Analysis of zz-www.sudokuwiki.org-0142-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=142
level: medium
position: ..7...3...9...6..58....5..21.85.........7.........87.94..8....13......4...2.9.6.. initial
Autosolve
position: ..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13......477.2.9.6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 5,6 => CTR => B1: 1,4 * DIS # B5: 5,6 => CTR => B5: 2,3,4 * DIS # B6: 5,6 => CTR => B6: 2,3,4 * DIS # G5: 2,4 => CTR => G5: 1,5,8 * DIS # B8: 5,6 => CTR => B8: 1,8 * DIS # C8: 5,6 => CTR => C8: 1,9 * DIS # E7: 5,6 => CTR => E7: 2,3 * DIS # B1: 5,6 => CTR => B1: 1,4 * DIS # B5: 5,6 => CTR => B5: 2,3,4 * DIS # B6: 5,6 => CTR => B6: 2,3,4 * DIS # D8: 1,2 => CTR => D8: 6 * DIS # E8: 1,2 => CTR => E8: 5,6 * DIS # F5: 1,2 => CTR => F5: 3,4 * PRF # H9: 3,8 => SOL * CNT 14 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 # B1: 5,6 => CTR => B1: 1,4 * DIS B1: 1,4 # G5: 2,4 => CTR => G5: 1,5,8 * DIS B1: 1,4 + G5: 1,5,8 # E4: 2,4 => CTR => E4: 3,6 * DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 # C7: 5,6 => CTR => C7: 9 * DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 # C8: 5,6 => CTR => C8: 1 * PRF B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1 => SOL * STA B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1 * CNT 6 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..7...3...9...6..58....5..21.85.........7.........87.94..8....13......4...2.9.6.. | initial |
| ..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13......477.2.9.6.. | autosolve |
| 517924368294386175836715492178569234945273816623148759469837521381652947752491683 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) A1: 5,6 A6: 5,6 G4: 2,4 B7: 5,6 F8: 1,2 I9: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,B6: 2.. / B5 = 2 => 6 pairs (_) / B6 = 2 => 6 pairs (_) E7,H7: 3.. / E7 = 3 => 18 pairs (_) / H7 = 3 => 0 pairs (X) F5,F9: 3.. / F5 = 3 => 7 pairs (_) / F9 = 3 => 0 pairs (X) D9,F9: 4.. / D9 = 4 => 7 pairs (_) / F9 = 4 => 8 pairs (_) A1,B1: 5.. / A1 = 5 => 4 pairs (_) / B1 = 5 => 0 pairs (X) E7,E8: 5.. / E7 = 5 => 0 pairs (X) / E8 = 5 => 6 pairs (_) B9,H9: 5.. / B9 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) A1,A6: 5.. / A1 = 5 => 4 pairs (_) / A6 = 5 => 0 pairs (X) A1,A6: 6.. / A1 = 6 => 0 pairs (X) / A6 = 6 => 4 pairs (_) D2,D3: 7.. / D2 = 7 => 6 pairs (_) / D3 = 7 => 6 pairs (_) H2,H3: 7.. / H2 = 7 => 6 pairs (_) / H3 = 7 => 6 pairs (_) D2,H2: 7.. / D2 = 7 => 6 pairs (_) / H2 = 7 => 6 pairs (_) D3,H3: 7.. / D3 = 7 => 6 pairs (_) / H3 = 7 => 6 pairs (_) E1,E2: 8.. / E1 = 8 => 7 pairs (_) / E2 = 8 => 8 pairs (_) B8,B9: 8.. / B8 = 8 => 7 pairs (_) / B9 = 8 => 0 pairs (X) B8,G8: 8.. / B8 = 8 => 7 pairs (_) / G8 = 8 => 0 pairs (X) D1,D3: 9.. / D1 = 9 => 6 pairs (_) / D3 = 9 => 0 pairs (X) C7,C8: 9.. / C7 = 9 => 10 pairs (_) / C8 = 9 => 14 pairs (_) D1,H1: 9.. / D1 = 9 => 6 pairs (_) / H1 = 9 => 0 pairs (X) C8,G8: 9.. / C8 = 9 => 14 pairs (_) / G8 = 9 => 10 pairs (_) * DURATION: 0:00:23.780562 START: 06:09:18.918695 END: 06:09:42.699257 2017-05-01 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B7,F8,G4,I9) * ..