Analysis of xx-top500-100-base.sdk
Contents
Original Sudoku
level: medium
position: ...2..8.4...9..3..1........5....6.1.....4.........8....84.3.......7...5..2....... initial
Autosolve
position: ...2..8.4...9..3.11........5..3.6.1.....4.........8....846351.....7...5..25...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F3: 4,7 => SOL * DIS # B2: 4,7 => CTR => B2: 5,6 * DIS # C4: 2,8 => CTR => C4: 7,9 * PRF # C4: 7,9 => SOL * DIS # C5: 2,8 => CTR => C5: 1,3,6,7,9 * DIS # I5: 2,8 => CTR => I5: 3,5,6,7,9 * DIS # A2: 2,8 => CTR => A2: 4 * PRF # A2: 4 => SOL * DIS # G6: 2,4 => CTR => G6: 5,6,7,9 * PRF # A2: 2,4 => SOL * DIS # A2: 8 => CTR => A2: 2,4 * DIS # I5: 3,8 => CTR => I5: 2,5,6,7,9 * DIS # C5: 3,8 => CTR => C5: 1,2,6,7,9 * PRF # H9: 3,8 => SOL * DIS # H9: 4 => CTR => H9: 3,8 * DIS # B6: 3,4 => CTR => B6: 1,6,7,9 * DIS # H9: 3,4 => CTR => H9: 8 * PRF # H9: 8 => SOL * DIS # H9: 3 => CTR => H9: 4,8 * CNT 19 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F3: 4,7 => SOL * STA F3: 4,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2..8.4...9..3..1........5....6.1.....4.........8....84.3.......7...5..2....... | initial |
| ...2..8.4...9..3.11........5..3.6.1.....4.........8....846351.....7...5..25...... | autosolve |
| 957213864468957321132864579549326718876149235213578946784635192691782453325491687 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) F2: 4,7 D3: 4,8 A5: 2,8 A6: 2,4 D5: 1,5 D6: 1,5 H5: 3,8 H6: 3,4 A7: 7,9 D9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 1.. / E1 = 1 => 0 pairs (*) / F1 = 1 => 0 pairs (X) D5,D6: 1.. / D5 = 1 => 8 pairs (_) / D6 = 1 => 8 pairs (_) B8,C8: 1.. / B8 = 1 => 10 pairs (_) / C8 = 1 => 10 pairs (_) E9,F9: 1.. / E9 = 1 => 11 pairs (_) / F9 = 1 => 0 pairs (*) E1,E9: 1.. / E1 = 1 => 0 pairs (*) / E9 = 1 => 0 pairs (X) F1,F9: 1.. / F1 = 1 => 11 pairs (_) / F9 = 1 => 0 pairs (*) E8,F8: 2.. / E8 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) H7,I7: 2.. / H7 = 2 => 14 pairs (_) / I7 = 2 => 11 pairs (_) F5,F8: 2.. / F5 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) F1,F3: 3.. / F1 = 3 => 0 pairs (*) / F3 = 3 => 0 pairs (X) B4,G4: 4.. / B4 = 4 => 0 pairs (*) / G4 = 4 => 0 pairs (X) F8,G8: 4.. / F8 = 4 => 0 pairs (X) / G8 = 4 => 0 pairs (_) A2,A6: 4.. / A2 = 4 => 0 pairs (*) / A6 = 4 => 0 pairs (X) D3,D9: 4.. / D3 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) H6,H9: 4.. / H6 = 4 => 0 pairs (*) / H9 = 4 => 0 pairs (X) B1,B2: 5.. / B1 = 5 => 10 pairs (_) / B2 = 5 => 11 pairs (_) E1,E2: 5.. / E1 = 5 => 11 pairs (_) / E2 = 5 => 10 pairs (_) G3,I3: 5.. / G3 = 5 => 10 pairs (_) / I3 = 5 => 10 pairs (_) D5,D6: 5.. / D5 = 5 => 8 pairs (_) / D6 = 5 => 8 pairs (_) B1,E1: 5.. / B1 = 5 => 10 pairs (_) / E1 = 5 => 11 pairs (_) B2,E2: 5.. / B2 = 5 => 11 pairs (_) / E2 = 5 => 10 pairs (_) A7,A9: 7.. / A7 = 7 => 12 pairs (_) / A9 = 7 => 15 pairs (_) C4,I4: 8.. / C4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) E8,I8: 8.. / E8 = 8 => 0 pairs (*) / I8 = 8 => 0 pairs (X) A2,A5: 8.. / A2 = 8 => 0 pairs (X) / A5 = 8 => 0 pairs (_) D3,D9: 8.. / D3 = 8 => 0 pairs (*) / D9 = 8 => 0 pairs (X) H5,H9: 8.. / H5 = 8 => 0 pairs (X) / H9 = 8 => 0 pairs (_) * DURATION: 0:00:48.905109 START: 06:10:59.998366 END: 06:11:48.903475 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A7,D3,D5,D6,D9,F2,H5,H6) * ...2..8.4...9..3.11........5..3.6.1.....4.........8....846351.....7...5..25...... * PAIR F2: 4,7 BLK 2 F3: 4,7,3 # reduction candidate for 4,7 F3: 4,7 => SOLVED * 957213864468957321132864579549326718876149235213578946784635192691782453325491687 F3: 3 # 11 pairs * PAIR F2: 4,7 ROW 2 B2: 4,7,5,6 # reduction candidate for 4,7 B2: 4,7 => CTR * .5.2618.484.9573.11..483...5.83.641.2...49.8.4....8.3..846351.....7.4.58.258...43 B2: 5,6 # 11 pairs * PAIR A5: 2,8 BLK 4 C4: 2,8,7,9 # reduction candidate for 2,8 C4: 2,8 => CTR * ...2..8.484.9573.11..483...5.83.641.2...49.8.4....8.3..846351.....724.58.25891.4. C4: 7,9 => SOLVED * 957213864468957321132864579549326718876149235213578946784635192691782453325491687 C5: 2,8,1,3,6,7,9 # reduction candidate for 2,8 C5: 2,8 => CTR * ...2..8.4...9..3.11........5..3.6.18....4..3.4....8....846351.....7...5..25...... C5: 1,3,6,7,9 # 10 pairs * PAIR A5: 2,8 ROW 5 I5: 2,8,3,5,6,7,9 # reduction candidate for 2,8 I5: 2,8 => CTR * ...2..8.44..9.73.11..864...54.3.6.1.8...49.322...78.4..8463512....78245..25491.8. I5: 3,5,6,7,9 # 10 pairs * PAIR A5: 2,8 COL A A2: 2,8,4 # reduction candidate for 2,8 A2: 2,8 => CTR * ...2..8.484.9573.11..483...5.83.641.2...49.8.4....8.3..846351.....724.58.25891.4. A2: 4 => SOLVED * 957213864468957321132864579549326718876149235213578946784635192691782453325491687 * PAIR A6: 2,4 ROW 6 G6: 2,4,5,6,7,9 # reduction candidate for 2,4 G6: 2,4 => CTR * ...2..8.484.9573.11..483...5.83.641.2...49.8.4...7823..846351.....724.5..258...4. G6: 5,6,7,9 # 10 pairs * PAIR A6: 2,4 COL A A2: 2,4,8 # reduction candidate for 2,4 A2: 2,4 => SOLVED * 957213864468957321132864579549326718876149235213578946784635192691782453325491687 A2: 8 => CTR * ...2..8.48..9..3.11........5..3.6.1.2...4....4....8.3..846351.....7.245..25....8. * PAIR H5: 3,8 BLK 6 I5: 3,8,2,5,6,7,9 # reduction candidate for 3,8 I5: 3,8 => CTR * ...2..8.48..9..3.11........5.83.6.1.2...4....4....8....846351.....7...5..25...... I5: 2,5,6,7,9 # 10 pairs * PAIR H5: 3,8 ROW 5 C5: 3,8,1,2,6,7,9 # reduction candidate for 3,8 C5: 3,8 => CTR * ...2..8.48..9..3.11........5..3.6.1.2...4....4....8.3..846351.....7.245..25....8. C5: 1,2,6,7,9 # 10 pairs * PAIR H5: 3,8 COL H H9: 3,8,4 # reduction candidate for 3,8 H9: 3,8 => SOLVED * 957213864468957321132864579549326718876149235213578946784635192691782453325491687 H9: 4 => CTR * ...2..8.48..9..3.11..48....5.83.6.1.2...4..8.4....8.3..846351.....7...5..25....4. * PAIR H6: 3,4 ROW 6 B6: 3,4,1,6,7,9 # reduction candidate for 3,4 B6: 3,4 => CTR * ...2.38.44.89573211..864...54.3.6.188...4..3.23...8.4..846351.....78245..254...8. B6: 1,6,7,9 # 10 pairs * PAIR H6: 3,4 COL H H9: 3,4,8 # reduction candidate for 3,4 H9: 3,4 => CTR * ...2..8.48..9..3.11........5.83.6.1.2...4..8.4....8.3..846351.....7.245..25...... H9: 8 => SOLVED * 