Analysis of zz-www.sudokuwiki.org-0017-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=17
level: medium
position: ..6...7...1.8...6...2.46.9..8......6...954...5......4..4.18.2.......9.1...7...5.. initial
Autosolve
position: 4.6...7...1.8..46.8.2.46.9..84....56.6.9548..5....8.4.64.18.2....8..961.1.7...5.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B8: 2,3 => CTR => B8: 5 * DIS # D9: 2,3 => CTR => D9: 4,6 * DIS # E9: 2,3 => CTR => E9: 6 * DIS # F1: 2,3 => CTR => F1: 1,5 * DIS # I8: 3,7 => CTR => I8: 4 * DIS # F7: 3,7 => CTR => F7: 5 * CNT 6 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B8: 2,3 => CTR => B8: 5 * DIS B8: 5 # D9: 2,3 => CTR => D9: 4,6 * DIS B8: 5 + D9: 4,6 # E9: 2,3 => CTR => E9: 6 * PRF B8: 5 + D9: 4,6 + E9: 6 # B9: 9 => SOL * STA B8: 5 + D9: 4,6 + E9: 6 + B9: 9 * CNT 4 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6...7...1.8...6...2.46.9..8......6...954...5......4..4.18.2.......9.1...7...5.. | initial |
| 4.6...7...1.8..46.8.2.46.9..84....56.6.9548..5....8.4.64.18.2....8..961.1.7...5.. | autosolve |
| 436591782915827463872346195784213956361954827529678341643185279258739614197462538 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) G3: 1,3 C5: 1,3 A8: 2,3 F9: 2,3 H7: 3,7 H9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 1.. / E1 = 1 => 0 pairs (X) / F1 = 1 => 6 pairs (_) G3,I3: 1.. / G3 = 1 => 10 pairs (_) / I3 = 1 => 11 pairs (_) C5,C6: 1.. / C5 = 1 => 6 pairs (_) / C6 = 1 => 12 pairs (_) C5,I5: 1.. / C5 = 1 => 6 pairs (_) / I5 = 1 => 12 pairs (_) F1,F4: 1.. / F1 = 1 => 6 pairs (_) / F4 = 1 => 0 pairs (X) H1,H5: 2.. / H1 = 2 => 8 pairs (_) / H5 = 2 => 10 pairs (_) D8,D9: 4.. / D8 = 4 => 0 pairs (X) / D9 = 4 => 7 pairs (_) I8,I9: 4.. / I8 = 4 => 7 pairs (_) / I9 = 4 => 0 pairs (X) D8,I8: 4.. / D8 = 4 => 0 pairs (X) / I8 = 4 => 7 pairs (_) D9,I9: 4.. / D9 = 4 => 7 pairs (_) / I9 = 4 => 0 pairs (X) C7,B8: 5.. / C7 = 5 => 0 pairs (X) / B8 = 5 => 11 pairs (_) F7,D8: 5.. / F7 = 5 => 11 pairs (_) / D8 = 5 => 0 pairs (X) C7,F7: 5.. / C7 = 5 => 0 pairs (X) / F7 = 5 => 11 pairs (_) B8,D8: 5.. / B8 = 5 => 11 pairs (_) / D8 = 5 => 0 pairs (X) C2,C7: 5.. / C2 = 5 => 11 pairs (_) / C7 = 5 => 0 pairs (X) D6,E6: 6.. / D6 = 6 => 6 pairs (_) / E6 = 6 => 0 pairs (X) D9,E9: 6.. / D9 = 6 => 0 pairs (X) / E9 = 6 => 6 pairs (_) D6,D9: 6.. / D6 = 6 => 6 pairs (_) / D9 = 6 => 0 pairs (X) E6,E9: 6.. / E6 = 6 => 0 pairs (X) / E9 = 6 => 6 pairs (_) A2,B3: 7.. / A2 = 7 => 18 pairs (_) / B3 = 7 => 8 pairs (_) B3,D3: 7.. / B3 = 7 => 8 pairs (_) / D3 = 7 => 18 pairs (_) B3,B6: 7.. / B3 = 7 => 8 pairs (_) / B6 = 7 => 18 pairs (_) H5,H7: 7.. / H5 = 7 => 14 pairs (_) / H7 = 7 => 9 pairs (_) H1,I1: 8.. / H1 = 8 => 9 pairs (_) / I1 = 8 => 6 pairs (_) H9,I9: 8.. / H9 = 8 => 6 pairs (_) / I9 = 8 => 9 pairs (_) H1,H9: 8.. / H1 = 8 => 9 pairs (_) / H9 = 8 => 6 pairs (_) I1,I9: 8.. / I1 = 8 => 6 pairs (_) / I9 = 8 => 9 pairs (_) E1,E2: 9.. / E1 = 9 => 7 pairs (_) / E2 = 9 => 17 pairs (_) G4,G6: 9.. / G4 = 9 => 10 pairs (_) / G6 = 9 => 15 pairs (_) C7,B9: 9.. / C7 = 9 => 15 pairs (_) / B9 = 9 => 9 pairs (_) I7,I9: 9.. / I7 = 9 => 9 pairs (_) / I9 = 9 => 15 pairs (_) B1,E1: 9.. / B1 = 9 => 17 pairs (_) / E1 = 9 => 7 pairs (_) A4,G4: 9.. / A4 = 9 => 15 pairs (_) / G4 = 9 => 10 pairs (_) C7,I7: 9.. / C7 = 9 => 15 pairs (_) / I7 = 9 => 9 pairs (_) B9,I9: 9.. / B9 = 9 => 9 pairs (_) / I9 = 9 => 15 pairs (_) A2,A4: 9.. / A2 = 9 => 10 pairs (_) / A4 = 9 => 15 pairs (_) * DURATION: 0:00:50.906673 START: 03:42:21.400827 END: 03:43:12.307500 2017-05-01 * CP COUNT: (36) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C5,F9,G3,H7,H9) * 4.6...7...1.8..46.8.2.46.9..84....56.6.9548..5....8.4.64.18.2....8..961.1.7...5.. * PAIR G3: 1,3 BLK 3 I3: 1,3,5 # reduction candidate for 1,3 I3: 5 # 12 pairs I3: 1,3 # 11 pairs * PAIR G3: 1,3 COL G G4: 1,3,9 # reduction candidate for 1,3 G4: 1,3 # 15 pairs G6: 1,3,9 # reduction candidate for 1,3 G6: 1,3 # 10 pairs * PAIR C5: 1,3 BLK 4 C6: 1,3,9 # reduction candidate for 1,3 C6: 9 # 12 pairs C6: 1,3 # 10 pairs * PAIR C5: 1,3 ROW 5 I5: 1,3,2,7 # reduction candidate for 1,3 I5: 1,3 # 10 pairs I5: 2,7 # 7 pairs * PAIR A8: 2,3 BLK 7 B8: 2,3,5 # reduction candidate for 2,3 B8: 2,3 => CTR * 4.6.917..7198.546.8.2746.9.984..7.562619548375736.8942645183279328579614197462583 B8: 5 # 11 pairs B9: 2,3,9 # reduction candidate for 2,3 B9: 2,3 # 15 pairs * PAIR A8: 2,3 ROW 8 D8: 2,3,4,5,7 # reduction candidate for 2,3 D8: 2,3 # 11 pairs E8: 2,3,7 # reduction candidate for 2,3 E8: 2,3 # 13 pairs * PAIR A8: 2,3 COL A A4: 2,3,7,9 # reduction candidate for 2,3 A4: 2,3 # 14 pairs A5: 2,3,7 # reduction candidate for 2,3 A5: 2,3 # 9 pairs * PAIR F9: 2,3 BLK 8 D8: 2,3,4,5,7 # reduction candidate for 2,3 D8: 2,3 # 11 pairs E8: 2,3,7 # reduction candidate for 2,3 E8: 2,3 # 13 pairs D9: 2,3,4,6 # reduction candidate for 2,3 D9: 2,3 => CTR * 436591728.158..46.8.2.46.9..84....56.6.9548..5..6.8.4.64.1852.9.58479613197.6.584 D9: 4,6 # 7 pairs E9: 2,3,6 # reduction candidate for 2,3 E9: 2,3 => CTR * 436591728.158..46.8.2.46.9..84.1..56.6.9548..5...68.4.64.185279.584796131976..584 E9: 6 # 6 pairs * PAIR F9: 2,3 ROW 9 B9: 2,3,9 # reduction candidate for 2,3 B9: 2,3 # 15 pairs B9: 9 # 9 pairs * PAIR F9: 2,3 COL F F1: 2,3,1,5 # reduction candidate for 2,3 F1: 