Analysis of xx-top95-094-base.sdk
Contents
Original Sudoku
level: medium
position: .....2.......7...17..3...9.8..7......2.89.6...13..6....9..5.824.....891.......... initial
Autosolve
position: .....2.......7...17..3...9.8..7..1...278916...13..6...39..57824.....891.......... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D1: 4,5 => SOL * DIS # C3: 4,5 => CTR => C3: 1,2,6,8 * DIS # F4: 4,5 => CTR => F4: 3 * DIS # B4: 4,5 => CTR => B4: 6 * DIS # A1: 4,5 => CTR => A1: 1,6,9 * DIS # A9: 4,5 => CTR => A9: 1,2,6 * DIS # D6: 2,4 => CTR => D6: 5 * DIS # E8: 2,4 => CTR => E8: 3,6 * DIS # E9: 2,4 => CTR => E9: 1,3,6 * DIS # B4: 4,5 => CTR => B4: 6 * DIS # F4: 4,5 => CTR => F4: 3 * DIS # C9: 1,6 => CTR => C9: 2,4,5,8 * DIS # C1: 1,6 => CTR => C1: 4,5,8,9 * DIS # D9: 1,6 => CTR => D9: 2,4,9 * CNT 14 HDP CHAINS / 60 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D1: 4,5 => SOL * STA D1: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....2.......7...17..3...9.8..7......2.89.6...13..6....9..5.824.....891.......... | initial |
| .....2.......7...17..3...9.8..7..1...278916...13..6...39..57824.....891.......... | autosolve |
| 659412378238679451741385296865723149427891635913546782396157824574268913182934567 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) F3: 4,5 A5: 4,5 E6: 2,4 H4: 4,5 I4: 2,9 I5: 3,5 G6: 2,7 H6: 7,8 C7: 1,6 D7: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C3,E3: 1.. / C3 = 1 => 17 pairs (_) / E3 = 1 => 0 pairs (X) C7,D7: 1.. / C7 = 1 => 0 pairs (X) / D7 = 1 => 17 pairs (_) A1,A9: 1.. / A1 = 1 => 0 pairs (X) / A9 = 1 => 17 pairs (_) E4,I4: 2.. / E4 = 2 => 11 pairs (_) / I4 = 2 => 21 pairs (_) B1,B2: 3.. / B1 = 3 => 10 pairs (_) / B2 = 3 => 10 pairs (_) E4,F4: 3.. / E4 = 3 => 0 pairs (X) / F4 = 3 => 15 pairs (_) H5,I5: 3.. / H5 = 3 => 11 pairs (_) / I5 = 3 => 15 pairs (_) E8,I8: 3.. / E8 = 3 => 15 pairs (_) / I8 = 3 => 15 pairs (_) F4,F9: 3.. / F4 = 3 => 15 pairs (_) / F9 = 3 => 0 pairs (X) H4,H5: 4.. / H4 = 4 => 13 pairs (_) / H5 = 4 => 13 pairs (_) A5,H5: 4.. / A5 = 4 => 13 pairs (_) / H5 = 4 => 13 pairs (_) F4,D6: 5.. / F4 = 5 => 0 pairs (X) / D6 = 5 => 12 pairs (_) A6,D6: 5.. / A6 = 5 => 0 pairs (X) / D6 = 5 => 12 pairs (_) B4,C4: 6.. / B4 = 6 => 10 pairs (_) / C4 = 6 => 0 pairs (X) C7,D7: 6.. / C7 = 6 => 17 pairs (_) / D7 = 6 => 0 pairs (X) B8,B9: 7.. / B8 = 7 => 10 pairs (_) / B9 = 7 => 0 pairs (X) B8,I8: 7.. / B8 = 7 => 10 pairs (_) / I8 = 7 => 0 pairs (X) E1,E3: 8.. / E1 = 8 => 11 pairs (_) / E3 = 8 => 17 pairs (_) H6,I6: 8.. / H6 = 8 => 9 pairs (_) / I6 = 8 => 11 pairs (_) B9,C9: 8.. / B9 = 8 => 10 pairs (_) / C9 = 8 => 10 pairs (_) C4,A6: 9.. / C4 = 9 => 21 pairs (_) / A6 = 9 => 11 pairs (_) I4,I6: 9.. / I4 = 9 => 11 pairs (_) / I6 = 9 => 21 pairs (_) D9,F9: 9.. / D9 = 9 => 11 pairs (_) / F9 = 9 => 17 pairs (_) C4,I4: 9.. / C4 = 9 => 21 pairs (_) / I4 = 9 => 11 pairs (_) A6,I6: 9.. / A6 = 9 => 11 pairs (_) / I6 = 9 => 21 pairs (_) F2,F9: 9.. / F2 = 9 => 11 pairs (_) / F9 = 9 => 17 pairs (_) * DURATION: 0:00:35.647595 START: 01:12:51.119083 END: 01:13:26.766678 2017-05-04 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C7,D7,E6,F3,G6,H4,H6,I4,I5) * .....2.......7...17..3...9.8..7..1...278916...13..6...39..57824.....891.......... * PAIR F3: 4,5 BLK 2 D1: 4,5,1,6,9 # reduction candidate for 4,5 D1: 4,5 => SOLVED * 659412378238679451741385296865723149427891635913546782396157824574268913182934567 D1: 1,6,9 # 10 pairs D2: 4,5,6,9 # reduction candidate for 4,5 D2: 4,5 # 14 pairs F2: 4,5,9 # reduction candidate for 4,5 F2: 4,5 # 17 pairs * PAIR F3: 4,5 ROW 3 B3: 4,5,6,8 # reduction candidate for 4,5 B3: 4,5 # 13 pairs C3: 4,5,1,2,6,8 # reduction candidate for 4,5 C3: 4,5 => CTR * ....82.......7...17..31..9686.7..1...278916...13..6..8396157824....68913......... C3: 1,2,6,8 # 10 pairs G3: 4,5,2 # reduction candidate for 4,5 G3: 4,5 # 12 pairs * PAIR F3: 4,5 COL F F4: 4,5,3 # reduction candidate for 4,5 F4: 4,5 => CTR * 9....2...6.2579..175.3.429.869735142427891635513..6789396157824275..89131..9235.. F4: 3 # 15 pairs * PAIR A5: 4,5 BLK 4 B4: 4,5,6 # reduction candidate for 4,5 B4: 4,5 => CTR * 1....2.......7...17..31..9.8.672.1.9.278916..913546...391657824.....891.......... B4: 6 # 10 pairs C4: 4,5,6,9 # reduction candidate for 4,5 C4: 4,5 # 12 pairs A6: 4,5,9 # reduction candidate for 4,5 A6: 4,5 # 21 pairs * PAIR A5: 4,5 ROW 5 H5: 4,5,3 # reduction candidate for 4,5 H5: 4,5 # 15 pairs H5: 3 # 11 pairs * PAIR A5: 4,5 COL A A1: 4,5,1,6,9 # reduction candidate for 4,5 A1: 4,5 => CTR * ..9612..86..97...17.138.296864723159.278916..913546..23961578242.54689131..239.6. A1: 1,6,9 # 10 pairs A2: 4,5,2,6,9 # reduction candidate for 4,5 A2: 4,5 # 15 pairs A8: 4,5,2,6 # reduction candidate for 4,5 A8: 4,5 # 14 pairs A9: 4,5,1,2,6 # reduction candidate for 4,5 A9: 4,5 => CTR * 1...82...6...7...17..31..9686.7..1...278916..913546..83961578242..468913..1...... A9: 1,2,6 # 10 pairs * PAIR E6: 2,4 BLK 5 E4: 2,4,3 # reduction candidate for 2,4 E4: 2,4 # 15 pairs D6: 2,4,5 # reduction candidate for 2,4 D6: 2,4 => CTR * 9....2...6.2579..175.3.429.869735142427891635513..6789396157824275..89131..9235.. D6: 5 # 12 pairs * PAIR E6: 2,4 COL E E8: 2,4,3,6 # reduction candidate for 2,4 E8: 2,4 => CTR * ...1.2.......7...17.13...9.8..735142427891635513..6789396.57824.7...8913......... E8: 