Analysis of xx-top500-179-base.sdk
Contents
Original Sudoku
level: medium
position: .7...3....4..8..........6..6..5..1......7..4...1......5..6.1..........73...2..... initial
Autosolve
position: 276413...345986712.1.7..6346345.81.7.5.17.3467.1364...5.76314..16.84..734.32.7.61 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C5: 8,9 => CTR => C5: 2 * PRF # C5: 2 => SOL * PRF # G6: 8,9 => SOL * DIS # G6: 2 => CTR => G6: 8,9 * DIS # G9: 8,9 => CTR => G9: 5 * PRF # G9: 5 => SOL * DIS # C5: 8,9 => CTR => C5: 2 * PRF # C5: 2 => SOL * DIS # C5: 8 => CTR => C5: 2,9 * PRF # H6: 2,9 => SOL * DIS # B7: 8 => CTR => B7: 2,9 * DIS # C5: 8 => CTR => C5: 2,9 * PRF # H6: 2,9 => SOL * PRF # H7: 8 => SOL * DIS # B7: 8 => CTR => B7: 2,9 * PRF # G8: 2,9 => SOL * DIS # G8: 5 => CTR => G8: 2,9 * DIS # C5: 8 => CTR => C5: 2,9 * DIS # B7: 8,9 => CTR => B7: 2 * PRF # B7: 2 => SOL * DIS # G9: 8,9 => CTR => G9: 5 * PRF # G9: 5 => SOL * DIS # G8: 5,9 => CTR => G8: 2 * PRF # G8: 2 => SOL * DIS # G9: 8 => CTR => G9: 5,9 * PRF # H7: 8,9 => SOL * DIS # H7: 2 => CTR => H7: 8,9 * DIS # G9: 8,9 => CTR => G9: 5 * PRF # G9: 5 => SOL * DIS # B7: 8,9 => CTR => B7: 2 * PRF # B7: 2 => SOL * CNT 31 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C5: 8,9 => CTR => C5: 2 * PRF C5: 2 => SOL * STA C5: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7...3....4..8..........6..6..5..1......7..4...1......5..6.1..........73...2..... | initial |
| 276413...345986712.1.7..6346345.81.7.5.17.3467.1364...5.76314..16.84..734.32.7.61 | autosolve |
| 276413958345986712918752634634528197852179346791364825527631489169845273483297561 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A3: 8,9 C3: 8,9 E3: 2,5 F3: 2,5 G1: 8,9 A5: 8,9 B6: 2,9 E4: 2,9 F5: 2,9 H4: 2,9 C8: 2,9 B9: 8,9 F8: 5,9 E9: 5,9 I7: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 2.. / E3 = 2 => 0 pairs (X) / F3 = 2 => 0 pairs (_) C5,B6: 2.. / C5 = 2 => 0 pairs (*) / B6 = 2 => 0 pairs (X) E4,F5: 2.. / E4 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) B7,C8: 2.. / B7 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) H7,G8: 2.. / H7 = 2 => 0 pairs (X) / G8 = 2 => 0 pairs (_) E4,H4: 2.. / E4 = 2 => 0 pairs (*) / H4 = 2 => 0 pairs (X) C5,F5: 2.. / C5 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) B7,H7: 2.. / B7 = 2 => 0 pairs (*) / H7 = 2 => 0 pairs (X) C8,G8: 2.. / C8 = 2 => 0 pairs (X) / G8 = 2 => 0 pairs (_) B6,B7: 2.. / B6 = 2 => 0 pairs (X) / B7 = 2 => 0 pairs (_) C5,C8: 2.. / C5 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) E3,E4: 2.. / E3 = 2 => 0 pairs (X) / E4 = 2 => 0 pairs (_) F3,F5: 2.. / F3 = 2 => 0 pairs (*) / F5 = 2 => 0 pairs (X) G6,G8: 2.. / G6 = 2 => 0 pairs (X) / G8 = 2 => 0 pairs (_) E3,F3: 5.. / E3 = 5 => 0 pairs (*) / F3 = 5 => 0 pairs (X) H1,I1: 5.. / H1 = 5 => 16 pairs (_) / I1 = 5 => 17 pairs (_) H6,I6: 5.. / H6 = 5 => 17 pairs (_) / I6 = 5 => 16 pairs (_) F8,E9: 5.. / F8 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) G8,G9: 5.. / G8 