2,3 => CTR * 496.1.7.8.15897462872.46195984..1356763954821521..8947649185273258..9614137462589 F1: 1,5 # 7 pairs F2: 2,3,5,7 # reduction candidate for 2,3 F2: 2,3 # 10 pairs F4: 2,3,1,7 # reduction candidate for 2,3 F4: 2,3 # 9 pairs * PAIR H7: 3,7 BLK 9 I7: 3,7,9 # reduction candidate for 3,7 I7: 3,7 # 15 pairs I8: 3,7,4 # reduction candidate for 3,7 I8: 3,7 => CTR * 436591728.158..46.8.2.46.9..84....56.6.9548..5....8.4.64.1852.9.58479613197...584 I8: 4 # 7 pairs * PAIR H7: 3,7 ROW 7 F7: 3,7,5 # reduction candidate for 3,7 F7: 3,7 => CTR * 4.6.917..7198.546.8.2746.9.984..7.562619548375736.8942645183279328579614197462583 F7: 5 # 11 pairs * PAIR H7: 3,7 COL H H5: 3,7,2 # reduction candidate for 3,7 H5: 2 # 10 pairs H5: 3,7 # 8 pairs * PAIR H9: 3,8 BLK 9 I9: 3,8,4,9 # reduction candidate for 3,8 I9: 3,8 # 11 pairs I9: 4,9 # 7 pairs * PAIR H9: 3,8 COL H H1: 3,8,2 # reduction candidate for 3,8 H1: 3,8 # 10 pairs H1: 2 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0017-base-pr-000.dot * REASONING * DIS # B8: 2,3 => CTR => B8: 5 * DIS # D9: 2,3 => CTR => D9: 4,6 * DIS # E9: 2,3 => CTR => E9: 6 * DIS # F1: 2,3 => CTR => F1: 1,5 * DIS # I8: 3,7 => CTR => I8: 4 * DIS # F7: 3,7 => CTR => F7: 5 * CNT 6 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C5,F9,G3,H7,H9) * 4.6...7...1.8..46.8.2.46.9..84....56.6.9548..5....8.4.64.18.2....8..961.1.7...5.. * PAIR G3: 1,3 BLK 3 I3: 1,3,5 # reduction candidate for 1,3 I3: 5 # 12 pairs I3: 1,3 # 11 pairs * PAIR G3: 1,3 COL G G4: 1,3,9 # reduction candidate for 1,3 G4: 1,3 # 15 pairs G6: 1,3,9 # reduction candidate for 1,3 G6: 1,3 # 10 pairs * PAIR C5: 1,3 BLK 4 C6: 1,3,9 # reduction candidate for 1,3 C6: 9 # 12 pairs C6: 1,3 # 10 pairs * PAIR C5: 1,3 ROW 5 I5: 1,3,2,7 # reduction candidate for 1,3 I5: 1,3 # 10 pairs I5: 2,7 # 7 pairs * PAIR A8: 2,3 BLK 7 B8: 2,3,5 # reduction candidate for 2,3 B8: 2,3 => CTR * 4.6.917..7198.546.8.2746.9.984..7.562619548375736.8942645183279328579614197462583 B9: 2,3,9 # reduction candidate for 2,3 B9: 2,3 # 15 pairs * RESTART * PAIR A8: 2,3 BLK 7 B9: 2,3,9 # reduction candidate for 2,3 B9: 2,3 # 15 pairs B9: 9 # 13 pairs * PAIR A8: 2,3 ROW 8 D8: 2,3,4,7 # reduction candidate for 2,3 D8: 2,3 # 11 pairs E8: 2,3,7 # reduction candidate for 2,3 E8: 2,3 # 13 pairs * PAIR A8: 2,3 COL A A4: 2,3,7,9 # reduction candidate for 2,3 A4: 2,3 # 17 pairs A5: 2,3,7 # reduction candidate for 2,3 A5: 2,3 # 15 pairs * PAIR F9: 2,3 BLK 8 D8: 2,3,4,7 # reduction candidate for 2,3 D8: 2,3 # 11 pairs E8: 2,3,7 # reduction candidate for 2,3 E8: 2,3 # 13 pairs D9: 2,3,4,6 # reduction candidate for 2,3 D9: 2,3 => CTR * 4.6...7.8.158..4628.2.46.95.84....56.6.95482.5..6.8.4.643185279258479613197.6.584 E9: 2,3,6 # reduction candidate for 2,3 E9: 2,3 => CTR * 436591728.158..46.8.2.46.95.84....56.6.9548..5...68.4.64.1852.9.584796131976..584 * PAIR F9: 2,3 ROW 9 B9: 2,3,9 # reduction candidate for 2,3 B9: 9 => SOLVED * 436591782915827463872346195784213956361954827529678341643185279258739614197462538 * DURATION: 0:00:19.465958 START: 03:43:41.193608 END: 03:44:00.659566 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0017-base-pr-001.dot * REASONING * DIS # B8: 2,3 => CTR => B8: 5 * DIS B8: 5 # D9: 2,3 => CTR => D9: 4,6 * DIS B8: 5 + D9: 4,6 # E9: 2,3 => CTR => E9: 6 * PRF B8: 5 + D9: 4,6 + E9: 6 # B9: 9 => SOL * STA B8: 5 + D9: 4,6 + E9: 6 + B9: 9 * CNT 4 HDP CHAINS / 22 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=17
Solution
position: 436591782915827463872346195784213956361954827529678341643185279258739614197462538 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 # I3: 1,3 => UNS * INC # I3: 5 => UNS * INC # G4: 1,3 => UNS * INC # G6: 1,3 => UNS * INC # C6: 1,3 => UNS * INC # C6: 9 => UNS * INC # I5: 1,3 => UNS * INC # I5: 2,7 => UNS * DIS # B8: 2,3 => CTR => B8: 5 * INC # B8: 5 => UNS * INC # B9: 2,3 => UNS * INC # D8: 2,3 => UNS * INC # E8: 2,3 => UNS * INC # A4: 2,3 => UNS * INC # A5: 2,3 => UNS * INC # D8: 2,3 => UNS * INC # E8: 2,3 => UNS * DIS # D9: 2,3 => CTR => D9: 4,6 * INC # D9: 4,6 => UNS * DIS # E9: 2,3 => CTR => E9: 6 * INC # E9: 6 => UNS * INC # B9: 2,3 => UNS * INC # B9: 9 => UNS * DIS # F1: 2,3 => CTR => F1: 1,5 * INC # F1: 1,5 => UNS * INC # F2: 2,3 => UNS * INC # F4: 2,3 => UNS * INC # I7: 3,7 => UNS * DIS # I8: 3,7 => CTR => I8: 4 * INC # I8: 4 => UNS * DIS # F7: 3,7 => CTR => F7: 5 * INC # F7: 5 => UNS * INC # H5: 3,7 => UNS * INC # H5: 2 => UNS * INC # I9: 3,8 => UNS * INC # I9: 4,9 => UNS * INC # H1: 3,8 => UNS * INC # H1: 2 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I3: 1,3 => UNS * INC # I3: 5 => UNS * INC # G4: 1,3 => UNS * INC # G6: 1,3 => UNS * INC # C6: 1,3 => UNS * INC # C6: 9 => UNS * INC # I5: 1,3 => UNS * INC # I5: 2,7 => UNS * DIS # B8: 2,3 => CTR => B8: 5 * INC B8: 5 # B9: 2,3 => UNS * INC B8: 5 # B9: 2,3 => UNS * INC B8: 5 # B9: 9 => UNS * INC B8: 5 # D8: 2,3 => UNS * INC B8: 5 # E8: 2,3 => UNS * INC B8: 5 # A4: 2,3 => UNS * INC B8: 5 # A5: 2,3 => UNS * INC B8: 5 # D8: 2,3 => UNS * INC B8: 5 # E8: 2,3 => UNS * DIS B8: 5 # D9: 2,3 => CTR => D9: 4,6 * DIS B8: 5 + D9: 4,6 # E9: 2,3 => CTR => E9: 6 * INC B8: 5 + D9: 4,6 + E9: 6 # B9: 2,3 => UNS * PRF B8: 5 + D9: 4,6 + E9: 6 # B9: 9 => SOL * STA B8: 5 + D9: 4,6 + E9: 6 + B9: 9 * CNT 22 HDP CHAINS / 22 HYP OPENED