Analysis of xx-top500-159-base.sdk
Contents
Original Sudoku
level: medium
position: 6.7.....5...8..4..1........2......6..1.3........4.....54..7........6..1.......3.. initial
Autosolve
position: 637.4.1859..831476184657..32.371.86441.3..75.87.4...3154.1736.83.8.645177615..34. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F5: 2,9 => CTR => F5: 6,8 * PRF # F9: 2,9 => SOL * DIS # F5: 6,9 => CTR => F5: 2,8 * PRF # F5: 2,8 => SOL * PRF # E5: 2,9 => SOL * DIS # F5: 2,9 => CTR => F5: 6,8 * PRF # E9: 8 => SOL * PRF # E5: 2,9 => SOL * DIS # F5: 2,9 => CTR => F5: 6,8 * PRF # F9: 2,9 => SOL * PRF # F9: 2,9 => SOL * CNT 11 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F5: 2,9 => CTR => F5: 6,8 * PRF F5: 6,8 # F9: 2,9 => SOL * STA F5: 6,8 + F9: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.7.....5...8..4..1........2......6..1.3........4.....54..7........6..1.......3.. | initial |
| 637.4.1859..831476184657..32.371.86441.3..75.87.4...3154.1736.83.8.645177615..34. | autosolve |
| 637249185952831476184657293293715864416398752875426931549173628328964517761582349 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) B2: 2,5 C2: 2,5 D1: 2,9 F1: 2,9 G3: 2,9 H3: 2,9 B4: 5,9 C5: 6,9 C6: 5,6 F4: 5,9 E6: 2,9 F6: 5,6 I5: 2,9 G6: 2,9 C7: 2,9 B8: 2,9 D8: 2,9 H7: 2,9 I9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 2.. / B2 = 2 => 0 pairs (X) / C2 = 2 => 0 pairs (_) D1,F1: 2.. / D1 = 2 => 0 pairs (*) / F1 = 2 => 0 pairs (X) G3,H3: 2.. / G3 = 2 => 0 pairs (*) / H3 = 2 => 0 pairs (X) I5,G6: 2.. / I5 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) C7,B8: 2.. / C7 = 2 => 0 pairs (X) / B8 = 2 => 0 pairs (_) H7,I9: 2.. / H7 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) E6,G6: 2.. / E6 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) C7,H7: 2.. / C7 = 2 => 0 pairs (X) / H7 = 2 => 0 pairs (_) B8,D8: 2.. / B8 = 2 => 0 pairs (*) / D8 = 2 => 0 pairs (X) B2,B8: 2.. / B2 = 2 => 0 pairs (X) / B8 = 2 => 0 pairs (_) C2,C7: 2.. / C2 = 2 => 0 pairs (*) / C7 = 2 => 0 pairs (X) D1,D8: 2.. / D1 = 2 => 0 pairs (*) / D8 = 2 => 0 pairs (X) G3,G6: 2.. / G3 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) H3,H7: 2.. / H3 = 2 => 0 pairs (X) / H7 = 2 => 0 pairs (_) I5,I9: 2.. / I5 = 2 => 0 pairs (*) / I9 = 2 => 0 pairs (X) B2,C2: 5.. / B2 = 5 => 0 pairs (*) / C2 = 5 => 0 pairs (X) B4,C6: 5.. / B4 = 5 => 0 pairs (X) / C6 = 5 => 0 pairs (_) F4,F6: 5.. / F4 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) B4,F4: 5.. / B4 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) C6,F6: 5.. / C6 = 5 => 0 pairs (*) / F6 = 5 => 0 pairs (X) B2,B4: 5.. / B2 = 5 => 0 pairs (*) / B4 = 5 => 0 pairs (X) C2,C6: 5.. / C2 = 5 => 0 pairs (X) / C6 = 5 => 0 pairs (_) C5,C6: 6.. / C5 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) F5,F6: 6.. / F5 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) C5,F5: 6.. / C5 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) C6,F6: 6.. / C6 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) E5,F5: 8.. / E5 = 8 => 20 pairs (_) / F5 = 8 => 0 pairs (*) E9,F9: 8.. / E9 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) E5,E9: 8.. / E5 = 8 => 20 pairs (_) / E9 = 8 => 0 pairs (*) F5,F9: 8.. / F5 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) D1,F1: 9.. / D1 = 9 => 0 pairs (X) / F1 = 9 => 0 pairs (_) G3,H3: 9.. / G3 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B4,C5: 9.. / B4 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) I5,G6: 9.. / I5 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) C7,B8: 9.. / C7 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) H7,I9: 9.. / H7 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) B4,F4: 9.. / B4 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) E6,G6: 9.. / E6 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) C7,H7: 9.. / C7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) B8,D8: 9.. / B8 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) B4,B8: 9.. / B4 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) C5,C7: 9.. / C5 = 9 => 0 pairs (X) / C7 = 9 => 0 pairs (_) D1,D8: 9.. / D1 = 9 => 0 pairs (X) / D8 = 9 => 0 pairs (_) G3,G6: 9.. / G3 = 9 => 0 pairs (X) / G6 = 9 => 0 pairs (_) H3,H7: 9.. / H3 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) I5,I9: 9.. / I5 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) * DURATION: 0:01:20.659168 START: 