Analysis of xx-top500-006-base.sdk
Contents
Original Sudoku
level: medium
position: ....15..97.....4.............389.7...5..........7...........32.1......5..9.6..... initial
Autosolve
position: 3...156797.59..4139.13..582.1389.765.571.329...975.13..765.932113....956592631847 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 4,8 => CTR => B1: 2 * PRF # B1: 2 => SOL * DIS # E2: 8 => CTR => E2: 2,6 * DIS # E3: 4,6 => CTR => E3: 7 * PRF # B1: 2,4 => SOL * DIS # B1: 8 => CTR => B1: 2,4 * DIS # E2: 6,8 => CTR => E2: 2 * PRF # E2: 2 => SOL * DIS # A5: 6 => CTR => A5: 4,8 * DIS # B1: 4,8 => CTR => B1: 2 * PRF # B1: 2 => SOL * PRF # A5: 4,6 => SOL * DIS # A5: 8 => CTR => A5: 4,6 * DIS # E3: 4,6 => CTR => E3: 7 * DIS # A5: 6 => CTR => A5: 4,8 * DIS # A5: 6 => CTR => A5: 4,8 * PRF # E8: 4,8 => SOL * DIS # F8: 4,8 => CTR => F8: 7 * PRF # E8: 4,8 => SOL * DIS # F8: 4,8 => CTR => F8: 7 * DIS # E8: 2,4 => CTR => E8: 7,8 * PRF # E8: 7,8 => SOL * CNT 22 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 4,8 => CTR => B1: 2 * PRF B1: 2 => SOL * STA B1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....15..97.....4.............389.7...5..........7...........32.1......5..9.6..... | initial |
| 3...156797.59..4139.13..582.1389.765.571.329...975.13..765.932113....956592631847 | autosolve |
| 328415679765928413941376582213894765457163298689752134876549321134287956592631847 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 4,8 B2: 2,6 B3: 4,6 D1: 2,4 F2: 6,8 A4: 2,4 A6: 2,6 B6: 4,8 F4: 2,4 E5: 4,6 F6: 2,6 I5: 4,8 I6: 4,8 A7: 4,8 C8: 4,8 E7: 4,8 D8: 2,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B2: 2.. / B1 = 2 => 0 pairs (*) / B2 = 2 => 0 pairs (X) D1,E2: 2.. / D1 = 2 => 0 pairs (X) / E2 = 2 => 0 pairs (_) A4,A6: 2.. / A4 = 2 => 17 pairs (_) / A6 = 2 => 0 pairs (X) F4,F6: 2.. / F4 = 2 => 0 pairs (X) / F6 = 2 => 17 pairs (_) D8,E8: 2.. / D8 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) B1,D1: 2.. / B1 = 2 => 0 pairs (*) / D1 = 2 => 0 pairs (X) B2,E2: 2.. / B2 = 2 => 0 pairs (X) / E2 = 2 => 0 pairs (_) A4,F4: 2.. / A4 = 2 => 17 pairs (_) / F4 = 2 => 0 pairs (X) A6,F6: 2.. / A6 = 2 => 0 pairs (X) / F6 = 2 => 17 pairs (_) D1,D8: 2.. / D1 = 2 => 0 pairs (X) / D8 = 2 => 0 pairs (_) E2,E8: 2.. / E2 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) F4,E5: 4.. / F4 = 4 => 17 pairs (_) / E5 = 4 => 0 pairs (X) I5,I6: 4.. / I5 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) A7,C8: 4.. / A7 = 4 => 0 pairs (X) / C8 = 4 => 0 pairs (_) A4,F4: 4.. / A4 = 4 => 0 pairs (X) / F4 = 4 => 17 pairs (_) B6,I6: 4.. / B6 = 4 => 0 pairs (X) / I6 = 4 => 0 pairs (_) A7,E7: 4.. / A7 = 4 => 0 pairs (X) / E7 = 4 => 0 pairs (_) C1,C8: 4.. / C1 = 4 => 0 pairs (X) / C8 = 4 => 0 pairs (_) D1,D8: 4.. / D1 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) B2,B3: 6.. / B2 = 6 => 0 pairs (*) / B3 = 6 => 0 pairs (X) A5,A6: 6.. / A5 = 6 => 0 pairs (X) / A6 = 6 => 17 pairs (_) E5,F6: 6.. / E5 = 6 => 17 pairs (_) / F6 = 6 => 0 pairs (X) A5,E5: 6.. / A5 = 6 => 0 pairs (X) / E5 = 6 => 17 pairs (_) A6,F6: 6.. / A6 = 6 => 17 pairs (_) / F6 = 6 => 0 pairs (X) E3,F3: 7.. / E3 = 7 => 18 pairs (_) / F3 = 7 => 0 pairs (X) E8,F8: 7.. / E8 = 7 => 0 pairs (X) / F8 = 7 => 18 pairs (_) E3,E8: 7.. / E3 = 7 => 18 pairs (_) / E8 = 7 => 0 pairs (X) F3,F8: 7.. / F3 = 7 => 0 pairs (X) / F8 = 7 => 18 pairs (_) B1,C1: 8.. / B1 = 8 => 0 pairs (X) / C1 = 8 => 0 pairs (_) E2,F2: 8.. / E2 = 8 => 0 pairs (X) / F2 = 8 => 18 pairs (_) A5,B6: 8.. / A5 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) I5,I6: 8.. / I5 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) A7,C8: 8.. / A7 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) A5,I5: 8.. / A5 = 8 => 0 pairs (X) / I5 = 8 => 0 pairs (_) B6,I6: 8.. / B6 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) A7,E7: 8.. / A7 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) A5,A7: 8.. / A5 = 8 => 0 pairs (X) / A7 = 8 => 0 pairs (_) B1,B6: 8.. / B1 = 8 => 0 pairs (X) / B6 = 8 => 0 pairs (_) C1,C8: 8.. / C1 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) F2,F8: 8.. / F2 = 8 => 18 pairs (_) / F8 = 8 => 0 pairs (X) * DURATION: 0:01:16.070416 START: 02:46:48.845961 END: 02:48:04.916377 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B2,B3,B6,C1,C8,D1,D8,E5,E7,F2,F4,F6,I5,I6) * 3...156797.59..4139.13..582.1389.765.571.329...975.13..765.932113....956592631847 * PAIR C1: 4,8 BLK 1 B1: 4,8,2 # reduction candidate for 4,8 B1: 4,8 => CTR * 3.42156797259.8413961374582413892765.5714329828975.13..765.932113.427956592631847 B1: 2 => SOLVED * 328415679765928413941376582213894765457163298689752134876549321134287956592631847 * PAIR B2: 2,6 ROW 2 E2: 2,6,8 # reduction candidate for 2,6 E2: 8 => CTR * 3..2156797259864139613..582.1389.765.5716329.6.975213.87654932113....956592631847 E2: 2,6 # 18 pairs * PAIR B3: 4,6 ROW 3 E3: 4,6,7 # reduction candidate for 4,6 E3: 4,6 => CTR * 3...156797.59284139.1367582.1389.7656571432982.975.13..765.932113..7.956592631847 E3: 7 # 18 pairs F3: 4,6,7 # reduction candidate for 4,6 F3: 4,6 # 18 pairs * PAIR D1: 2,4 ROW 1 B1: 2,4,8 # reduction candidate for 2,4 B1: 2,4 => SOLVED * 328415679765928413941376582213894765457163298689752134876549321134287956592631847 B1: 8 => CTR * 3842156797259..4139613..582.1389.76585716329464975213847658932113....956592631847 * PAIR F2: 6,8 BLK 2 E2: 6,8,2 # reduction candidate for 6,8 E2: 6,8 => CTR * 3.42156797259.8413961374582413892765.5714329828975.13..765.932113.427956592631847 E2: 2 => SOLVED * 328415679765928413941376582213894765457163298689752134876549321134287956592631847 * PAIR B6: 4,8 BLK 4 A5: 4,8,6 # reduction candidate for 4,8 A5: 6 => CTR * 3...156797.59..4139.13..582.1389.7656571432982.975.13..765.932113....956592631847 A5: 4,8 # 17 pairs * PAIR B6: 4,8 COL B B1: 4,8,2 # reduction candidate for 4,8 B1: 4,8 => CTR * 3.42156797259.8413961374582413892765.5714329828975.13..765.932113.427956592631847 B1: 2 => SOLVED * 328415679765928413941376582213894765457163298689752134876549321134287956592631847 * PAIR E5: 4,6 ROW 5 A5: 4,6,8 # reduction candidate for 4,6 A5: 4,6 => SOLVED * 328415679765928413941376582213894765457163298689752134876549321134287956592631847 A5: 8 => CTR * 3842156797.59..4139.13..582.1389.765857163294649752138476589321138...956592631847 * PAIR E5: 4,6 COL E E3: 4,6,7 # reduction candidate for 4,6 E3: 4,6 => CTR * 3...156797.59284139.1367582.1389.7656571432982.975.13..765.932113..7.956592631847 E3: 7 # 18 pairs * PAIR I5: 4,8 ROW 5 A5: 4,8,6 # reduction candidate for 4,8 A5: 6 => CTR * 3...156797.59..4139.13..582.1389.7656571432982.975.13..765.932113....956592631847 A5: 4,8 # 17 pairs * PAIR A7: 4,8 COL A A5: 4,8,6 # reduction candidate for 4,8 A5: 6 => CTR * 3...156797.59..4139.13..582.1389.7656571432982.975.13..765.932113....956592631847 A5: 4,8 # 17 pairs * PAIR C8: 4,8 ROW 8 E8: 4,8,2,7 # reduction candidate for 4,8 E8: 4,8 => SOLVED * 328415679765928413941376582213894765457163298689752134876549321134287956592631847 E8: 2,7 # 18 pairs F8: 4,8,7 # reduction candidate