Analysis of xx-top95-085-base.sdk
Contents
Original Sudoku
level: medium
position: ....6...4..6.3....1..4..5.77.....8.5...8.....6.8....9...2.9....4....32....97..1.. initial
Autosolve
position: ....6.3.4.46.379..1.34..5677.....8.5...8.....6.8....9...2.9....4....32.9..97..1.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 2,8 => CTR => F1: 1,5,9 * DIS # F3: 2,8 => CTR => F3: 9 * DIS # B3: 9 => CTR => B3: 2,8 * DIS # F4: 1,4 => CTR => F4: 2,6,9 * CNT 4 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 2,8 => CTR => F1: 1,5,9 * DIS F1: 1,5,9 # F3: 2,8 => CTR => F3: 9 * PRF F1: 1,5,9 + F3: 9 # C5: 5 => SOL * STA F1: 1,5,9 + F3: 9 + C5: 5 * CNT 3 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....6...4..6.3....1..4..5.77.....8.5...8.....6.8....9...2.9....4....32....97..1.. | initial |
| ....6.3.4.46.379..1.34..5677.....8.5...8.....6.8....9...2.9....4....32.9..97..1.. | autosolve |
| 957261384846537921123489567734926815295814736618375492572198643481653279369742158 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) C1: 5,7 E3: 2,8 C4: 1,4 G6: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E9,F9: 2.. / E9 = 2 => 11 pairs (_) / F9 = 2 => 5 pairs (_) D4,D6: 3.. / D4 = 3 => 0 pairs (X) / D6 = 3 => 5 pairs (_) C4,C5: 4.. / C4 = 4 => 5 pairs (_) / C5 = 4 => 6 pairs (_) A2,D2: 5.. / A2 = 5 => 11 pairs (_) / D2 = 5 => 12 pairs (_) D4,F4: 6.. / D4 = 6 => 0 pairs (X) / F4 = 6 => 4 pairs (_) G5,I5: 6.. / G5 = 6 => 5 pairs (_) / I5 = 6 => 12 pairs (_) B8,D8: 6.. / B8 = 6 => 7 pairs (_) / D8 = 6 => 5 pairs (_) G5,G7: 6.. / G5 = 6 => 5 pairs (_) / G7 = 6 => 12 pairs (_) B1,C1: 7.. / B1 = 7 => 18 pairs (_) / C1 = 7 => 4 pairs (_) E5,E6: 7.. / E5 = 7 => 6 pairs (_) / E6 = 7 => 5 pairs (_) E6,G6: 7.. / E6 = 7 => 5 pairs (_) / G6 = 7 => 6 pairs (_) C1,C8: 7.. / C1 = 7 => 4 pairs (_) / C8 = 7 => 18 pairs (_) B3,F3: 9.. / B3 = 9 => 0 pairs (X) / F3 = 9 => 10 pairs (_) A1,A5: 9.. / A1 = 9 => 10 pairs (_) / A5 = 9 => 0 pairs (X) D1,D4: 9.. / D1 = 9 => 0 pairs (X) / D4 = 9 => 10 pairs (_) * DURATION: 0:00:15.737785 START: 00:54:56.913844 END: 00:55:12.651629 2017-05-04 * CP COUNT: (15) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,C4,E3,G6) * ....6.3.4.46.379..1.34..5677.....8.5...8.....6.8....9...2.9....4....32.9..97..1.. * PAIR C1: 5,7 BLK 1 B1: 5,7,2,8,9 # reduction candidate for 5,7 B1: 5,7 # 18 pairs B1: 2,8,9 # 10 pairs * PAIR C1: 5,7 COL C C8: 5,7,1 # reduction candidate for 5,7 C8: 5,7 # 6 pairs C8: 1 # 5 pairs * PAIR E3: 2,8 BLK 2 F1: 2,8,1,5,9 # reduction candidate for 2,8 F1: 2,8 => CTR * ....6.3.4.46.379..1.34..5677.....8.5...8.....6.8....9...2.9....4....32.9..97..1.. F1: 1,5,9 # 5 pairs F3: 2,8,9 # reduction candidate for 2,8 F3: 2,8 => CTR * ....6.3.4.46.379..1934..5677.....8.59..8.....6.8....9...2.9....4....32.9..97..1.. F3: 9 # 10 pairs * PAIR E3: 2,8 ROW 3 B3: 2,8,9 # reduction candidate for 2,8 B3: 9 => CTR * ....6.3.4.46.379..1934..5677.....8.59..8.....6.8....9...2.9....4....32.9..97..1.. B3: 2,8 # 10 pairs * PAIR E3: 2,8 COL E E9: 2,8,4,5 # reduction candidate for 2,8 E9: 2,8 # 10 pairs E9: 4,5 # 6 pairs * PAIR C4: 1,4 BLK 4 C5: 1,4,5 # reduction candidate for 1,4 C5: 1,4 # 6 pairs C5: 5 # 5 pairs * PAIR C4: 1,4 ROW 4 E4: 1,4,2 # reduction candidate for 1,4 E4: 1,4 # 6 pairs F4: 1,4,2,6,9 # reduction candidate for 1,4 F4: 1,4 => CTR * 9...6.3.4.46.379..1.34..56779.6..835...8.9...6.83...9...2.9....46...32.9..97..1.. F4: 2,6,9 # 4 pairs H4: 1,4,2,3 # reduction candidate for 1,4 H4: 1,4 # 11 pairs * PAIR G6: 4,7 BLK 6 G5: 4,7,6 # reduction candidate for 4,7 G5: 4,7 # 12 pairs H5: 4,7,1,2,3 # reduction candidate for 4,7 H5: 4,7 # 6 pairs * PAIR G6: 4,7 ROW 6 E6: 4,7,1,2,5 # reduction candidate for 4,7 E6: 1,2,5 # 7 pairs E6: 4,7 # 5 pairs * PAIR G6: 4,7 COL G G7: 4,7,6 # reduction candidate for 4,7 G7: 6 # 12 pairs G7: 4,7 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-085-base-pr-000.dot * REASONING * DIS # F1: 2,8 => CTR => F1: 1,5,9 * DIS # F3: 2,8 => CTR => F3: 9 * DIS # B3: 9 => CTR => B3: 2,8 * DIS # F4: 1,4 => CTR => F4: 2,6,9 * CNT 4 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,C4,E3,G6) * ....6.3.4.46.379..1.34..5677.....8.5...8.....6.8....9...2.9....4....32.9..97..1.. * PAIR C1: 5,7 BLK 1 B1: 5,7,2,8,9 # reduction candidate for 5,7 B1: 5,7 # 18 pairs B1: 2,8,9 # 10 pairs * PAIR C1: 5,7 COL C C8: 5,7,1 # reduction candidate for 5,7 C8: 5,7 # 6 pairs C8: 1 # 5 pairs * PAIR E3: 2,8 BLK 2 F1: 2,8,1,5,9 # reduction candidate for 2,8 F1: 2,8 => CTR * ....6.3.4.46.379..1.34..5677.....8.5...8.....6.8....9...2.9....4....32.9..97..1.. F3: 2,8,9 # reduction candidate for 2,8 F3: 2,8 => CTR * ....6.3.4.46.379..1934..5677.....8.59..8.....6.8....9...2.9....4....32.9..97..1.. * PAIR C4: 1,4 BLK 4 C5: 1,4,5 # reduction candidate for 1,4 C5: 5 => SOLVED * 957261384846537921123489567734926815295814736618375492572198643481653279369742158 * DURATION: 0:00:06.892750 START: 00:55:27.049553 END: 00:55:33.942303 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-085-base-pr-001.dot * REASONING * DIS # F1: 2,8 => CTR => F1: 1,5,9 * DIS F1: 1,5,9 # F3: 2,8 => CTR => F3: 9 * PRF F1: 1,5,9 + F3: 9 # C5: 5 => SOL * STA F1: 1,5,9 + F3: 9 + C5: 5 * CNT 3 HDP CHAINS / 8 HYP OPENED
Header Info
Top 95 Sudokus 085 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 957261384846537921123489567734926815295814736618375492572198643481653279369742158 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 # B1: 5,7 => UNS * INC # B1: 2,8,9 => UNS * INC # C8: 5,7 => UNS * INC # C8: 1 => UNS * DIS # F1: 2,8 => CTR => F1: 1,5,9 * INC # F1: 1,5,9 => UNS * DIS # F3: 2,8 => CTR => F3: 9 * INC # F3: 9 => UNS * INC # B3: 2,8 => UNS * DIS # B3: 9 => CTR => B3: 2,8 * INC # E9: 2,8 => UNS * INC # E9: 4,5 => UNS * INC # C5: 1,4 => UNS * INC # C5: 5 => UNS * INC # E4: 1,4 => UNS * DIS # F4: 1,4 => CTR => F4: 2,6,9 * INC # F4: 2,6,9 => UNS * INC # H4: 1,4 => UNS * INC # G5: 4,7 => UNS * INC # H5: 4,7 => UNS * INC # E6: 4,7 => UNS * INC # E6: 1,2,5 => UNS * INC # G7: 4,7 => UNS * INC # G7: 6 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 5,7 => UNS * INC # B1: 2,8,9 => UNS * INC # C8: 5,7 => UNS * INC # C8: 1 => UNS * DIS # F1: 2,8 => CTR => F1: 1,5,9 * DIS F1: 1,5,9 # F3: 2,8 => CTR => F3: 9 * INC F1: 1,5,9 + F3: 9 # C5: 1,4 => UNS * PRF F1: 1,5,9 + F3: 9 # C5: 5 => SOL * STA F1: 1,5,9 + F3: 9 + C5: 5 * CNT 8 HDP CHAINS / 8 HYP OPENED