Analysis of xx-top95-090-base.sdk
Contents
Original Sudoku
level: medium
position: ..........72.6.1....51...82.8...13..4.........37.9..1.....238..5.4..9.........79. initial
Autosolve
position: 1.........72.6.1....51...82.8...13..451.......37.9..1.7...238..5.4..9....2..1.79. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 9 => CTR => A2: 3,8 * DIS # E1: 3,8 => CTR => E1: 4,5 * DIS # E3: 4,7 => CTR => E3: 3 * DIS # G6: 2,6 => CTR => G6: 4,5 * DIS # A2: 9 => CTR => A2: 3,8 * DIS # D5: 7,8 => CTR => D5: 2,3,6 * DIS # E5: 3 => CTR => E5: 7,8 * DIS # G6: 2,6 => CTR => G6: 4,5 * CNT 8 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 # A2: 9 => CTR => A2: 3,8 * DIS A2: 3,8 # G6: 2,6 => CTR => G6: 4,5 * PRF A2: 3,8 + G6: 4,5 # B3: 6,9 => SOL * STA A2: 3,8 + G6: 4,5 + B3: 6,9 * CNT 3 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..........72.6.1....51...82.8...13..4.........37.9..1.....238..5.4..9.........79. | initial |
| 1.........72.6.1....51...82.8...13..451.......37.9..1.7...238..5.4..9....2..1.79. | autosolve |
| 143258679872964153695137482986541327451372968237896514719623845564789231328415796 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) C1: 3,8 F3: 4,7 C4: 6,9 A6: 2,6 C7: 6,9 B8: 1,6 A9: 3,8 C9: 3,8 D8: 7,8 E8: 7,8 G8: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,B8: 1.. / B7 = 1 => 14 pairs (_) / B8 = 1 => 15 pairs (_) I7,I8: 1.. / I7 = 1 => 15 pairs (_) / I8 = 1 => 14 pairs (_) B7,I7: 1.. / B7 = 1 => 14 pairs (_) / I7 = 1 => 15 pairs (_) B8,I8: 1.. / B8 = 1 => 15 pairs (_) / I8 = 1 => 14 pairs (_) D1,F1: 2.. / D1 = 2 => 16 pairs (_) / F1 = 2 => 11 pairs (_) A4,A6: 2.. / A4 = 2 => 14 pairs (_) / A6 = 2 => 11 pairs (_) G8,H8: 2.. / G8 = 2 => 12 pairs (_) / H8 = 2 => 21 pairs (_) D5,E5: 3.. / D5 = 3 => 13 pairs (_) / E5 = 3 => 0 pairs (X) A9,C9: 3.. / A9 = 3 => 14 pairs (_) / C9 = 3 => 9 pairs (_) H8,I8: 3.. / H8 = 3 => 13 pairs (_) / I8 = 3 => 15 pairs (_) A3,E3: 3.. / A3 = 3 => 0 pairs (X) / E3 = 3 => 15 pairs (_) C1,C9: 3.. / C1 = 3 => 14 pairs (_) / C9 = 3 => 9 pairs (_) B1,B3: 4.. / B1 = 4 => 13 pairs (_) / B3 = 4 => 20 pairs (_) E1,E4: 5.. / E1 = 5 => 0 pairs (*) / E4 = 5 => 0 pairs (X) G1,G6: 5.. / G1 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) C4,C7: 6.. / C4 = 6 => 15 pairs (_) / C7 = 6 => 16 pairs (_) E3,F3: 7.. / E3 = 7 => 0 pairs (X) / F3 = 7 => 11 pairs (_) H1,I1: 7.. / H1 = 7 => 12 pairs (_) / I1 = 7 => 11 pairs (_) D8,E8: 7.. / D8 = 7 => 10 pairs (_) / E8 = 7 => 11 pairs (_) F3,F5: 7.. / F3 = 7 => 11 pairs (_) / F5 = 7 => 0 pairs (X) C1,A2: 8.. / C1 = 8 => 9 pairs (_) / A2 = 8 => 14 pairs (_) I5,I6: 