02:55:17.788834 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,B3,B6,B7,C2,C3,C4,C7,D1,D9,G3,H5,H9,I8) * .31...8.55..893421...1.5.3.25.3..14.7.341.5..1.45...838..6319546459..31.319.54..8 * PAIR D1: 2,7 BLK 2 E1: 2,7,4,6 # reduction candidate for 2,7 E1: 2,7 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 E1: 4,6 # 17 pairs F1: 2,7,6 # reduction candidate for 2,7 F1: 2,7 => CTR * .317.28.55..893421...1.573.25.3..1477.341.5.21.45...838..6319546459..31.319.54678 F1: 6 # 18 pairs * PAIR G3: 6,7 BLK 3 H1: 6,7,9 # reduction candidate for 6,7 H1: 6,7 # 20 pairs I3: 6,7,9 # reduction candidate for 6,7 I3: 6,7 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 I3: 9 # 20 pairs * PAIR G3: 6,7 ROW 3 E3: 6,7,4 # reduction candidate for 6,7 E3: 4 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 E3: 6,7 # 20 pairs * PAIR G3: 6,7 COL G G6: 6,7,2 # reduction candidate for 6,7 G6: 6,7 => CTR * .312..8755..893421...17563925.3..14.7.341.5.21.45...838..6319546459..317319754268 G6: 2 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 G9: 6,7,2 # reduction candidate for 6,7 G9: 6,7 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 G9: 2 => CTR * .312..8755..893421...17563925.3.91477.341.5..1.45...838..6319546459..31.319.54268 * PAIR C4: 6,8 BLK 4 B5: 6,8,9 # reduction candidate for 6,8 B5: 9 => CTR * .31...8.55..893421.821.5.3.2583..14.7934185621645.97838..6319546459..31.319.54..8 B5: 6,8 # 16 pairs * PAIR C4: 6,8 ROW 4 E4: 6,8,7 # reduction candidate for 6,8 E4: 6,8 # 19 pairs F4: 6,8,7,9 # reduction candidate for 6,8 F4: 6,8 => CTR * .31...8.55..893421...1.5.3.25.3..1497.341.5621.45..7838..6319546459..31.319.54..8 F4: 7,9 # 17 pairs * PAIR B6: 6,9 BLK 4 B5: 6,9,8 # reduction candidate for 6,9 B5: 6,9 => CTR * .312..875576893421.8217563925836.14.7.34185.21.45...83827631954645982317319754268 B5: 8 # 10 pairs * PAIR B6: 6,9 ROW 6 F6: 6,9,2,7 # reduction candidate for 6,9 F6: 6,9 # 19 pairs F6: 2,7 # 17 pairs * PAIR H5: 6,9 BLK 6 I4: 6,9,7 # reduction candidate for 6,9 I4: 6,9 => CTR * .312..8755..893421...17563925.3..14.7.341.5..1.45..7838..6319546459..31.319.54268 I4: 7 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 I5: 6,9,2 # reduction candidate for 6,9 I5: 6,9 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 I5: 2 => CTR * .312..8755..893421...17563925.3..14.7.341.5.21.45...838..6319546459..317319754268 * PAIR H5: 6,9 ROW 5 B5: 6,9,8 # reduction candidate for 6,9 B5: 6,9 => CTR * .312..875576893421.8217563925836.14.7.34185.21.45...83827631954645982317319754268 B5: 8 # 10 pairs F5: 6,9,2,8 # reduction candidate for 6,9 F5: 6,9 => CTR * .312..875567893421.281756392563..14.78341.5.21945...838..6319546459..317319754268 F5: 2,8 # 17 pairs * PAIR H5: 6,9 COL H H1: 6,9,7 # reduction candidate for 6,9 H1: 6,9 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 H1: 7 => CTR * 931.468755..8934214..17563925.3.91477.341.5961945672838..63195464592.31.319.54..8 * PAIR D9: 2,7 BLK 8 E8: 2,7,8 # reduction candidate for 2,7 E8: 2,7 # 11 pairs F8: 2,7,8 # reduction candidate for 2,7 F8: 2,7 # 18 pairs * PAIR D9: 2,7 ROW 9 G9: 2,7,6 # reduction candidate for 2,7 G9: 2,7 => CTR * .31...8755..893421...17563925.3.91477.341.5961945.72838..6319546459..312319.54.68 G9: 6 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 * PAIR I8: 2,7 BLK 9 G9: 2,7,6 # reduction candidate for 2,7 G9: 2,7 => CTR * .31...8755..893421...17563925.3.91477.341.5961945.72838..6319546459..312319.54.68 G9: 6 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 * PAIR I8: 2,7 ROW 8 E8: 2,7,8 # reduction candidate for 2,7 E8: 2,7 # 11 pairs F8: 2,7,8 # reduction candidate for 2,7 F8: 2,7 # 18 pairs * PAIR H9: 6,7 BLK 9 G9: 6,7,2 # reduction candidate for 6,7 G9: 6,7 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 G9: 2 => CTR * .312..8755..893421...17563925.3.91477.341.5..1.45...838..6319546459..31.319.54268 * PAIR H9: 6,7 COL H H1: 6,7,9 # reduction candidate for 6,7 H1: 9 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 H1: 6,7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-009-base-pr-000.dot * REASONING * PRF # E1: 2,7 => SOL * DIS # F1: 2,7 => CTR => F1: 6 * PRF # I3: 6,7 => SOL * PRF # E3: 4 => SOL * DIS # G6: 6,7 => CTR => G6: 2 * PRF # G6: 2 => SOL * PRF # G9: 6,7 => SOL * DIS # G9: 2 => CTR => G9: 6,7 * DIS # B5: 9 => CTR => B5: 6,8 * DIS # F4: 6,8 => CTR => F4: 7,9 * DIS # B5: 6,9 => CTR => B5: 8 * DIS # I4: 6,9 => CTR => I4: 7 * PRF # I4: 7 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 2 => CTR => I5: 6,9 * DIS # B5: 6,9 => CTR => B5: 8 * DIS # F5: 6,9 => CTR => F5: 2,8 * PRF # H1: 6,9 => SOL * DIS # H1: 7 => CTR => H1: 6,9 * DIS # G9: 2,7 => CTR => G9: 6 * PRF # G9: 6 => SOL * DIS # G9: 2,7 => CTR => G9: 6 * PRF # G9: 6 => SOL * PRF # G9: 6,7 => SOL * DIS # G9: 2 => CTR => G9: 6,7 * PRF # H1: 9 => SOL * CNT 26 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,B3,B6,B7,C2,C3,C4,C7,D1,D9,G3,H5,H9,I8) * .31...8.55..893421...1.5.3.25.3..14.7.341.5..1.45...838..6319546459..31.319.54..8 * PAIR D1: 2,7 BLK 2 E1: 2,7,4,6 # reduction candidate for 2,7 E1: 2,7 => SOLVED * 431726895567893421928145736256389147783412569194567283872631954645978312319254678 * DURATION: 0:00:02.521341 START: 02:56:04.417491 END: 02:56:06.938832 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-009-base-pr-001.dot * REASONING * PRF # E1: 2,7 => SOL * STA E1: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 009 solution: 431726895567893421928145736256389147783412569194567283872631954645978312319254678 info: 1307 FNBWXY S8.f 18192 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 431726895567893421928145736256389147783412569194567283872631954645978312319254678 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 # E1: 2,7 => SOL * INC # E1: 4,6 => UNS * DIS # F1: 2,7 => CTR => F1: 6 * INC # F1: 6 => UNS * INC # H1: 6,7 => UNS * PRF # I3: 6,7 => SOL * INC # I3: 9 => UNS * INC # E3: 6,7 => UNS * PRF # E3: 4 => SOL * DIS # G6: 6,7 => CTR => G6: 2 * PRF # G6: 2 => SOL * PRF # G9: 6,7 => SOL * DIS # G9: 2 => CTR => G9: 6,7 * INC # B5: 6,8 => UNS * DIS # B5: 9 => CTR => B5: 6,8 * INC # E4: 6,8 => UNS * DIS # F4: 6,8 => CTR => F4: 7,9 * INC # F4: 7,9 => UNS * DIS # B5: 6,9 => CTR => B5: 8 * INC # B5: 8 => UNS * INC # F6: 6,9 => UNS * INC # F6: 2,7 => UNS * DIS # I4: 6,9 => CTR => I4: 7 * PRF # I4: 7 => SOL * PRF # I5: 6,9 => SOL * DIS # I5: 2 => CTR => I5: 6,9 * DIS # B5: 6,9 => CTR => B5: 8 * INC # B5: 8 => UNS * DIS # F5: 6,9 => CTR => F5: 2,8 * INC # F5: 2,8 => UNS * PRF # H1: 6,9 => SOL * DIS # H1: 7 => CTR => H1: 6,9 * INC # E8: 2,7 => UNS * INC # F8: 2,7 => UNS * DIS # G9: 2,7 => CTR => G9: 6 * PRF # G9: 6 => SOL * DIS # G9: 2,7 => CTR => G9: 6 * PRF # G9: 6 => SOL * INC # E8: 2,7 => UNS * INC # F8: 2,7 => UNS * PRF # G9: 6,7 => SOL * DIS # G9: 2 => CTR => G9: 6,7 * INC # H1: 6,7 => UNS * PRF # H1: 9 => SOL * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # E1: 2,7 => SOL * STA E1: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED