Analysis of xx-top500-385-base.sdk
Contents
Original Sudoku
level: medium
position: .1...46......9...3..........2.8..7.....35....4..............21...35.....9.....4.. initial
Autosolve
position: 519.346.....19.5.3.3...59.1325841796.9.35.1.44.19..35..5.4.32191435298679.2.1.435 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 6 => CTR => D3: 2,7 * PRF # E3: 6,7 => SOL * PRF # F9: 6,7 => SOL * PRF # B9: 8 => SOL * CNT 4 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 6 => CTR => D3: 2,7 * DIS D3: 2,7 # H1: 2,7 => CTR => H1: 8 * PRF D3: 2,7 + H1: 8 # C2: 6,8 => SOL * STA D3: 2,7 + H1: 8 + C2: 6,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1...46......9...3..........2.8..7.....35....4..............21...35.....9.....4.. | initial |
| 519.346.....19.5.3.3...59.1325841796.9.35.1.44.19..35..5.4.32191435298679.2.1.435 | autosolve |
| 519734682276198543834265971325841796798356124461972358657483219143529867982617435 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) D1: 2,7 I1: 2,8 E6: 6,7 H5: 2,8 I6: 2,8 D9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 2.. / A2 = 2 => 7 pairs (_) / A3 = 2 => 12 pairs (_) D1,D3: 2.. / D1 = 2 => 14 pairs (_) / D3 = 2 => 12 pairs (_) F5,F6: 2.. / F5 = 2 => 14 pairs (_) / F6 = 2 => 10 pairs (_) H5,I6: 2.. / H5 = 2 => 10 pairs (_) / I6 = 2 => 14 pairs (_) A2,H2: 2.. / A2 = 2 => 7 pairs (_) / H2 = 2 => 12 pairs (_) F5,H5: 2.. / F5 = 2 => 14 pairs (_) / H5 = 2 => 10 pairs (_) F6,I6: 2.. / F6 = 2 => 10 pairs (_) / I6 = 2 => 14 pairs (_) I1,I6: 2.. / I1 = 2 => 10 pairs (_) / I6 = 2 => 14 pairs (_) C2,C3: 4.. / C2 = 4 => 7 pairs (_) / C3 = 4 => 7 pairs (_) H2,H3: 4.. / H2 = 4 => 7 pairs (_) / H3 = 4 => 7 pairs (_) C2,H2: 4.. / C2 = 4 => 7 pairs (_) / H2 = 4 => 7 pairs (_) C3,H3: 4.. / C3 = 4 => 7 pairs (_) / H3 = 4 => 7 pairs (_) D3,D9: 6.. / D3 = 6 => 0 pairs (X) / D9 = 6 => 11 pairs (_) D1,H1: 7.. / D1 = 7 => 12 pairs (_) / H1 = 7 => 14 pairs (_) F2,E3: 8.. / F2 = 8 => 0 pairs (*) / E3 = 8 => 0 pairs (X) H1,I1: 8.. / H1 = 8 => 10 pairs (_) / I1 = 8 => 14 pairs (_) H5,I6: 8.. / H5 = 8 => 14 pairs (_) / I6 = 8 => 10 pairs (_) E7,F9: 8.. / E7 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) B6,I6: 8.. / B6 = 8 => 14 pairs (_) / I6 = 8 => 10 pairs (_) B9,F9: 8.. / B9 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) E3,E7: 8.. / E3 = 8 => 9 pairs (_) / E7 = 8 => 0 pairs (*) F2,F9: 8.. / F2 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) H1,H5: 8.. / H1 = 8 => 10 pairs (_) / H5 = 8 => 14 pairs (_) I1,I6: 8.. / I1 = 8 => 14 pairs (_) / I6 = 8 => 10 pairs (_) * DURATION: 0:00:41.600000 START: 16:00:35.116133 END: 16:01:16.716133 2017-05-04 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,D9,E6,H5,I1,I6) * 519.346.....19.5.3.3...59.1325841796.9.35.1.44.19..35..5.4.32191435298679.2.1.435 * PAIR D1: 2,7 BLK 2 D3: 2,7,6 # reduction candidate for 2,7 D3: 6 => CTR * 519234678.7.19.5.3.3.6.59.1325841796.9.35.1844819..352.5.4.32191435298679.2718435 D3: 2,7 # 11 pairs * PAIR D1: 2,7 ROW 1 H1: 2,7,8 # reduction candidate for 2,7 H1: 2,7 # 14 pairs H1: 8 # 10 pairs * PAIR I1: 2,8 BLK 3 H1: 2,8,7 # reduction candidate for 2,8 H1: 7 # 14 pairs H1: 2,8 # 12 pairs * PAIR E6: 6,7 BLK 5 F5: 6,7,2 # reduction candidate for 6,7 F5: 6,7 # 10 pairs F6: 6,7,2 # reduction candidate for 6,7 F6: 6,7 # 14 pairs * PAIR E6: 6,7 ROW 6 B6: 6,7,8 # reduction candidate for 6,7 B6: 8 # 14 pairs B6: 6,7 # 10 pairs * PAIR E6: 6,7 COL E E3: 6,7,8 # reduction candidate for 6,7 E3: 6,7 => SOLVED * 519734682276198543834265971325841796798356124461972358657483219143529867982617435 E3: 8 # 9 pairs E7: 6,7,8 # reduction candidate for 6,7 E7: 6,7 # 9 pairs * PAIR H5: 2,8 COL H H1: 2,8,7 # reduction candidate for 2,8 H1: 7 # 14 pairs H1: 2,8 # 12 pairs * PAIR D9: 6,7 BLK 8 E7: 6,7,8 # reduction candidate for 6,7 E7: 6,7 # 9 pairs F9: 6,7,8 # reduction candidate for 6,7 F9: 6,7 => SOLVED * 519734682276198543834265971325841796798356124461972358657483219143529867982617435 F9: 8 # 9 pairs * PAIR D9: 6,7 ROW 9 B9: 6,7,8 # reduction candidate for 6,7 B9: 8 => SOLVED * 519734682276198543834265971325841796798356124461972358657483219143529867982617435 B9: 6,7 # 9 pairs * PAIR D9: 6,7 COL D D3: 6,7,2 # reduction candidate for 6,7 D3: 6,7 # 14 pairs D3: 2 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-385-base-pr-000.dot * REASONING * DIS # D3: 6 => CTR => D3: 2,7 * PRF # E3: 6,7 => SOL * PRF # F9: 6,7 => SOL * PRF # B9: 8 => SOL * CNT 4 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,D9,E6,H5,I1,I6) * 519.346.....19.5.3.3...59.1325841796.9.35.1.44.19..35..5.4.32191435298679.2.1.435 * PAIR D1: 2,7 BLK 2 D3: 2,7,6 # reduction candidate for 2,7 D3: 6 => CTR * 519234678.7.19.5.3.3.6.59.1325841796.9.35.1844819..352.5.4.32191435298679.2718435 * PAIR D1: 2,7 ROW 1 H1: 2,7,8 # reduction candidate for 2,7 H1: 2,7 => CTR * 519.346.8...19.5.3.3...59.1325841796.9.35.1844819..352.5.4.3219143529867972618435 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B6,B9,E3,E6,E7,F2,F5,F9,H2,H3) * 5197346822..19.5.3.3.2.59.1325841796.9.35.1244.19.2358.5.4.32191435298679.261.435 * PAIR F2: 6,8 ROW 2 B2: 6,8,7 # reduction candidate for 6,8 B2: 6,8 # 12 pairs C2: 6,8,4,7 # reduction candidate for 6,8 C2: 6,8 => SOLVED * 519734682276198543834265971325841796798356124461972358657483219143529867982617435 * DURATION: 0:00:07.359717 START: 16:01:39.375297 END: 16:01:46.735014 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-385-base-pr-001.dot * REASONING * DIS # D3: 6 => CTR => D3: 2,7 * DIS D3: 2,7 # H1: 2,7 => CTR => H1: 8 * PRF D3: 2,7 + H1: 8 # C2: 6,8 => SOL * STA D3: 2,7 + H1: 8 + C2: 6,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 385 solution: 519734682276198543834265971325841796798356124461972358657483219143529867982617435 info: 34331 FNBXYK S8.f 15172 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 519734682276198543834265971325841796798356124461972358657483219143529867982617435 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 # D3: 2,7 => UNS * DIS # D3: 6 => CTR => D3: 2,7 * INC # H1: 2,7 => UNS * INC # H1: 8 => UNS * INC # H1: 2,8 => UNS * INC # H1: 7 => UNS * INC # F5: 6,7 => UNS * INC # F6: 6,7 => UNS * INC # B6: 6,7 => UNS * INC # B6: 8 => UNS * PRF # E3: 6,7 => SOL * INC # E3: 8 => UNS * INC # E7: 6,7 => UNS * INC # H1: 2,8 => UNS * INC # H1: 7 => UNS * INC # E7: 6,7 => UNS * PRF # F9: 6,7 => SOL * INC # F9: 8 => UNS * INC # B9: 6,7 => UNS * PRF # B9: 8 => SOL * INC # D3: 6,7 => UNS * INC # D3: 2 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 2,7 => UNS * DIS # D3: 6 => CTR => D3: 2,7 * DIS D3: 2,7 # H1: 2,7 => CTR => H1: 8 * INC D3: 2,7 + H1: 8 # B2: 6,8 => UNS * PRF D3: 2,7 + H1: 8 # C2: 6,8 => SOL * STA D3: 2,7 + H1: 8 + C2: 6,8 * CNT 5 HDP CHAINS / 5 HYP OPENED