Analysis of zz-www.sudokuwiki.org-0067-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=67
level: medium
position: .....6....9.15...6..7...18..5..1...2...9.5...6...3..4..84...6..5...81.9....2..... initial
Autosolve
position: ..5..6....9.15...6.67...185.5..1...2...9.5...6...3.54..845..6..5...81.9....2...5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 3,4 => CTR => D1: 7,8 * DIS # F2: 3,4 => CTR => F2: 2,7,8 * DIS # F3: 3,4 => CTR => F3: 2,9 * DIS # A3: 2 => CTR => A3: 3,4 * DIS # D4: 7,8 => CTR => D4: 4,6 * PRF # F6: 7,8 => SOL * DIS # I6: 7,8 => CTR => I6: 1,9 * DIS # D1: 3,4 => CTR => D1: 7,8 * DIS # E9: 7,9 => CTR => E9: 4,6 * DIS # A7: 7,9 => CTR => A7: 1,2,3 * CNT 10 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 3,4 => CTR => D1: 7,8 * DIS D1: 7,8 # F2: 3,4 => CTR => F2: 2,7,8 * DIS D1: 7,8 + F2: 2,7,8 # F3: 3,4 => CTR => F3: 2,9 * DIS D1: 7,8 + F2: 2,7,8 + F3: 2,9 # F4: 7,8 => CTR => F4: 4 * PRF D1: 7,8 + F2: 2,7,8 + F3: 2,9 + F4: 4 => SOL * STA D1: 7,8 + F2: 2,7,8 + F3: 2,9 + F4: 4 * CNT 5 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....6....9.15...6..7...18..5..1...2...9.5...6...3..4..84...6..5...81.9....2..... | initial |
| ..5..6....9.15...6.67...185.5..1...2...9.5...6...3.54..845..6..5...81.9....2...5. | autosolve |
| 815746329392158476467392185758614932143925768629837541284579613536481297971263854 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) D3: 3,4 D6: 7,8 E7: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,B1: 1.. / A1 = 1 => 6 pairs (_) / B1 = 1 => 9 pairs (_) H5,H7: 1.. / H5 = 1 => 0 pairs (X) / H7 = 1 => 10 pairs (_) E5,F6: 2.. / E5 = 2 => 0 pairs (*) / F6 = 2 => 0 pairs (X) H7,G8: 2.. / H7 = 2 => 0 pairs (X) / G8 = 2 => 9 pairs (_) A7,H7: 2.. / A7 = 2 => 9 pairs (_) / H7 = 2 => 0 pairs (X) B1,B5: 4.. / B1 = 4 => 9 pairs (_) / B5 = 4 => 3 pairs (_) D4,E5: 6.. / D4 = 6 => 10 pairs (_) / E5 = 6 => 0 pairs (X) H4,H5: 6.. / H4 = 6 => 0 pairs (X) / H5 = 6 => 10 pairs (_) C8,C9: 6.. / C8 = 6 => 10 pairs (_) / C9 = 6 => 0 pairs (X) D8,E9: 6.. / D8 = 6 => 0 pairs (X) / E9 = 6 => 10 pairs (_) D4,H4: 6.. / D4 = 6 => 10 pairs (_) / H4 = 6 => 0 pairs (X) E5,H5: 6.. / E5 = 6 => 0 pairs (X) / H5 = 6 => 10 pairs (_) C8,D8: 6.. / C8 = 6 => 10 pairs (_) / D8 = 6 => 0 pairs (X) C9,E9: 6.. / C9 = 6 => 0 pairs (X) / E9 = 6 => 10 pairs (_) D4,D8: 6.. / D4 = 6 => 10 pairs (_) / D8 = 6 => 0 pairs (X) E5,E9: 6.. / E5 = 6 => 0 pairs (X) / E9 = 6 => 10 pairs (_) D1,F2: 8.. / D1 = 8 => 6 pairs (_) / F2 = 8 => 11 pairs (_) G9,I9: 8.. / G9 = 8 => 4 pairs (_) / I9 = 8 => 3 pairs (_) A1,D1: 8.. / A1 = 8 => 11 pairs (_) / D1 = 8 => 6 pairs (_) E3,F3: 9.. / E3 = 9 => 10 pairs (_) / F3 = 9 => 5 pairs (_) G1,I1: 9.. / G1 = 9 => 3 pairs (_) / I1 = 9 => 4 pairs (_) G4,I6: 9.. / G4 = 9 => 4 pairs (_) / I6 = 9 => 3 pairs (_) C6,I6: 9.. / C6 = 9 => 4 pairs (_) / I6 = 9 => 3 pairs (_) G1,G4: 9.. / G1 = 9 => 3 pairs (_) / G4 = 9 => 4 pairs (_) I1,I6: 9.. / I1 = 9 => 4 pairs (_) / I6 = 9 => 3 pairs (_) * DURATION: 0:00:29.996824 START: 04:36:22.632212 END: 04:36:52.629036 2017-05-01 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D3,D6,E7) * ..5..6....9.15...6.67...185.5..1...2...9.5...6...3.54..845..6..5...81.9....2...5. * PAIR D3: 3,4 BLK 2 D1: 3,4,7,8 # reduction candidate for 3,4 D1: 3,4 => CTR * 815.76....9.158..6.67.29185.5..1...2.4.965...67.83254..8459362.526.81.9..3.247.5. D1: 7,8 # 5 pairs F2: 3,4,2,7,8 # reduction candidate for 3,4 F2: 3,4 => CTR * 145876.2..9.15.47636742918545.618732.2394586161873254928459.61.5.638129493126..5. F2: 2,7,8 # 3 pairs F3: 3,4,2,9 # reduction candidate for 3,4 F3: 3,4 => CTR * ..5.269.449.15.2.6267.9.185.59.1..62.42965.1.671832549.8457.62.523681497716249.5. F3: 2,9 # 4 pairs * PAIR D3: 3,4 ROW 3 A3: 3,4,2 # reduction candidate for 3,4 A3: 2 => CTR * ..5.269.449.15.2.6267...185.59.1..62.42965.1.671832549.845..62.523681497.162...5. A3: 3,4 # 7 pairs * PAIR D3: 3,4 COL D D8: 3,4,6,7 # reduction candidate for 3,4 D8: 3,4 # 12 pairs D8: 6,7 # 4 pairs * PAIR D6: 7,8 BLK 5 D4: 7,8,4,6 # reduction candidate for 7,8 D4: 7,8 => CTR * 815..6....9.158..6.67...185.5..14.62.4.965...67.83254..845..6..523681.9...624..5. D4: 4,6 # 4 pairs F4: 7,8,4 # reduction candidate for 7,8 F4: 7,8 # 7 pairs F6: 7,8,2 # reduction candidate for 7,8 F6: 7,8 => SOLVED * 815746329392158476467392185758614932143925768629837541284579613536481297971263854 F6: 2 # 4 pairs * PAIR D6: 7,8 ROW 6 I6: 7,8,1,9 # reduction candidate for 7,8 I6: 7,8 => CTR * 1458.673989215.4.6.67...185453618972.289453616197325482845..61.5.6.8129.9.126.85. I6: 1,9 # 4 pairs * PAIR D6: 7,8 COL D D1: 7,8,3,4 # reduction candidate for 7,8 D1: 3,4 => CTR * 815.76....9.158..6.67.29185.5..1...2.4.965...67.83254..8459362.526.81.9..3.247.5. D1: 7,8 # 5 pairs * PAIR E7: 7,9 BLK 8 F7: 7,9,3 # reduction candidate for 7,9 F7: 7,9 # 7 pairs E9: 7,9,4,6 # reduction candidate for 7,9 E9: 7,9 => CTR * 8157.6....9.158..6.673.918535.417.62.4.965...67.83254..845.36..523681.9...62.4.5. E9: 4,6 # 4 pairs F9: 7,9,3,4 # reduction candidate for 7,9 F9: 7,9 # 7 pairs * PAIR E7: 7,9 ROW 7 A7: 7,9,1,2,3 # reduction candidate for 7,9 A7: 7,9 => CTR * 