Analysis of zz-www.sudokuwiki.org-0107-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=107
level: medium
position: .8...9.........2.69...5..3...24..17.3...2...5..7..3....3..9...12.4.........6...5. initial
Autosolve
position: .8.2.951.......29692..5..3..924..1733...2...5..7..3....3..9...12.4........96...5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F5: 6,8 => CTR => F5: 1,7 * DIS # E6: 6,8 => CTR => E6: 1 * DIS # B8: 1,7 => CTR => B8: 5,6 * DIS # E9: 1,7 => CTR => E9: 3,4,8 * DIS # F9: 1,7 => CTR => F9: 2,4,8 * CNT 5 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F5: 6,8 => CTR => F5: 1,7 * DIS F5: 1,7 # E6: 6,8 => CTR => E6: 1 * DIS F5: 1,7 + E6: 1 # F4: 5 => CTR => F4: 6,8 * DIS F5: 1,7 + E6: 1 + F4: 6,8 # B8: 1,7 => CTR => B8: 5,6 * PRF F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 # A9: 1,7 => SOL * STA F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 + A9: 1,7 * CNT 5 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8...9.........2.69...5..3...24..17.3...2...5..7..3....3..9...12.4.........6...5. | initial |
| .8.2.951.......29692..5..3..924..1733...2...5..7..3....3..9...12.4........96...5. | autosolve |
| 783269514415378296926154837592486173341927685867513942638795421254831769179642358 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) C1: 3,6 C3: 1,6 D3: 1,7 I1: 4,7 E4: 6,8 B9: 1,7 H8: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H6,I6: 2.. / H6 = 2 => 7 pairs (_) / I6 = 2 => 7 pairs (_) F7,F9: 2.. / F7 = 2 => 7 pairs (_) / F9 = 2 => 7 pairs (_) H7,I9: 2.. / H7 = 2 => 7 pairs (_) / I9 = 2 => 7 pairs (_) F7,H7: 2.. / F7 = 2 => 7 pairs (_) / H7 = 2 => 7 pairs (_) F9,I9: 2.. / F9 = 2 => 7 pairs (_) / I9 = 2 => 7 pairs (_) H6,H7: 2.. / H6 = 2 => 7 pairs (_) / H7 = 2 => 7 pairs (_) I6,I9: 2.. / I6 = 2 => 7 pairs (_) / I9 = 2 => 7 pairs (_) C1,C2: 3.. / C1 = 3 => 7 pairs (_) / C2 = 3 => 0 pairs (X) G8,G9: 3.. / G8 = 3 => 15 pairs (_) / G9 = 3 => 7 pairs (_) C1,E1: 3.. / C1 = 3 => 7 pairs (_) / E1 = 3 => 0 pairs (X) E9,G9: 3.. / E9 = 3 => 15 pairs (_) / G9 = 3 => 7 pairs (_) D2,D8: 3.. / D2 = 3 => 7 pairs (_) / D8 = 3 => 7 pairs (_) F4,D6: 5.. / F4 = 5 => 8 pairs (_) / D6 = 5 => 10 pairs (_) A4,F4: 5.. / A4 = 5 => 10 pairs (_) / F4 = 5 => 8 pairs (_) C2,C7: 5.. / C2 = 5 => 7 pairs (_) / C7 = 5 => 14 pairs (_) E1,F3: 6.. / E1 = 6 => 14 pairs (_) / F3 = 6 => 13 pairs (_) C3,F3: 6.. / C3 = 6 => 14 pairs (_) / F3 = 6 => 13 pairs (_) D5,F5: 7.. / D5 = 7 => 0 pairs (X) / F5 = 7 => 7 pairs (_) G3,I3: 8.. / G3 = 8 => 10 pairs (_) / I3 = 8 => 9 pairs (_) C5,C7: 8.. / C5 = 8 => 11 pairs (_) / C7 = 8 => 11 pairs (_) D5,D6: 9.. / D5 = 9 => 7 pairs (_) / D6 = 9 => 8 pairs (_) G8,I8: 9.. / G8 = 9 => 9 pairs (_) / I8 = 9 => 7 pairs (_) D5,G5: 9.. / D5 = 9 => 7 pairs (_) / G5 = 9 => 8 pairs (_) I6,I8: 9.. / I6 = 9 => 9 pairs (_) / I8 = 9 => 7 pairs (_) * DURATION: 0:00:27.582277 START: 05:23:18.758277 END: 05:23:46.340554 2017-05-01 * CP COUNT: (24) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C1,C3,D3,E4,H8,I1) * .8.2.951.......29692..5..3..924..1733...2...5..7..3....3..9...12.4........96...5. * PAIR C1: 3,6 ROW 1 E1: 3,6,4,7 # reduction candidate for 3,6 E1: 4,7 # 16 pairs E1: 3,6 # 11 pairs * PAIR C3: 1,6 ROW 3 F3: 1,6,4,7 # reduction candidate for 1,6 F3: 4,7 # 14 pairs F3: 1,6 # 11 pairs * PAIR C3: 1,6 COL C C5: 1,6,8 # reduction candidate for 1,6 C5: 8 # 11 pairs C5: 1,6 # 11 pairs * PAIR D3: 1,7 BLK 2 D2: 1,7,3,8 # reduction candidate for 1,7 D2: 1,7 # 17 pairs E2: 1,7,3,4,8 # reduction candidate for 1,7 E2: 1,7 # 11 pairs F2: 1,7,4,8 # reduction candidate for 1,7 F2: 1,7 # 11 pairs F3: 1,7,4,6 # reduction candidate for 1,7 F3: 1,7 # 22 pairs * PAIR D3: 1,7 COL D D5: 1,7,8,9 # reduction candidate for 1,7 D5: 1,7 # 11 pairs D8: 1,7,3,5,8 # reduction candidate for 1,7 D8: 1,7 # 11 pairs * PAIR I1: 4,7 BLK 3 G3: 4,7,8 # reduction candidate for 4,7 G3: 4,7 # 9 pairs I3: 4,7,8 # reduction candidate for 4,7 I3: 4,7 # 10 pairs * PAIR I1: 4,7 ROW 1 A1: 4,7,6 # reduction candidate for 4,7 A1: 4,7 # 11 pairs E1: 4,7,3,6 # reduction candidate for 4,7 E1: 4,7 # 16 pairs * PAIR I1: 4,7 COL I I9: 4,7,2,8 # reduction candidate for 4,7 I9: 4,7 # 9 pairs I9: 2,8 # 8 pairs * PAIR E4: 6,8 BLK 5 F4: 6,8,5 # reduction candidate for 6,8 F4: 6,8 # 10 pairs F5: 6,8,1,7 # reduction candidate for 6,8 F5: 6,8 => CTR * .8326951....3.829692615..3.6924851733.8726945..7913....3589...12645.1.898196...5. F5: 1,7 # 8 pairs E6: 6,8,1 # reduction candidate for 6,8 E6: 6,8 => CTR * .8.2.9517...3.8296921756.3..924.51733...27..5..7..3....3.89...12645.1.898196...5. E6: 1 # 7 pairs * PAIR E4: 6,8 ROW 4 A4: 6,8,5 # reduction candidate for 6,8 A4: 5 # 10 pairs A4: 6,8 # 8 pairs * PAIR B9: 1,7 BLK 7 B8: 1,7,5,6 # reduction candidate for 1,7 B8: 1,7 => CTR * .8.2.951.......29692..5..3..924..1733.8.2...51.7.83...635.9...12.4......8.96...5. B8: 5,6 # 8 pairs A9: 1,7,8 # reduction candidate for 1,7 A9: 1,7 # 10 pairs * PAIR B9: 1,7 ROW 9 E9: 1,7,3,4,8 # reduction candidate for 1,7 E9: 1,7 => CTR * .8.2.9517......29692..56.3.692485173348.27.65157963....3..9...126453178981967.35. E9: 3,4,8 # 7 pairs F9: 1,7,2,4,8 # reduction candidate for 1,7 F9: 1,7 => CTR * .8.2.951.......29692..56.3.692485173348.2..65157963.2..3..92.41264531.89819647352 F9: 2,4,8 # 7 pairs * PAIR B9: 1,7 COL B B2: 1,7,4,5 # reduction candidate for 1,7 B2: 1,7 # 10 pairs B2: 4,5 # 9 pairs * PAIR H8: 6,8 BLK 9 G7: 6,8,4,7 # reduction candidate for 6,8 G7: 6,8 # 11 pairs H7: 6,8,2,4 # reduction candidate for 6,8 H7: 6,8 # 13 pairs G8: 6,8,3,7,9 # reduction candidate for 6,8 G8: 6,8 # 13 pairs * PAIR H8: 6,8 COL H H5: 6,8,4 # reduction candidate for 6,8 H5: 6,8 # 10 pairs H6: 6,8,2,4 # reduction candidate for 6,8 H6: 6,8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0107-base-pr-000.dot * REASONING * DIS # F5: 6,8 => CTR => F5: 1,7 * DIS # E6: 6,8 => CTR => E6: 1 * DIS # B8: 1,7 => CTR => B8: 5,6 * DIS # E9: 1,7 => CTR => E9: 3,4,8 * DIS # F9: 1,7 => CTR => F9: 2,4,8 * CNT 5 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,C1,C3,D3,E4,H8,I1) * .8.2.951.......29692..5..3..924..1733...2...5..7..3....3..9...12.4........96...5. * PAIR C1: 3,6 ROW 1 E1: 3,6,4,7 # reduction candidate for 3,6 E1: 4,7 # 16 pairs E1: 3,6 # 11 pairs * PAIR C3: 1,6 ROW 3 F3: 1,6,4,7 # reduction candidate for 1,6 F3: 4,7 # 14 pairs F3: 1,6 # 11 pairs * PAIR C3: 1,6 COL C C5: 1,6,8 # reduction candidate for 1,6 C5: 8 # 11 pairs C5: 1,6 # 11 pairs * PAIR D3: 1,7 BLK 2 D2: 1,7,3,8 # reduction candidate for 1,7 D2: 1,7 # 17 pairs E2: 1,7,3,4,8 # reduction candidate for 1,7 E2: 1,7 # 11 pairs F2: 1,7,4,8 # reduction candidate for 1,7 F2: 1,7 # 11 pairs F3: 1,7,4,6 # reduction candidate for 1,7 F3: 1,7 # 22 pairs * PAIR D3: 1,7 COL D D5: 1,7,8,9 # reduction candidate for 1,7 D5: 1,7 # 11 pairs D8: 1,7,3,5,8 # reduction candidate for 1,7 D8: 1,7 # 11 pairs * PAIR I1: 4,7 BLK 3 G3: 4,7,8 # reduction candidate for 4,7 G3: 4,7 # 9 pairs I3: 4,7,8 # reduction candidate for 4,7 I3: 4,7 # 10 pairs * PAIR I1: 4,7 ROW 1 A1: 4,7,6 # reduction candidate for 4,7 A1: 4,7 # 11 pairs E1: 4,7,3,6 # reduction candidate for 4,7 E1: 4,7 # 16 pairs * PAIR I1: 4,7 COL I I9: 4,7,2,8 # reduction candidate for 4,7 I9: 4,7 # 9 pairs I9: 2,8 # 8 pairs * PAIR E4: 6,8 BLK 5 F4: 6,8,5 # reduction candidate for 6,8 F4: 6,8 # 10 pairs F5: 6,8,1,7 # reduction candidate for 6,8 F5: 6,8 => CTR * .8326951....3.829692615..3.6924851733.8726945..7913....3589...12645.1.898196...5. E6: 6,8,1 # reduction candidate for 6,8 E6: 6,8 => CTR * .8.2.9517...3.8296921756.3..924.51733...27..5..7..3....3.89...12645.1.898196...5. * RESTART * PAIR E4: 6,8 BLK 5 F4: 6,8,5 # reduction candidate for 6,8 F4: 5 => CTR * .8.2.951.......296921756.3.892465173316.27..5..7.13....3859...12.4........96...5. * PAIR B9: 1,7 BLK 7 B8: 1,7,5,6 # reduction candidate for 1,7 B8: 1,7 => CTR * .8.2.951.153...29692..5..3.5924..1733.8927..5..7513...635.9...12.4..5...8.96...5. A9: 1,7,8 # reduction candidate for 1,7 A9: 1,7 => SOLVED * 783269514415378296926154837592486173341927685867513942638795421254831769179642358 * DURATION: 0:00:18.419982 START: 05:24:11.626500 END: 05:24:30.046482 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0107-base-pr-001.dot * REASONING * DIS # F5: 6,8 => CTR => F5: 1,7 * DIS F5: 1,7 # E6: 6,8 => CTR => E6: 1 * DIS F5: 1,7 + E6: 1 # F4: 5 => CTR => F4: 6,8 * DIS F5: 1,7 + E6: 1 + F4: 6,8 # B8: 1,7 => CTR => B8: 5,6 * PRF F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 # A9: 1,7 => SOL * STA F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 + A9: 1,7 * CNT 5 HDP CHAINS / 25 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=107
Solution
position: 783269514415378296926154837592486173341927685867513942638795421254831769179642358 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 # E1: 3,6 => UNS * INC # E1: 4,7 => UNS * INC # F3: 1,6 => UNS * INC # F3: 4,7 => UNS * INC # C5: 1,6 => UNS * INC # C5: 8 => UNS * INC # D2: 1,7 => UNS * INC # E2: 1,7 => UNS * INC # F2: 1,7 => UNS * INC # F3: 1,7 => UNS * INC # D5: 1,7 => UNS * INC # D8: 1,7 => UNS * INC # G3: 4,7 => UNS * INC # I3: 4,7 => UNS * INC # A1: 4,7 => UNS * INC # E1: 4,7 => UNS * INC # I9: 4,7 => UNS * INC # I9: 2,8 => UNS * INC # F4: 6,8 => UNS * DIS # F5: 6,8 => CTR => F5: 1,7 * INC # F5: 1,7 => UNS * DIS # E6: 6,8 => CTR => E6: 1 * INC # E6: 1 => UNS * INC # A4: 6,8 => UNS * INC # A4: 5 => UNS * DIS # B8: 1,7 => CTR => B8: 5,6 * INC # B8: 5,6 => UNS * INC # A9: 1,7 => UNS * DIS # E9: 1,7 => CTR => E9: 3,4,8 * INC # E9: 3,4,8 => UNS * DIS # F9: 1,7 => CTR => F9: 2,4,8 * INC # F9: 2,4,8 => UNS * INC # B2: 1,7 => UNS * INC # B2: 4,5 => UNS * INC # G7: 6,8 => UNS * INC # H7: 6,8 => UNS * INC # G8: 6,8 => UNS * INC # H5: 6,8 => UNS * INC # H6: 6,8 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 3,6 => UNS * INC # E1: 4,7 => UNS * INC # F3: 1,6 => UNS * INC # F3: 4,7 => UNS * INC # C5: 1,6 => UNS * INC # C5: 8 => UNS * INC # D2: 1,7 => UNS * INC # E2: 1,7 => UNS * INC # F2: 1,7 => UNS * INC # F3: 1,7 => UNS * INC # D5: 1,7 => UNS * INC # D8: 1,7 => UNS * INC # G3: 4,7 => UNS * INC # I3: 4,7 => UNS * INC # A1: 4,7 => UNS * INC # E1: 4,7 => UNS * INC # I9: 4,7 => UNS * INC # I9: 2,8 => UNS * INC # F4: 6,8 => UNS * DIS # F5: 6,8 => CTR => F5: 1,7 * DIS F5: 1,7 # E6: 6,8 => CTR => E6: 1 * INC F5: 1,7 + E6: 1 # F4: 6,8 => UNS * DIS F5: 1,7 + E6: 1 # F4: 5 => CTR => F4: 6,8 * DIS F5: 1,7 + E6: 1 + F4: 6,8 # B8: 1,7 => CTR => B8: 5,6 * PRF F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 # A9: 1,7 => SOL * STA F5: 1,7 + E6: 1 + F4: 6,8 + B8: 5,6 + A9: 1,7 * CNT 25 HDP CHAINS / 25 HYP OPENED