Analysis of xx-top500-257-base.sdk
Contents
Original Sudoku
level: medium
position: .95....4.....1.....2.......8.....1.6...4.2.........3..3...6....1..9........7...5. initial
Autosolve
position: 6953...41....1.....21....3.8..5..126916432...5721863943...6..1.1..9.3...2..741.53 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G3: 5,7,9 => CTR => G3: 6,8 * DIS # F3: 5,9 => CTR => F3: 4 * DIS # G3: 5,9 => CTR => G3: 6,7,8 * DIS # G8: 2,8 => CTR => G8: 4,6,7 * PRF # G2: 6,7 => SOL * DIS # H8: 8 => CTR => H8: 6,7 * DIS # H8: 7,8 => CTR => H8: 6 * DIS # B8: 6,8 => CTR => B8: 4,5 * DIS # B8: 6,8 => CTR => B8: 4,5 * DIS # G9: 6 => CTR => G9: 8,9 * CNT 10 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G3: 5,7,9 => CTR => G3: 6,8 * DIS G3: 6,8 # F3: 5,9 => CTR => F3: 4 * PRF G3: 6,8 + F3: 4 # G2: 6,7 => SOL * STA G3: 6,8 + F3: 4 + G2: 6,7 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .95....4.....1.....2.......8.....1.6...4.2.........3..3...6....1..9........7...5. | initial |
| 6953...41....1.....21....3.8..5..126916432...5721863943...6..1.1..9.3...2..741.53 | autosolve |
| 695378241483219675721654839834597126916432587572186394349865712157923468268741953 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (22) A2: 4,7 B2: 3,8 C2: 3,8 A3: 4,7 E1: 2,7 F1: 7,8 D2: 2,6 D3: 6,8 E3: 5,9 G1: 2,8 H2: 6,7 B4: 3,4 C4: 3,4 E4: 7,9 F4: 7,9 H5: 7,8 B7: 4,5 B9: 6,8 C9: 8,9 D7: 2,8 F7: 5,8 E8: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,D2: 2.. / E1 = 2 => 0 pairs (X) / D2 = 2 => 0 pairs (_) D7,E8: 2.. / D7 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) E1,G1: 2.. / E1 = 2 => 0 pairs (X) / G1 = 2 => 0 pairs (_) D2,D7: 2.. / D2 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) E1,E8: 2.. / E1 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) B2,C2: 3.. / B2 = 3 => 0 pairs (X) / C2 = 3 => 21 pairs (_) B4,C4: 3.. / B4 = 3 => 21 pairs (_) / C4 = 3 => 0 pairs (X) B2,B4: 3.. / B2 = 3 => 0 pairs (X) / B4 = 3 => 21 pairs (_) C2,C4: 3.. / C2 = 3 => 21 pairs (_) / C4 = 3 => 0 pairs (X) A2,A3: 4.. / A2 = 4 => 21 pairs (_) / A3 = 4 => 0 pairs (X) F2,F3: 4.. / F2 = 4 => 0 pairs (X) / F3 = 4 => 21 pairs (_) B4,C4: 4.. / B4 = 4 => 0 pairs (X) / C4 = 4 => 21 pairs (_) G7,G8: 4.. / G7 = 4 => 0 pairs (X) / G8 = 4 => 23 pairs (_) A2,F2: 4.. / A2 = 4 => 21 pairs (_) / F2 = 4 => 0 pairs (X) A3,F3: 4.. / A3 = 4 => 0 pairs (X) / F3 = 4 => 21 pairs (_) G5,I5: 5.. / G5 = 5 => 23 pairs (_) / I5 = 5 => 23 pairs (_) B7,B8: 5.. / B7 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) F7,E8: 5.. / F7 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) B7,F7: 5.. / B7 = 5 => 0 pairs (X) / F7 = 5 => 0 pairs (_) B8,E8: 5.. / B8 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) E3,E8: 5.. / E3 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) D2,D3: 6.. / D2 = 6 => 0 pairs (X) / D3 = 6 => 0 pairs (_) B8,B9: 6.. / B8 = 6 => 0 pairs (X) / B9 = 6 => 22 pairs (_) D3,G3: 6.. / D3 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) B9,G9: 6.. / B9 = 6 => 22 pairs (_) / G9 = 6 => 0 pairs (X) H2,H8: 6.. / H2 = 6 => 0 pairs (X) / H8 = 6 => 21 pairs (_) A2,A3: 7.. / A2 = 7 => 0 pairs (X) / A3 = 7 => 21 pairs (_) E1,F1: 7.. / E1 = 7 => 0 pairs (*) / F1 = 7 => 0 pairs (X) E4,F4: 7.. / E4 = 7 => 0 pairs (X) / F4 = 7 => 0 pairs (_) C7,C8: 7.. / C7 = 7 => 24 pairs (_) / C8 = 7 => 25 pairs (_) E1,E4: 7.. / E1 = 7 => 0 pairs (*) / E4 = 7 => 0 pairs (X) F1,F4: 7.. / F1 = 7 => 0 pairs (X) / F4 = 7 => 0 pairs (_) B2,C2: 8.. / B2 = 8 => 21 pairs (_) / C2 = 8 => 0 pairs (X) F1,D3: 8.. / F1 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) D7,F7: 8.. / D7 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) F1,G1: 8.. / F1 = 8 => 0 pairs (*) / G1 = 8 => 0 pairs (X) D3,D7: 8.. / D3 = 8 => 0 pairs (X) / D7 = 8 => 0 pairs (_) F1,F7: 8.. / F1 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) H5,H8: 8.. / H5 = 8 => 24 pairs (_) / H8 = 8 => 0 pairs (X) E4,F4: 9.. / E4 = 9 => 0 pairs (*) / F4 = 9 => 0 pairs (X) C7,C9: 9.. / C7 = 9 => 20 pairs (_) / C9 = 9 => 23 pairs (_) C9,G9: 9.. / C9 = 9 => 23 pairs (_) / G9 = 9 => 20 pairs (_) E3,E4: 9.. / E3 = 9 => 0 pairs (X) / E4 = 9 => 0 pairs (_) * DURATION: 0:01:30.105284 START: 11:34:28.954043 END: 11:35:59.059327 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B2,B4,B7,B9,C2,C4,C9,D2,D3,D7,E1,E3,E4,E8,F1,F4,F7,G1,H2,H5) * 6953...41....1.....21....3.8..5..126916432...5721863943...6..1.1..9.3...2..741.53 * PAIR D2: 2,6 ROW 2 G2: 2,6,5,7,9 # reduction candidate for 2,6 G2: 2,6 # 23 pairs G2: 5,7,9 # 22 pairs * PAIR D3: 6,8 ROW 3 G3: 6,8,5,7,9 # reduction candidate for 6,8 G3: 5,7,9 => CTR * 695378241.8321.....2165..38834597126916432..5572186394347865912158923467269741853 G3: 6,8 # 26 pairs * PAIR E3: 5,9 BLK 2 F2: 5,9,4 # reduction candidate for 5,9 F2: 5,9 # 21 pairs F3: 5,9,4 # reduction candidate for 5,9 F3: 5,9 => CTR * 695378241783214.6.421659.3.834597126916432...57218639434.865.1215.9236..26.741.53 F3: 4 # 21 pairs * PAIR E3: 5,9 ROW 3 G3: 5,9,6,7,8 # reduction candidate for 5,9 G3: 5,9 => CTR * 695378241.8321....721654938834597126916432..55721863943..865.1.15.923..726.741.53 G3: 6,7,8 # 22 pairs I3: 5,9,7,8 # reduction candidate for 5,9 I3: 5,9 # 26 pairs * PAIR G1: 2,8 COL G G8: 2,8,4,6,7 # reduction candidate for 2,8 G8: 2,8 => CTR * 695327841...61..7.7218946358..579126916432...57218639435..6841.1..953...2..741.53 G8: 4,6,7 # 22 pairs * PAIR H2: 6,7 BLK 3 G2: 6,7,2,5,9 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 695378241483219675721654839834597126916432587572186394349865712157923468268741953 G2: 2,5,9 # 22 pairs G3: 6,7,5,8,9 # reduction candidate for 6,7 G3: 6,7 # 23 pairs * PAIR H2: 6,7 COL H H8: 6,7,8 # reduction candidate for 6,7 H8: 8 => CTR * 6953...41....1..6..216...3.8..5..126916432.7.5721863943..865.1.15.923687268741953 H8: 6,7 # 24 pairs * PAIR H5: 7,8 BLK 6 G5: 7,8,5 # reduction candidate for 7,8 G5: 7,8 # 23 pairs I5: 7,8,5 # reduction candidate for 7,8 I5: 7,8 # 23 pairs * PAIR H5: 7,8 COL H H8: 7,8,6 # reduction candidate for 7,8 H8: 7,8 => CTR * 695378241.8321..6..2165..3.834597126916432...57218639434.865.1215.9236..26.741.53 H8: 6 # 21 pairs * PAIR B7: 4,5 BLK 7 B8: 4,5,6,8 # reduction candidate for 4,5 B8: 6,8 => CTR * 695327841...61..7.72189463584357912691643258757218639435.268.191..953...2..741.53 B8: 4,5 # 21 pairs * PAIR B9: 6,8 BLK 7 B8: 6,8,4,5 # reduction candidate for 6,8 B8: 6,8 => CTR * 695327841...61..7.72189463584357912691643258757218639435.268.191..953...2..741.53 B8: 4,5 # 21 pairs * PAIR B9: 6,8 ROW 9 G9: 6,8,9 # reduction candidate for 6,8 G9: 6,8 # 23 pairs G9: 9 # 20 pairs * PAIR C9: 8,9 ROW 9 G9: 8,9,6 # reduction candidate for 8,9 G9: 6 => CTR * 6953...41....1..6..216...3.8..5..126916432...5721863943..865.1.1..9.3...2.9741653 G9: 8,9 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-257-base-pr-000.dot * REASONING * DIS # G3: 5,7,9 => CTR => G3: 6,8 * DIS # F3: 5,9 => CTR => F3: 4 * DIS # G3: 5,9 => CTR => G3: 6,7,8 * DIS # G8: 2,8 => CTR => G8: 4,6,7 * PRF # G2: 6,7 => SOL * DIS # H8: 8 => CTR => H8: 6,7 * DIS # H8: 7,8 => CTR => H8: 6 * DIS # B8: 6,8 => CTR => B8: 4,5 * DIS # B8: 6,8 => CTR => B8: 4,5 * DIS # G9: 6 => CTR => G9: 8,9 * CNT 10 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,B2,B4,B7,B9,C2,C4,C9,D2,D3,D7,E1,E3,E4,E8,F1,F4,F7,G1,H2,H5) * 6953...41....1.....21....3.8..5..126916432...5721863943...6..1.1..9.3...2..741.53 * PAIR D2: 2,6 ROW 2 G2: 2,6,5,7,9 # reduction candidate for 2,6 G2: 2,6 # 23 pairs G2: 5,7,9 # 22 pairs * PAIR D3: 6,8 ROW 3 G3: 6,8,5,7,9 # reduction candidate for 6,8 G3: 5,7,9 => CTR * 695378241.8321.....2165..38834597126916432..5572186394347865912158923467269741853 * PAIR RESTART * PAIR E3: 5,9 BLK 2 F2: 5,9,4 # reduction candidate for 5,9 F2: 5,9 # 26 pairs F3: 5,9,4 # reduction candidate for 5,9 F3: 5,9 => CTR * 69537824178321456942165983783459712691643278557218639434.865.1.15.9236.8268741953 * RESTART * PAIR H2: 6,7 BLK 3 G2: 6,7,2,5,9 # reduction candidate for 6,7 G2: 6,7 => SOLVED * 695378241483219675721654839834597126916432587572186394349865712157923468268741953 * DURATION: 0:00:10.631508 START: 11:36:32.774582 END: 11:36:43.406090 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-257-base-pr-001.dot * REASONING * DIS # G3: 5,7,9 => CTR => G3: 6,8 * DIS G3: 6,8 # F3: 5,9 => CTR => F3: 4 * PRF G3: 6,8 + F3: 4 # G2: 6,7 => SOL * STA G3: 6,8 + F3: 4 + G2: 6,7 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 257 solution: 695378241483219675721654839834597126916432587572186394349865712157923468268741953 info: 2080 FNBHWXY S8.f 24718 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 695378241483219675721654839834597126916432587572186394349865712157923468268741953 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 # G2: 2,6 => UNS * INC # G2: 5,7,9 => UNS * INC # G3: 6,8 => UNS * DIS # G3: 5,7,9 => CTR => G3: 6,8 * INC # F2: 5,9 => UNS * DIS # F3: 5,9 => CTR => F3: 4 * INC # F3: 4 => UNS * DIS # G3: 5,9 => CTR => G3: 6,7,8 * INC # G3: 6,7,8 => UNS * INC # I3: 5,9 => UNS * DIS # G8: 2,8 => CTR => G8: 4,6,7 * INC # G8: 4,6,7 => UNS * PRF # G2: 6,7 => SOL * INC # G2: 2,5,9 => UNS * INC # G3: 6,7 => UNS * INC # H8: 6,7 => UNS * DIS # H8: 8 => CTR => H8: 6,7 * INC # G5: 7,8 => UNS * INC # I5: 7,8 => UNS * DIS # H8: 7,8 => CTR => H8: 6 * INC # H8: 6 => UNS * INC # B8: 4,5 => UNS * DIS # B8: 6,8 => CTR => B8: 4,5 * DIS # B8: 6,8 => CTR => B8: 4,5 * INC # B8: 4,5 => UNS * INC # G9: 6,8 => UNS * INC # G9: 9 => UNS * INC # G9: 8,9 => UNS * DIS # G9: 6 => CTR => G9: 8,9 * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G2: 2,6 => UNS * INC # G2: 5,7,9 => UNS * INC # G3: 6,8 => UNS * DIS # G3: 5,7,9 => CTR => G3: 6,8 * INC G3: 6,8 # F2: 5,9 => UNS * DIS G3: 6,8 # F3: 5,9 => CTR => F3: 4 * PRF G3: 6,8 + F3: 4 # G2: 6,7 => SOL * STA G3: 6,8 + F3: 4 + G2: 6,7 * CNT 7 HDP CHAINS / 7 HYP OPENED