Analysis of xx-top500-365-base.sdk
Contents
Original Sudoku
level: medium
position: .1..7.......8..5...........6......123.45..................12.7.5.....3..4....9... initial
Autosolve
position: .15.7....7..82.591..81.5..765.....123245.17.918.2...538..412975591...3244723591.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 3,6 => CTR => B2: 4 * DIS # F2: 4 => CTR => F2: 3,6 * DIS # F2: 3,4 => CTR => F2: 6 * PRF # F2: 6 => SOL * PRF # E3: 3,4 => SOL * DIS # E3: 9 => CTR => E3: 3,4 * DIS # F4: 3,4 => CTR => F4: 8 * PRF # F4: 8 => SOL * PRF # G1: 6,8 => SOL * DIS # G1: 2 => CTR => G1: 6,8 * DIS # G1: 2,6 => CTR => G1: 8 * PRF # G1: 8 => SOL * DIS # B3: 3,4 => CTR => B3: 6 * PRF # B3: 6 => SOL * PRF # E3: 3,4 => SOL * DIS # E3: 9 => CTR => E3: 3,4 * DIS # F4: 3,4 => CTR => F4: 8 * PRF # F4: 8 => SOL * PRF # E3: 3,4 => SOL * DIS # E3: 9 => CTR => E3: 3,4 * DIS # E3: 3 => CTR => E3: 4,9 * DIS # F4: 3 => CTR => F4: 4,8 * PRF # F6: 4,6 => SOL * DIS # F6: 7 => CTR => F6: 4,6 * DIS # B2: 3,6 => CTR => B2: 4 * PRF # F8: 6,7 => SOL * DIS # F8: 8 => CTR => F8: 6,7 * DIS # F8: 6,8 => CTR => F8: 7 * PRF # F8: 7 => SOL * CNT 29 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 3,6 => CTR => B2: 4 * PRF B2: 4 # E3: 3,4 => SOL * STA B2: 4 + E3: 3,4 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1..7.......8..5...........6......123.45..................12.7.5.....3..4....9... | initial |
| .15.7....7..82.591..81.5..765.....123245.17.918.2...538..412975591...3244723591.. | autosolve |
| 215973846743826591968145237659738412324561789187294653836412975591687324472359168 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (24) A1: 2,9 C2: 3,6 A3: 2,9 D1: 6,9 F1: 3,4 H1: 3,4 I1: 6,8 G3: 2,6 H3: 3,4 C4: 7,9 C6: 7,9 D4: 7,9 E4: 3,4 E5: 6,8 E6: 4,9 G4: 4,8 H5: 6,8 G6: 4,6 B7: 3,6 C7: 3,6 D8: 6,7 E8: 6,8 H9: 6,8 I9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 2.. / A1 = 2 => 0 pairs (*) / A3 = 2 => 0 pairs (X) G1,G3: 2.. / G1 = 2 => 0 pairs (X) / G3 = 2 => 0 pairs (_) A1,G1: 2.. / A1 = 2 => 0 pairs (*) / G1 = 2 => 0 pairs (X) A3,G3: 2.. / A3 = 2 => 0 pairs (X) / G3 = 2 => 0 pairs (_) H1,H3: 3.. / H1 = 3 => 26 pairs (_) / H3 = 3 => 24 pairs (_) E4,F4: 3.. / E4 = 3 => 25 pairs (_) / F4 = 3 => 0 pairs (X) B7,C7: 3.. / B7 = 3 => 24 pairs (_) / C7 = 3 => 0 pairs (X) F1,H1: 3.. / F1 = 3 => 24 pairs (_) / H1 = 3 => 26 pairs (_) C2,C7: 3.. / C2 = 3 => 24 pairs (_) / C7 = 3 => 0 pairs (X) E3,E4: 3.. / E3 = 3 => 0 pairs (X) / E4 = 3 => 25 pairs (_) B2,B3: 4.. / B2 = 4 => 26 pairs (_) / B3 = 4 => 0 pairs (X) H1,H3: 4.. / H1 = 4 => 24 pairs (_) / H3 = 4 => 26 pairs (_) G4,G6: 4.. / G4 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) F1,H1: 4.. / F1 = 4 => 26 pairs (_) / H1 = 4 => 24 pairs (_) B2,F2: 4.. / B2 = 4 => 26 pairs (_) / F2 = 4 => 0 pairs (X) D1,F2: 6.. / D1 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) E5,F6: 6.. / E5 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) H5,G6: 6.. / H5 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) B7,C7: 6.. / B7 = 6 => 0 pairs (X) / C7 = 6 => 24 pairs (_) H9,I9: 6.. / H9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) B3,G3: 6.. / B3 = 6 => 0 pairs (*) / G3 = 6 => 0 pairs (X) E5,H5: 6.. / E5 = 6 => 0 pairs (*) / H5 = 6 => 0 pairs (X) F6,G6: 6.. / F6 = 6 => 0 pairs (X) / G6 = 6 => 0 pairs (_) C2,C7: 6.. / C2 = 6 => 0 pairs (X) / C7 = 6 => 24 pairs (_) D1,D8: 6.. / D1 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) E5,E8: 6.. / E5 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) H5,H9: 6.. / H5 = 6 => 0 pairs (X) / H9 = 6 => 0 pairs (_) I1,I9: 6.. / I1 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) C4,C6: 7.. / C4 = 7 => 0 pairs (X) / C6 = 7 => 0 pairs (_) D4,F6: 7.. / D4 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) D8,F8: 7.. / D8 = 7 => 0 pairs (X) / F8 = 7 => 0 pairs (_) C4,D4: 7.. / C4 = 7 => 0 pairs (X) / D4 = 7 => 0 pairs (_) C6,F6: 7.. / C6 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) D4,D8: 7.. / D4 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) F6,F8: 7.. / F6 = 7 => 0 pairs (X) / F8 = 7 => 0 pairs (_) G1,I1: 8.. / G1 = 8 => 0 pairs (*) / I1 = 8 => 0 pairs (X) F4,E5: 8.. / F4 = 8 => 0 pairs (*) / E5 = 8 => 0 pairs (X) G4,H5: 8.. / G4 = 8 => 0 pairs (X) / H5 = 8 => 0 pairs (_) E8,F8: 8.. / E8 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) H9,I9: 8.. / H9 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) F4,G4: 8.. / F4 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) E5,H5: 8.. / E5 = 8 => 0 pairs (X) / H5 = 8 => 0 pairs (_) E5,E8: 8.. / E5 = 8 => 0 pairs (X) / E8 = 8 => 0 pairs (_) F4,F8: 8.. / F4 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) G1,G4: 8.. / G1 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) H5,H9: 8.. / H5 = 8 => 0 pairs (*) / H9 = 8 => 0 pairs (X) I1,I9: 8.. / I1 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) A1,A3: 9.. / A1 = 9 => 0 pairs (X) / A3 = 9 => 0 pairs (_) D1,E3: 9.. / D1 = 9 => 0 pairs (*) / E3 = 9 => 0 pairs (X) C4,C6: 9.. / C4 = 9 => 0 pairs (*) / C6 = 9 => 0 pairs (X) D4,E6: 9.. / D4 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) A1,D1: 9.. / A1 = 9 => 0 pairs (X) / D1 = 9 => 0 pairs (_) A3,E3: 9.. / A3 = 9 => 0 pairs (*) / E3 = 9 => 0 pairs (X) C4,D4: 9.. / C4 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) C6,E6: 9.. / C6 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) D1,D4: 9.. / D1 = 9 => 0 pairs (*) / D4 = 9 => 0 pairs (X) E3,E6: 9.. / E3 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) * DURATION: 0:02:13.540256 START: 15:17:27.943563 END: 15:19:41.483819 2017-05-04 * CP COUNT: (57) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,C2,C4,C6,C7,D1,D4,D8,E4,E5,E6,E8,F1,G3,G4,G6,H1,H3,H5,H9,I1,I9) * .15.7....7..82.591..81.5..765.....123245.17.918.2...538..412975591...3244723591.. * PAIR C2: 3,6 BLK 1 B2: 3,6,4 # reduction candidate for 3,6 B2: 3,6 => CTR * .15.7....7..824591.481.563765..384123245.17.918.2...538..412975591...3244723591.. B2: 4 # 26 pairs B3: 3,6,4 # reduction candidate for 3,6 B3: 3,6 # 26 pairs * PAIR C2: 3,6 ROW 2 F2: 3,6,4 # reduction candidate for 3,6 F2: 4 => CTR * .1567...87..824591.4819563765.93..123245.17.918.2...538..412975591...3244723591.. F2: 3,6 # 26 pairs * PAIR F1: 3,4 BLK 2 F2: 3,4,6 # reduction