3,6 # 11 pairs E9: 2,4,1,3,6 # reduction candidate for 2,4 E9: 2,4 => CTR * 9....2...6...79.517..3...96869735142427891635513..6789396157824275468913...9.35.. E9: 1,3,6 # 10 pairs * PAIR H4: 4,5 BLK 6 H5: 4,5,3 # reduction candidate for 4,5 H5: 4,5 # 15 pairs H5: 3 # 11 pairs * PAIR H4: 4,5 ROW 4 B4: 4,5,6 # reduction candidate for 4,5 B4: 4,5 => CTR * 1....2.......7...17..31..9.8.672.1.9.278916..913546...391657824.....891.......... B4: 6 # 10 pairs C4: 4,5,6,9 # reduction candidate for 4,5 C4: 4,5 # 12 pairs F4: 4,5,3 # reduction candidate for 4,5 F4: 4,5 => CTR * 9....2...6.2579..175.3.429.869735142427891635513..6789396157824275..89131..9235.. F4: 3 # 15 pairs * PAIR I4: 2,9 BLK 6 I6: 2,9,7,8 # reduction candidate for 2,9 I6: 7,8 # 13 pairs I6: 2,9 # 10 pairs * PAIR I5: 3,5 BLK 6 H5: 3,5,4 # reduction candidate for 3,5 H5: 4 # 13 pairs H5: 3,5 # 13 pairs * PAIR I5: 3,5 COL I I1: 3,5,6,7,8 # reduction candidate for 3,5 I1: 3,5 # 22 pairs I8: 3,5,6,7 # reduction candidate for 3,5 I8: 3,5 # 12 pairs I9: 3,5,6,7 # reduction candidate for 3,5 I9: 3,5 # 17 pairs * PAIR G6: 2,7 BLK 6 I6: 2,7,8,9 # reduction candidate for 2,7 I6: 8,9 # 11 pairs I6: 2,7 # 11 pairs * PAIR H6: 7,8 BLK 6 I6: 7,8,2,9 # reduction candidate for 7,8 I6: 7,8 # 13 pairs I6: 2,9 # 10 pairs * PAIR H6: 7,8 COL H H1: 7,8,3,5,6 # reduction candidate for 7,8 H1: 7,8 # 11 pairs H1: 3,5,6 # 10 pairs * PAIR C7: 1,6 BLK 7 A9: 1,6,2,4,5 # reduction candidate for 1,6 A9: 1,6 # 11 pairs C9: 1,6,2,4,5,8 # reduction candidate for 1,6 C9: 1,6 => CTR * 1...82...6...7..817.831.29686.7231.9.278916..913546...39..57824.7...891..8.....6. C9: 2,4,5,8 # 10 pairs * PAIR C7: 1,6 COL C C1: 1,6,4,5,8,9 # reduction candidate for 1,6 C1: 1,6 => CTR * ....82.......7...17..31..9686.7..1...278916...13..6..839..57824.....891........6. C1: 4,5,8,9 # 10 pairs C3: 1,6,2,4,5,8 # reduction candidate for 1,6 C3: 1,6 # 11 pairs * PAIR D7: 1,6 BLK 8 D9: 1,6,2,4,9 # reduction candidate for 1,6 D9: 1,6 => CTR * .....2.......7...17..3...9.8..7.31...278916...135.6...39..57824...2.891......9... D9: 2,4,9 # 10 pairs E9: 1,6,2,3,4 # reduction candidate for 1,6 E9: 1,6 # 12 pairs * PAIR D7: 1,6 COL D D1: 1,6,4,5,9 # reduction candidate for 1,6 D1: 4,5,9 # 17 pairs D1: 1,6 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-094-base-pr-000.dot * REASONING * PRF # D1: 4,5 => SOL * DIS # C3: 4,5 => CTR => C3: 1,2,6,8 * DIS # F4: 4,5 => CTR => F4: 3 * DIS # B4: 4,5 => CTR => B4: 6 * DIS # A1: 4,5 => CTR => A1: 1,6,9 * DIS # A9: 4,5 => CTR => A9: 1,2,6 * DIS # D6: 2,4 => CTR => D6: 5 * DIS # E8: 2,4 => CTR => E8: 3,6 * DIS # E9: 2,4 => CTR => E9: 1,3,6 * DIS # B4: 4,5 => CTR => B4: 6 * DIS # F4: 4,5 => CTR => F4: 3 * DIS # C9: 1,6 => CTR => C9: 2,4,5,8 * DIS # C1: 1,6 => CTR => C1: 4,5,8,9 * DIS # D9: 1,6 => CTR => D9: 2,4,9 * CNT 14 HDP CHAINS / 60 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C7,D7,E6,F3,G6,H4,H6,I4,I5) * .....2.......7...17..3...9.8..7..1...278916...13..6...39..57824.....891.......... * PAIR F3: 4,5 BLK 2 D1: 4,5,1,6,9 # reduction candidate for 4,5 D1: 4,5 => SOLVED * 659412378238679451741385296865723149427891635913546782396157824574268913182934567 * DURATION: 0:00:02.686809 START: 01:14:09.885583 END: 01:14:12.572392 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-094-base-pr-001.dot * REASONING * PRF # D1: 4,5 => SOL * STA D1: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 95 Sudokus 094 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 659412378238679451741385296865723149427891635913546782396157824574268913182934567 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 # D1: 4,5 => SOL * INC # D1: 1,6,9 => UNS * INC # D2: 4,5 => UNS * INC # F2: 4,5 => UNS * INC # B3: 4,5 => UNS * DIS # C3: 4,5 => CTR => C3: 1,2,6,8 * INC # C3: 1,2,6,8 => UNS * INC # G3: 4,5 => UNS * DIS # F4: 4,5 => CTR => F4: 3 * INC # F4: 3 => UNS * DIS # B4: 4,5 => CTR => B4: 6 * INC # B4: 6 => UNS * INC # C4: 4,5 => UNS * INC # A6: 4,5 => UNS * INC # H5: 4,5 => UNS * INC # H5: 3 => UNS * DIS # A1: 4,5 => CTR => A1: 1,6,9 * INC # A1: 1,6,9 => UNS * INC # A2: 4,5 => UNS * INC # A8: 4,5 => UNS * DIS # A9: 4,5 => CTR => A9: 1,2,6 * INC # A9: 1,2,6 => UNS * INC # E4: 2,4 => UNS * DIS # D6: 2,4 => CTR => D6: 5 * INC # D6: 5 => UNS * DIS # E8: 2,4 => CTR => E8: 3,6 * INC # E8: 3,6 => UNS * DIS # E9: 2,4 => CTR => E9: 1,3,6 * INC # E9: 1,3,6 => UNS * INC # H5: 4,5 => UNS * INC # H5: 3 => UNS * DIS # B4: 4,5 => CTR => B4: 6 * INC # B4: 6 => UNS * INC # C4: 4,5 => UNS * DIS # F4: 4,5 => CTR => F4: 3 * INC # F4: 3 => UNS * INC # I6: 2,9 => UNS * INC # I6: 7,8 => UNS * INC # H5: 3,5 => UNS * INC # H5: 4 => UNS * INC # I1: 3,5 => UNS * INC # I8: 3,5 => UNS * INC # I9: 3,5 => UNS * INC # I6: 2,7 => UNS * INC # I6: 8,9 => UNS * INC # I6: 7,8 => UNS * INC # I6: 2,9 => UNS * INC # H1: 7,8 => UNS * INC # H1: 3,5,6 => UNS * INC # A9: 1,6 => UNS * DIS # C9: 1,6 => CTR => C9: 2,4,5,8 * INC # C9: 2,4,5,8 => UNS * DIS # C1: 1,6 => CTR => C1: 4,5,8,9 * INC # C1: 4,5,8,9 => UNS * INC # C3: 1,6 => UNS * DIS # D9: 1,6 => CTR => D9: 2,4,9 * INC # D9: 2,4,9 => UNS * INC # E9: 1,6 => UNS * INC # D1: 1,6 => UNS * INC # D1: 4,5,9 => UNS * CNT 60 HDP CHAINS / 60 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D1: 4,5 => SOL * STA D1: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED