Analysis of xx-top500-455-base.sdk
Contents
Original Sudoku
level: medium
position: ....94.3.51................6.3..8......7..9........1.....5...2....6....84...1.... initial
Autosolve
position: ....9453151.376.94....51.76693128745...7.59.....4.91.....58.429...64.3184..91.657 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C7: 6,7 => CTR => C7: 1 * PRF # C7: 1 => SOL * PRF # C8: 5,7 => SOL * DIS # C8: 9 => CTR => C8: 5,7 * PRF # B9: 3 => SOL * PRF # A7: 3,7 => SOL * DIS # A7: 1 => CTR => A7: 3,7 * DIS # B7: 3,7 => CTR => B7: 6 * DIS # A8: 2,7 => CTR => A8: 9 * PRF # A8: 9 => SOL * PRF # B8: 2,7 => SOL * CNT 11 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C7: 6,7 => CTR => C7: 1 * PRF C7: 1 => SOL * STA C7: 1 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....94.3.51................6.3..8......7..9........1.....5...2....6....84...1.... | initial |
| ....9453151.376.94....51.76693128745...7.59.....4.91.....58.429...64.3184..91.657 | autosolve |
| 876294531512376894349851276693128745184735962257469183761583429925647318438912657 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) C1: 6,7 C2: 2,8 A3: 3,9 B3: 3,4 C3: 4,9 D1: 2,8 D3: 2,8 G2: 2,8 G3: 2,8 C5: 1,4 C6: 5,7 E5: 3,6 E6: 3,6 H5: 6,8 I5: 2,3 H6: 6,8 I6: 2,3 C9: 2,8 F7: 3,7 F8: 2,7 F9: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,C5: 1.. / A5 = 1 => 0 pairs (*) / C5 = 1 => 0 pairs (X) A7,C7: 1.. / A7 = 1 => 0 pairs (X) / C7 = 1 => 0 pairs (_) A5,A7: 1.. / A5 = 1 => 0 pairs (*) / A7 = 1 => 0 pairs (X) C5,C7: 1.. / C5 = 1 => 0 pairs (X) / C7 = 1 => 0 pairs (_) D1,D3: 2.. / D1 = 2 => 17 pairs (_) / D3 = 2 => 19 pairs (_) G2,G3: 2.. / G2 = 2 => 19 pairs (_) / G3 = 2 => 17 pairs (_) I5,I6: 2.. / I5 = 2 => 18 pairs (_) / I6 = 2 => 18 pairs (_) F8,F9: 2.. / F8 = 2 => 24 pairs (_) / F9 = 2 => 0 pairs (*) C2,G2: 2.. / C2 = 2 => 17 pairs (_) / G2 = 2 => 19 pairs (_) D3,G3: 2.. / D3 = 2 => 19 pairs (_) / G3 = 2 => 17 pairs (_) C2,C9: 2.. / C2 = 2 => 17 pairs (_) / C9 = 2 => 19 pairs (_) A3,B3: 3.. / A3 = 3 => 0 pairs (*) / B3 = 3 => 0 pairs (X) E5,E6: 3.. / E5 = 3 => 18 pairs (_) / E6 = 3 => 18 pairs (_) I5,I6: 3.. / I5 = 3 => 18 pairs (_) / I6 = 3 => 18 pairs (_) F7,F9: 3.. / F7 = 3 => 0 pairs (*) / F9 = 3 => 0 pairs (X) E5,I5: 3.. / E5 = 3 => 18 pairs (_) / I5 = 3 => 18 pairs (_) E6,I6: 3.. / E6 = 3 => 18 pairs (_) / I6 = 3 => 18 pairs (_) B9,F9: 3.. / B9 = 3 => 0 pairs (*) / F9 = 3 => 0 pairs (X) A3,A7: 3.. / A3 = 3 => 0 pairs (*) / A7 = 3 => 0 pairs (X) B3,C3: 4.. / B3 = 4 => 0 pairs (*) / C3 = 4 => 0 pairs (X) B5,C5: 4.. / B5 = 4 => 0 pairs (X) / C5 = 4 => 0 pairs (_) B3,B5: 4.. / B3 = 4 => 0 pairs (*) / B5 = 4 => 0 pairs (X) C3,C5: 4.. / C3 = 4 => 0 pairs (X) / C5 = 4 => 0 pairs (_) B6,C6: 5.. / B6 = 5 => 0 pairs (*) / C6 = 5 => 0 pairs (X) B8,C8: 5.. / B8 = 5 => 21 pairs (_) / C8 = 5 => 0 pairs (*) B6,B8: 5.. / B6 = 5 => 0 pairs (*) / B8 = 5 => 0 pairs (X) C6,C8: 5.. / C6 = 5 => 21 pairs (_) / C8 = 5 => 0 pairs (*) B1,C1: 6.. / B1 = 6 => 0 pairs (X) / C1 = 6 => 21 pairs (_) E5,E6: 6.. / E5 = 6 => 18 pairs (_) / E6 = 6 => 18 pairs (_) H5,H6: 6.. / H5 = 6 => 18 pairs (_) / H6 = 6 => 18 pairs (_) B7,C7: 6.. / B7 = 6 => 21 pairs (_) / C7 = 6 => 0 pairs (X) E5,H5: 6.. / E5 = 6 => 18 pairs (_) / H5 = 6 => 18 pairs (_) E6,H6: 6.. / E6 = 6 => 18 pairs (_) / H6 = 6 => 18 pairs (_) B1,B7: 6.. / B1 = 6 => 0 pairs (X) / B7 = 6 => 21 pairs (_) C1,C7: 6.. / C1 = 6 => 21 pairs (_) / C7 = 6 => 0 pairs (X) F7,F8: 7.. / F7 = 7 => 24 pairs (_) / F8 = 7 => 0 pairs (*) D1,D3: 8.. / D1 = 8 => 19 pairs (_) / D3 = 8 => 17 pairs (_) G2,G3: 8.. / G2 = 8 => 17 pairs (_) / G3 = 8 => 19 pairs (_) H5,H6: 8.. / H5 = 8 => 18 pairs (_) / H6 = 8 => 18 pairs (_) B9,C9: 8.. / B9 = 8 => 19 pairs (_) / C9 = 8 => 17 pairs (_) C2,G2: 8.. / C2 = 8 => 19 pairs (_) / G2 = 8 => 17 pairs (_) D3,G3: 8.. / D3 = 8 => 17 pairs (_) / G3 = 8 => 19 pairs (_) C2,C9: 8.. / C2 = 8 => 19 pairs (_) / C9 = 8 => 17 pairs (_) A3,C3: 9.. / A3 = 9 => 0 pairs (X) / C3 = 9 => 0 pairs (_) A8,C8: 9.. / A8 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) A3,A8: 9.. / A3 = 9 => 0 pairs (X) / A8 = 9 => 0 pairs (_) C3,C8: 9.. / C3 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) * DURATION: 0:01:42.138601 START: 18:16:50.892134 END: 18:18:33.030735 2017-05-04 * CP COUNT: (47) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,C1,C2,C3,C5,C6,C9,D1,D3,E5,E6,F7,F8,F9,G2,G3,H5,H6,I5,I6) * ....9453151.376.94....51.76693128745...7.59.....4.91.....58.429...64.3184..91.657 * PAIR C1: 6,7 BLK 1 B1: 6,7,2,8 # reduction candidate for 6,7 B1: 2,8 # 28 pairs B1: 6,7 # 23 pairs * PAIR C1: 6,7 COL C C7: 6,7,1 # reduction candidate for 6,7 C7: 6,7 => CTR * ....9453151.376.9434..51.76693128745..17.59.....4.91..1..58.429...64.3184..91.657 C7: 1 => SOLVED * 876294531512376894349851276693128745184735962257469183761583429925647318438912657 * PAIR C2: 2,8 BLK 1 A1: 2,8,7 # reduction candidate for 2,8 A1: 2,8 # 23 pairs B1: 2,8,6,7 # reduction candidate for 2,8 B1: 2,8 # 28 pairs * PAIR D1: 2,8 ROW 1 A1: 2,8,7 # reduction candidate for 2,8 A1: 2,8 # 23 pairs B1: 2,8,6,7 # reduction candidate for 2,8 B1: 2,8 # 28 pairs * PAIR C6: 5,7 BLK 4 B6: 5,7,2,8 # reduction candidate for 5,7 B6: 2,8 # 27 pairs B6: 5,7 # 23 pairs * PAIR C6: 5,7 COL C C8: 5,7,9 # reduction candidate for 5,7 C8: 5,7 => SOLVED * 876294531512376894349851276693128745184735962257469183761583429925647318438912657 C8: 9 => CTR * ....9453151.376.94934.51.76693128745.417.59....54.91.....58.429.5964.3184..91.657 * PAIR C9: 2,8 BLK 7 B9: 2,8,3 # reduction candidate for 2,8 B9: 3 => SOLVED * 876294531512376894349851276693128745184735962257469183761583429925647318438912657 B9: 2,8 # 24 pairs * PAIR F7: 3,7 ROW 7 A7: 3,7,1 # reduction candidate for 3,7 A7: 3,7 => SOLVED * 876294531512376894349851276693128745184735962257469183761583429925647318438912657 A7: 1 => CTR * ....9453151.376.94349.51.76693128745..47.59.....4.91..1..58.4299..64.3184..91.657 B7: 3,7,6 # reduction candidate for 3,7 B7: 3,7 => CTR * .67.9453151.376.94934.51.76693128745.417.59....54.91....658.429.5964.3184..91.657 B7: 6 # 21 pairs * PAIR F8: 2,7 ROW 8 A8: 2,7,9 # reduction candidate for 2,7 A8: 2,7 => CTR * ....9453151.376.94934.51.76693128745.417.59.....4.91.....58.429...64.3184..91.657 A8: 9 => SOLVED * 876294531512376894349851276693128745184735962257469183761583429925647318438912657 B8: 2,7,5 # reduction candidate for 2,7 B8: 2,7 => SOLVED * 876294531512376894349851276693128745184735962257469183761583429925647318438912657 B8: 5 # 21 pairs * PAIR F9: 2,3 ROW 9 B9: 2,3,8 # reduction candidate for 2,3 B9: 8 # 19 pairs B9: 2,3 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-455-base-pr-000.dot * REASONING * DIS # C7: 6,7 => CTR => C7: 1 * PRF # C7: 1 => SOL * PRF # C8: 5,7 => SOL * DIS # C8: 9 => CTR => C8: 5,7 * PRF # B9: 3 => SOL * PRF # A7: 3,7 => SOL * DIS # A7: 1 => CTR => A7: 3,7 * DIS # B7: 3,7 => CTR => B7: 6 * DIS # A8: 2,7 => CTR => A8: 9 * PRF # A8: 9 => SOL * PRF # B8: 2,7 => SOL * CNT 11 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,C1,C2,C3,C5,C6,C9,D1,D3,E5,E6,F7,F8,F9,G2,G3,H5,H6,I5,I6) * ....9453151.376.94....51.76693128745...7.59.....4.91.....58.429...64.3184..91.657 * PAIR C1: 6,7 BLK 1 B1: 6,7,2,8 # reduction candidate for 6,7 B1: 2,8 # 28 pairs B1: 6,7 # 23 pairs * PAIR C1: 6,7 COL C C7: 6,7,1 # reduction candidate for 6,7 C7: 6,7 => CTR * ....9453151.376.9434..51.76693128745..17.59.....4.91..1..58.429...64.3184..91.657 C7: 1 => SOLVED * 876294531512376894349851276693128745184735962257469183761583429925647318438912657 * DURATION: 0:00:05.867499 START: 18:19:04.824991 END: 18:19:10.692490 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-455-base-pr-001.dot * REASONING * DIS # C7: 6,7 => CTR => C7: 1 * PRF C7: 1 => SOL * STA C7: 1 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 455 solution: 876294531512376894349851276693128745184735962257469183761583429925647318438912657 info: 95498 FNBTK S8.f 6702 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 876294531512376894349851276693128745184735962257469183761583429925647318438912657 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 # B1: 6,7 => UNS * INC # B1: 2,8 => UNS * DIS # C7: 6,7 => CTR => C7: 1 * PRF # C7: 1 => SOL * INC # A1: 2,8 => UNS * INC # B1: 2,8 => UNS * INC # A1: 2,8 => UNS * INC # B1: 2,8 => UNS * INC # B6: 5,7 => UNS * INC # B6: 2,8 => UNS * PRF # C8: 5,7 => SOL * DIS # C8: 9 => CTR => C8: 5,7 * INC # B9: 2,8 => UNS * PRF # B9: 3 => SOL * PRF # A7: 3,7 => SOL * DIS # A7: 1 => CTR => A7: 3,7 * DIS # B7: 3,7 => CTR => B7: 6 * INC # B7: 6 => UNS * DIS # A8: 2,7 => CTR => A8: 9 * PRF # A8: 9 => SOL * PRF # B8: 2,7 => SOL * INC # B8: 5 => UNS * INC # B9: 2,3 => UNS * INC # B9: 8 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 6,7 => UNS * INC # B1: 2,8 => UNS * DIS # C7: 6,7 => CTR => C7: 1 * PRF C7: 1 => SOL * STA C7: 1 * CNT 4 HDP CHAINS / 3 HYP OPENED