Analysis of xx-top500-234-base.sdk
Contents
Original Sudoku
level: medium
position: .41......6...3.......2.....7..5....8.....4......1......2....91.....9.2..8....3... initial
Autosolve
position: 24195.83.69.43.5215.321.4.97325691481..3.4.929.41.23.532.84591.4...91283819.23.54 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F3: 7,8 => SOL * DIS # F3: 6 => CTR => F3: 7,8 * DIS # F3: 6,7 => CTR => F3: 8 * PRF # F3: 8 => SOL * PRF # F3: 7,8 => SOL * DIS # F3: 6 => CTR => F3: 7,8 * DIS # F3: 6,7 => CTR => F3: 8 * PRF # F3: 8 => SOL * PRF # B5: 6,8 => SOL * PRF # C8: 6,7 => SOL * PRF # C8: 6,7 => SOL * CNT 11 HDP CHAINS / 17 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F3: 7,8 => SOL * STA F3: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .41......6...3.......2.....7..5....8.....4......1......2....91.....9.2..8....3... | initial |
| 24195.83.69.43.5215.321.4.97325691481..3.4.929.41.23.532.84591.4...91283819.23.54 | autosolve |
| 241956837698437521573218469732569148185374692964182375327845916456791283819623754 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C2: 7,8 B3: 7,8 F1: 6,7 F2: 7,8 I1: 6,7 H3: 6,7 B6: 6,8 E5: 7,8 E6: 7,8 G5: 6,7 H6: 6,7 C7: 6,7 D8: 6,7 D9: 6,7 I7: 6,7 G9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C5: 5.. / B5 = 5 => 18 pairs (_) / C5 = 5 => 0 pairs (*) B8,C8: 5.. / B8 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) B5,B8: 5.. / B5 = 5 => 18 pairs (_) / B8 = 5 => 0 pairs (*) C5,C8: 5.. / C5 = 5 => 0 pairs (*) / C8 = 5 => 0 pairs (X) F1,F3: 6.. / F1 = 6 => 0 pairs (*) / F3 = 6 => 0 pairs (X) I1,H3: 6.. / I1 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) G5,H6: 6.. / G5 = 6 => 0 pairs (*) / H6 = 6 => 0 pairs (X) D8,D9: 6.. / D8 = 6 => 0 pairs (X) / D9 = 6 => 0 pairs (_) I7,G9: 6.. / I7 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) F1,I1: 6.. / F1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) F3,H3: 6.. / F3 = 6 => 0 pairs (X) / H3 = 6 => 0 pairs (_) B6,H6: 6.. / B6 = 6 => 0 pairs (*) / H6 = 6 => 0 pairs (X) C7,I7: 6.. / C7 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) D9,G9: 6.. / D9 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) G5,G9: 6.. / G5 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) H3,H6: 6.. / H3 = 6 => 0 pairs (*) / H6 = 6 => 0 pairs (X) I1,I7: 6.. / I1 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) C2,B3: 7.. / C2 = 7 => 0 pairs (X) / B3 = 7 => 0 pairs (_) I1,H3: 7.. / I1 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) E5,E6: 7.. / E5 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) G5,H6: 7.. / G5 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) D8,D9: 7.. / D8 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) I7,G9: 7.. / I7 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) F1,I1: 7.. / F1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) C2,F2: 7.. / C2 = 7 => 0 pairs (X) / F2 = 7 => 0 pairs (_) E5,G5: 7.. / E5 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) E6,H6: 7.. / E6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) C7,I7: 7.. / C7 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) D9,G9: 7.. / D9 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) B3,B8: 7.. / B3 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) G5,G9: 7.. / G5 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) H3,H6: 7.. / H3 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) I1,I7: 7.. / I1 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) C2,B3: 8.. / C2 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) F2,F3: 8.. / F2 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) E5,E6: 8.. / E5 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) C2,F2: 8.. / C2 = 8 => 0 pairs (*) / F2 = 8 => 0 pairs (X) B3,F3: 8.. / B3 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) B6,E6: 8.. / B6 = 8 => 0 pairs (X) / E6 = 8 => 0 pairs (_) C2,C5: 8.. / C2 = 8 => 0 