957213864468957321132864579549326718876149235213578946784635192691782453325491687 * PAIR A7: 7,9 BLK 7 A9: 7,9,3,6 # reduction candidate for 7,9 A9: 3,6 # 17 pairs A9: 7,9 # 15 pairs * PAIR A7: 7,9 ROW 7 H7: 7,9,2 # reduction candidate for 7,9 H7: 7,9 # 11 pairs I7: 7,9,2 # reduction candidate for 7,9 I7: 7,9 # 14 pairs * PAIR D9: 4,8 ROW 9 H9: 4,8,3 # reduction candidate for 4,8 H9: 3 => CTR * ...2..8.4...9..3.11........5..3.6.1.....4..8......8.4..846351.....7...5..25....3. H9: 4,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-100-base-pr-000.dot * REASONING * PRF # F3: 4,7 => SOL * DIS # B2: 4,7 => CTR => B2: 5,6 * DIS # C4: 2,8 => CTR => C4: 7,9 * PRF # C4: 7,9 => SOL * DIS # C5: 2,8 => CTR => C5: 1,3,6,7,9 * DIS # I5: 2,8 => CTR => I5: 3,5,6,7,9 * DIS # A2: 2,8 => CTR => A2: 4 * PRF # A2: 4 => SOL * DIS # G6: 2,4 => CTR => G6: 5,6,7,9 * PRF # A2: 2,4 => SOL * DIS # A2: 8 => CTR => A2: 2,4 * DIS # I5: 3,8 => CTR => I5: 2,5,6,7,9 * DIS # C5: 3,8 => CTR => C5: 1,2,6,7,9 * PRF # H9: 3,8 => SOL * DIS # H9: 4 => CTR => H9: 3,8 * DIS # B6: 3,4 => CTR => B6: 1,6,7,9 * DIS # H9: 3,4 => CTR => H9: 8 * PRF # H9: 8 => SOL * DIS # H9: 3 => CTR => H9: 4,8 * CNT 19 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A7,D3,D5,D6,D9,F2,H5,H6) * ...2..8.4...9..3.11........5..3.6.1.....4.........8....846351.....7...5..25...... * PAIR F2: 4,7 BLK 2 F3: 4,7,3 # reduction candidate for 4,7 F3: 4,7 => SOLVED * 957213864468957321132864579549326718876149235213578946784635192691782453325491687 * DURATION: 0:00:02.738315 START: 06:12:21.173026 END: 06:12:23.911341 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-100-base-pr-001.dot * REASONING * PRF # F3: 4,7 => SOL * STA F3: 4,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 100 solution: 957213864468957321132864579549326718876149235213578946784635192691782453325491687 info: 1579 FNBTHXY S8.f 7762 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 957213864468957321132864579549326718876149235213578946784635192691782453325491687 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:
* PRF # F3: 4,7 => SOL * INC # F3: 3 => UNS * DIS # B2: 4,7 => CTR => B2: 5,6 * INC # B2: 5,6 => UNS * DIS # C4: 2,8 => CTR => C4: 7,9 * PRF # C4: 7,9 => SOL * DIS # C5: 2,8 => CTR => C5: 1,3,6,7,9 * INC # C5: 1,3,6,7,9 => UNS * DIS # I5: 2,8 => CTR => I5: 3,5,6,7,9 * INC # I5: 3,5,6,7,9 => UNS * DIS # A2: 2,8 => CTR => A2: 4 * PRF # A2: 4 => SOL * DIS # G6: 2,4 => CTR => G6: 5,6,7,9 * INC # G6: 5,6,7,9 => UNS * PRF # A2: 2,4 => SOL * DIS # A2: 8 => CTR => A2: 2,4 * DIS # I5: 3,8 => CTR => I5: 2,5,6,7,9 * INC # I5: 2,5,6,7,9 => UNS * DIS # C5: 3,8 => CTR => C5: 1,2,6,7,9 * INC # C5: 1,2,6,7,9 => UNS * PRF # H9: 3,8 => SOL * DIS # H9: 4 => CTR => H9: 3,8 * DIS # B6: 3,4 => CTR => B6: 1,6,7,9 * INC # B6: 1,6,7,9 => UNS * DIS # H9: 3,4 => CTR => H9: 8 * PRF # H9: 8 => SOL * INC # A9: 7,9 => UNS * INC # A9: 3,6 => UNS * INC # H7: 7,9 => UNS * INC # I7: 7,9 => UNS * INC # H9: 4,8 => UNS * DIS # H9: 3 => CTR => H9: 4,8 * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F3: 4,7 => SOL * STA F3: 4,7 * CNT 1 HDP CHAINS / 1 HYP OPENED