Analysis of zz-www.sudokuwiki.org-0062-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=62
level: medium
position: .3...8....6.....272.4...9.......3.4...6.9.1...5.71......2...3.554.....1....8...9. initial
Autosolve
position: .3...8....6.....272.4...9......83.4...6.9.1...5.71......2...3.554.....1....8...9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H3: 5,6 => CTR => H3: 3,8 * DIS # A7: 1,7 => CTR => A7: 6,8,9 * DIS # B7: 1,7 => CTR => B7: 8,9 * PRF # A9: 1,7 => SOL * CNT 4 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H3: 5,6 => CTR => H3: 3,8 * DIS H3: 3,8 # A7: 1,7 => CTR => A7: 6,8,9 * DIS H3: 3,8 + A7: 6,8,9 # B7: 1,7 => CTR => B7: 8,9 * PRF H3: 3,8 + A7: 6,8,9 + B7: 8,9 # A9: 1,7 => SOL * STA H3: 3,8 + A7: 6,8,9 + B7: 8,9 + A9: 1,7 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3...8....6.....272.4...9.......3.4...6.9.1...5.71......2...3.554.....1....8...9. | initial |
| .3...8....6.....272.4...9......83.4...6.9.1...5.71......2...3.554.....1....8...9. | autosolve |
| 937248651865931427214567938721683549386495172459712863692174385548329716173856294 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) H1: 5,6 G4: 5,7 H5: 5,7 B9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I3: 1.. / I1 = 1 => 5 pairs (_) / I3 = 1 => 0 pairs (X) D1,E1: 2.. / D1 = 2 => 7 pairs (_) / E1 = 2 => 5 pairs (_) B4,B5: 2.. / B4 = 2 => 7 pairs (_) / B5 = 2 => 13 pairs (_) D2,E2: 3.. / D2 = 3 => 5 pairs (_) / E2 = 3 => 4 pairs (_) H3,I3: 3.. / H3 = 3 => 6 pairs (_) / I3 = 3 => 8 pairs (_) A5,I5: 3.. / A5 = 3 => 7 pairs (_) / I5 = 3 => 7 pairs (_) D2,D8: 3.. / D2 = 3 => 5 pairs (_) / D8 = 3 => 4 pairs (_) H3,H6: 3.. / H3 = 3 => 6 pairs (_) / H6 = 3 => 8 pairs (_) A5,A6: 4.. / A5 = 4 => 0 pairs (X) / A6 = 4 => 5 pairs (_) G9,I9: 4.. / G9 = 4 => 0 pairs (X) / I9 = 4 => 5 pairs (_) A6,F6: 4.. / A6 = 4 => 5 pairs (_) / F6 = 4 => 0 pairs (X) I1,I9: 4.. / I1 = 4 => 0 pairs (X) / I9 = 4 => 5 pairs (_) C1,C2: 5.. / C1 = 5 => 10 pairs (_) / C2 = 5 => 6 pairs (_) G4,H5: 5.. / G4 = 5 => 7 pairs (_) / H5 = 5 => 0 pairs (X) E9,F9: 5.. / E9 = 5 => 6 pairs (_) / F9 = 5 => 6 pairs (_) D4,G4: 5.. / D4 = 5 => 0 pairs (X) / G4 = 5 => 7 pairs (_) D4,F6: 6.. / D4 = 6 => 9 pairs (_) / F6 = 6 => 11 pairs (_) A7,A9: 6.. / A7 = 6 => 8 pairs (_) / A9 = 6 => 8 pairs (_) D4,I4: 6.. / D4 = 6 => 9 pairs (_) / I4 = 6 => 11 pairs (_) G4,H5: 7.. / G4 = 7 => 0 pairs (X) / H5 = 7 => 7 pairs (_) H5,H7: 7.. / H5 = 7 => 7 pairs (_) / H7 = 7 => 0 pairs (X) I4,I6: 9.. / I4 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) B4,B7: 9.. / B4 = 9 => 15 pairs (_) / B7 = 9 => 4 pairs (_) * DURATION: 0:00:25.874391 START: 04:32:24.364989 END: 04:32:50.239380 2017-05-01 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,G4,H1,H5) * .3...8....6.....272.4...9......83.4...6.9.1...5.71......2...3.554.....1....8...9. * PAIR H1: 5,6 BLK 3 G1: 5,6,4 # reduction candidate for 5,6 G1: 5,6 # 9 pairs H3: 5,6,3,8 # reduction candidate for 5,6 H3: 5,6 => CTR * .3...8..186.....272.4...9.3....83.4.386.9.172459712836..2...385548....1...38...9. H3: 3,8 # 6 pairs * PAIR H1: 5,6 ROW 1 D1: 5,6,1,2,4,9 # reduction candidate for 5,6 D1: 5,6 # 23 pairs E1: 5,6,2,4,7 # reduction candidate for 5,6 E1: 5,6 # 24 pairs * PAIR B9: 1,7 BLK 7 A7: 1,7,6,8,9 # reduction candidate for 1,7 A7: 1,7 => CTR * 937..8651865139427214...9..7.1.8354...6.9.17..5.71.8..1.2...3.5548....1.6738.1294 A7: 6,8,9 # 4 pairs B7: 1,7,8,9 # reduction candidate for 1,7 B7: 1,7 => CTR * .3...8....6....827284...9...9..83.4..26.9.1...5871...98.2...3.5549....186.38...9. B7: 8,9 # 5 pairs A9: 1,7,3,6 # reduction candidate for 1,7 A9: 1,7 => SOLVED * 937248651865931427214567938721683549386495172459712863692174385548329716173856294 A9: 3,6 # 5 pairs C9: 1,7,3 # reduction candidate for 1,7 C9: 1,7 # 7 pairs * PAIR B9: 1,7 ROW 9 F9: 1,7,2,5,6 # reduction candidate for 1,7 F9: 1,7 # 13 pairs F9: 2,5,6 # 4 pairs * PAIR B9: 1,7 COL B B3: 1,7,8 # reduction candidate for 1,7 B3: 1,7 # 13 pairs B4: 1,7,2,9 # reduction candidate for 1,7 B4: 1,7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0062-base-pr-000.dot * REASONING * DIS # H3: 5,6 => CTR => H3: 3,8 * DIS # A7: 1,7 => CTR => A7: 6,8,9 * DIS # B7: 1,7 => CTR => B7: 8,9 * PRF # A9: 1,7 => SOL * CNT 4 HDP CHAINS / 16 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,G4,H1,H5) * .3...8....6.....272.4...9......83.4...6.9.1...5.71......2...3.554.....1....8...9. * PAIR H1: 5,6 BLK 3 G1: 5,6,4 # reduction candidate for 5,6 G1: 5,6 # 9 pairs H3: 5,6,3,8 # reduction candidate for 5,6 H3: 5,6 => CTR * .3...8..186.....272.4...9.3....83.4.386.9.172459712836..2...385548....1...38...9. * RESTART * PAIR H1: 5,6 BLK 3 G1: 5,6,4 # reduction candidate for 5,6 G1: 5,6 # 9 pairs G1: 4 # 8 pairs * PAIR B9: 1,7 BLK 7 A7: 1,7,6,8,9 # reduction candidate for 1,7 A7: 1,7 => CTR * 937..8651865139427214...9..7.1.8354...6.9.17..5.71.8..1.2...3.5548....1.6738.1294 B7: 1,7,8,9 # reduction candidate for 1,7 B7: 1,7 => CTR * .3...8....6....827284...93..9..83.4.826.9.17345371..89..2...36554.....18...8...9. A9: 1,7,3,6 # reduction candidate for 1,7 A9: 1,7 => SOLVED * 937248651865931427214567938721683549386495172459712863692174385548329716173856294 * DURATION: 0:00:07.360732 START: 04:33:02.162046 END: 04:33:09.522778 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0062-base-pr-001.dot * REASONING * DIS # H3: 5,6 => CTR => H3: 3,8 * DIS H3: 3,8 # A7: 1,7 => CTR => A7: 6,8,9 * DIS H3: 3,8 + A7: 6,8,9 # B7: 1,7 => CTR => B7: 8,9 * PRF H3: 3,8 + A7: 6,8,9 + B7: 8,9 # A9: 1,7 => SOL * STA H3: 3,8 + A7: 6,8,9 + B7: 8,9 + A9: 1,7 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=62
Solution
position: 937248651865931427214567938721683549386495172459712863692174385548329716173856294 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 # G1: 5,6 => UNS * DIS # H3: 5,6 => CTR => H3: 3,8 * INC # H3: 3,8 => UNS * INC # D1: 5,6 => UNS * INC # E1: 5,6 => UNS * DIS # A7: 1,7 => CTR => A7: 6,8,9 * INC # A7: 6,8,9 => UNS * DIS # B7: 1,7 => CTR => B7: 8,9 * INC # B7: 8,9 => UNS * PRF # A9: 1,7 => SOL * INC # A9: 3,6 => UNS * INC # C9: 1,7 => UNS * INC # F9: 1,7 => UNS * INC # F9: 2,5,6 => UNS * INC # B3: 1,7 => UNS * INC # B4: 1,7 => UNS * CNT 16 HDP CHAINS / 16 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 5,6 => UNS * DIS # H3: 5,6 => CTR => H3: 3,8 * INC H3: 3,8 # G1: 5,6 => UNS * INC H3: 3,8 # G1: 4 => UNS * DIS H3: 3,8 # A7: 1,7 => CTR => A7: 6,8,9 * DIS H3: 3,8 + A7: 6,8,9 # B7: 1,7 => CTR => B7: 8,9 * PRF H3: 3,8 + A7: 6,8,9 + B7: 8,9 # A9: 1,7 => SOL * STA H3: 3,8 + A7: 6,8,9 + B7: 8,9 + A9: 1,7 * CNT 7 HDP CHAINS / 7 HYP OPENED