Analysis of xx-top500-389-base.sdk
Contents
Original Sudoku
level: medium
position: .3....41.8..5..9............9...1.......3..2.4.......82.68...........1.....2..... initial
Autosolve
position: .3592841.8215..9.3...1.3285392781654..84397214176523982.681.539.8.3..1.21.329.8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B9: 4,7 => SOL * PRF # B3: 6 => SOL * PRF # F8: 4,7 => SOL * DIS # F9: 4,7 => CTR => F9: 5,6 * PRF # F2: 6 => SOL * CNT 5 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B9: 4,7 => SOL * STA B9: 4,7 * CNT 1 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3....41.8..5..9............9...1.......3..2.4.......82.68...........1.....2..... | initial |
| .3592841.8215..9.3...1.3285392781654..84397214176523982.681.539.8.3..1.21.329.8.. | autosolve |
| 735928416821546973964173285392781654658439721417652398276814539589367142143295867 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A1: 6,7 C3: 4,9 E3: 6,7 I1: 6,7 H2: 6,7 A5: 5,6 B5: 5,6 B7: 4,7 C8: 4,9 F7: 4,7 I9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 4.. / B3 = 4 => 10 pairs (_) / C3 = 4 => 11 pairs (_) E2,F2: 4.. / E2 = 4 => 13 pairs (_) / F2 = 4 => 14 pairs (_) H8,H9: 4.. / H8 = 4 => 16 pairs (_) / H9 = 4 => 13 pairs (_) B7,F7: 4.. / B7 = 4 => 12 pairs (_) / F7 = 4 => 14 pairs (_) C3,C8: 4.. / C3 = 4 => 11 pairs (_) / C8 = 4 => 10 pairs (_) E2,E8: 4.. / E2 = 4 => 13 pairs (_) / E8 = 4 => 14 pairs (_) A5,B5: 5.. / A5 = 5 => 11 pairs (_) / B5 = 5 => 0 pairs (*) A8,B9: 5.. / A8 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) F8,F9: 5.. / F8 = 5 => 11 pairs (_) / F9 = 5 => 0 pairs (*) A8,F8: 5.. / A8 = 5 => 0 pairs (*) / F8 = 5 => 0 pairs (X) B9,F9: 5.. / B9 = 5 => 11 pairs (_) / F9 = 5 => 0 pairs (*) A5,A8: 5.. / A5 = 5 => 11 pairs (_) / A8 = 5 => 0 pairs (*) B5,B9: 5.. / B5 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) I1,H2: 6.. / I1 = 6 => 0 pairs (*) / H2 = 6 => 0 pairs (X) A5,B5: 6.. / A5 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) A1,I1: 6.. / A1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) B3,B5: 6.. / B3 = 6 => 0 pairs (*) / B5 = 6 => 0 pairs (X) I1,I9: 6.. / I1 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) I1,H2: 7.. / I1 = 7 => 0 pairs (X) / H2 = 7 => 0 pairs (_) A1,I1: 7.. / A1 = 7 => 0 pairs (*) / I1 = 7 => 0 pairs (X) B7,F7: 7.. / B7 = 7 => 14 pairs (_) / F7 = 7 => 12 pairs (_) I1,I9: 7.. / I1 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) A3,C3: 9.. / A3 = 9 => 11 pairs (_) / C3 = 9 => 10 pairs (_) A8,C8: 9.. / A8 = 9 => 10 pairs (_) / C8 = 9 => 11 pairs (_) A3,A8: 9.. / A3 = 9 => 11 pairs (_) / A8 = 9 => 10 pairs (_) C3,C8: 9.. / C3 = 9 => 10 pairs (_) / C8 = 9 => 11 pairs (_) * DURATION: 0:00:51.329731 START: 16:08:44.879694 END: 16:09:36.209425 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B5,B7,C3,C8,E3,F7,H2,I1,I9) * .3592841.8215..9.3...1.3285392781654..84397214176523982.681.539.8.3..1.21.329.8.. * PAIR A1: 6,7 BLK 1 A3: 6,7,9 # reduction candidate for 6,7 A3: 6,7 # 10 pairs B3: 6,7,4 # reduction candidate for 6,7 B3: 6,7 # 11 pairs * PAIR E3: 6,7 BLK 2 E2: 6,7,4 # reduction candidate for 6,7 E2: 6,7 # 14 pairs F2: 6,7,4 # reduction candidate for 6,7 F2: 6,7 # 13 pairs * PAIR E3: 6,7 ROW 3 A3: 6,7,9 # reduction candidate for 6,7 A3: 6,7 # 10 pairs B3: 6,7,4 # reduction candidate for 6,7 B3: 6,7 # 11 pairs * PAIR E3: 6,7 COL E E8: 6,7,4 # reduction candidate for 6,7 E8: 4 # 14 pairs E8: 6,7 # 13 pairs * PAIR H2: 6,7 ROW 2 E2: 6,7,4 # reduction candidate for 6,7 E2: 6,7 # 14 pairs F2: 6,7,4 # reduction candidate for 6,7 F2: 6,7 # 13 pairs * PAIR H2: 6,7 COL H H8: 6,7,4 # reduction candidate for 6,7 H8: 6,7 # 13 pairs H9: 6,7,4 # reduction candidate for 6,7 H9: 6,7 # 16 pairs * PAIR B7: 4,7 BLK 7 B9: 4,7,5 # reduction candidate for 4,7 B9: 4,7 => SOLVED * 735928416821546973964173285392781654658439721417652398276814539589367142143295867 B9: 5 # 11 pairs * PAIR B7: 