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13......477.2.9.6.. * PAIR A1: 5,6 BLK 1 B1: 5,6,1,4 # reduction candidate for 5,6 B1: 5,6 => CTR * ..79..3..29.3861758.17459621785.94369...735.8..3.687.94.5837291319652847782.94653 B1: 1,4 # 5 pairs * PAIR A6: 5,6 BLK 4 B5: 5,6,2,3,4 # reduction candidate for 5,6 B5: 5,6 => CTR * 547...3..291..6..5836..5..21785.9...95..7....62...875946.8.7..13......477.2.9.6.. B5: 2,3,4 # 6 pairs C5: 5,6,3,4 # reduction candidate for 5,6 C5: 5,6 # 8 pairs B6: 5,6,2,3,4 # reduction candidate for 5,6 B6: 5,6 => CTR * 547...3..291..64.5836.451.217856923492..735..65342871946583792131965284778219.653 B6: 2,3,4 # 6 pairs C6: 5,6,3,4 # reduction candidate for 5,6 C6: 5,6 # 8 pairs * PAIR A6: 5,6 ROW 6 H6: 5,6,1,2,3 # reduction candidate for 5,6 H6: 5,6 # 8 pairs H6: 1,2,3 # 6 pairs * PAIR G4: 2,4 BLK 6 G5: 2,4,1,5,8 # reduction candidate for 2,4 G5: 2,4 => CTR * 5179..3..29...68758.67.51921785.9...9...7....6....87.94698.7521381652947752.9.6.. G5: 1,5,8 # 6 pairs * PAIR G4: 2,4 ROW 4 E4: 2,4,3,6 # reduction candidate for 2,4 E4: 2,4 # 10 pairs E4: 3,6 # 7 pairs * PAIR B7: 5,6 BLK 7 C7: 5,6,9 # reduction candidate for 5,6 C7: 5,6 # 14 pairs B8: 5,6,1,8 # reduction candidate for 5,6 B8: 5,6 => CTR * ..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13.....847782.9.653 B8: 1,8 # 7 pairs C8: 5,6,1,9 # reduction candidate for 5,6 C8: 5,6 => CTR * ..798.3..29...68758..7.51921785.942.9...7.58......87194.98.723138....947712.9.658 C8: 1,9 # 7 pairs * PAIR B7: 5,6 ROW 7 E7: 5,6,2,3 # reduction candidate for 5,6 E7: 5,6 => CTR * ..798.3.429...68758..7.51921785.942.9...7.58......87194.98.723138....947712.9.658 E7: 2,3 # 9 pairs * PAIR B7: 5,6 COL B B1: 5,6,1,4 # reduction candidate for 5,6 B1: 5,6 => CTR * ..79..3..29.3861758.17459621785.94369...735.8..3.687.94.5837291319652847782.94653 B1: 1,4 # 5 pairs B5: 5,6,2,3,4 # reduction candidate for 5,6 B5: 5,6 => CTR * 547...3..291..6..5836..5..21785.9...95..7....62...875946.8.7..13......477.2.9.6.. B5: 2,3,4 # 6 pairs B6: 5,6,2,3,4 # reduction candidate for 5,6 B6: 5,6 => CTR * 547...3..291..64.5836.451.217856923492..735..65342871946583792131965284778219.653 B6: 2,3,4 # 6 pairs * PAIR F8: 1,2 BLK 8 D8: 1,2,6 # reduction candidate for 1,2 D8: 1,2 => CTR * ..798.3.429...68758..7.51921785394269...74583....287194.98.723138....947712493658 D8: 6 # 6 pairs E8: 1,2,5,6 # reduction candidate for 1,2 E8: 1,2 => CTR * .5798.3.429...68758..7.51921785.942.9...7.58......87194698572313856..947712.9.658 E8: 5,6 # 7 pairs * PAIR F8: 1,2 COL F F1: 1,2,4 # reduction candidate for 1,2 F1: 1,2 # 9 pairs F5: 1,2,3,4 # reduction candidate for 1,2 F5: 1,2 => CTR * 517..43.629...6..58....5..21785.9...9...7....6....87.94..8.7.3138.....477.2493658 F5: 3,4 # 7 pairs * PAIR I9: 3,8 BLK 9 H9: 3,8,5 # reduction candidate for 3,8 H9: 3,8 => SOLVED * 517924368294386175836715492178569234945273816623148759469837521381652947752491683 H9: 5 # 9 pairs * PAIR I9: 3,8 COL I I5: 3,8,4,6 # reduction candidate for 3,8 I5: 4,6 # 9 pairs I5: 3,8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0142-base-pr-000.dot * REASONING * DIS # B1: 5,6 => CTR => B1: 1,4 * DIS # B5: 5,6 => CTR => B5: 2,3,4 * DIS # B6: 5,6 => CTR => B6: 2,3,4 * DIS # G5: 2,4 => CTR => G5: 1,5,8 * DIS # B8: 5,6 => CTR => B8: 1,8 * DIS # C8: 5,6 => CTR => C8: 1,9 * DIS # E7: 5,6 => CTR => E7: 2,3 * DIS # B1: 5,6 => CTR => B1: 1,4 * DIS # B5: 5,6 => CTR => B5: 2,3,4 * DIS # B6: 5,6 => CTR => B6: 2,3,4 * DIS # D8: 1,2 => CTR => D8: 6 * DIS # E8: 1,2 => CTR => E8: 5,6 * DIS # F5: 1,2 => CTR => F5: 3,4 * PRF # H9: 3,8 => SOL * CNT 14 HDP CHAINS / 38 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B7,F8,G4,I9) * ..