pairs (*) / C5 = 8 => 0 pairs (X) * DURATION: 0:01:05.700466 START: 10:49:47.796821 END: 10:50:53.497287 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B6,C2,C7,D8,D9,E5,E6,F1,F2,G5,G9,H3,H6,I1,I7) * 24195.83.69.43.5215.321.4.97325691481..3.4.929.41.23.532.84591.4...91283819.23.54 * PAIR B3: 7,8 ROW 3 F3: 7,8,6 # reduction candidate for 7,8 F3: 7,8 => SOLVED * 241956837698437521573218469732569148185374692964182375327845916456791283819623754 F3: 6 => CTR * 24195.83.69.4385215832164797325691481.8374.929.41.23.532.84591.4...91283819.23.54 * PAIR F1: 6,7 BLK 2 F3: 6,7,8 # reduction candidate for 6,7 F3: 6,7 => CTR * 24195.83.69.43852158321.4.97325691481.837469296418237532.84591647..91283819.23.54 F3: 8 => SOLVED * 241956837698437521573218469732569148185374692964182375327845916456791283819623754 * PAIR F2: 7,8 BLK 2 F3: 7,8,6 # reduction candidate for 7,8 F3: 7,8 => SOLVED * 241956837698437521573218469732569148185374692964182375327845916456791283819623754 F3: 6 => CTR * 24195.83.69.4385215832164797325691481.8374.929.41.23.532.84591.4...91283819.23.54 * PAIR H3: 6,7 ROW 3 F3: 6,7,8 # reduction candidate for 6,7 F3: 6,7 => CTR * 24195.83.69.43852158321.4.97325691481.837469296418237532.84591647..91283819.23.54 F3: 8 => SOLVED * 241956837698437521573218469732569148185374692964182375327845916456791283819623754 * PAIR B6: 6,8 BLK 4 B5: 6,8,5 # reduction candidate for 6,8 B5: 6,8 => SOLVED * 241956837698437521573218469732569148185374692964182375327845916456791283819623754 B5: 5 # 18 pairs C5: 6,8,5 # reduction candidate for 6,8 C5: 6,8 # 18 pairs * PAIR C7: 6,7 BLK 7 B8: 6,7,5 # reduction candidate for 6,7 B8: 6,7 # 18 pairs C8: 6,7,5 # reduction candidate for 6,7 C8: 6,7 => SOLVED * 241956837698437521573218469732569148185374692964182375327845916456791283819623754 C8: 5 # 18 pairs * PAIR D8: 6,7 ROW 8 B8: 6,7,5 # reduction candidate for 6,7 B8: 6,7 # 18 pairs C8: 6,7,5 # reduction candidate for 6,7 C8: 6,7 => SOLVED * 241956837698437521573218469732569148185374692964182375327845916456791283819623754 C8: 5 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-234-base-pr-000.dot * REASONING * PRF # F3: 7,8 => SOL * DIS # F3: 6 => CTR => F3: 7,8 * DIS # F3: 6,7 => CTR => F3: 8 * PRF # F3: 8 => SOL * PRF # F3: 7,8 => SOL * DIS # F3: 6 => CTR => F3: 7,8 * DIS # F3: 6,7 => CTR => F3: 8 * PRF # F3: 8 => SOL * PRF # B5: 6,8 => SOL * PRF # C8: 6,7 => SOL * PRF # C8: 6,7 => SOL * CNT 11 HDP CHAINS / 17 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B6,C2,C7,D8,D9,E5,E6,F1,F2,G5,G9,H3,H6,I1,I7) * 24195.83.69.43.5215.321.4.97325691481..3.4.929.41.23.532.84591.4...91283819.23.54 * PAIR B3: 7,8 ROW 3 F3: 7,8,6 # reduction candidate for 7,8 F3: 7,8 => SOLVED * 241956837698437521573218469732569148185374692964182375327845916456791283819623754 * DURATION: 0:00:01.918812 START: 10:51:12.646726 END: 10:51:14.565538 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-234-base-pr-001.dot * REASONING * PRF # F3: 7,8 => SOL * STA F3: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 234 solution: 241956837698437521573218469732569148185374692964182375327845916456791283819623754 info: 2067 FNWXY S8.f 48635 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 241956837698437521573218469732569148185374692964182375327845916456791283819623754 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 # F3: 7,8 => SOL * DIS # F3: 6 => CTR => F3: 7,8 * DIS # F3: 6,7 => CTR => F3: 8 * PRF # F3: 8 => SOL * PRF # F3: 7,8 => SOL * DIS # F3: 6 => CTR => F3: 7,8 * DIS # F3: 6,7 => CTR => F3: 8 * PRF # F3: 8 => SOL * PRF # B5: 6,8 => SOL * INC # B5: 5 => UNS * INC # C5: 6,8 => UNS * INC # B8: 6,7 => UNS * PRF # C8: 6,7 => SOL * INC # C8: 5 => UNS * INC # B8: 6,7 => UNS * PRF # C8: 6,7 => SOL * INC # C8: 5 => UNS * CNT 17 HDP CHAINS / 17 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F3: 7,8 => SOL * STA F3: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED