Analysis of xx-top95-089-base.sdk
Contents
Original Sudoku
level: medium
position: ..5..8..18......9.......78....4.....64....9......53..2.6.........138..5....9.714. initial
Autosolve
position: ..5..8..18.....59.......78....4.....64....9.5....534.2.6.........138..5....9.714. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 6,7 => CTR => E1: 3,4,9 * PRF # F8: 2,6 => SOL * DIS # F8: 4 => CTR => F8: 2,6 * PRF # F8: 2,6 => SOL * DIS # F8: 4 => CTR => F8: 2,6 * DIS # G1: 3 => CTR => G1: 2,6 * CNT 6 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 6,7 => CTR => E1: 3,4,9 * PRF E1: 3,4,9 # F8: 2,6 => SOL * STA E1: 3,4,9 + F8: 2,6 * CNT 2 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..5..8..18......9.......78....4.....64....9......53..2.6.........138..5....9.714. | initial |
| ..5..8..18.....59.......78....4.....64....9.5....534.2.6.........138..5....9.714. | autosolve |
| 935748621876231594124695783512469378643872915789153462267514839491386257358927146 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) D1: 6,7 F5: 1,2 E9: 2,6 G8: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G1,H1: 2.. / G1 = 2 => 0 pairs (X) / H1 = 2 => 7 pairs (_) H1,H7: 2.. / H1 = 2 => 7 pairs (_) / H7 = 2 => 0 pairs (X) C5,H5: 3.. / C5 = 3 => 7 pairs (_) / H5 = 3 => 7 pairs (_) I2,I3: 4.. / I2 = 4 => 5 pairs (_) / I3 = 4 => 5 pairs (_) A1,E1: 4.. / A1 = 4 => 0 pairs (X) / E1 = 4 => 5 pairs (_) A8,F8: 4.. / A8 = 4 => 0 pairs (*) / F8 = 4 => 0 pairs (X) D3,F3: 5.. / D3 = 5 => 5 pairs (_) / F3 = 5 => 4 pairs (_) A4,B4: 5.. / A4 = 5 => 6 pairs (_) / B4 = 5 => 4 pairs (_) A9,B9: 5.. / A9 = 5 => 4 pairs (_) / B9 = 5 => 6 pairs (_) D7,F7: 5.. / D7 = 5 => 4 pairs (_) / F7 = 5 => 5 pairs (_) A4,A9: 5.. / A4 = 5 => 6 pairs (_) / A9 = 5 => 4 pairs (_) B4,B9: 5.. / B4 = 5 => 4 pairs (_) / B9 = 5 => 6 pairs (_) D3,D7: 5.. / D3 = 5 => 5 pairs (_) / D7 = 5 => 4 pairs (_) F3,F7: 5.. / F3 = 5 => 4 pairs (_) / F7 = 5 => 5 pairs (_) C2,C3: 6.. / C2 = 6 => 5 pairs (_) / C3 = 6 => 5 pairs (_) F8,E9: 6.. / F8 = 6 => 0 pairs (*) / E9 = 6 => 0 pairs (X) D6,H6: 6.. / D6 = 6 => 6 pairs (_) / H6 = 6 => 8 pairs (_) E9,I9: 6.. / E9 = 6 => 6 pairs (_) / I9 = 6 => 0 pairs (*) D5,D6: 8.. / D5 = 8 => 4 pairs (_) / D6 = 8 => 15 pairs (_) G4,I4: 8.. / G4 = 8 => 5 pairs (_) / I4 = 8 => 9 pairs (_) C5,D5: 8.. / C5 = 8 => 15 pairs (_) / D5 = 8 => 4 pairs (_) B6,B9: 8.. / B6 = 8 => 5 pairs (_) / B9 = 8 => 8 pairs (_) G4,G7: 8.. / G4 = 8 => 5 pairs (_) / G7 = 8 => 9 pairs (_) E4,F4: 9.. / E4 = 9 => 5 pairs (_) / F4 = 9 => 4 pairs (_) I7,I8: 9.. / I7 = 9 => 5 pairs (_) / I8 = 9 => 5 pairs (_) F3,F4: 9.. / F3 = 9 => 5 pairs (_) / F4 = 9 => 4 pairs (_) * DURATION: 0:00:29.960444 START: 01:02:17.568794 END: 01:02:47.529238 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E9,F5,G8) * ..5..8..18.....59.......78....4.....64....9.5....534.2.6.........138..5....9.714. * PAIR D1: 6,7 BLK 2 E1: 6,7,3,4,9 # reduction candidate for 6,7 E1: 6,7 => CTR * 495678..18.....59....5.978....496...64....9.5..9.53462.64..5.....138465....96714. E1: 3,4,9 # 4 pairs D2: 6,7,1,2 # reduction candidate for 6,7 D2: 6,7 # 17 pairs E2: 6,7,1,2,3,4 # reduction candidate for 6,7 E2: 6,7 # 7 pairs * PAIR D1: 6,7 COL D D6: 6,7,1,8 # reduction candidate for 6,7 D6: 1,8 # 16 pairs D6: 6,7 # 6 pairs * PAIR F5: 1,2 BLK 5 E4: 1,2,6,7,9 # reduction candidate for 1,2 E4: 1,2 # 9 pairs F4: 1,2,6,9 # reduction candidate for 1,2 F4: 1,2 # 12 pairs D5: 1,2,7,8 # reduction candidate for 1,2 D5: 1,2 # 16 pairs E5: 1,2,7 # reduction candidate for 1,2 E5: 1,2 # 9 pairs * PAIR F5: 1,2 COL F F2: 1,2,4,6 # reduction candidate for 1,2 F2: 1,2 # 8 pairs F3: 1,2,4,5,6,9 # reduction candidate for 1,2 F3: 1,2 # 8 pairs F7: 1,2,4,5 # reduction candidate for 1,2 F7: 1,2 # 7 pairs * PAIR E9: 2,6 BLK 8 F8: 2,6,4 # reduction candidate for 2,6 F8: 2,6 => SOLVED * 935748621876231594124695783512469378643872915789153462267514839491386257358927146 F8: 4 => CTR * ..57486218.7...594......78....4..8.764.87.9.5.89.534.2468...379..1384256...967148 * PAIR E9: 2,6 COL E E2: 2,6,1,3,4,7 # reduction candidate for 2,6 E2: 2,6 # 7 pairs E3: 2,6,1,3,4,9 # reduction candidate for 2,6 E3: 2,6 # 7 pairs E4: 2,6,1,7,9 # reduction candidate for 2,6 E4: 2,6 # 7 pairs * PAIR G8: 2,6 ROW 8 F8: 2,6,4 # reduction candidate for 2,6 F8: 2,6 => SOLVED * 935748621876231594124695783512469378643872915789153462267514839491386257358927146 F8: 4 => CTR * ..57486218.7...594......78....4..8.764.87.9.5.89.534.2468...379..1384256...967148 * PAIR G8: 2,6 COL G G1: 2,6,3 # reduction candidate for 2,6 G1: 3 => CTR * ..56483218.....59......978....4968..64...19.5....53462.6...52..4.138265....96714. G1: 2,6 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-089-base-pr-000.dot * REASONING * DIS # E1: 6,7 => CTR => E1: 3,4,9 * PRF # F8: 2,6 => SOL * DIS # F8: 4 => CTR => F8: 2,6 * PRF # F8: 2,6 => SOL * DIS # F8: 4 => CTR => F8: 2,6 * DIS # G1: 3 => CTR => G1: 2,6 * CNT 6 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E9,F5,G8) * ..5..8..18.....59.......78....4.....64....9.5....534.2.6.........138..5....9.714. * PAIR D1: 6,7 BLK 2 E1: 6,7,3,4,9 # reduction candidate for 6,7 E1: 6,7 => CTR * 495678..18.....59....5.978....496...64....9.5..9.53462.64..5.....138465....96714. D2: 6,7,1,2 # reduction candidate for 6,7 D2: 6,7 # 17 pairs E2: 6,7,1,2,3,4 # reduction candidate for 6,7 E2: 6,7 # 7 pairs * PAIR D1: 6,7 COL D D6: 6,7,1,8 # reduction candidate for 6,7 D6: 1,8 # 16 pairs D6: 6,7 # 6 pairs * PAIR F5: 1,2 BLK 5 E4: 1,2,6,7,9 # reduction candidate for 1,2 E4: 1,2 # 16 pairs F4: 1,2,6,9 # reduction candidate for 1,2 F4: 1,2 # 20 pairs D5: 1,2,7,8 # reduction candidate for 1,2 D5: 1,2 # 16 pairs E5: 1,2,7 # reduction candidate for 1,2 E5: 1,2 # 9 pairs * PAIR F5: 1,2 COL F F2: 1,2,4,6 # reduction candidate for 1,2 F2: 1,2 # 8 pairs F3: 1,2,4,5,6,9 # reduction candidate for 1,2 F3: 1,2 # 8 pairs F7: 1,2,4,5 # reduction candidate for 1,2 F7: 1,2 # 7 pairs * PAIR E9: 2,6 BLK 8 F8: 2,6,4 # reduction candidate for 2,6 F8: 2,6 => SOLVED * 935748621876231594124695783512469378643872915789153462267514839491386257358927146 * DURATION: 0:00:11.087876 START: 01:03:04.266242 END: 01:03:15.354118 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-089-base-pr-001.dot * REASONING * DIS # E1: 6,7 => CTR => E1: 3,4,9 * PRF E1: 3,4,9 # F8: 2,6 => SOL * STA E1: 3,4,9 + F8: 2,6 * CNT 2 HDP CHAINS / 13 HYP OPENED
Header Info
Top 95 Sudokus 089 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 935748621876231594124695783512469378643872915789153462267514839491386257358927146 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 # E1: 6,7 => CTR => E1: 3,4,9 * INC # E1: 3,4,9 => UNS * INC # D2: 6,7 => UNS * INC # E2: 6,7 => UNS * INC # D6: 6,7 => UNS * INC # D6: 1,8 => UNS * INC # E4: 1,2 => UNS * INC # F4: 1,2 => UNS * INC # D5: 1,2 => UNS * INC # E5: 1,2 => UNS * INC # F2: 1,2 => UNS * INC # F3: 1,2 => UNS * INC # F7: 1,2 => UNS * PRF # F8: 2,6 => SOL * DIS # F8: 4 => CTR => F8: 2,6 * INC # E2: 2,6 => UNS * INC # E3: 2,6 => UNS * INC # E4: 2,6 => UNS * PRF # F8: 2,6 => SOL * DIS # F8: 4 => CTR => F8: 2,6 * INC # G1: 2,6 => UNS * DIS # G1: 3 => CTR => G1: 2,6 * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 6,7 => CTR => E1: 3,4,9 * INC E1: 3,4,9 # D2: 6,7 => UNS * INC E1: 3,4,9 # E2: 6,7 => UNS * INC E1: 3,4,9 # D6: 6,7 => UNS * INC E1: 3,4,9 # D6: 1,8 => UNS * INC E1: 3,4,9 # E4: 1,2 => UNS * INC E1: 3,4,9 # F4: 1,2 => UNS * INC E1: 3,4,9 # D5: 1,2 => UNS * INC E1: 3,4,9 # E5: 1,2 => UNS * INC E1: 3,4,9 # F2: 1,2 => UNS * INC E1: 3,4,9 # F3: 1,2 => UNS * INC E1: 3,4,9 # F7: 1,2 => UNS * PRF E1: 3,4,9 # F8: 2,6 => SOL * STA E1: 3,4,9 + F8: 2,6 * CNT 13 HDP CHAINS / 13 HYP OPENED