Analysis of xx-top500-017-base.sdk
Contents
Original Sudoku
level: medium
position: .1..4.67.3..8...........5......71...9......3...........4....2.....9....8..73..... initial
Autosolve
position: .18.4967337.81.9244.973.581.34.718.99.14..73.78..9341..431..2971..9.7348.973.41.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A4: 6 => CTR => A4: 2,5 * DIS # C8: 5,6 => CTR => C8: 2 * DIS # B8: 2,6 => CTR => B8: 5 * DIS # D6: 2,5 => CTR => D6: 6 * DIS # F5: 5,8 => CTR => F5: 2 * PRF # F5: 2 => SOL * DIS # E7: 6 => CTR => E7: 5,8 * DIS # I6: 5,6 => CTR => I6: 2 * DIS # A4: 5,6 => CTR => A4: 2 * PRF # A4: 2 => SOL * PRF # D4: 5,6 => SOL * DIS # D4: 2 => CTR => D4: 5,6 * DIS # E7: 6 => CTR => E7: 5,8 * DIS # A7: 5,8 => CTR => A7: 6 * DIS # F5: 5,8 => CTR => F5: 2 * PRF # F5: 2 => SOL * DIS # I6: 5,6 => CTR => I6: 2 * CNT 17 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A4: 6 => CTR => A4: 2,5 * DIS A4: 2,5 # C6: 2 => CTR => C6: 5,6 * PRF A4: 2,5 + C6: 5,6 # D4: 2,5 => SOL * STA A4: 2,5 + C6: 5,6 + D4: 2,5 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1..4.67.3..8...........5......71...9......3...........4....2.....9....8..73..... | initial |
| .18.4967337.81.9244.973.581.34.718.99.14..73.78..9341..431..2971..9.7348.973.41.. | autosolve |
| 518249673376815924429736581234571869961482735785693412643158297152967348897324156 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 2,5 C2: 5,6 B3: 2,6 D1: 2,5 F2: 5,6 F3: 2,6 E5: 5,8 H4: 5,6 A9: 2,8 F7: 5,8 E9: 2,8 H9: 5,6 I9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B3: 2.. / A1 = 2 => 0 pairs (X) / B3 = 2 => 0 pairs (_) D1,F3: 2.. / D1 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) I5,I6: 2.. / I5 = 2 => 0 pairs (X) / I6 = 2 => 17 pairs (_) E8,E9: 2.. / E8 = 2 => 0 pairs (X) / E9 = 2 => 13 pairs (_) A1,D1: 2.. / A1 = 2 => 0 pairs (X) / D1 = 2 => 0 pairs (_) B3,F3: 2.. / B3 = 2 => 0 pairs (*) / F3 = 2 => 0 pairs (X) A4,D4: 2.. / A4 = 2 => 0 pairs (*) / D4 = 2 => 0 pairs (X) A9,E9: 2.. / A9 = 2 => 0 pairs (X) / E9 = 2 => 13 pairs (_) C6,C8: 2.. / C6 = 2 => 0 pairs (X) / C8 = 2 => 15 pairs (_) F3,F5: 2.. / F3 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) A1,C2: 5.. / A1 = 5 => 0 pairs (*) / C2 = 5 => 0 pairs (X) D1,F2: 5.. / D1 = 5 => 0 pairs (X) / F2 = 5 => 0 pairs (_) H9,I9: 5.. / H9 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) A1,D1: 5.. / A1 = 5 => 0 pairs (*) / D1 = 5 => 0 pairs (X) C2,F2: 5.. / C2 = 5 => 0 pairs (X) / F2 = 5 => 0 pairs (_) B5,B8: 5.. / B5 = 5 => 0 pairs (X) / B8 = 5 => 17 pairs (_) H4,H9: 5.. / H4 = 5 => 14 pairs (_) / H9 = 5 => 0 pairs (*) C2,B3: 6.. / C2 = 6 => 0 pairs (*) / B3 = 6 => 0 pairs (X) F2,F3: 6.. / F2 = 6 => 0 pairs (X) / F3 = 6 => 0 pairs (_) D4,D6: 6.. / D4 = 6 => 0 pairs (X) / D6 = 6 => 16 pairs (_) E7,E8: 6.. / E7 = 6 => 0 pairs (X) / E8 = 6 => 15 pairs (_) H9,I9: 6.. / H9 = 6 => 14 pairs (_) / I9 = 6 => 0 pairs (*) C2,F2: 6.. / C2 = 6 => 0 pairs (*) / F2 = 6 => 0 pairs (X) B3,F3: 6.. / B3 = 6 => 0 pairs (X) / F3 = 6 => 0 pairs (_) B5,I5: 6.. / B5 = 6 => 0 pairs (*) / I5 = 6 => 0 pairs (X) A7,E7: 6.. / A7 = 6 => 15 pairs (_) / E7 = 6 => 0 pairs (X) A4,A7: 6.. / A4 = 6 => 0 pairs (X) / A7 = 6 => 15 pairs (_) H4,H9: 6.. / H4 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) E5,F5: 8.. / E5 = 8 => 13 pairs (_) / F5 = 8 => 0 pairs (X) A7,A9: 8.. / A7 = 8 => 0 pairs (X) / A9 = 8 => 13 pairs (_) A9,E9: 8.. / A9 = 8 => 13 pairs (_) / E9 = 8 => 0 pairs (X) F5,F7: 8.. / F5 = 8 => 0 pairs (X) / F7 = 8 => 13 pairs (_) * DURATION: 0:01:01.155703 START: 03:09:45.851597 END: 03:10:47.007300 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A9,B3,C2,D1,E5,E9,F2,F3,F7,H4,H9,I9) * .18.4967337.81.9244.973.581.34.718.99.14..73.78..9341..431..2971..9.7348.973.41.. * PAIR A1: 2,5 COL A A4: 2,5,6 # reduction candidate for 2,5 A4: 6 => CTR * .18.4967337.81.9244.973.5816342718599.14..73678.693412.4316.2971.2957348897324165 A4: 2,5 # 15 pairs * PAIR C2: 5,6 COL C C6: 5,6,2 # reduction candidate for 5,6 C6: 5,6 # 15 pairs C8: 5,6,2 # reduction candidate for 5,6 C8: 5,6 => CTR * 218549673375816924469732581.342718.99.14..732782693415.431..2971..9.7348.973.4156 C8: 2 # 15 pairs * PAIR B3: 2,6 COL B B5: 2,6,5 # reduction candidate for 2,6 B5: 2,6 # 17 pairs B8: 2,6,5 # reduction candidate for 2,6 B8: 2,6 => CTR * .1824967337581.9244.973.581.34.718.995148273678..93412.431.82971.2957348897324165 B8: 5 # 17 pairs * PAIR D1: 2,5 COL D D4: 2,5,6 # reduction candidate for 2,5 D4: 2,5 # 16 pairs D6: 2,5,6 # reduction candidate for 2,5 D6: 2,5 => CTR * 51824967337681592442973658123467185996145.73.78..9341.6431..2971..967348897324165 D6: 6 # 16 pairs * PAIR E5: 5,8 BLK 5 F5: 5,8,2 # reduction candidate for 5,8 F5: 5,8 => CTR * 218549673375816924469732581.342718.99.14..73678.69341..431..2971..9.7348.973.41.. F5: 2 => SOLVED * 518249673376815924429736581234571869961482735785693412643158297152967348897324156 * PAIR E5: 5,8 COL E E7: 5,8,6 # reduction candidate for 5,8 E7: 6 => CTR * .18.4967337.81.9244.973.5816342718599.14..73678.693412.4316.2971.2957348897324165 E7: 5,8 # 15 pairs * PAIR H4: 5,6 BLK 6 I5: 5,6,2 # reduction candidate for 5,6 I5: 5,6 # 17 pairs I6: 5,6,2 # reduction candidate for 5,6 I6: 5,6 => CTR * .18.4967337.81.9244.9732581.34.718.99614..73278..9341..431..2971..9.7348.973.41.. I6: 2 # 17 pairs * PAIR H4: 5,6 ROW 4 A4: 5,6,2 # reduction candidate for 5,6 A4: 5,6 => CTR * 21854967337581692446973258163427185995148.73.78.69341..431..2971..9.7348.973.41.. A4: 2 => SOLVED * 518249673376815924429736581234571869961482735785693412643158297152967348897324156 D4: 5,6,2 # reduction candidate for 5,6 D4: 5,6 => SOLVED * 518249673376815924429736581234571869961482735785693412643158297152967348897324156 D4: 2 => CTR * 21854967337581692446973258163427185995148.73.78.69341..431..2971..9.7348.973.41.. * PAIR F7: 5,8 BLK 8 E7: 5,8,6 # reduction candidate for 5,8 E7: 6 => CTR * .18.4967337.81.9244.973.5816342718599.14..73678.693412.4316.2971.2957348897324165 E7: 5,8 # 15 pairs * PAIR F7: 5,8 ROW 7 A7: 5,8,6 # reduction candidate for 5,8 A7: 5,8 => CTR * .18.4967337.81.9244.973.5816342718599.14..73678.693412.4316.2971.2957348897324165 A7: 6 # 15 pairs * PAIR F7: 5,8 COL F F5: 5,8,2 # reduction candidate for 5,8 F5: 5,8 => CTR * 218549673375816924469732581.342718.99.14..73678.69341..431..2971..9.7348.973.41.. F5: 2 => SOLVED * 518249673376815924429736581234571869961482735785693412643158297152967348897324156 * PAIR I9: 5,6 COL I I5: 5,6,2 # reduction candidate for 5,6 I5: 5,6 # 17 pairs I6: 5,6,2 # reduction candidate for 5,6 I6: 5,6 => CTR * .18.4967337.81.9244.9732581.34.718.99614..73278..9341..431..2971..9.7348.973.41.. I6: 2 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-017-base-pr-000.dot * REASONING * DIS # A4: 6 => CTR => A4: 2,5 * DIS # C8: 5,6 => CTR => C8: 2 * DIS # B8: 2,6 => CTR => B8: 5 * DIS # D6: 2,5 => CTR => D6: 6 * DIS # F5: 5,8 => CTR => F5: 2 * PRF # F5: 2 => SOL * DIS # E7: 6 => CTR => E7: 5,8 * DIS # I6: 5,6 => CTR => I6: 2 * DIS # A4: 5,6 => CTR => A4: 2 * PRF # A4: 2 => SOL * PRF # D4: 5,6 => SOL * DIS # D4: 2 => CTR => D4: 5,6 * DIS # E7: 6 => CTR => E7: 5,8 * DIS # A7: 5,8 => CTR => A7: 6 * DIS # F5: 5,8 => CTR => F5: 2 * PRF # F5: 2 => SOL * DIS # I6: 5,6 => CTR => I6: 2 * CNT 17 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A9,B3,C2,D1,E5,E9,F2,F3,F7,H4,H9,I9) * .18.4967337.81.9244.973.581.34.718.99.14..73.78..9341..431..2971..9.7348.973.41.. * PAIR A1: 2,5 COL A A4: 2,5,6 # reduction candidate for 2,5 A4: 6 => CTR * .18.4967337.81.9244.973.5816342718599.14..73678.693412.4316.2971.2957348897324165 * PAIR RESTART * PAIR C2: 5,6 COL C C6: 5,6,2 # reduction candidate for 5,6 C6: 2 => CTR * .18.49673376815924429736581234.718.99.14..73.78..9341.6431..2971..9673488973241.. * PAIR RESTART * PAIR D1: 2,5 COL D D4: 2,5,6 # reduction candidate for 2,5 D4: 2,5 => SOLVED * 518249673376815924429736581234571869961482735785693412643158297152967348897324156 * DURATION: 0:00:06.715196 START: 03:11:22.643619 END: 03:11:29.358815 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-017-base-pr-001.dot * REASONING * DIS # A4: 6 => CTR => A4: 2,5 * DIS A4: 2,5 # C6: 2 => CTR => C6: 5,6 * PRF A4: 2,5 + C6: 5,6 # D4: 2,5 => SOL * STA A4: 2,5 + C6: 5,6 + D4: 2,5 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 017 solution: 518249673376815924429736581234571869961482735785693412643158297152967348897324156 info: 1310 FNBWXY S8.f 47982 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 518249673376815924429736581234571869961482735785693412643158297152967348897324156 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 # A4: 2,5 => UNS * DIS # A4: 6 => CTR => A4: 2,5 * INC # C6: 5,6 => UNS * DIS # C8: 5,6 => CTR => C8: 2 * INC # C8: 2 => UNS * INC # B5: 2,6 => UNS * DIS # B8: 2,6 => CTR => B8: 5 * INC # B8: 5 => UNS * INC # D4: 2,5 => UNS * DIS # D6: 2,5 => CTR => D6: 6 * INC # D6: 6 => UNS * DIS # F5: 5,8 => CTR => F5: 2 * PRF # F5: 2 => SOL * INC # E7: 5,8 => UNS * DIS # E7: 6 => CTR => E7: 5,8 * INC # I5: 5,6 => UNS * DIS # I6: 5,6 => CTR => I6: 2 * INC # I6: 2 => UNS * DIS # A4: 5,6 => CTR => A4: 2 * PRF # A4: 2 => SOL * PRF # D4: 5,6 => SOL * DIS # D4: 2 => CTR => D4: 5,6 * INC # E7: 5,8 => UNS * DIS # E7: 6 => CTR => E7: 5,8 * DIS # A7: 5,8 => CTR => A7: 6 * INC # A7: 6 => UNS * DIS # F5: 5,8 => CTR => F5: 2 * PRF # F5: 2 => SOL * INC # I5: 5,6 => UNS * DIS # I6: 5,6 => CTR => I6: 2 * INC # I6: 2 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A4: 2,5 => UNS * DIS # A4: 6 => CTR => A4: 2,5 * INC A4: 2,5 # C6: 5,6 => UNS * DIS A4: 2,5 # C6: 2 => CTR => C6: 5,6 * PRF A4: 2,5 + C6: 5,6 # D4: 2,5 => SOL * STA A4: 2,5 + C6: 5,6 + D4: 2,5 * CNT 5 HDP CHAINS / 5 HYP OPENED