4,7 COL B B3: 4,7,6 # reduction candidate for 4,7 B3: 6 => SOLVED * 735928416821546973964173285392781654658439721417652398276814539589367142143295867 B3: 4,7 # 11 pairs * PAIR F7: 4,7 BLK 8 E8: 4,7,6 # reduction candidate for 4,7 E8: 4,7 # 15 pairs F8: 4,7,5,6 # reduction candidate for 4,7 F8: 4,7 => SOLVED * 735928416821546973964173285392781654658439721417652398276814539589367142143295867 F8: 5,6 # 12 pairs F9: 4,7,5,6 # reduction candidate for 4,7 F9: 4,7 => CTR * .3592841.8215.6973...1732853927816545684397214176523982768145399843651.215329.8.. F9: 5,6 # 12 pairs * PAIR F7: 4,7 COL F F2: 4,7,6 # reduction candidate for 4,7 F2: 6 => SOLVED * 735928416821546973964173285392781654658439721417652398276814539589367142143295867 F2: 4,7 # 15 pairs * PAIR I9: 6,7 BLK 9 H8: 6,7,4 # reduction candidate for 6,7 H8: 6,7 # 13 pairs H9: 6,7,4 # reduction candidate for 6,7 H9: 6,7 # 16 pairs * PAIR I9: 6,7 ROW 9 F9: 6,7,4,5 # reduction candidate for 6,7 F9: 6,7 # 13 pairs F9: 4,5 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-389-base-pr-000.dot * REASONING * PRF # B9: 4,7 => SOL * PRF # B3: 6 => SOL * PRF # F8: 4,7 => SOL * DIS # F9: 4,7 => CTR => F9: 5,6 * PRF # F2: 6 => SOL * CNT 5 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B5,B7,C3,C8,E3,F7,H2,I1,I9) * .3592841.8215..9.3...1.3285392781654..84397214176523982.681.539.8.3..1.21.329.8.. * PAIR A1: 6,7 BLK 1 A3: 6,7,9 # reduction candidate for 6,7 A3: 6,7 # 10 pairs B3: 6,7,4 # reduction candidate for 6,7 B3: 6,7 # 11 pairs * PAIR E3: 6,7 BLK 2 E2: 6,7,4 # reduction candidate for 6,7 E2: 6,7 # 14 pairs F2: 6,7,4 # reduction candidate for 6,7 F2: 6,7 # 13 pairs * PAIR E3: 6,7 ROW 3 A3: 6,7,9 # reduction candidate for 6,7 A3: 6,7 # 10 pairs B3: 6,7,4 # reduction candidate for 6,7 B3: 6,7 # 11 pairs * PAIR E3: 6,7 COL E E8: 6,7,4 # reduction candidate for 6,7 E8: 4 # 14 pairs E8: 6,7 # 13 pairs * PAIR H2: 6,7 ROW 2 E2: 6,7,4 # reduction candidate for 6,7 E2: 6,7 # 14 pairs F2: 6,7,4 # reduction candidate for 6,7 F2: 6,7 # 13 pairs * PAIR H2: 6,7 COL H H8: 6,7,4 # reduction candidate for 6,7 H8: 6,7 # 13 pairs H9: 6,7,4 # reduction candidate for 6,7 H9: 6,7 # 16 pairs * PAIR B7: 4,7 BLK 7 B9: 4,7,5 # reduction candidate for 4,7 B9: 4,7 => SOLVED * 735928416821546973964173285392781654658439721417652398276814539589367142143295867 * DURATION: 0:00:15.709091 START: 16:10:08.580967 END: 16:10:24.290058 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-389-base-pr-001.dot * REASONING * PRF # B9: 4,7 => SOL * STA B9: 4,7 * CNT 1 HDP CHAINS / 13 HYP OPENED
Header Info
Top 500 Minimum 17 389 solution: 735928416821546973964173285392781654658439721417652398276814539589367142143295867 info: 42012 FNBK S8.f 48624 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 735928416821546973964173285392781654658439721417652398276814539589367142143295867 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:
* INC # A3: 6,7 => UNS * INC # B3: 6,7 => UNS * INC # E2: 6,7 => UNS * INC # F2: 6,7 => UNS * INC # A3: 6,7 => UNS * INC # B3: 6,7 => UNS * INC # E8: 6,7 => UNS * INC # E8: 4 => UNS * INC # E2: 6,7 => UNS * INC # F2: 6,7 => UNS * INC # H8: 6,7 => UNS * INC # H9: 6,7 => UNS * PRF # B9: 4,7 => SOL * INC # B9: 5 => UNS * INC # B3: 4,7 => UNS * PRF # B3: 6 => SOL * INC # E8: 4,7 => UNS * PRF # F8: 4,7 => SOL * INC # F8: 5,6 => UNS * DIS # F9: 4,7 => CTR => F9: 5,6 * INC # F9: 5,6 => UNS * INC # F2: 4,7 => UNS * PRF # F2: 6 => SOL * INC # H8: 6,7 => UNS * INC # H9: 6,7 => UNS * INC # F9: 6,7 => UNS * INC # F9: 4,5 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 6,7 => UNS * INC # B3: 6,7 => UNS * INC # E2: 6,7 => UNS * INC # F2: 6,7 => UNS * INC # A3: 6,7 => UNS * INC # B3: 6,7 => UNS * INC # E8: 6,7 => UNS * INC # E8: 4 => UNS * INC # E2: 6,7 => UNS * INC # F2: 6,7 => UNS * INC # H8: 6,7 => UNS * INC # H9: 6,7 => UNS * PRF # B9: 4,7 => SOL * STA B9: 4,7 * CNT 13 HDP CHAINS / 13 HYP OPENED