Analysis of zz-www.sudokuwiki.org-0042-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=42
level: medium
position: ...7..3...4.....9...3..9..1.9.1.7.82..8.6.4..35.8.2.6.1..5..9...6.....7...5..8... initial
Autosolve
position: ...7..3...4.....9...3..9..1.9.137582..89654..35.842.691..5..9...6.....75..5..8... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 2,7 => CTR => B5: 1 * DIS # B5: 2 => CTR => B5: 1,7 * DIS # H9: 2,4 => CTR => H9: 1,3 * DIS # B7: 2,7 => CTR => B7: 3,8 * DIS # I7: 4,6 => CTR => I7: 3,8 * PRF # F1: 1 => SOL * 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 # B5: 2,7 => CTR => B5: 1 * DIS B5: 1 # B3: 2,8 => CTR => B3: 7 * DIS B5: 1 + B3: 7 # F8: 3 => CTR => F8: 1,4 * PRF B5: 1 + B3: 7 + F8: 1,4 # I1: 6,8 => SOL * STA B5: 1 + B3: 7 + F8: 1,4 + I1: 6,8 * CNT 4 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...7..3...4.....9...3..9..1.9.1.7.82..8.6.4..35.8.2.6.1..5..9...6.....7...5..8... | initial |
| ...7..3...4.....9...3..9..1.9.137582..89654..35.842.691..5..9...6.....75..5..8... | autosolve |
| 829751346541623798673489251496137582218965437357842169184576923962314875735298614 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A4: 4,6 C4: 4,6 A5: 2,7 C6: 1,7 H5: 1,3 I5: 3,7 G6: 1,7 E7: 2,7 F7: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C6: 1.. / B5 = 1 => 14 pairs (_) / C6 = 1 => 0 pairs (X) H5,G6: 1.. / H5 = 1 => 0 pairs (X) / G6 = 1 => 14 pairs (_) B5,H5: 1.. / B5 = 1 => 14 pairs (_) / H5 = 1 => 0 pairs (X) C6,G6: 1.. / C6 = 1 => 0 pairs (X) / G6 = 1 => 14 pairs (_) B1,B5: 1.. / B1 = 1 => 0 pairs (X) / B5 = 1 => 14 pairs (_) H5,H9: 1.. / H5 = 1 => 0 pairs (X) / H9 = 1 => 14 pairs (_) A5,B5: 2.. / A5 = 2 => 9 pairs (_) / B5 = 2 => 0 pairs (X) D2,F2: 3.. / D2 = 3 => 14 pairs (_) / F2 = 3 => 11 pairs (_) H5,I5: 3.. / H5 = 3 => 14 pairs (_) / I5 = 3 => 0 pairs (X) B7,B9: 3.. / B7 = 3 => 17 pairs (_) / B9 = 3 => 13 pairs (_) D8,F8: 3.. / D8 = 3 => 11 pairs (_) / F8 = 3 => 14 pairs (_) D2,D8: 3.. / D2 = 3 => 14 pairs (_) / D8 = 3 => 11 pairs (_) F2,F8: 3.. / F2 = 3 => 11 pairs (_) / F8 = 3 => 14 pairs (_) F1,D3: 4.. / F1 = 4 => 16 pairs (_) / D3 = 4 => 13 pairs (_) A4,C4: 4.. / A4 = 4 => 7 pairs (_) / C4 = 4 => 11 pairs (_) D3,H3: 4.. / D3 = 4 => 13 pairs (_) / H3 = 4 => 16 pairs (_) H1,H3: 5.. / H1 = 5 => 10 pairs (_) / H3 = 5 => 14 pairs (_) A2,E2: 5.. / A2 = 5 => 9 pairs (_) / E2 = 5 => 10 pairs (_) A4,C4: 6.. / A4 = 6 => 11 pairs (_) / C4 = 6 => 7 pairs (_) F7,D9: 6.. / F7 = 6 => 11 pairs (_) / D9 = 6 => 0 pairs (X) F7,I7: 6.. / F7 = 6 => 11 pairs (_) / I7 = 6 => 0 pairs (X) I5,G6: 7.. / I5 = 7 => 14 pairs (_) / G6 = 7 => 0 pairs (X) E7,E9: 7.. / E7 = 7 => 9 pairs (_) / E9 = 7 => 0 pairs (X) C6,G6: 7.. / C6 = 7 => 14 pairs (_) / G6 = 7 => 0 pairs (X) I2,I5: 7.. / I2 = 7 => 0 pairs (X) / I5 = 7 => 14 pairs (_) B7,A8: 8.. / B7 = 8 => 14 pairs (_) / A8 = 8 => 14 pairs (_) I7,G8: 8.. / I7 = 8 => 14 pairs (_) / G8 = 8 => 14 pairs (_) B7,I7: 8.. / B7 = 8 => 14 pairs (_) / I7 = 8 => 14 pairs (_) A8,G8: 8.. / A8 = 8 => 14 pairs (_) / G8 = 8 => 14 pairs (_) A1,C1: 9.. / A1 = 9 => 11 pairs (_) / C1 = 9 => 10 pairs (_) E8,E9: 9.. / E8 = 9 => 10 pairs (_) / E9 = 9 => 11 pairs (_) A9,E9: 9.. / A9 = 9 => 10 pairs (_) / E9 = 9 => 11 pairs (_) C1,C8: 9.. / C1 = 9 => 10 pairs (_) / C8 = 9 => 11 pairs (_) * DURATION: 0:00:44.521841 START: 04:15:08.732785 END: 04:15:53.254626 2017-05-01 * CP COUNT: (33) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,C4,C6,E7,F7,G6,H5,I5) * ...7..3...4.....9...3..9..1.9.137582..89654..35.842.691..5..9...6.....75..5..8... * PAIR A5: 2,7 BLK 4 B5: 2,7,1 # reduction candidate for 2,7 B5: 2,7 => CTR * .1978.354542613897..3..96.1.9.137582..89654133518427691.752.9.8864391275925.78136 B5: 1 # 14 pairs * PAIR A5: 2,7 COL A A2: 2,7,5,6,8 # reduction candidate for 2,7 A2: 2,7 # 13 pairs A3: 2,7,5,6,8 # reduction candidate for 2,7 A3: 2,7 # 11 pairs A9: 2,7,4,9 # reduction candidate for 2,7 A9: 2,7 # 12 pairs * PAIR C6: 1,7 BLK 4 B5: 1,7,2 # reduction candidate for 1,7 B5: 2 => CTR * .197..3.8.4..13.97.73..9..1.9.13758272896541335184276918752.93..6..91875935.7812. B5: 1,7 # 9 pairs * PAIR C6: 1,7 COL C C2: 1,7,2,6 # reduction candidate for 1,7 C2: 2,6 # 13 pairs C2: 1,7 # 11 pairs * PAIR H5: 1,3 COL H H9: 1,3,2,4 # reduction candidate for 1,3 H9: 2,4 => CTR * .197..3.8.4..13.97..3..9..1.9.137582..896541335184276918752.93..6..91875935.7812. H9: 1,3 # 15 pairs * PAIR E7: 2,7 BLK 8 E9: 2,7,1,9 # reduction candidate for 2,7 E9: 2,7 # 19 pairs E9: 1,9 # 10 pairs * PAIR E7: 2,7 ROW 7 B7: 2,7,3,8 # reduction candidate for 2,7 B7: 2,7 => CTR * ...7..3...4.....97..3..9..1.9.137582..89654133518427691..5.693886.....75.35..8... B7: 3,8 # 10 pairs C7: 2,7,4 # reduction candidate for 2,7 C7: 2,7 # 12 pairs * PAIR F7: 4,6 BLK 8 D9: 4,6,2 # reduction candidate for 4,6 D9: 2 # 19 pairs D9: 4,6 # 15 pairs * PAIR F7: 4,6 ROW 7 I7: 4,6,3,8 # reduction candidate for 4,6 I7: 4,6 => CTR * .1975.34854.....97..3..9..1.9.137582..896541335184276918752.93..6..91875935.7812. I7: 3,8 # 12 pairs * PAIR F7: 4,6 COL F F1: 4,6,1 # reduction candidate for 4,6 F1: 1 => SOLVED * 829751346541623798673489251496137582218965437357842169184576923962314875735298614 F1: 4,6 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0042-base-pr-000.dot * REASONING * DIS # B5: 2,7 => CTR => B5: 1 * DIS # B5: 2 => CTR => B5: 1,7 * DIS # H9: 2,4 => CTR => H9: 1,3 * DIS # B7: 2,7 => CTR => B7: 3,8 * DIS # I7: 4,6 => CTR => I7: 3,8 * PRF # F1: 1 => SOL * CNT 6 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,C4,C6,E7,F7,G6,H5,I5) * ...7..3...4.....9...3..9..1.9.137582..89654..35.842.691..5..9...6.....75..5..8... * PAIR A5: 2,7 BLK 4 B5: 2,7,1 # reduction candidate for 2,7 B5: 2,7 => CTR * .1978.354542613897..3..96.1.9.137582..89654133518427691.752.9.8864391275925.78136 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,B1,B7,C4,C7,D9,E9,F1,F2,G8,G9,H7,I2,I7) * ...7..3...4.....9...3..9..1.9.1375822189654373578421691..5769...6.....75..5..8.1. * PAIR B1: 2,8 BLK 1 B3: 2,8,7 # reduction candidate for 2,8 B3: 2,8 => CTR * ...7..3.4.4.....96..3..9..1.9.1375822189654373578421691..5769...6.....75.75..8.13 * PAIR B1: 2,8 ROW 1 E1: 2,8,1,5 # reduction candidate for 2,8 E1: 2,8 # 20 pairs E1: 1,5 # 16 pairs * PAIR F1: 1,4 COL F F8: 1,4,3 # reduction candidate for 1,4 F8: 3 => CTR * .217.435..46..179..73..9.41.9.1375822189654373578421691.457692..6.4138757.5298614 * PAIR RESTART * PAIR I2: 6,8 BLK 3 I1: 6,8,4 # reduction candidate for 6,8 I1: 6,8 => SOLVED * 829751346541623798673489251496137582218965437357842169184576923962314875735298614 * DURATION: 0:00:10.035251 START: 04:16:09.614085 END: 04:16:19.649336 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0042-base-pr-001.dot * REASONING * DIS # B5: 2,7 => CTR => B5: 1 * DIS B5: 1 # B3: 2,8 => CTR => B3: 7 * DIS B5: 1 + B3: 7 # F8: 3 => CTR => F8: 1,4 * PRF B5: 1 + B3: 7 + F8: 1,4 # I1: 6,8 => SOL * STA B5: 1 + B3: 7 + F8: 1,4 + I1: 6,8 * CNT 4 HDP CHAINS / 7 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=42
Solution
position: 829751346541623798673489251496137582218965437357842169184576923962314875735298614 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 # B5: 2,7 => CTR => B5: 1 * INC # B5: 1 => UNS * INC # A2: 2,7 => UNS * INC # A3: 2,7 => UNS * INC # A9: 2,7 => UNS * INC # B5: 1,7 => UNS * DIS # B5: 2 => CTR => B5: 1,7 * INC # C2: 1,7 => UNS * INC # C2: 2,6 => UNS * INC # H9: 1,3 => UNS * DIS # H9: 2,4 => CTR => H9: 1,3 * INC # E9: 2,7 => UNS * INC # E9: 1,9 => UNS * DIS # B7: 2,7 => CTR => B7: 3,8 * INC # B7: 3,8 => UNS * INC # C7: 2,7 => UNS * INC # D9: 4,6 => UNS * INC # D9: 2 => UNS * DIS # I7: 4,6 => CTR => I7: 3,8 * INC # I7: 3,8 => UNS * INC # F1: 4,6 => UNS * PRF # F1: 1 => SOL * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B5: 2,7 => CTR => B5: 1 * DIS B5: 1 # B3: 2,8 => CTR => B3: 7 * INC B5: 1 + B3: 7 # E1: 2,8 => UNS * INC B5: 1 + B3: 7 # E1: 1,5 => UNS * INC B5: 1 + B3: 7 # F8: 1,4 => UNS * DIS B5: 1 + B3: 7 # F8: 3 => CTR => F8: 1,4 * PRF B5: 1 + B3: 7 + F8: 1,4 # I1: 6,8 => SOL * STA B5: 1 + B3: 7 + F8: 1,4 + I1: 6,8 * CNT 7 HDP CHAINS / 7 HYP OPENED