8.. / I5 = 8 => 16 pairs (_) / I6 = 8 => 11 pairs (_) A9,C9: 8.. / A9 = 8 => 9 pairs (_) / C9 = 8 => 14 pairs (_) D8,E8: 8.. / D8 = 8 => 11 pairs (_) / E8 = 8 => 10 pairs (_) A2,A9: 8.. / A2 = 8 => 14 pairs (_) / A9 = 8 => 9 pairs (_) C1,C9: 8.. / C1 = 8 => 9 pairs (_) / C9 = 8 => 14 pairs (_) D1,D2: 9.. / D1 = 9 => 12 pairs (_) / D2 = 9 => 15 pairs (_) A4,C4: 9.. / A4 = 9 => 15 pairs (_) / C4 = 9 => 16 pairs (_) G5,I5: 9.. / G5 = 9 => 17 pairs (_) / I5 = 9 => 18 pairs (_) B7,C7: 9.. / B7 = 9 => 16 pairs (_) / C7 = 9 => 15 pairs (_) C4,C7: 9.. / C4 = 9 => 16 pairs (_) / C7 = 9 => 15 pairs (_) * DURATION: 0:00:45.727218 START: 01:03:30.128261 END: 01:04:15.855479 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B8,C1,C4,C7,C9,D8,E8,F3,G8) * 1.........72.6.1....51...82.8...13..451.......37.9..1.7...238..5.4..9....2..1.79. * PAIR C1: 3,8 BLK 1 A2: 3,8,9 # reduction candidate for 3,8 A2: 9 => CTR * 1489.25..972.6.1..3651..982.89.513..451.....9.37.96418796.23851514..9...823615794 A2: 3,8 # 15 pairs * PAIR C1: 3,8 ROW 1 D1: 3,8,2,4,5,9 # reduction candidate for 3,8 D1: 3,8 # 11 pairs E1: 3,8,4,5 # reduction candidate for 3,8 E1: 3,8 => CTR * 14........72.6.1..365147982.8..513..451.....9.37.9.41.7...238..5.4..9....2..1.79. E1: 4,5 # 12 pairs * PAIR F3: 4,7 BLK 2 E3: 4,7,3 # reduction candidate for 4,7 E3: 4,7 => CTR * 1489.25..972.6.1..3651..982.89.513..451.....9.37.96418796.23851514..9...823615794 E3: 3 # 15 pairs * PAIR C4: 6,9 BLK 4 A4: 6,9,2 # reduction candidate for 6,9 A4: 2 # 14 pairs A4: 6,9 # 11 pairs * PAIR A6: 2,6 BLK 4 A4: 2,6,9 # reduction candidate for 2,6 A4: 2,6 # 16 pairs A4: 9 # 15 pairs * PAIR A6: 2,6 ROW 6 D6: 2,6,4,5,8 # reduction candidate for 2,6 D6: 2,6 # 13 pairs F6: 2,6,4,5,8 # reduction candidate for 2,6 F6: 2,6 # 13 pairs G6: 2,6,4,5 # reduction candidate for 2,6 G6: 2,6 => CTR * 14....5...72.6.139..51.7482.8..5134.451...9.8.37.9..157...2385.5.4..9..3.2..1.79. G6: 4,5 # 12 pairs * PAIR C7: 6,9 BLK 7 B7: 6,9,1 # reduction candidate for 6,9 B7: 6,9 # 15 pairs B7: 1 # 14 pairs * PAIR B8: 1,6 BLK 7 B7: 1,6,9 # reduction candidate for 1,6 B7: 9 # 16 pairs B7: 1,6 # 15 pairs * PAIR B8: 1,6 ROW 8 I8: 1,6,3 # reduction candidate for 1,6 I8: 3 # 15 pairs I8: 1,6 # 13 pairs * PAIR A9: 3,8 COL A A2: 3,8,9 # reduction candidate for 3,8 A2: 9 => CTR * 1489.25..972.6.1..3651..982.89.513..451.....9.37.96418796.23851514..9...823615794 A2: 3,8 # 15 pairs * PAIR D8: 7,8 COL D D5: 7,8,2,3,6 # reduction candidate for 7,8 D5: 7,8 => CTR * 1489526..9723681..3651..982.89..13..45183...9.37.9..18796.238.1514789...823.1.79. D5: 2,3,6 # 11 pairs * PAIR