Analysis of xx-top95-051-base.sdk
Contents
Original Sudoku
level: medium
position: 1.....9...64..1.7..7..4.......3.....3.89..5....7....2.....6.7.9.....4.1....129.3. initial
Autosolve
position: 1.....9...64.91.7..7..4.......3...9.3.89..5....74...2.....6.7.9.....4.1.7..129.3. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C8: 5,6 => CTR => C8: 3,9 * DIS # F7: 5,8 => CTR => F7: 3 * PRF # D8: 5,8 => SOL * DIS # A7: 5,8 => CTR => A7: 2,4 * DIS # B7: 5,8 => CTR => B7: 1,2,3,4 * CNT 5 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C8: 5,6 => CTR => C8: 3,9 * DIS C8: 3,9 # F7: 5,8 => CTR => F7: 3 * PRF C8: 3,9 + F7: 3 # D8: 5,8 => SOL * STA C8: 3,9 + F7: 3 + D8: 5,8 * CNT 3 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.....9...64..1.7..7..4.......3.....3.89..5....7....2.....6.7.9.....4.1....129.3. | initial |
| 1.....9...64.91.7..7..4.......3...9.3.89..5....74...2.....6.7.9.....4.1.7..129.3. | autosolve |
| 152738946864291375973645281216357498348912567597486123421863759639574812785129634 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) E5: 1,7 H5: 4,6 C9: 5,6 D7: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,I3: 1.. / G3 = 1 => 4 pairs (_) / I3 = 1 => 4 pairs (_) B7,C7: 1.. / B7 = 1 => 6 pairs (_) / C7 = 1 => 4 pairs (_) C4,C7: 1.. / C4 = 1 => 6 pairs (_) / C7 = 1 => 4 pairs (_) F4,F5: 2.. / F4 = 2 => 16 pairs (_) / F5 = 2 => 5 pairs (_) G8,I8: 2.. / G8 = 2 => 5 pairs (_) / I8 = 2 => 5 pairs (_) B5,F5: 2.. / B5 = 2 => 16 pairs (_) / F5 = 2 => 5 pairs (_) G2,I2: 3.. / G2 = 3 => 4 pairs (_) / I2 = 3 => 5 pairs (_) G6,I6: 3.. / G6 = 3 => 5 pairs (_) / I6 = 3 => 4 pairs (_) F7,E8: 3.. / F7 = 3 => 7 pairs (_) / E8 = 3 => 0 pairs (X) C3,F3: 3.. / C3 = 3 => 7 pairs (_) / F3 = 3 => 0 pairs (X) E1,E8: 3.. / E1 = 3 => 7 pairs (_) / E8 = 3 => 0 pairs (X) G2,G6: 3.. / G2 = 3 => 4 pairs (_) / G6 = 3 => 5 pairs (_) I2,I6: 3.. / I2 = 3 => 5 pairs (_) / I6 = 3 => 4 pairs (_) H1,I1: 4.. / H1 = 4 => 13 pairs (_) / I1 = 4 => 4 pairs (_) A4,A7: 4.. / A4 = 4 => 11 pairs (_) / A7 = 4 => 11 pairs (_) G4,G9: 4.. / G4 = 4 => 16 pairs (_) / G9 = 4 => 11 pairs (_) D1,D3: 6.. / D1 = 6 => 4 pairs (_) / D3 = 6 => 17 pairs (_) I4,I5: 7.. / I4 = 7 => 4 pairs (_) / I5 = 7 => 6 pairs (_) D8,E8: 7.. / D8 = 7 => 4 pairs (_) / E8 = 7 => 0 pairs (*) D1,D8: 7.. / D1 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) A3,C3: 9.. / A3 = 9 => 5 pairs (_) / C3 = 9 => 0 pairs (X) A6,B6: 9.. / A6 = 9 => 0 pairs (X) / B6 = 9 => 5 pairs (_) B6,B8: 9.. / B6 = 9 => 5 pairs (_) / B8 = 9 => 0 pairs (X) C3,C8: 9.. / C3 = 9 => 0 pairs (X) / C8 = 9 => 5 pairs (_) * DURATION: 0:00:29.914998 START: 23:53:37.764910 END: 23:54:07.679908 2017-05-03 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,D7,E5,H5) * 1.....9...64.91.7..7..4.......3...9.3.89..5....74...2.....6.7.9.....4.1.7..129.3. * PAIR E5: 1,7 BLK 5 E4: 1,7,5,8 # reduction candidate for 1,7 E4: 1,7 # 7 pairs E4: 5,8 # 5 pairs * PAIR E5: 1,7 ROW 5 I5: 1,7,4,6 # reduction candidate for 1,7 I5: 4,6 # 15 pairs I5: 1,7 # 7 pairs * PAIR H5: 4,6 BLK 6 G4: 4,6,1,8 # reduction candidate for 4,6 G4: 4,6 # 8 pairs I4: 4,6,1,7,8 # reduction candidate for 4,6 I4: 4,6 # 19 pairs I5: 4,6,1,7 # reduction candidate for 4,6 I5: 4,6 # 15 pairs * PAIR H5: 4,6 COL H H1: 4,6,5,8 # reduction candidate for 4,6 H1: 4,6 # 14 pairs H1: 5,8 # 8 pairs * PAIR C9: 5,6 BLK 7 A8: 5,6,8,9 # reduction candidate for 5,6 A8: 5,6 # 7 pairs C8: 5,6,3,9 # reduction candidate for 5,6 C8: 5,6 => CTR * 1.....9.4.64.91.7..79.43...4..3...9.3.89..56...74...2.2...6.749...734.1.74.129.3. C8: 3,9 # 5 pairs * PAIR C9: 5,6 ROW 9 I9: 5,6,4,8 # reduction candidate for 5,6 I9: 5,6 # 7 pairs I9: 4,8 # 5 pairs * PAIR C9: 5,6 COL C C4: 5,6,1,2 # reduction candidate for 5,6 C4: 5,6 # 10 pairs C4: 1,2 # 5 pairs * PAIR D7: 5,8 BLK 8 F7: 5,8,3 # reduction candidate for 5,8 F7: 5,8 => CTR * 1.....9.4.64.91.7..7..4....4..3...9.3.89..56...74...2.2...6.749...734.1.74.129.3. F7: 3 # 7 pairs D8: 5,8,7 # reduction candidate for 5,8 D8: 5,8 => SOLVED * 152738946864291375973645281216357498348912567597486123421863759639574812785129634 D8: 7 # 4 pairs E8: 5,8,3,7 # reduction candidate for 5,8 E8: 5,8 # 9 pairs * PAIR D7: 5,8 ROW 7 A7: 5,8,2,4 # reduction candidate for 5,8 A7: 5,8 => CTR * 1.....9...64.91.7..7..4....4..3...9.3.89..5....74...2..4..6.7.9.....4.1.7..12943. A7: 2,4 # 5 pairs B7: 5,8,1,2,3,4 # reduction candidate for 5,8 B7: 5,8 => CTR * 1...3.9.4.64.91.7.973.4....4..3...9.3.89..56..974...2.2.1.63749.39..4.1.74.129.3. B7: 1,2,3,4 # 4 pairs H7: 5,8,4 # reduction candidate for 5,8 H7: 5,8 # 11 pairs * PAIR D7: 5,8 COL D D1: 5,8,2,6,7 # reduction candidate for 5,8 D1: 5,8 # 22 pairs D2: 5,8,2 # reduction candidate for 5,8 D2: 5,8 # 7 pairs D3: 5,8,2,6 # reduction candidate for 5,8 D3: 5,8 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-051-base-pr-000.dot * REASONING * DIS # C8: 5,6 => CTR => C8: 3,9 * DIS # F7: 5,8 => CTR => F7: 3 * PRF # D8: 5,8 => SOL * DIS # A7: 5,8 => CTR => A7: 2,4 * DIS # B7: 5,8 => CTR => B7: 1,2,3,4 * CNT 5 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,D7,E5,H5) * 1.....9...64.91.7..7..4.......3...9.3.89..5....74...2.....6.7.9.....4.1.7..129.3. * PAIR E5: 1,7 BLK 5 E4: 1,7,5,8 # reduction candidate for 1,7 E4: 1,7 # 7 pairs E4: 5,8 # 5 pairs * PAIR E5: 1,7 ROW 5 I5: 1,7,4,6 # reduction candidate for 1,7 I5: 4,6 # 15 pairs I5: 1,7 # 7 pairs * PAIR H5: 4,6 BLK 6 G4: 4,6,1,8 # reduction candidate for 4,6 G4: 4,6 # 8 pairs I4: 4,6,1,7,8 # reduction candidate for 4,6 I4: 4,6 # 19 pairs I5: 4,6,1,7 # reduction candidate for 4,6 I5: 4,6 # 15 pairs * PAIR H5: 4,6 COL H H1: 4,6,5,8 # reduction candidate for 4,6 H1: 4,6 # 14 pairs H1: 5,8 # 8 pairs * PAIR C9: 5,6 BLK 7 A8: 5,6,8,9 # reduction candidate for 5,6 A8: 5,6 # 7 pairs C8: 5,6,3,9 # reduction candidate for 5,6 C8: 5,6 => CTR * 1.....9.4.64.91.7..79.43...4..3...9.3.89..56...74...2.2...6.749...734.1.74.129.3. * RESTART * PAIR C9: 5,6 BLK 7 A8: 5,6,8,9 # reduction candidate for 5,6 A8: 8,9 # 8 pairs A8: 5,6 # 7 pairs * PAIR C9: 5,6 ROW 9 I9: 5,6,4,8 # reduction candidate for 5,6 I9: 5,6 # 8 pairs I9: 4,8 # 6 pairs * PAIR C9: 5,6 COL C C4: 5,6,1,2 # reduction candidate for 5,6 C4: 5,6 # 10 pairs C4: 1,2 # 8 pairs * PAIR D7: 5,8 BLK 8 F7: 5,8,3 # reduction candidate for 5,8 F7: 5,8 => CTR * 1.....9.4.64.91.7.97..4....4..3...9.3.89..56..974...2.2...6.749..9734.1.74.129.3. D8: 5,8,7 # reduction candidate for 5,8 D8: 5,8 => SOLVED * 152738946864291375973645281216357498348912567597486123421863759639574812785129634 * DURATION: 0:00:15.048159 START: 23:54:28.020755 END: 23:54:43.068914 2017-05-03 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-051-base-pr-001.dot * REASONING * DIS # C8: 5,6 => CTR => C8: 3,9 * DIS C8: 3,9 # F7: 5,8 => CTR => F7: 3 * PRF C8: 3,9 + F7: 3 # D8: 5,8 => SOL * STA C8: 3,9 + F7: 3 + D8: 5,8 * CNT 3 HDP CHAINS / 19 HYP OPENED
Header Info
Top 95 Sudokus 051 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 152738946864291375973645281216357498348912567597486123421863759639574812785129634 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 # E4: 1,7 => UNS * INC # E4: 5,8 => UNS * INC # I5: 1,7 => UNS * INC # I5: 4,6 => UNS * INC # G4: 4,6 => UNS * INC # I4: 4,6 => UNS * INC # I5: 4,6 => UNS * INC # H1: 4,6 => UNS * INC # H1: 5,8 => UNS * INC # A8: 5,6 => UNS * DIS # C8: 5,6 => CTR => C8: 3,9 * INC # C8: 3,9 => UNS * INC # I9: 5,6 => UNS * INC # I9: 4,8 => UNS * INC # C4: 5,6 => UNS * INC # C4: 1,2 => UNS * DIS # F7: 5,8 => CTR => F7: 3 * INC # F7: 3 => UNS * PRF # D8: 5,8 => SOL * INC # D8: 7 => UNS * INC # E8: 5,8 => UNS * DIS # A7: 5,8 => CTR => A7: 2,4 * INC # A7: 2,4 => UNS * DIS # B7: 5,8 => CTR => B7: 1,2,3,4 * INC # B7: 1,2,3,4 => UNS * INC # H7: 5,8 => UNS * INC # D1: 5,8 => UNS * INC # D2: 5,8 => UNS * INC # D3: 5,8 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E4: 1,7 => UNS * INC # E4: 5,8 => UNS * INC # I5: 1,7 => UNS * INC # I5: 4,6 => UNS * INC # G4: 4,6 => UNS * INC # I4: 4,6 => UNS * INC # I5: 4,6 => UNS * INC # H1: 4,6 => UNS * INC # H1: 5,8 => UNS * INC # A8: 5,6 => UNS * DIS # C8: 5,6 => CTR => C8: 3,9 * INC C8: 3,9 # A8: 5,6 => UNS * INC C8: 3,9 # A8: 8,9 => UNS * INC C8: 3,9 # I9: 5,6 => UNS * INC C8: 3,9 # I9: 4,8 => UNS * INC C8: 3,9 # C4: 5,6 => UNS * INC C8: 3,9 # C4: 1,2 => UNS * DIS C8: 3,9 # F7: 5,8 => CTR => F7: 3 * PRF C8: 3,9 + F7: 3 # D8: 5,8 => SOL * STA C8: 3,9 + F7: 3 + D8: 5,8 * CNT 19 HDP CHAINS / 19 HYP OPENED