for 4,8 F8: 4,8 => CTR * 3...156797.59284139.1367582.1389.7656571432982.975.13..765.932113..7.956592631847 F8: 7 # 18 pairs * PAIR E7: 4,8 BLK 8 E8: 4,8,2,7 # reduction candidate for 4,8 E8: 4,8 => SOLVED * 328415679765928413941376582213894765457163298689752134876549321134287956592631847 E8: 2,7 # 18 pairs F8: 4,8,7 # reduction candidate for 4,8 F8: 4,8 => CTR * 3...156797.59284139.1367582.1389.7656571432982.975.13..765.932113..7.956592631847 F8: 7 # 18 pairs * PAIR D8: 2,4 BLK 8 E8: 2,4,7,8 # reduction candidate for 2,4 E8: 2,4 => CTR * 38421567972596841396137458241389.765.571.329...975.13..76589321138..7956592631847 E8: 7,8 => SOLVED * 328415679765928413941376582213894765457163298689752134876549321134287956592631847 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-006-base-pr-000.dot * REASONING * DIS # B1: 4,8 => CTR => B1: 2 * PRF # B1: 2 => SOL * DIS # E2: 8 => CTR => E2: 2,6 * DIS # E3: 4,6 => CTR => E3: 7 * PRF # B1: 2,4 => SOL * DIS # B1: 8 => CTR => B1: 2,4 * DIS # E2: 6,8 => CTR => E2: 2 * PRF # E2: 2 => SOL * DIS # A5: 6 => CTR => A5: 4,8 * DIS # B1: 4,8 => CTR => B1: 2 * PRF # B1: 2 => SOL * PRF # A5: 4,6 => SOL * DIS # A5: 8 => CTR => A5: 4,6 * DIS # E3: 4,6 => CTR => E3: 7 * DIS # A5: 6 => CTR => A5: 4,8 * DIS # A5: 6 => CTR => A5: 4,8 * PRF # E8: 4,8 => SOL * DIS # F8: 4,8 => CTR => F8: 7 * PRF # E8: 4,8 => SOL * DIS # F8: 4,8 => CTR => F8: 7 * DIS # E8: 2,4 => CTR => E8: 7,8 * PRF # E8: 7,8 => SOL * CNT 22 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B2,B3,B6,C1,C8,D1,D8,E5,E7,F2,F4,F6,I5,I6) * 3...156797.59..4139.13..582.1389.765.571.329...975.13..765.932113....956592631847 * PAIR C1: 4,8 BLK 1 B1: 4,8,2 # reduction candidate for 4,8 B1: 4,8 => CTR * 3.42156797259.8413961374582413892765.5714329828975.13..765.932113.427956592631847 B1: 2 => SOLVED * 328415679765928413941376582213894765457163298689752134876549321134287956592631847 * DURATION: 0:00:03.090000 START: 02:48:42.156669 END: 02:48:45.246669 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-006-base-pr-001.dot * REASONING * DIS # B1: 4,8 => CTR => B1: 2 * PRF B1: 2 => SOL * STA B1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 006 solution: 328415679765928413941376582213894765457163298689752134876549321134287956592631847 info: 1306 FNBTWXY S8.f 40669 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 328415679765928413941376582213894765457163298689752134876549321134287956592631847 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 # B1: 4,8 => CTR => B1: 2 * PRF # B1: 2 => SOL * INC # E2: 2,6 => UNS * DIS # E2: 8 => CTR => E2: 2,6 * DIS # E3: 4,6 => CTR => E3: 7 * INC # E3: 7 => UNS * INC # F3: 4,6 => UNS * PRF # B1: 2,4 => SOL * DIS # B1: 8 => CTR => B1: 2,4 * DIS # E2: 6,8 => CTR => E2: 2 * PRF # E2: 2 => SOL * INC # A5: 4,8 => UNS * DIS # A5: 6 => CTR => A5: 4,8 * DIS # B1: 4,8 => CTR => B1: 2 * PRF # B1: 2 => SOL * PRF # A5: 4,6 => SOL * DIS # A5: 8 => CTR => A5: 4,6 * DIS # E3: 4,6 => CTR => E3: 7 * INC # E3: 7 => UNS * INC # A5: 4,8 => UNS * DIS # A5: 6 => CTR => A5: 4,8 * INC # A5: 4,8 => UNS * DIS # A5: 6 => CTR => A5: 4,8 * PRF # E8: 4,8 => SOL * INC # E8: 2,7 => UNS * DIS # F8: 4,8 => CTR => F8: 7 * INC # F8: 7 => UNS * PRF # E8: 4,8 => SOL * INC # E8: 2,7 => UNS * DIS # F8: 4,8 => CTR => F8: 7 * INC # F8: 7 => UNS * DIS # E8: 2,4 => CTR => E8: 7,8 * PRF # E8: 7,8 => SOL * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 4,8 => CTR => B1: 2 * PRF B1: 2 => SOL * STA B1: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED