Analysis of xx-top95-059-base.sdk
Contents
Original Sudoku
level: medium
position: .47.2....8....1....3....9.2.....5...6..81..5.....4.....7....3.4...9...1.4..27.8.. initial
Autosolve
position: .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 1,5 => CTR => A6: 2,3,7,9 * DIS # F3: 6,8 => CTR => F3: 7 * DIS # H3: 6,8 => CTR => H3: 4,7 * DIS # C5: 2,9 => CTR => C5: 3,4 * DIS # F5: 3,7 => CTR => F5: 2,9 * DIS # F3: 6,8 => CTR => F3: 7 * DIS # I9: 6,9 => CTR => I9: 5 * CNT 7 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 1,5 => CTR => A6: 2,3,7,9 * DIS A6: 2,3,7,9 # F3: 6,8 => CTR => F3: 7 * DIS A6: 2,3,7,9 + F3: 7 # H3: 6,8 => CTR => H3: 4 * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 # B4: 2,9 => CTR => B4: 1,8 * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 # C5: 2,9 => CTR => C5: 3,4 * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 # B6: 2,9 => CTR => B6: 1,5,8 * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # F5: 3 => CTR => F5: 2,9 * PRF A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 # B2: 5,6 => SOL * STA A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 + B2: 5,6 * CNT 8 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .47.2....8....1....3....9.2.....5...6..81..5.....4.....7....3.4...9...1.4..27.8.. | initial |
| .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8.. | autosolve |
| 947326581852491673136587942284735169693812457715649238579168324328954716461273895 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A1: 5,9 A3: 1,5 E3: 6,8 B5: 2,9 F7: 6,8 F9: 3,6 H9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,C3: 1.. / A3 = 1 => 7 pairs (_) / C3 = 1 => 0 pairs (X) G1,I1: 1.. / G1 = 1 => 7 pairs (_) / I1 = 1 => 8 pairs (_) B9,C9: 1.. / B9 = 1 => 7 pairs (_) / C9 = 1 => 8 pairs (_) B2,C2: 2.. / B2 = 2 => 8 pairs (_) / C2 = 2 => 7 pairs (_) F5,F6: 2.. / F5 = 2 => 9 pairs (_) / F6 = 2 => 7 pairs (_) H7,G8: 2.. / H7 = 2 => 9 pairs (_) / G8 = 2 => 13 pairs (_) E8,F9: 3.. / E8 = 3 => 15 pairs (_) / F9 = 3 => 8 pairs (_) C9,F9: 3.. / C9 = 3 => 15 pairs (_) / F9 = 3 => 8 pairs (_) D2,D3: 4.. / D2 = 4 => 7 pairs (_) / D3 = 4 => 0 pairs (X) C4,C5: 4.. / C4 = 4 => 7 pairs (_) / C5 = 4 => 8 pairs (_) D3,H3: 4.. / D3 = 4 => 0 pairs (X) / H3 = 4 => 7 pairs (_) C5,G5: 4.. / C5 = 4 => 8 pairs (_) / G5 = 4 => 7 pairs (_) E7,E8: 5.. / E7 = 5 => 8 pairs (_) / E8 = 5 => 12 pairs (_) A4,A6: 7.. / A4 = 7 => 8 pairs (_) / A6 = 7 => 8 pairs (_) G8,I8: 7.. / G8 = 7 => 11 pairs (_) / I8 = 7 => 8 pairs (_) F1,E2: 9.. / F1 = 9 => 14 pairs (_) / E2 = 9 => 13 pairs (_) A1,F1: 9.. / A1 = 9 => 13 pairs (_) / F1 = 9 => 14 pairs (_) E2,E4: 9.. / E2 = 9 => 13 pairs (_) / E4 = 9 => 14 pairs (_) * DURATION: 0:00:19.162709 START: 00:07:16.105536 END: 00:07:35.268245 2017-05-04 * CP COUNT: (18) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,E3,F7,F9,H9) * .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8.. * PAIR A1: 5,9 BLK 1 B2: 5,9,2,6 # reduction candidate for 5,9 B2: 5,9 # 9 pairs C2: 5,9,2,6 # reduction candidate for 5,9 C2: 5,9 # 10 pairs * PAIR A1: 5,9 COL A A6: 5,9,1,2,3,7 # reduction candidate for 5,9 A6: 5,9 # 15 pairs A7: 5,9,2 # reduction candidate for 5,9 A7: 5,9 # 9 pairs * PAIR A3: 1,5 BLK 1 C3: 1,5,6 # reduction candidate for 1,5 C3: 1,5 # 19 pairs C3: 6 # 7 pairs * PAIR A3: 1,5 COL A A6: 1,5,2,3,7,9 # reduction candidate for 1,5 A6: 1,5 => CTR * 947.2..3.8..391476.364879.27..635...6.481.753..374....27.1..3.43..9.42174..2738.5 A6: 2,3,7,9 # 7 pairs * PAIR E3: 6,8 BLK 2 F1: 6,8,3,9 # reduction candidate for 6,8 F1: 6,8 # 16 pairs F3: 6,8,7 # reduction candidate for 6,8 F3: 6,8 => CTR * .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8.. F3: 7 # 7 pairs * PAIR E3: 6,8 ROW 3 H3: 6,8,4,7 # reduction candidate for 6,8 H3: 6,8 => CTR * 94752..3.8..391475.3.4.79.2....35.4.6.481.753....4.....7.15.324...9.45174..2738.. H3: 4,7 # 8 pairs * PAIR E3: 6,8 COL E E7: 6,8,5 # reduction candidate for 6,8 E7: 6,8 # 12 pairs E8: 6,8,3,5 # reduction candidate for 6,8 E8: 6,8 # 10 pairs * PAIR B5: 2,9 BLK 4 A4: 2,9,1,3,7 # reduction candidate for 2,9 A4: 2,9 # 12 pairs B4: 2,9,1,8 # reduction candidate for 2,9 B4: 2,9 # 15 pairs C4: 2,9,1,3,4,8 # reduction candidate for 2,9 C4: 2,9 # 10 pairs C5: 2,9,3,4 # reduction candidate for 2,9 C5: 2,9 => CTR * 547.29...8....1...136587942..4.952..6..813457....42...97.1.83242..93471.4.32768.. C5: 3,4 # 8 pairs A6: 2,9,1,3,5,7 # reduction candidate for 2,9 A6: 2,9 # 13 pairs B6: 2,9,1,5,8 # reduction candidate for 2,9 B6: 2,9 # 17 pairs C6: 2,9,1,3,5,8 # reduction candidate for 2,9 C6: 2,9 # 11 pairs * PAIR B5: 2,9 ROW 5 F5: 2,9,3,7 # reduction candidate for 2,9 F5: 3,7 => CTR * 547.29...8..4615..136587942....95...6..813.5.....42....7.15836426.934.1.4.3276895 F5: 2,9 # 11 pairs * PAIR B5: 2,9 COL B B2: 2,9,5,6 # reduction candidate for 2,9 B2: 5,6 # 14 pairs B2: 2,9 # 9 pairs * PAIR F7: 6,8 BLK 8 E7: 6,8,5 # reduction candidate for 6,8 E7: 6,8 # 12 pairs E8: 6,8,3,5 # reduction candidate for 6,8 E8: 6,8 # 10 pairs * PAIR F7: 6,8 ROW 7 C7: 6,8,2,5,9 # reduction candidate for 6,8 C7: 6,8 # 10 pairs C7: 2,5,9 # 7 pairs * PAIR F7: 6,8 COL F F1: 6,8,3,9 # reduction candidate for 6,8 F1: 6,8 # 16 pairs F3: 6,8,7 # reduction candidate for 6,8 F3: 6,8 => CTR * .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8.. F3: 7 # 7 pairs * PAIR F9: 3,6 BLK 8 E8: 3,6,5,8 # reduction candidate for 3,6 E8: 5,8 # 10 pairs E8: 3,6 # 8 pairs * PAIR F9: 3,6 ROW 9 C9: 3,6,1,5,9 # reduction candidate for 3,6 C9: 3,6 # 9 pairs C9: 1,5,9 # 8 pairs * PAIR F9: 3,6 COL F F1: 3,6,8,9 # reduction candidate for 3,6 F1: 3,6 # 14 pairs F6: 3,6,2,7,9 # reduction candidate for 3,6 F6: 3,6 # 15 pairs * PAIR H9: 6,9 BLK 9 H7: 6,9,2 # reduction candidate for 6,9 H7: 6,9 # 13 pairs I9: 6,9,5 # reduction candidate for 6,9 I9: 6,9 => CTR * 547.29...8....1...1365879.2.....5...6..81..5.....4....97.15.324...9.4.1.4..2738.. I9: 5 # 8 pairs * PAIR H9: 6,9 ROW 9 B9: 6,9,1,5 # reduction candidate for 6,9 B9: 6,9 # 10 pairs C9: 6,9,1,3,5 # reduction candidate for 6,9 C9: 6,9 # 10 pairs * PAIR H9: 6,9 COL H H4: 6,9,2,3,4,7,8 # reduction candidate for 6,9 H4: 6,9 # 11 pairs H6: 6,9,2,3,7,8 # reduction candidate for 6,9 H6: 6,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-059-base-pr-000.dot * REASONING * DIS # A6: 1,5 => CTR => A6: 2,3,7,9 * DIS # F3: 6,8 => CTR => F3: 7 * DIS # H3: 6,8 => CTR => H3: 4,7 * DIS # C5: 2,9 => CTR => C5: 3,4 * DIS # F5: 3,7 => CTR => F5: 2,9 * DIS # F3: 6,8 => CTR => F3: 7 * DIS # I9: 6,9 => CTR => I9: 5 * CNT 7 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B5,E3,F7,F9,H9) * .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8.. * PAIR A1: 5,9 BLK 1 B2: 5,9,2,6 # reduction candidate for 5,9 B2: 5,9 # 9 pairs C2: 5,9,2,6 # reduction candidate for 5,9 C2: 5,9 # 10 pairs * PAIR A1: 5,9 COL A A6: 5,9,1,2,3,7 # reduction candidate for 5,9 A6: 5,9 # 15 pairs A7: 5,9,2 # reduction candidate for 5,9 A7: 5,9 # 9 pairs * PAIR A3: 1,5 BLK 1 C3: 1,5,6 # reduction candidate for 1,5 C3: 1,5 # 19 pairs C3: 6 # 7 pairs * PAIR A3: 1,5 COL A A6: 1,5,2,3,7,9 # reduction candidate for 1,5 A6: 1,5 => CTR * 947.2..3.8..391476.364879.27..635...6.481.753..374....27.1..3.43..9.42174..2738.5 * PAIR RESTART * PAIR A3: 1,5 BLK 1 C3: 1,5,6 # reduction candidate for 1,5 C3: 1,5 # 19 pairs C3: 6 # 7 pairs * PAIR E3: 6,8 BLK 2 F1: 6,8,3,9 # reduction candidate for 6,8 F1: 6,8 # 16 pairs F3: 6,8,7 # reduction candidate for 6,8 F3: 6,8 => CTR * .47.2....8....1....3....9.2.....5...6..81..5.....4.....7.1..3.4...9.4.1.4..27.8.. * RESTART * PAIR E3: 6,8 BLK 2 F1: 6,8,3,9 # reduction candidate for 6,8 F1: 6,8 # 16 pairs F1: 3,9 # 8 pairs * PAIR E3: 6,8 ROW 3 H3: 6,8,4 # reduction candidate for 6,8 H3: 6,8 => CTR * 94752..3.8..391475.3.4.79.2....35.4.6.481.753....4.....7.15.324...9.45174..2738.. * PAIR RESTART * PAIR B5: 2,9 BLK 4 A4: 2,9,1,3,7 # reduction candidate for 2,9 A4: 2,9 # 19 pairs B4: 2,9,1,8 # reduction candidate for 2,9 B4: 2,9 => CTR * 947.2....8.2491.73.3..87942.....5...6.381.4577...4.....7.1.83.43..9.4.1.4..27.8.. C4: 2,9,1,3,4,8 # reduction candidate for 2,9 C4: 2,9 # 12 pairs C5: 2,9,3,4 # reduction candidate for 2,9 C5: 2,9 => CTR * .47329...8..461573.36587942..4.952..6..813457..1.426.99751.8324...93471.4.3276895 A6: 2,9,3,7 # reduction candidate for 2,9 A6: 2,9 # 22 pairs B6: 2,9,1,5,8 # reduction candidate for 2,9 B6: 2,9 => CTR * 947.2....8.2491.73.3..87942..4..52..6.381.4577.5.4....5791683242..9.471.4..27.8.. C6: 2,9,1,3,5,8 # reduction candidate for 2,9 C6: 2,9 # 20 pairs * PAIR B5: 2,9 ROW 5 F5: 2,9,3 # reduction candidate for 2,9 F5: 3 => CTR * .47329...8..461573.36587942....95...6.4813.5.....42....7.158364.68934217413276895 * PAIR B5: 2,9 COL B B2: 2,9,5,6 # reduction candidate for 2,9 B2: 5,6 => SOLVED * 947326581852491673136587942284735169693812457715649238579168324328954716461273895 * DURATION: 0:00:22.585343 START: 00:08:04.215848 END: 00:08:26.801191 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-059-base-pr-001.dot * REASONING * DIS # A6: 1,5 => CTR => A6: 2,3,7,9 * DIS A6: 2,3,7,9 # F3: 6,8 => CTR => F3: 7 * DIS A6: 2,3,7,9 + F3: 7 # H3: 6,8 => CTR => H3: 4 * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 # B4: 2,9 => CTR => B4: 1,8 * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 # C5: 2,9 => CTR => C5: 3,4 * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 # B6: 2,9 => CTR => B6: 1,5,8 * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # F5: 3 => CTR => F5: 2,9 * PRF A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 # B2: 5,6 => SOL * STA A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 + B2: 5,6 * CNT 8 HDP CHAINS / 25 HYP OPENED
Header Info
Top 95 Sudokus 059 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 947326581852491673136587942284735169693812457715649238579168324328954716461273895 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 # B2: 5,9 => UNS * INC # C2: 5,9 => UNS * INC # A6: 5,9 => UNS * INC # A7: 5,9 => UNS * INC # C3: 1,5 => UNS * INC # C3: 6 => UNS * DIS # A6: 1,5 => CTR => A6: 2,3,7,9 * INC # A6: 2,3,7,9 => UNS * INC # F1: 6,8 => UNS * DIS # F3: 6,8 => CTR => F3: 7 * INC # F3: 7 => UNS * DIS # H3: 6,8 => CTR => H3: 4,7 * INC # H3: 4,7 => UNS * INC # E7: 6,8 => UNS * INC # E8: 6,8 => UNS * INC # A4: 2,9 => UNS * INC # B4: 2,9 => UNS * INC # C4: 2,9 => UNS * DIS # C5: 2,9 => CTR => C5: 3,4 * INC # C5: 3,4 => UNS * INC # A6: 2,9 => UNS * INC # B6: 2,9 => UNS * INC # C6: 2,9 => UNS * INC # F5: 2,9 => UNS * DIS # F5: 3,7 => CTR => F5: 2,9 * INC # B2: 2,9 => UNS * INC # B2: 5,6 => UNS * INC # E7: 6,8 => UNS * INC # E8: 6,8 => UNS * INC # C7: 6,8 => UNS * INC # C7: 2,5,9 => UNS * INC # F1: 6,8 => UNS * DIS # F3: 6,8 => CTR => F3: 7 * INC # F3: 7 => UNS * INC # E8: 3,6 => UNS * INC # E8: 5,8 => UNS * INC # C9: 3,6 => UNS * INC # C9: 1,5,9 => UNS * INC # F1: 3,6 => UNS * INC # F6: 3,6 => UNS * INC # H7: 6,9 => UNS * DIS # I9: 6,9 => CTR => I9: 5 * INC # I9: 5 => UNS * INC # B9: 6,9 => UNS * INC # C9: 6,9 => UNS * INC # H4: 6,9 => UNS * INC # H6: 6,9 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 5,9 => UNS * INC # C2: 5,9 => UNS * INC # A6: 5,9 => UNS * INC # A7: 5,9 => UNS * INC # C3: 1,5 => UNS * INC # C3: 6 => UNS * DIS # A6: 1,5 => CTR => A6: 2,3,7,9 * INC A6: 2,3,7,9 # C3: 1,5 => UNS * INC A6: 2,3,7,9 # C3: 6 => UNS * INC A6: 2,3,7,9 # F1: 6,8 => UNS * DIS A6: 2,3,7,9 # F3: 6,8 => CTR => F3: 7 * INC A6: 2,3,7,9 + F3: 7 # F1: 6,8 => UNS * INC A6: 2,3,7,9 + F3: 7 # F1: 3,9 => UNS * DIS A6: 2,3,7,9 + F3: 7 # H3: 6,8 => CTR => H3: 4 * INC A6: 2,3,7,9 + F3: 7 + H3: 4 # A4: 2,9 => UNS * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 # B4: 2,9 => CTR => B4: 1,8 * INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 # C4: 2,9 => UNS * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 # C5: 2,9 => CTR => C5: 3,4 * INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 # A6: 2,9 => UNS * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 # B6: 2,9 => CTR => B6: 1,5,8 * INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # C6: 2,9 => UNS * INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # F5: 2,9 => UNS * DIS A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 # F5: 3 => CTR => F5: 2,9 * INC A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 # B2: 2,9 => UNS * PRF A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 # B2: 5,6 => SOL * STA A6: 2,3,7,9 + F3: 7 + H3: 4 + B4: 1,8 + C5: 3,4 + B6: 1,5,8 + F5: 2,9 + B2: 5,6 * CNT 25 HDP CHAINS / 25 HYP OPENED