candidate for 3,4 F2: 3,4 => CTR * .1567...87..82.591..81956.765.93..123245.17.918.2...538..412975591...3244723591.. F2: 6 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 E3: 3,4,9 # reduction candidate for 3,4 E3: 3,4 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 E3: 9 => CTR * .15.7....7..82.591..8195..765.93..123245.17.91892476538..4129755917..324472359168 * PAIR F1: 3,4 COL F F4: 3,4,8 # reduction candidate for 3,4 F4: 3,4 => CTR * .15.7....7..82.591..81.5..765....81232458176918.2.64538..412975591.6.3244723591.. F4: 8 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 * PAIR I1: 6,8 BLK 3 G1: 6,8,2 # reduction candidate for 6,8 G1: 6,8 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 G1: 2 => CTR * .15.7.2.87..82.5912.81956.765.93..123245.17.918.2...538..412975591...3244723591.. * PAIR G3: 2,6 BLK 3 G1: 2,6,8 # reduction candidate for 2,6 G1: 2,6 => CTR * .15.7...87..82.591..81.5..765....81232458176918.2.64538..412975591.6.3244723591.. G1: 8 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 * PAIR H3: 3,4 ROW 3 B3: 3,4,6 # reduction candidate for 3,4 B3: 3,4 => CTR * .15.7....7..82.591..81.56.765.....123245.176918.2.64538..412975591.6.3244723591.. B3: 6 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 E3: 3,4,9 # reduction candidate for 3,4 E3: 3,4 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 E3: 9 => CTR * .15.7....7..82.591..8195..765.93..123245.17.91892476538..4129755917..324472359168 * PAIR E4: 3,4 BLK 5 F4: 3,4,8 # reduction candidate for 3,4 F4: 3,4 => CTR * .15.7....7..82.591..81.5..765....81232458176918.2.64538..412975591.6.3244723591.. F4: 8 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 * PAIR E4: 3,4 COL E E3: 3,4,9 # reduction candidate for 3,4 E3: 3,4 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 E3: 9 => CTR * .15.7....7..82.591..8195..765.93..123245.17.91892476538..4129755917..324472359168 * PAIR E6: 4,9 COL E E3: 4,9,3 # reduction candidate for 4,9 E3: 3 => CTR * .1597....7..82659196813524765974..123245.17.918.2...538..412975591...3244723591.. E3: 4,9 # 25 pairs * PAIR G4: 4,8 ROW 4 F4: 4,8,3 # reduction candidate for 4,8 F4: 3 => CTR * .15.7....7..82.591..81.5..765...381232458176918.2.64538..412975591.6.3244723591.. F4: 4,8 # 25 pairs * PAIR G6: 4,6 ROW 6 F6: 4,6,7 # reduction candidate for 4,6 F6: 4,6 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 F6: 7 => CTR * .1567....7..82.591..81.5..765.....1232456178918.2.76538..412975591786324472359168 * PAIR B7: 3,6 COL B B2: 3,6,4 # reduction candidate for 3,6 B2: 3,6 => CTR * .15.7....7..824591.481.563765..384123245.17.918.2...538..412975591...3244723591.. B2: 4 # 26 pairs B3: 3,6,4 # reduction candidate for 3,6 B3: 3,6 # 26 pairs * PAIR D8: 6,7 BLK 8 F8: 6,7,8 # reduction candidate for 6,7 F8: 6,7 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 F8: 8 => CTR * .15.7....7..82.591..81.5..765.....123245.17.918.2.76538..412975591768324472359168 * PAIR E8: 6,8 BLK 8 F8: 6,8,7 # reduction candidate for 6,8 F8: 6,8 => CTR * .1567....7..82.591..81.5..765.....123245.17.918.2.76538..4129755917..324472359168 F8: 7 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-365-base-pr-000.dot * REASONING * DIS # B2: 3,6 => CTR => B2: 4 * DIS # F2: 4 => CTR => F2: 3,6 * DIS # F2: 3,4 => CTR => F2: 6 * PRF # F2: 6 => SOL * PRF # E3: 3,4 => SOL * DIS # E3: 9 => CTR => E3: 3,4 * DIS # F4: 3,4 => CTR => F4: 8 * PRF # F4: 8 => SOL * PRF # G1: 6,8 => SOL * DIS # G1: 2 => CTR => G1: 6,8 * DIS # G1: 2,6 => CTR => G1: 8 * PRF # G1: 8 => SOL * DIS # B3: 3,4 => CTR => B3: 6 * PRF # B3: 6 => SOL * PRF # E3: 3,4 => SOL * DIS # E3: 9 => CTR => E3: 3,4 * DIS # F4: 3,4 => CTR => F4: 8 * PRF # F4: 8 => SOL * PRF # E3: 3,4 => SOL * DIS # E3: 9 => CTR => E3: 3,4 * DIS # E3: 3 => CTR => E3: 4,9 * DIS # F4: 3 => CTR => F4: 4,8 * PRF # F6: 4,6 => SOL * DIS # F6: 7 => CTR => F6: 4,6 * DIS # B2: 3,6 => CTR => B2: 4 * PRF # F8: 6,7 => SOL * DIS # F8: 8 => CTR => F8: 6,7 * DIS # F8: 6,8 => CTR => F8: 7 * PRF # F8: 7 => SOL * CNT 29 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B7,C2,C4,C6,C7,D1,D4,D8,E4,E5,E6,E8,F1,G3,G4,G6,H1,H3,H5,H9,I1,I9) * .15.7....7..82.591..81.5..765.....123245.17.918.2...538..412975591...3244723591.. * PAIR C2: 3,6 BLK 1 B2: 3,6,4 # reduction candidate for 3,6 B2: 3,6 => CTR * .15.7....7..824591.481.563765..384123245.17.918.2...538..412975591...3244723591.. * RESTART * PAIR F1: 3,4 BLK 2 E3: 3,4,9 # reduction candidate for 3,4 E3: 3,4 => SOLVED * 215973846743826591968145237659738412324561789187294653836412975591687324472359168 * DURATION: 0:00:04.113645 START: 15:20:34.792755 END: 15:20:38.906400 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-365-base-pr-001.dot * REASONING * DIS # B2: 3,6 => CTR => B2: 4 * PRF B2: 4 # E3: 3,4 => SOL * STA B2: 4 + E3: 3,4 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 365 solution: 215973846743826591968145237659738412324561789187294653836412975591687324472359168 info: 4984 FNBTHWY S8.f 15372 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 215973846743826591968145237659738412324561789187294653836412975591687324472359168 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 # B2: 3,6 => CTR => B2: 4 * INC # B2: 4 => UNS * INC # B3: 3,6 => UNS * INC # F2: 3,6 => UNS * DIS # F2: 4 => CTR => F2: 3,6 * DIS # F2: 3,4 => CTR => F2: 6 * PRF # F2: 6 => SOL * PRF # E3: 3,4 => SOL * DIS # E3: 9 => CTR => E3: 3,4 * DIS # F4: 3,4 => CTR => F4: 8 * PRF # F4: 8 => SOL * PRF # G1: 6,8 => SOL * DIS # G1: 2 => CTR => G1: 6,8 * DIS # G1: 2,6 => CTR => G1: 8 * PRF # G1: 8 => SOL * DIS # B3: 3,4 => CTR => B3: 6 * PRF # B3: 6 => SOL * PRF # E3: 3,4 => SOL * DIS # E3: 9 => CTR => E3: 3,4 * DIS # F4: 3,4 => CTR => F4: 8 * PRF # F4: 8 => SOL * PRF # E3: 3,4 => SOL * DIS # E3: 9 => CTR => E3: 3,4 * INC # E3: 4,9 => UNS * DIS # E3: 3 => CTR => E3: 4,9 * INC # F4: 4,8 => UNS * DIS # F4: 3 => CTR => F4: 4,8 * PRF # F6: 4,6 => SOL * DIS # F6: 7 => CTR => F6: 4,6 * DIS # B2: 3,6 => CTR => B2: 4 * INC # B2: 4 => UNS * INC # B3: 3,6 => UNS * PRF # F8: 6,7 => SOL * DIS # F8: 8 => CTR => F8: 6,7 * DIS # F8: 6,8 => CTR => F8: 7 * PRF # F8: 7 => SOL * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 3,6 => CTR => B2: 4 * PRF B2: 4 # E3: 3,4 => SOL * STA B2: 4 + E3: 3,4 * CNT 2 HDP CHAINS / 2 HYP OPENED