Analysis of xx-top500-448-base.sdk
Contents
Original Sudoku
level: medium
position: 1......28...3.5......6.....82..1..........34...........64...5....3...7.1......... initial
Autosolve
position: 135.4.628486325179972681435827413956651...34.349...81..641..5.3.93..47.1.18.3.2.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D5: 7,9 => CTR => D5: 2,8 * DIS # D9: 7,9 => CTR => D9: 5 * PRF # D9: 5 => SOL * DIS # F5: 7,9 => CTR => F5: 2,8 * PRF # F9: 7,9 => SOL * DIS # F9: 6 => CTR => F9: 7,9 * DIS # D5: 7,9 => CTR => D5: 2,8 * DIS # F5: 7,9 => CTR => F5: 2,8 * DIS # D5: 2,7 => CTR => D5: 8,9 * PRF # F5: 2,7 => SOL * PRF # D6: 2,7 => SOL * DIS # D6: 5 => CTR => D6: 2,7 * DIS # F6: 2,7 => CTR => F6: 6 * PRF # F6: 6 => SOL * DIS # D9: 9 => CTR => D9: 5,7 * DIS # D9: 7,9 => CTR => D9: 5 * PRF # D9: 5 => SOL * PRF # F9: 7,9 => SOL * DIS # F9: 6 => CTR => F9: 7,9 * DIS # F5: 7,9 => CTR => F5: 2,8 * DIS # D5: 7,9 => CTR => D5: 2,8 * DIS # F9: 7 => CTR => F9: 6,9 * CNT 22 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D5: 7,9 => CTR => D5: 2,8 * DIS D5: 2,8 # D9: 7,9 => CTR => D9: 5 * PRF D5: 2,8 + D9: 5 => SOL * STA D5: 2,8 + D9: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1......28...3.5......6.....82..1..........34...........64...5....3...7.1......... | initial |
| 135.4.628486325179972681435827413956651...34.349...81..641..5.3.93..47.1.18.3.2.4 | autosolve |
| 135947628486325179972681435827413956651892347349756812264178593593264781718539264 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) D1: 7,9 F1: 7,9 E5: 7,9 E6: 5,6 I5: 2,7 I6: 2,7 A7: 2,7 A8: 2,5 A9: 5,7 E7: 7,9 F7: 2,8 D8: 2,8 E8: 5,6 H7: 8,9 H8: 6,8 H9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I5,I6: 2.. / I5 = 2 => 16 pairs (_) / I6 = 2 => 0 pairs (*) A7,A8: 2.. / A7 = 2 => 0 pairs (*) / A8 = 2 => 0 pairs (X) F7,D8: 2.. / F7 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) A7,F7: 2.. / A7 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) A8,D8: 2.. / A8 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) D6,E6: 5.. / D6 = 5 => 0 pairs (X) / E6 = 5 => 0 pairs (_) A8,A9: 5.. / A8 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) E8,D9: 5.. / E8 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) A8,E8: 5.. / A8 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) A9,D9: 5.. / A9 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) D6,D9: 5.. / D6 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) E6,E8: 5.. / E6 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) E6,F6: 6.. / E6 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) E8,F9: 6.. / E8 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) H8,H9: 6.. / H8 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) E8,H8: 6.. / E8 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) F9,H9: 6.. / F9 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) E6,E8: 6.. / E6 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) F6,F9: 6.. / F6 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) D1,F1: 7.. / D1 = 7 => 17 pairs (_) / F1 = 7 => 17 pairs (_) I5,I6: 7.. / I5 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) A7,A9: 7.. / A7 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) A7,E7: 7.. / A7 = 7 => 0 pairs (X) / E7 = 7 => 0 pairs (_) E5,E7: 7.. / E5 = 7 => 0 pairs (X) / E7 = 7 => 0 pairs (_) D5,F5: 8.. / D5 = 8 => 0 pairs (*) / F5 = 8 => 0 pairs (X) F7,D8: 8.. / F7 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) H7,H8: 8.. / H7 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) F7,H7: 