Analysis of xx-top500-420-base.sdk
Contents
Original Sudoku
level: medium
position: ....81...6......3...4.......2....8.57..4...........1.....65..4.3.9.......8....... initial
Autosolve
position: ....814..6......3...4......42....8.57..4...........1.4...65..4.349......586...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 2,9 => CTR => A3: 1,8 * DIS # H1: 2,9 => CTR => H1: 5,6 * DIS # F6: 8,9 => CTR => F6: 2,3,5,6,7 * DIS # A3: 1,2 => CTR => A3: 8,9 * DIS # C7: 7 => CTR => C7: 1,2 * DIS # A3: 1,2 => CTR => A3: 8,9 * DIS # C7: 1,7 => CTR => C7: 2 * DIS # B3: 1,7 => CTR => B3: 3,5,9 * PRF # I7: 3,9 => SOL * DIS # I7: 8 => CTR => I7: 3,9 * DIS # G9: 3,9 => CTR => G9: 2,7 * DIS # I9: 3,9 => CTR => I9: 1,2,7 * DIS # F7: 3,9 => CTR => F7: 8 * PRF # F7: 8 => SOL * DIS # G5: 3,9 => CTR => G5: 2,6 * CNT 15 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:
* DIS # A3: 2,9 => CTR => A3: 1,8 * DIS A3: 1,8 # H1: 2,9 => CTR => H1: 5,6 * DIS A3: 1,8 + H1: 5,6 # F6: 8,9 => CTR => F6: 2,3,5,6,7 * DIS A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 # D6: 2,3,5,7 => CTR => D6: 8,9 * DIS A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 # C7: 7 => CTR => C7: 1,2 * PRF A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 + C7: 1,2 # I7: 3,9 => SOL * STA A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 + C7: 1,2 + I7: 3,9 * CNT 6 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....81...6......3...4.......2....8.57..4...........1.....65..4.3.9.......8....... | initial |
| ....814..6......3...4......42....8.57..4...........1.4...65..4.349......586...... | autosolve |
| 295381467617594238834267951421736895758419623963825174172658349349172586586943712 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) A1: 2,9 C4: 1,3 A6: 8,9 A7: 1,2 B7: 1,7 G7: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,A7: 1.. / A3 = 1 => 0 pairs (X) / A7 = 1 => 4 pairs (_) A7,C7: 2.. / A7 = 2 => 0 pairs (X) / C7 = 2 => 4 pairs (_) G5,I5: 3.. / G5 = 3 => 0 pairs (X) / I5 = 3 => 7 pairs (_) E2,F2: 4.. / E2 = 4 => 6 pairs (_) / F2 = 4 => 6 pairs (_) E9,F9: 4.. / E9 = 4 => 6 pairs (_) / F9 = 4 => 6 pairs (_) E2,E9: 4.. / E2 = 4 => 6 pairs (_) / E9 = 4 => 6 pairs (_) F2,F9: 4.. / F2 = 4 => 6 pairs (_) / F9 = 4 => 6 pairs (_) G8,H8: 5.. / G8 = 5 => 12 pairs (_) / H8 = 5 => 0 pairs (X) E3,F3: 6.. / E3 = 6 => 6 pairs (_) / F3 = 6 => 6 pairs (_) H1,I1: 6.. / H1 = 6 => 12 pairs (_) / I1 = 6 => 0 pairs (X) B5,B6: 6.. / B5 = 6 => 0 pairs (X) / B6 = 6 => 6 pairs (_) G5,G8: 6.. / G5 = 6 => 11 pairs (_) / G8 = 6 => 0 pairs (X) H4,H6: 7.. / H4 = 7 => 7 pairs (_) / H6 = 7 => 7 pairs (_) B7,C7: 7.. / B7 = 7 => 6 pairs (_) / C7 = 7 => 0 pairs (X) C2,A3: 8.. / C2 = 8 => 0 pairs (X) / A3 = 8 => 0 pairs (_) C2,I2: 8.. / C2 = 8 => 0 pairs (X) / I2 = 8 => 0 pairs (_) C5,F5: 8.. / C5 = 8 => 0 pairs (*) / F5 = 8 => 0 pairs (X) F7,I7: 8.. / F7 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) A3,A6: 8.. / A3 = 8 => 0 pairs (*) / A6 = 8 => 0 pairs (X) D6,D8: 8.. / D6 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) H3,H8: 8.. / H3 = 8 => 0 pairs (X) / H8 = 8 => 0 pairs (_) * DURATION: 0:00:31.554511 START: 17:10:53.250241 END: 17:11:24.804752 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,A7,B7,C4,G7) * ....814..6......3...4......42....8.57..4...........1.4...65..4.349......586...... * PAIR A1: 2,9 BLK 1 A3: 2,9,1,8 # reduction candidate for 2,9 A3: 2,9 => CTR * ..7.814566.8....3...4....8.421...8.57.5418...8.3...1.417265..483498...1.5861..... A3: 1,8 # 7 pairs * PAIR A1: 2,9 ROW 1 D1: 2,9,3,5,7 # reduction candidate for 2,9 D1: 2,9 # 9 pairs H1: 2,9,5,6 # reduction candidate for 2,9 H1: 2,9 => CTR * ..7.814.66.8....3...4....8.4231..8.57.14.8...8.5...1.417265..4834981.65.586....1. H1: 5,6 # 7 pairs I1: 2,9,6,7 # reduction candidate for 2,9 I1: 2,9 # 14 pairs * PAIR C4: 1,3 ROW 4 D4: 1,3,7,9 # reduction candidate for 1,3 D4: 1,3 # 7 pairs E4: 1,3,6,7,9 # reduction candidate for 1,3 E4: 1,3 # 9 pairs * PAIR A6: 8,9 ROW 6 D6: 8,9,2,3,5,7 # reduction candidate for 8,9 D6: 8,9 # 8 pairs F6: 8,9,2,3,5,6,7 # reduction candidate for 8,9 F6: 8,9 => CTR * ....814..6.8.4..3...4....8.421...895795418.6.863529174...6539483498726..586194.2. F6: 2,3,5,6,7 # 6 pairs * PAIR A6: 8,9 COL A A3: 8,9,1,2 # reduction candidate for 8,9 A3: 1,2 => CTR * 9...814566.8....3...4....8.421...8.57.5418...8.3...1.4...65..483498...1.5861..... A3: 8,9 # 4 pairs * PAIR A7: 1,2 BLK 7 C7: 1,2,7 # reduction candidate for 1,2 C7: 7 => CTR * 9.2.814566.8....311.4....8.421...8.57.5418...8.3...1.421765..483498...1.5861..... C7: 1,2 # 6 pairs * PAIR A7: 1,2 COL A A3: 1,2,8,9 # reduction candidate for 1,2 A3: 1,2 => CTR * 9...814566.8....3...4....8.421...8.57.5418...8.3...1.4...65..483498...1.5861..... A3: 8,9 # 4 pairs * PAIR B7: 1,7 BLK 7 C7: 1,7,2 # reduction candidate for 1,7 C7: 1,7 => CTR * 9.2.814566.8....311.4....8.421...8.57.5418...8.3...1.421765..483498...1.5861..... C7: 2 # 4 pairs * PAIR B7: 1,7 COL B B2: 1,7,5,9 # reduction candidate for 1,7 B2: 1,7 # 8 pairs B3: 1,7,3,5,9 # reduction candidate for 1,7 B3: 1,7 => CTR * .3..81456658....31..4....8.421...8.57.5418...8.3...1.4...65..483498...1.5861..... B3: 3,5,9 # 6 pairs * PAIR G7: 3,9 BLK 9 I7: 3,9,8 # reduction candidate for 3,9 I7: 3,9 => SOLVED * 295381467617594238834267951421736895758419623963825174172658349349172586586943712 I7: 8 => CTR * ....814566.8....3...4....8.421...8.57.5418...8.3...1.4...65..483498...1.5861..... G9: 3,9,2,7 # reduction candidate for 3,9 G9: 3,9 => CTR * ....814566.8....3...4....8.421...8.57.5418..38.3...1.4...65..483498...1.5861...27 G9: 2,7 # 7 pairs I9: 3,9,1,2,7 # reduction candidate for 3,9 I9: 3,9 => CTR * ....814566.8....3...4....8.421...8.57.5418...8.3...1.4...65..483498...1.5861...2. I9: 1,2,7 # 6 pairs * PAIR G7: 3,9 ROW 7 F7: 3,9,8 # reduction candidate for 3,9 F7: 3,9 => CTR * ....814566.8....3...4....8.421...8.57.5418...8.3...1.4...65..483498...1.5861..... F7: 8 => SOLVED * 295381467617594238834267951421736895758419623963825174172658349349172586586943712 * PAIR G7: 3,9 COL G G5: 3,9,2,6 # reduction candidate for 3,9 G5: 3,9 => CTR * ....814..6.8....3...4....8.4231..8.57..4.8...8.5...1.4...65..4834981.65.586....1. G5: 2,6 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-420-base-pr-000.dot * REASONING * DIS # A3: 2,9 => CTR => A3: 1,8 * DIS # H1: 2,9 => CTR => H1: 5,6 * DIS # F6: 8,9 => CTR => F6: 2,3,5,6,7 * DIS # A3: 1,2 => CTR => A3: 8,9 * DIS # C7: 7 => CTR => C7: 1,2 * DIS # A3: 1,2 => CTR => A3: 8,9 * DIS # C7: 1,7 => CTR => C7: 2 * DIS # B3: 1,7 => CTR => B3: 3,5,9 * PRF # I7: 3,9 => SOL * DIS # I7: 8 => CTR => I7: 3,9 * DIS # G9: 3,9 => CTR => G9: 2,7 * DIS # I9: 3,9 => CTR => I9: 1,2,7 * DIS # F7: 3,9 => CTR => F7: 8 * PRF # F7: 8 => SOL * DIS # G5: 3,9 => CTR => G5: 2,6 * CNT 15 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,A7,B7,C4,G7) * ....814..6......3...4......42....8.57..4...........1.4...65..4.349......586...... * PAIR A1: 2,9 BLK 1 A3: 2,9,1,8 # reduction candidate for 2,9 A3: 2,9 => CTR * ..7.814566.8....3...4....8.421...8.57.5418...8.3...1.417265..483498...1.5861..... * PAIR A1: 2,9 ROW 1 D1: 2,9,3,5,7 # reduction candidate for 2,9 D1: 2,9 # 10 pairs H1: 2,9,5,6 # reduction candidate for 2,9 H1: 2,9 => CTR * 9...814266......3...4....8.42....8.57..4.....8.....1.4...65..4.3498...5.586....1. I1: 2,9,6,7 # reduction candidate for 2,9 I1: 2,9 # 15 pairs * PAIR RESTART * PAIR A1: 2,9 ROW 1 D1: 2,9,3,5,7 # reduction candidate for 2,9 D1: 2,9 # 10 pairs I1: 2,9,6,7 # reduction candidate for 2,9 I1: 2,9 # 15 pairs * PAIR C4: 1,3 ROW 4 D4: 1,3,7,9 # reduction candidate for 1,3 D4: 1,3 # 9 pairs E4: 1,3,6,7,9 # reduction candidate for 1,3 E4: 1,3 # 11 pairs * PAIR A6: 8,9 ROW 6 D6: 8,9,2,3,5,7 # reduction candidate for 8,9 D6: 8,9 # 10 pairs F6: 8,9,2,3,5,6,7 # reduction candidate for 8,9 F6: 8,9 => CTR * 9.2.814..6.8....311.4....8942....895795418...863529174217653948349872.16586194.2. * RESTART * PAIR A6: 8,9 ROW 6 D6: 8,9,2,3,5,7 # reduction candidate for 8,9 D6: 2,3,5,7 => CTR * 9.2.814566.8....311.4....8.421...8.57.5418...8.3...1.421765..483498...1.5861..... * PAIR RESTART * PAIR A7: 1,2 BLK 7 C7: 1,2,7 # reduction candidate for 1,2 C7: 7 => CTR * 9.2.814..6.8....311.4....8.42....895795418...86392517421765..48349872.165861...2. * PAIR G7: 3,9 BLK 9 I7: 3,9,8 # reduction candidate for 3,9 I7: 3,9 => SOLVED * 295381467617594238834267951421736895758419623963825174172658349349172586586943712 * DURATION: 0:00:15.713642 START: 17:11:51.500157 END: 17:12:07.213799 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-420-base-pr-001.dot * REASONING * DIS # A3: 2,9 => CTR => A3: 1,8 * DIS A3: 1,8 # H1: 2,9 => CTR => H1: 5,6 * DIS A3: 1,8 + H1: 5,6 # F6: 8,9 => CTR => F6: 2,3,5,6,7 * DIS A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 # D6: 2,3,5,7 => CTR => D6: 8,9 * DIS A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 # C7: 7 => CTR => C7: 1,2 * PRF A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 + C7: 1,2 # I7: 3,9 => SOL * STA A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 + C7: 1,2 + I7: 3,9 * CNT 6 HDP CHAINS / 15 HYP OPENED
Header Info
Top 500 Minimum 17 420 solution: 295381467617594238834267951421736895758419623963825174172658349349172586586943712 info: 95094 FNBWYK S8.f 6374 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 295381467617594238834267951421736895758419623963825174172658349349172586586943712 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 # A3: 2,9 => CTR => A3: 1,8 * INC # A3: 1,8 => UNS * INC # D1: 2,9 => UNS * DIS # H1: 2,9 => CTR => H1: 5,6 * INC # H1: 5,6 => UNS * INC # I1: 2,9 => UNS * INC # D4: 1,3 => UNS * INC # E4: 1,3 => UNS * INC # D6: 8,9 => UNS * DIS # F6: 8,9 => CTR => F6: 2,3,5,6,7 * INC # F6: 2,3,5,6,7 => UNS * INC # A3: 8,9 => UNS * DIS # A3: 1,2 => CTR => A3: 8,9 * INC # C7: 1,2 => UNS * DIS # C7: 7 => CTR => C7: 1,2 * DIS # A3: 1,2 => CTR => A3: 8,9 * INC # A3: 8,9 => UNS * DIS # C7: 1,7 => CTR => C7: 2 * INC # C7: 2 => UNS * INC # B2: 1,7 => UNS * DIS # B3: 1,7 => CTR => B3: 3,5,9 * INC # B3: 3,5,9 => UNS * PRF # I7: 3,9 => SOL * DIS # I7: 8 => CTR => I7: 3,9 * DIS # G9: 3,9 => CTR => G9: 2,7 * INC # G9: 2,7 => UNS * DIS # I9: 3,9 => CTR => I9: 1,2,7 * INC # I9: 1,2,7 => UNS * DIS # F7: 3,9 => CTR => F7: 8 * PRF # F7: 8 => SOL * DIS # G5: 3,9 => CTR => G5: 2,6 * INC # G5: 2,6 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 2,9 => CTR => A3: 1,8 * INC A3: 1,8 # D1: 2,9 => UNS * DIS A3: 1,8 # H1: 2,9 => CTR => H1: 5,6 * INC A3: 1,8 + H1: 5,6 # I1: 2,9 => UNS * INC A3: 1,8 + H1: 5,6 # D1: 2,9 => UNS * INC A3: 1,8 + H1: 5,6 # I1: 2,9 => UNS * INC A3: 1,8 + H1: 5,6 # D4: 1,3 => UNS * INC A3: 1,8 + H1: 5,6 # E4: 1,3 => UNS * INC A3: 1,8 + H1: 5,6 # D6: 8,9 => UNS * DIS A3: 1,8 + H1: 5,6 # F6: 8,9 => CTR => F6: 2,3,5,6,7 * INC A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 # D6: 8,9 => UNS * DIS A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 # D6: 2,3,5,7 => CTR => D6: 8,9 * INC A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 # C7: 1,2 => UNS * DIS A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 # C7: 7 => CTR => C7: 1,2 * PRF A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 + C7: 1,2 # I7: 3,9 => SOL * STA A3: 1,8 + H1: 5,6 + F6: 2,3,5,6,7 + D6: 8,9 + C7: 1,2 + I7: 3,9 * CNT 15 HDP CHAINS / 15 HYP OPENED