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) F8,G8: 5.. / F8 = 5 => 0 pairs (*) / G8 = 5 => 0 pairs (X) E9,G9: 5.. / E9 = 5 => 0 pairs (X) / G9 = 5 => 0 pairs (_) E3,E9: 5.. / E3 = 5 => 0 pairs (*) / E9 = 5 => 0 pairs (X) F3,F8: 5.. / F3 = 5 => 0 pairs (X) / F8 = 5 => 0 pairs (_) H1,H6: 5.. / H1 = 5 => 16 pairs (_) / H6 = 5 => 17 pairs (_) I1,I6: 5.. / I1 = 5 => 17 pairs (_) / I6 = 5 => 16 pairs (_) A3,C3: 8.. / A3 = 8 => 0 pairs (X) / C3 = 8 => 13 pairs (_) A5,C5: 8.. / A5 = 8 => 13 pairs (_) / C5 = 8 => 0 pairs (X) B7,B9: 8.. / B7 = 8 => 0 pairs (X) / B9 = 8 => 16 pairs (_) B9,G9: 8.. / B9 = 8 => 16 pairs (_) / G9 = 8 => 0 pairs (X) A3,A5: 8.. / A3 = 8 => 0 pairs (X) / A5 = 8 => 13 pairs (_) C3,C5: 8.. / C3 = 8 => 13 pairs (_) / C5 = 8 => 0 pairs (X) A3,C3: 9.. / A3 = 9 => 13 pairs (_) / C3 = 9 => 0 pairs (X) E4,F5: 9.. / E4 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) F8,E9: 9.. / F8 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) E4,H4: 9.. / E4 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) A3,A5: 9.. / A3 = 9 => 13 pairs (_) / A5 = 9 => 0 pairs (X) E4,E9: 9.. / E4 = 9 => 0 pairs (X) / E9 = 9 => 0 pairs (_) F5,F8: 9.. / F5 = 9 => 0 pairs (*) / F8 = 9 => 0 pairs (X) * DURATION: 0:01:12.543254 START: 08:48:41.082655 END: 08:49:53.625909 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B9,C3,C8,E3,E4,E9,F3,F5,F8,G1,H4,I7) * 276413...345986712.1.7..6346345.81.7.5.17.3467.1364...5.76314..16.84..734.32.7.61 * PAIR C3: 8,9 COL C C5: 8,9,2 # reduction candidate for 8,9 C5: 8,9 => CTR * 276413...345986712.1.7..6346345.81.7.5.172346721364...5.763142.1628495734.3257.61 C5: 2 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 * PAIR G1: 8,9 BLK 3 H1: 8,9,5 # reduction candidate for 8,9 H1: 8,9 # 17 pairs I1: 8,9,5 # reduction candidate for 8,9 I1: 8,9 # 16 pairs * PAIR G1: 8,9 COL G G6: 8,9,2 # reduction candidate for 8,9 G6: 8,9 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 G6: 2 => CTR * 276413...345986712.1.7..6346345.81.7.5.17.3467.13642..5276314..169845.734.32.7.61 G9: 8,9,5 # reduction candidate for 8,9 G9: 8,9 => CTR * 276413...345986712.1.725634634598127.5.172346721364...5.76314..1628495734.3257.61 G9: 5 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 * PAIR A5: 8,9 BLK 4 C5: 8,9,2 # reduction candidate for 8,9 C5: 8,9 => CTR * 276413...345986712.1.7..6346345.81.7.5.172346721364...5.763142.1628495734.3257.61 C5: 2 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 * PAIR B6: 2,9 BLK 4 C5: 2,9,8 # reduction candidate for 2,9 C5: 8 => CTR * 276413...345986712.1.7..6346345.81.7.58172346721364...5.763142.1628495734.3257.61 C5: 2,9 # 13 pairs * PAIR B6: 2,9 ROW 6 G6: 2,9,8 # reduction candidate for 2,9 G6: 2,9 # 18 pairs H6: 2,9,5,8 # reduction candidate for 2,9 H6: 2,9 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 H6: 5,8 # 16 pairs * PAIR B6: 2,9 COL B B7: 2,9,8 # reduction candidate for 2,9 B7: 8 => CTR * 276413...345986712.1.7..6346345.81.7.5.17.346721364...587631429162849573493257.61 B7: 2,9 # 16 pairs * PAIR F5: 2,9 ROW 5 C5: 2,9,8 # reduction candidate for 2,9 C5: 8 => CTR * 276413...345986712.1.7..6346345.81.7.58172346721364...5.763142.1628495734.3257.61 C5: 2,9 # 13 pairs * PAIR H4: 2,9 BLK 6 G6: 2,9,8 # reduction candidate for 2,9 G6: 2,9 # 18 pairs H6: 2,9,5,8 # reduction candidate for 2,9 H6: 2,9 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 H6: 5,8 # 16 pairs * PAIR H4: 2,9 COL H H7: 2,9,8 # reduction candidate for 2,9 H7: 8 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 H7: 2,9 # 18 pairs * PAIR C8: 2,9 BLK 7 B7: 2,9,8 # reduction candidate for 2,9 B7: 8 => CTR * 276413...345986712.1.7..6346345.81.7.5.17.346721364...587631429162849573493257.61 B7: 2,9 # 16 pairs * PAIR C8: 2,9 ROW 8 G8: 2,9,5 # reduction candidate for 2,9 G8: 2,9 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 G8: 5 => CTR * 276413...345986712.1.7..6346345.81.7.5.17.3467.13642..5276314..169845.734.32.7.61 * PAIR C8: 2,9 COL C C5: 2,9,8 # reduction candidate for 2,9 C5: 8 => CTR * 276413...345986712.1.7..6346345.81.7.58172346721364...5.763142.1628495734.3257.61 C5: 2,9 # 13 pairs * PAIR B9: 8,9 BLK 7 B7: 8,9,2 # reduction candidate for 8,9 B7: 8,9 => CTR * 276413...345986712.1.7..6346345.81.7.5.17.346721364...5.763142.16284..734.32.7.61 B7: 2 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 * PAIR B9: 8,9 ROW 9 G9: 8,9,5 # reduction candidate for 8,9 G9: 8,9 => CTR * 276413...345986712.1.725634634598127.5.172346721364...5.76314..1628495734.3257.61 G9: 5 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 * PAIR F8: 5,9 ROW 8 G8: 5,9,2 # reduction candidate for 5,9 G8: 5,9 => CTR * 276413...345986712.1.7..6346345.81.7.5.17.3467.13642..5276314..169845.734.32.7.61 G8: 2 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 * PAIR E9: 5,9 ROW 9 G9: 5,9,8 # reduction candidate for 5,9 G9: 8 => CTR * 2764139..345986712.1.725634634598127.5.17.3467.1364...5.76314..16.84.5734.3257861 G9: 5,9 # 16 pairs * PAIR I7: 8,9 BLK 9 H7: 8,9,2 # reduction candidate for 8,9 H7: 8,9 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 H7: 2 => CTR * 276413...345986712.1.7..634634528197.5.1793467.1364...5.763142.16284..734.32.7.61 G9: 8,9,5 # reduction candidate for 8,9 G9: 8,9 => CTR * 276413...345986712.1.725634634598127.5.172346721364...5.76314..1628495734.3257.61 G9: 5 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 * PAIR I7: 8,9 ROW 7 B7: 8,9,2 # reduction candidate for 8,9 B7: 8,9 => CTR * 276413...345986712.1.7..6346345.81.7.5.17.346721364...5.763142.16284..734.32.7.61 B7: 2 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 * PAIR I7: 8,9 COL I I1: 8,9,5 # reduction candidate for 8,9 I1: 8,9 # 16 pairs I6: 8,9,5 # reduction candidate for 8,9 I6: 8,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-179-base-pr-000.dot * REASONING * DIS # C5: 8,9 => CTR => C5: 2 * PRF # C5: 2 => SOL * PRF # G6: 8,9 => SOL * DIS # G6: 2 => CTR => G6: 8,9 * DIS # G9: 8,9 => CTR => G9: 5 * PRF # G9: 5 => SOL * DIS # C5: 8,9 => CTR => C5: 2 * PRF # C5: 2 => SOL * DIS # C5: 8 => CTR => C5: 2,9 * PRF # H6: 2,9 => SOL * DIS # B7: 8 => CTR => B7: 2,9 * DIS # C5: 8 => CTR => C5: 2,9 * PRF # H6: 2,9 => SOL * PRF # H7: 8 => SOL * DIS # B7: 8 => CTR => B7: 2,9 * PRF # G8: 2,9 => SOL * DIS # G8: 5 => CTR => G8: 2,9 * DIS # C5: 8 => CTR => C5: 2,9 * DIS # B7: 8,9 => CTR => B7: 2 * PRF # B7: 2 => SOL * DIS # G9: 8,9 => CTR => G9: 5 * PRF # G9: 5 => SOL * DIS # G8: 5,9 => CTR => G8: 2 * PRF # G8: 2 => SOL * DIS # G9: 8 => CTR => G9: 5,9 * PRF # H7: 8,9 => SOL * DIS # H7: 2 => CTR => H7: 8,9 * DIS # G9: 8,9 => CTR => G9: 5 * PRF # G9: 5 => SOL * DIS # B7: 8,9 => CTR => B7: 2 * PRF # B7: 2 => SOL * CNT 31 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B9,C3,C8,E3,E4,E9,F3,F5,F8,G1,H4,I7) * 276413...345986712.1.7..6346345.81.7.5.17.3467.1364...5.76314..16.84..734.32.7.61 * PAIR C3: 8,9 COL C C5: 8,9,2 # reduction candidate for 8,9 C5: 8,9 => CTR * 276413...345986712.1.7..6346345.81.7.5.172346721364...5.763142.1628495734.3257.61 C5: 2 => SOLVED * 276413958345986712918752634634528197852179346791364825527631489169845273483297561 * DURATION: 0:00:03.173007 START: 08:50:47.807667 END: 08:50:50.980674 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-179-base-pr-001.dot * REASONING * DIS # C5: 8,9 => CTR => C5: 2 * PRF C5: 2 => SOL * STA C5: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 179 solution: 276413958345986712918752634634528197852179346791364825527631489169845273483297561 info: 1828 FNBWX S8.f 22333 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 276413958345986712918752634634528197852179346791364825527631489169845273483297561 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 # C5: 8,9 => CTR => C5: 2 * PRF # C5: 2 => SOL * INC # H1: 8,9 => UNS * INC # I1: 8,9 => UNS * PRF # G6: 8,9 => SOL * DIS # G6: 2 => CTR => G6: 8,9 * DIS # G9: 8,9 => CTR => G9: 5 * PRF # G9: 5 => SOL * DIS # C5: 8,9 => CTR => C5: 2 * PRF # C5: 2 => SOL * INC # C5: 2,9 => UNS * DIS # C5: 8 => CTR => C5: 2,9 * INC # G6: 2,9 => UNS * PRF # H6: 2,9 => SOL * INC # H6: 5,8 => UNS * INC # B7: 2,9 => UNS * DIS # B7: 8 => CTR => B7: 2,9 * INC # C5: 2,9 => UNS * DIS # C5: 8 => CTR => C5: 2,9 * INC # G6: 2,9 => UNS * PRF # H6: 2,9 => SOL * INC # H6: 5,8 => UNS * INC # H7: 2,9 => UNS * PRF # H7: 8 => SOL * INC # B7: 2,9 => UNS * DIS # B7: 8 => CTR => B7: 2,9 * PRF # G8: 2,9 => SOL * DIS # G8: 5 => CTR => G8: 2,9 * INC # C5: 2,9 => UNS * DIS # C5: 8 => CTR => C5: 2,9 * DIS # B7: 8,9 => CTR => B7: 2 * PRF # B7: 2 => SOL * DIS # G9: 8,9 => CTR => G9: 5 * PRF # G9: 5 => SOL * DIS # G8: 5,9 => CTR => G8: 2 * PRF # G8: 2 => SOL * INC # G9: 5,9 => UNS * DIS # G9: 8 => CTR => G9: 5,9 * PRF # H7: 8,9 => SOL * DIS # H7: 2 => CTR => H7: 8,9 * DIS # G9: 8,9 => CTR => G9: 5 * PRF # G9: 5 => SOL * DIS # B7: 8,9 => CTR => B7: 2 * PRF # B7: 2 => SOL * INC # I1: 8,9 => UNS * INC # I6: 8,9 => UNS * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C5: 8,9 => CTR => C5: 2 * PRF C5: 2 => SOL * STA C5: 2 * CNT 2 HDP CHAINS / 1 HYP OPENED