08:10:52.109552 END: 08:12:12.768720 2017-05-04 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B8,C2,C5,C6,C7,D1,D8,E6,F1,F4,F6,G3,G6,H3,H7,I5,I9) * 637.4.1859..831476184657..32.371.86441.3..75.87.4...3154.1736.83.8.645177615..34. * PAIR F1: 2,9 COL F F5: 2,9,6,8 # reduction candidate for 2,9 F5: 2,9 => CTR * 637.4.1859..831476184657..32.371.86441638.75.8754.6.31549173628328964517761528349 F5: 6,8 # 21 pairs F9: 2,9,8 # reduction candidate for 2,9 F9: 2,9 => SOLVED * 637249185952831476184657293293715864416398752875426931549173628328964517761582349 F9: 8 # 20 pairs * PAIR C5: 6,9 ROW 5 F5: 6,9,2,8 # reduction candidate for 6,9 F5: 6,9 => CTR * 637.4.1859..831476184657..32.371.86441.38.75287.42.93154.1736283289645177615..34. F5: 2,8 => SOLVED * 637249185952831476184657293293715864416398752875426931549173628328964517761582349 * PAIR E6: 2,9 BLK 5 E5: 2,9,8 # reduction candidate for 2,9 E5: 2,9 => SOLVED * 637249185952831476184657293293715864416398752875426931549173628328964517761582349 E5: 8 # 20 pairs F5: 2,9,6,8 # reduction candidate for 2,9 F5: 2,9 => CTR * 637.4.1859..831476184657..32.371.86441638.75.8754.6.31549173628328964517761528349 F5: 6,8 # 21 pairs * PAIR E6: 2,9 COL E E9: 2,9,8 # reduction candidate for 2,9 E9: 8 => SOLVED * 637249185952831476184657293293715864416398752875426931549173628328964517761582349 E9: 2,9 # 20 pairs * PAIR I5: 2,9 ROW 5 E5: 2,9,8 # reduction candidate for 2,9 E5: 2,9 => SOLVED * 637249185952831476184657293293715864416398752875426931549173628328964517761582349 E5: 8 # 20 pairs F5: 2,9,6,8 # reduction candidate for 2,9 F5: 2,9 => CTR * 637.4.1859..831476184657..32.371.86441638.75.8754.6.31549173628328964517761528349 F5: 6,8 # 21 pairs * PAIR D8: 2,9 BLK 8 E9: 2,9,8 # reduction candidate for 2,9 E9: 2,9 # 20 pairs F9: 2,9,8 # reduction candidate for 2,9 F9: 2,9 => SOLVED * 637249185952831476184657293293715864416398752875426931549173628328964517761582349 F9: 8 # 20 pairs * PAIR I9: 2,9 ROW 9 E9: 2,9,8 # reduction candidate for 2,9 E9: 2,9 # 20 pairs F9: 2,9,8 # reduction candidate for 2,9 F9: 2,9 => SOLVED * 637249185952831476184657293293715864416398752875426931549173628328964517761582349 F9: 8 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-159-base-pr-000.dot * REASONING * DIS # F5: 2,9 => CTR => F5: 6,8 * PRF # F9: 2,9 => SOL * DIS # F5: 6,9 => CTR => F5: 2,8 * PRF # F5: 2,8 => SOL * PRF # E5: 2,9 => SOL * DIS # F5: 2,9 => CTR => F5: 6,8 * PRF # E9: 8 => SOL * PRF # E5: 2,9 => SOL * DIS # F5: 2,9 => CTR => F5: 6,8 * PRF # F9: 2,9 => SOL * PRF # F9: 2,9 => SOL * CNT 11 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B4,B8,C2,C5,C6,C7,D1,D8,E6,F1,F4,F6,G3,G6,H3,H7,I5,I9) * 637.4.1859..831476184657..32.371.86441.3..75.87.4...3154.1736.83.8.645177615..34. * PAIR F1: 2,9 COL F F5: 2,9,6,8 # reduction candidate for 2,9 F5: 2,9 => CTR * 637.4.1859..831476184657..32.371.86441638.75.8754.6.31549173628328964517761528349 F9: 2,9,8 # reduction candidate for 2,9 F9: 2,9 => SOLVED * 637249185952831476184657293293715864416398752875426931549173628328964517761582349 * DURATION: 0:00:03.337136 START: 08:12:38.629479 END: 08:12:41.966615 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-159-base-pr-001.dot * REASONING * DIS # F5: 2,9 => CTR => F5: 6,8 * PRF F5: 6,8 # F9: 2,9 => SOL * STA F5: 6,8 + F9: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 159 solution: 637249185952831476184657293293715864416398752875426931549173628328964517761582349 info: 1819 FNBTWX S8.f 35542 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 637249185952831476184657293293715864416398752875426931549173628328964517761582349 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:
* DIS # F5: 2,9 => CTR => F5: 6,8 * INC # F5: 6,8 => UNS * PRF # F9: 2,9 => SOL * INC # F9: 8 => UNS * DIS # F5: 6,9 => CTR => F5: 2,8 * PRF # F5: 2,8 => SOL * PRF # E5: 2,9 => SOL * INC # E5: 8 => UNS * DIS # F5: 2,9 => CTR => F5: 6,8 * INC # F5: 6,8 => UNS * INC # E9: 2,9 => UNS * PRF # E9: 8 => SOL * PRF # E5: 2,9 => SOL * INC # E5: 8 => UNS * DIS # F5: 2,9 => CTR => F5: 6,8 * INC # F5: 6,8 => UNS * INC # E9: 2,9 => UNS * PRF # F9: 2,9 => SOL * INC # F9: 8 => UNS * INC # E9: 2,9 => UNS * PRF # F9: 2,9 => SOL * INC # F9: 8 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F5: 2,9 => CTR => F5: 6,8 * PRF F5: 6,8 # F9: 2,9 => SOL * STA F5: 6,8 + F9: 2,9 * CNT 2 HDP CHAINS / 2 HYP OPENED