E8: 7,8 COL E E5: 7,8,3 # reduction candidate for 7,8 E5: 3 => CTR * 1489526..9723681..3651..982.89..13..45183...9.37.9..18796.238.1514789...823.1.79. E5: 7,8 # 13 pairs * PAIR G8: 2,6 BLK 9 H8: 2,6,3 # reduction candidate for 2,6 H8: 2,6 # 15 pairs H8: 3 # 13 pairs * PAIR G8: 2,6 COL G G5: 2,6,9 # reduction candidate for 2,6 G5: 2,6 # 18 pairs G6: 2,6,4,5 # reduction candidate for 2,6 G6: 2,6 => CTR * 14....5...72.6.139..51.7482.8..5134.451...9.8.37.9..157...2385.5.4..9..3.2..1.79. G6: 4,5 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-090-base-pr-000.dot * REASONING * DIS # A2: 9 => CTR => A2: 3,8 * DIS # E1: 3,8 => CTR => E1: 4,5 * DIS # E3: 4,7 => CTR => E3: 3 * DIS # G6: 2,6 => CTR => G6: 4,5 * DIS # A2: 9 => CTR => A2: 3,8 * DIS # D5: 7,8 => CTR => D5: 2,3,6 * DIS # E5: 3 => CTR => E5: 7,8 * DIS # G6: 2,6 => CTR => G6: 4,5 * CNT 8 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A9,B8,C1,C4,C7,C9,D8,E8,F3,G8) * 1.........72.6.1....51...82.8...13..451.......37.9..1.7...238..5.4..9....2..1.79. * PAIR C1: 3,8 BLK 1 A2: 3,8,9 # reduction candidate for 3,8 A2: 9 => CTR * 1489.25..972.6.1..3651..982.89.513..451.....9.37.96418796.23851514..9...823615794 * PAIR C4: 6,9 BLK 4 A4: 6,9,2 # reduction candidate for 6,9 A4: 2 # 17 pairs A4: 6,9 # 15 pairs * PAIR A6: 2,6 BLK 4 A4: 2,6,9 # reduction candidate for 2,6 A4: 2,6 # 19 pairs A4: 9 # 15 pairs * PAIR A6: 2,6 ROW 6 D6: 2,6,4,5,8 # reduction candidate for 2,6 D6: 2,6 # 17 pairs F6: 2,6,4,5,8 # reduction candidate for 2,6 F6: 2,6 # 17 pairs G6: 2,6,4,5 # reduction candidate for 2,6 G6: 2,6 => CTR * 14....5...72.6.1....5137482.8..513..4513..9...37.9..157...2385.5.4..9....2..1.79. * PAIR RESTART * PAIR A6: 2,6 BLK 4 A4: 2,6,9 # reduction candidate for 2,6 A4: 2,6 # 20 pairs A4: 9 # 16 pairs * PAIR A6: 2,6 ROW 6 D6: 2,6,4,5,8 # reduction candidate for 2,6 D6: 2,6 # 17 pairs F6: 2,6,4,5,8 # reduction candidate for 2,6 F6: 2,6 # 17 pairs * PAIR C7: 6,9 BLK 7 B7: 6,9,1 # reduction candidate for 6,9 B7: 6,9 # 20 pairs B7: 1 # 15 pairs * PAIR B8: 1,6 BLK 7 B7: 1,6,9 # reduction candidate for 1,6 B7: 9 # 20 pairs B7: 1,6 # 16 pairs * PAIR B8: 1,6 ROW 8 I8: 1,6,3 # reduction candidate for 1,6 I8: 3 # 20 pairs I8: 1,6 # 18 pairs * PAIR G8: 2,6 BLK 9 H8: 2,6,3 # reduction candidate for 2,6 H8: 2,6 # 20 pairs H8: 3 # 18 pairs * PAIR G8: 2,6 COL G G5: 2,6,9 # reduction candidate for 2,6 G5: 2,6 # 20 pairs G5: 9 # 18 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A3,A6,A9,B8,C1,C4,C7,C9,D8,E1,E4,E5,E8,G6,G8) * 1.........72.6.1....5137.82.8...13..4513......37.9..1.7...238..5.4..9....2..1.79. * PAIR A3: 6,9 BLK 1 B1: 6,9,4 # reduction candidate for 6,9 B1: 6,9 # 20 pairs B3: 6,9,4 # reduction candidate for 6,9 B3: 6,9 => SOLVED * 143258679872964153695137482986541327451372968237896514719623845564789231328415796 * DURATION: 0:00:24.460627 START: 01:04:41.716679 END: 01:05:06.177306 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-090-base-pr-001.dot * REASONING * DIS # A2: 9 => CTR => A2: 3,8 * DIS A2: 3,8 # G6: 2,6 => CTR => G6: 4,5 * PRF A2: 3,8 + G6: 4,5 # B3: 6,9 => SOL * STA A2: 3,8 + G6: 4,5 + B3: 6,9 * CNT 3 HDP CHAINS / 25 HYP OPENED
Header Info
Top 95 Sudokus 090 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 143258679872964153695137482986541327451372968237896514719623845564789231328415796 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 # A2: 3,8 => UNS * DIS # A2: 9 => CTR => A2: 3,8 * INC # D1: 3,8 => UNS * DIS # E1: 3,8 => CTR => E1: 4,5 * INC # E1: 4,5 => UNS * DIS # E3: 4,7 => CTR => E3: 3 * INC # E3: 3 => UNS * INC # A4: 6,9 => UNS * INC # A4: 2 => UNS * INC # A4: 2,6 => UNS * INC # A4: 9 => UNS * INC # D6: 2,6 => UNS * INC # F6: 2,6 => UNS * DIS # G6: 2,6 => CTR => G6: 4,5 * INC # G6: 4,5 => UNS * INC # B7: 6,9 => UNS * INC # B7: 1 => UNS * INC # B7: 1,6 => UNS * INC # B7: 9 => UNS * INC # I8: 1,6 => UNS * INC # I8: 3 => UNS * INC # A2: 3,8 => UNS * DIS # A2: 9 => CTR => A2: 3,8 * DIS # D5: 7,8 => CTR => D5: 2,3,6 * INC # D5: 2,3,6 => UNS * INC # E5: 7,8 => UNS * DIS # E5: 3 => CTR => E5: 7,8 * INC # H8: 2,6 => UNS * INC # H8: 3 => UNS * INC # G5: 2,6 => UNS * DIS # G6: 2,6 => CTR => G6: 4,5 * INC # G6: 4,5 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 3,8 => UNS * DIS # A2: 9 => CTR => A2: 3,8 * INC A2: 3,8 # A4: 6,9 => UNS * INC A2: 3,8 # A4: 2 => UNS * INC A2: 3,8 # A4: 2,6 => UNS * INC A2: 3,8 # A4: 9 => UNS * INC A2: 3,8 # D6: 2,6 => UNS * INC A2: 3,8 # F6: 2,6 => UNS * DIS A2: 3,8 # G6: 2,6 => CTR => G6: 4,5 * INC A2: 3,8 + G6: 4,5 # A4: 2,6 => UNS * INC A2: 3,8 + G6: 4,5 # A4: 9 => UNS * INC A2: 3,8 + G6: 4,5 # D6: 2,6 => UNS * INC A2: 3,8 + G6: 4,5 # F6: 2,6 => UNS * INC A2: 3,8 + G6: 4,5 # B7: 6,9 => UNS * INC A2: 3,8 + G6: 4,5 # B7: 1 => UNS * INC A2: 3,8 + G6: 4,5 # B7: 1,6 => UNS * INC A2: 3,8 + G6: 4,5 # B7: 9 => UNS * INC A2: 3,8 + G6: 4,5 # I8: 1,6 => UNS * INC A2: 3,8 + G6: 4,5 # I8: 3 => UNS * INC A2: 3,8 + G6: 4,5 # H8: 2,6 => UNS * INC A2: 3,8 + G6: 4,5 # H8: 3 => UNS * INC A2: 3,8 + G6: 4,5 # G5: 2,6 => UNS * INC A2: 3,8 + G6: 4,5 # G5: 9 => UNS * INC A2: 3,8 + G6: 4,5 # B1: 6,9 => UNS * PRF A2: 3,8 + G6: 4,5 # B3: 6,9 => SOL * STA A2: 3,8 + G6: 4,5 + B3: 6,9 * CNT 25 HDP CHAINS / 25 HYP OPENED