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13......477.2.9.6.. * PAIR A1: 5,6 BLK 1 B1: 5,6,1,4 # reduction candidate for 5,6 B1: 5,6 => CTR * ..79..3..29.3861758.17459621785.94369...735.8..3.687.94.5837291319652847782.94653 * PAIR G4: 2,4 BLK 6 G5: 2,4,1,5,8 # reduction candidate for 2,4 G5: 2,4 => CTR * 5179..3..29...68758.67.51921785.9...9...7....6....87.94698.7521381652947752.9.6.. * PAIR G4: 2,4 ROW 4 E4: 2,4,3,6 # reduction candidate for 2,4 E4: 2,4 => CTR * 5.7...3..29...6..58....5..21785.9..39..67....6....87.94.98.72313.....947712.9.658 * PAIR RESTART * PAIR B7: 5,6 BLK 7 C7: 5,6,9 # reduction candidate for 5,6 C7: 5,6 => CTR * 547..13..29...6..58...451.21785692349241735..6....87194..837921319652847782.94653 C8: 5,6,1 # reduction candidate for 5,6 C8: 5,6 => CTR * 547...3.629...6..58....5..21785.9..49...7.5836....87194.98.72.138....947712.9.658 C8: 1 => SOLVED * 517924368294386175836715492178569234945273816623148759469837521381652947752491683 * DURATION: 0:00:07.490682 START: 06:10:07.450921 END: 06:10:14.941603 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0142-base-pr-001.dot * REASONING * DIS # B1: 5,6 => CTR => B1: 1,4 * DIS B1: 1,4 # G5: 2,4 => CTR => G5: 1,5,8 * DIS B1: 1,4 + G5: 1,5,8 # E4: 2,4 => CTR => E4: 3,6 * DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 # C7: 5,6 => CTR => C7: 9 * DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 # C8: 5,6 => CTR => C8: 1 * PRF B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1 => SOL * STA B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1 * CNT 6 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=142
Solution
position: 517924368294386175836715492178569234945273816623148759469837521381652947752491683 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 # B1: 5,6 => CTR => B1: 1,4 * INC # B1: 1,4 => UNS * DIS # B5: 5,6 => CTR => B5: 2,3,4 * INC # B5: 2,3,4 => UNS * INC # C5: 5,6 => UNS * DIS # B6: 5,6 => CTR => B6: 2,3,4 * INC # B6: 2,3,4 => UNS * INC # C6: 5,6 => UNS * INC # H6: 5,6 => UNS * INC # H6: 1,2,3 => UNS * DIS # G5: 2,4 => CTR => G5: 1,5,8 * INC # G5: 1,5,8 => UNS * INC # E4: 2,4 => UNS * INC # E4: 3,6 => UNS * INC # C7: 5,6 => UNS * DIS # B8: 5,6 => CTR => B8: 1,8 * INC # B8: 1,8 => UNS * DIS # C8: 5,6 => CTR => C8: 1,9 * INC # C8: 1,9 => UNS * DIS # E7: 5,6 => CTR => E7: 2,3 * INC # E7: 2,3 => UNS * DIS # B1: 5,6 => CTR => B1: 1,4 * INC # B1: 1,4 => UNS * DIS # B5: 5,6 => CTR => B5: 2,3,4 * INC # B5: 2,3,4 => UNS * DIS # B6: 5,6 => CTR => B6: 2,3,4 * INC # B6: 2,3,4 => UNS * DIS # D8: 1,2 => CTR => D8: 6 * INC # D8: 6 => UNS * DIS # E8: 1,2 => CTR => E8: 5,6 * INC # E8: 5,6 => UNS * INC # F1: 1,2 => UNS * DIS # F5: 1,2 => CTR => F5: 3,4 * INC # F5: 3,4 => UNS * PRF # H9: 3,8 => SOL * INC # H9: 5 => UNS * INC # I5: 3,8 => UNS * INC # I5: 4,6 => UNS * CNT 38 HDP CHAINS / 38 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B1: 5,6 => CTR => B1: 1,4 * DIS B1: 1,4 # G5: 2,4 => CTR => G5: 1,5,8 * DIS B1: 1,4 + G5: 1,5,8 # E4: 2,4 => CTR => E4: 3,6 * DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 # C7: 5,6 => CTR => C7: 9 * DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 # C8: 5,6 => CTR => C8: 1 * PRF B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1 => SOL * STA B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1 * CNT 6 HDP CHAINS / 5 HYP OPENED