8.. / F7 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) D8,H8: 8.. / D8 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) D5,D8: 8.. / D5 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) F5,F7: 8.. / F5 = 8 => 0 pairs (X) / F7 = 8 => 0 pairs (_) D1,F1: 9.. / D1 = 9 => 17 pairs (_) / F1 = 9 => 17 pairs (_) H7,H9: 9.. / H7 = 9 => 0 pairs (*) / H9 = 9 => 0 pairs (X) E7,H7: 9.. / E7 = 9 => 0 pairs (X) / H7 = 9 => 0 pairs (_) E5,E7: 9.. / E5 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) * DURATION: 0:01:06.900530 START: 18:03:23.927166 END: 18:04:30.827696 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,A9,D1,D8,E5,E6,E7,E8,F1,F7,H7,H8,H9,I5,I6) * 135.4.628486325179972681435827413956651...34.349...81..641..5.3.93..47.1.18.3.2.4 * PAIR D1: 7,9 COL D D5: 7,9,2,8 # reduction candidate for 7,9 D5: 7,9 => CTR * 135.4.628486325179972681435827413956651..8342349...817.641.2583293854761518.362.4 D5: 2,8 # 18 pairs D9: 7,9,5 # reduction candidate for 7,9 D9: 7,9 => CTR * 135.4.628486325179972681435827413956651...34.34956.81.764192583293854761518736294 D9: 5 => SOLVED * 135947628486325179972681435827413956651892347349756812264178593593264781718539264 * PAIR F1: 7,9 COL F F5: 7,9,2,8 # reduction candidate for 7,9 F5: 7,9 => CTR * 135.4.6284863251799726814358274139566518..342349...817.641.8593.932.4781.18.3.264 F5: 2,8 # 18 pairs F9: 7,9,6 # reduction candidate for 7,9 F9: 7,9 => SOLVED * 135947628486325179972681435827413956651892347349756812264178593593264781718539264 F9: 6 => CTR * 135947628486325179972681435827413956651...34.349.6.81..6419.583.93854761518736294 * PAIR E5: 7,9 BLK 5 D5: 7,9,2,8 # reduction candidate for 7,9 D5: 7,9 => CTR * 135.4.628486325179972681435827413956651..8342349...817.641.2583293854761518.362.4 D5: 2,8 # 18 pairs F5: 7,9,2,8 # reduction candidate for 7,9 F5: 7,9 => CTR * 135.4.6284863251799726814358274139566518..342349...817.641.8593.932.4781.18.3.264 F5: 2,8 # 18 pairs * PAIR I5: 2,7 ROW 5 D5: 2,7,8,9 # reduction candidate for 2,7 D5: 2,7 => CTR * 135947628486325179972681435827413956651..834.349...81..641.2583293854761518.36294 D5: 8,9 # 17 pairs F5: 2,7,8,9 # reduction candidate for 2,7 F5: 2,7 => SOLVED * 135947628486325179972681435827413956651892347349756812264178593593264781718539264 F5: 8,9 # 17 pairs * PAIR I6: 2,7 ROW 6 D6: 2,7,5 # reduction candidate for 2,7 D6: 2,7 => SOLVED * 135947628486325179972681435827413956651892347349756812264178593593264781718539264 D6: 5 => CTR * 135.4.628486325179972681435827413956651...34.34956.81.764192583293854761518736294 F6: 2,7,6 # reduction candidate for 2,7 F6: 2,7 => CTR * 135.4.628486325179972681435827413956651...34.34956.81.764192583293854761518736294 F6: 6 => SOLVED * 135947628486325179972681435827413956651892347349756812264178593593264781718539264 * PAIR A9: 5,7 ROW 9 D9: 5,7,9 # reduction candidate for 5,7 D9: 9 => CTR * 135.4.628486325179972681435827413956651...34.34956.81..641..5.3.93.5476151893.2.4 D9: 5,7 # 18 pairs * PAIR E7: 7,9 BLK 8 D9: 7,9,5 # reduction candidate for 7,9 D9: 7,9 => CTR * 135.4.628486325179972681435827413956651...34.34956.81.764192583293854761518736294 D9: 5 => SOLVED * 135947628486325179972681435827413956651892347349756812264178593593264781718539264 F9: 7,9,6 # reduction candidate for 7,9 F9: 7,9 => SOLVED * 135947628486325179972681435827413956651892347349756812264178593593264781718539264 F9: 6 => CTR * 135947628486325179972681435827413956651...34.349.6.81..6419.583.93854761518736294 * PAIR F7: 2,8 COL F F5: 2,8,7,9 # reduction candidate for 2,8 F5: 7,9 => CTR * 135.4.6284863251799726814358274139566518..342349...817.641.8593.932.4781.18.3.264 F5: 2,8 # 18 pairs * PAIR D8: 2,8 COL D D5: 2,8,7,9 # reduction candidate for 2,8 D5: 7,9 => CTR * 135.4.628486325179972681435827413956651..8342349...817.641.2583293854761518.362.4 D5: 2,8 # 18 pairs * PAIR H9: 6,9 ROW 9 F9: 6,9,7 # reduction candidate for 6,9 F9: 7 => CTR * 135.4.628486325179972681435827413956651...34.349..681..641..5.3.93.64781.185372.4 F9: 6,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-448-base-pr-000.dot * REASONING * DIS # D5: 7,9 => CTR => D5: 2,8 * DIS # D9: 7,9 => CTR => D9: 5 * PRF # D9: 5 => SOL * DIS # F5: 7,9 => CTR => F5: 2,8 * PRF # F9: 7,9 => SOL * DIS # F9: 6 => CTR => F9: 7,9 * DIS # D5: 7,9 => CTR => D5: 2,8 * DIS # F5: 7,9 => CTR => F5: 2,8 * DIS # D5: 2,7 => CTR => D5: 8,9 * PRF # F5: 2,7 => SOL * PRF # D6: 2,7 => SOL * DIS # D6: 5 => CTR => D6: 2,7 * DIS # F6: 2,7 => CTR => F6: 6 * PRF # F6: 6 => SOL * DIS # D9: 9 => CTR => D9: 5,7 * DIS # D9: 7,9 => CTR => D9: 5 * PRF # D9: 5 => SOL * PRF # F9: 7,9 => SOL * DIS # F9: 6 => CTR => F9: 7,9 * DIS # F5: 7,9 => CTR => F5: 2,8 * DIS # D5: 7,9 => CTR => D5: 2,8 * DIS # F9: 7 => CTR => F9: 6,9 * CNT 22 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,A9,D1,D8,E5,E6,E7,E8,F1,F7,H7,H8,H9,I5,I6) * 135.4.628486325179972681435827413956651...34.349...81..641..5.3.93..47.1.18.3.2.4 * PAIR D1: 7,9 COL D D5: 7,9,2,8 # reduction candidate for 7,9 D5: 7,9 => CTR * 135.4.628486325179972681435827413956651..8342349...817.641.2583293854761518.362.4 D9: 7,9,5 # reduction candidate for 7,9 D9: 7,9 => CTR * 135947628486325179972681435827413956651.79342349562817.641..5.3.93.54761518.36294 D9: 5 => SOLVED * 135947628486325179972681435827413956651892347349756812264178593593264781718539264 * DURATION: 0:00:03.025719 START: 18:05:07.821741 END: 18:05:10.847460 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-448-base-pr-001.dot * REASONING * DIS # D5: 7,9 => CTR => D5: 2,8 * DIS D5: 2,8 # D9: 7,9 => CTR => D9: 5 * PRF D5: 2,8 + D9: 5 => SOL * STA D5: 2,8 + D9: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 448 solution: 135947628486325179972681435827413956651892347349756812264178593593264781718539264 info: 95363 FNTHYK S8.f 42780 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 135947628486325179972681435827413956651892347349756812264178593593264781718539264 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 # D5: 7,9 => CTR => D5: 2,8 * INC # D5: 2,8 => UNS * DIS # D9: 7,9 => CTR => D9: 5 * PRF # D9: 5 => SOL * DIS # F5: 7,9 => CTR => F5: 2,8 * INC # F5: 2,8 => UNS * PRF # F9: 7,9 => SOL * DIS # F9: 6 => CTR => F9: 7,9 * DIS # D5: 7,9 => CTR => D5: 2,8 * INC # D5: 2,8 => UNS * DIS # F5: 7,9 => CTR => F5: 2,8 * INC # F5: 2,8 => UNS * DIS # D5: 2,7 => CTR => D5: 8,9 * INC # D5: 8,9 => UNS * PRF # F5: 2,7 => SOL * INC # F5: 8,9 => UNS * PRF # D6: 2,7 => SOL * DIS # D6: 5 => CTR => D6: 2,7 * DIS # F6: 2,7 => CTR => F6: 6 * PRF # F6: 6 => SOL * INC # D9: 5,7 => UNS * DIS # D9: 9 => CTR => D9: 5,7 * DIS # D9: 7,9 => CTR => D9: 5 * PRF # D9: 5 => SOL * PRF # F9: 7,9 => SOL * DIS # F9: 6 => CTR => F9: 7,9 * INC # F5: 2,8 => UNS * DIS # F5: 7,9 => CTR => F5: 2,8 * INC # D5: 2,8 => UNS * DIS # D5: 7,9 => CTR => D5: 2,8 * INC # F9: 6,9 => UNS * DIS # F9: 7 => CTR => F9: 6,9 * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D5: 7,9 => CTR => D5: 2,8 * DIS D5: 2,8 # D9: 7,9 => CTR => D9: 5 * PRF D5: 2,8 + D9: 5 => SOL * STA D5: 2,8 + D9: 5 * CNT 3 HDP CHAINS / 2 HYP OPENED