815.269.4.931582762673..185.59417862.4.965.1.671832549.845.36215..681.9...62...5. A7: 1,2,3 # 3 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0067-base-pr-000.dot * REASONING * DIS # D1: 3,4 => CTR => D1: 7,8 * DIS # F2: 3,4 => CTR => F2: 2,7,8 * DIS # F3: 3,4 => CTR => F3: 2,9 * DIS # A3: 2 => CTR => A3: 3,4 * DIS # D4: 7,8 => CTR => D4: 4,6 * PRF # F6: 7,8 => SOL * DIS # I6: 7,8 => CTR => I6: 1,9 * DIS # D1: 3,4 => CTR => D1: 7,8 * DIS # E9: 7,9 => CTR => E9: 4,6 * DIS # A7: 7,9 => CTR => A7: 1,2,3 * CNT 10 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D3,D6,E7) * ..5..6....9.15...6.67...185.5..1...2...9.5...6...3.54..845..6..5...81.9....2...5. * PAIR D3: 3,4 BLK 2 D1: 3,4,7,8 # reduction candidate for 3,4 D1: 3,4 => CTR * 815.76....9.158..6.67.29185.5..1...2.4.965...67.83254..8459362.526.81.9..3.247.5. F2: 3,4,2,7,8 # reduction candidate for 3,4 F2: 3,4 => CTR * 145876.2..9.15.47636742918545.618732.2394586161873254928459.61.5.638129493126..5. F3: 3,4,2,9 # reduction candidate for 3,4 F3: 3,4 => CTR * ..5.269.449.15.2.6267394185.5941..62.42965.1.671832549.8457.62.523681497716249.5. * PAIR D6: 7,8 BLK 5 F4: 7,8,4 # reduction candidate for 7,8 F4: 7,8 => CTR * 8157.6....9.158..6.673.918535.417.62.4.965...67.83254..845.36..523681.9...62.4.5. F4: 4 => SOLVED * 815746329392158476467392185758614932143925768629837541284579613536481297971263854 * DURATION: 0:00:05.613828 START: 04:37:10.370849 END: 04:37:15.984677 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0067-base-pr-001.dot * REASONING * DIS # D1: 3,4 => CTR => D1: 7,8 * DIS D1: 7,8 # F2: 3,4 => CTR => F2: 2,7,8 * DIS D1: 7,8 + F2: 2,7,8 # F3: 3,4 => CTR => F3: 2,9 * DIS D1: 7,8 + F2: 2,7,8 + F3: 2,9 # F4: 7,8 => CTR => F4: 4 * PRF D1: 7,8 + F2: 2,7,8 + F3: 2,9 + F4: 4 => SOL * STA D1: 7,8 + F2: 2,7,8 + F3: 2,9 + F4: 4 * CNT 5 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=67
Solution
position: 815746329392158476467392185758614932143925768629837541284579613536481297971263854 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 # D1: 3,4 => CTR => D1: 7,8 * INC # D1: 7,8 => UNS * DIS # F2: 3,4 => CTR => F2: 2,7,8 * INC # F2: 2,7,8 => UNS * DIS # F3: 3,4 => CTR => F3: 2,9 * INC # F3: 2,9 => UNS * INC # A3: 3,4 => UNS * DIS # A3: 2 => CTR => A3: 3,4 * INC # D8: 3,4 => UNS * INC # D8: 6,7 => UNS * DIS # D4: 7,8 => CTR => D4: 4,6 * INC # D4: 4,6 => UNS * INC # F4: 7,8 => UNS * PRF # F6: 7,8 => SOL * INC # F6: 2 => UNS * DIS # I6: 7,8 => CTR => I6: 1,9 * INC # I6: 1,9 => UNS * INC # D1: 7,8 => UNS * DIS # D1: 3,4 => CTR => D1: 7,8 * INC # F7: 7,9 => UNS * DIS # E9: 7,9 => CTR => E9: 4,6 * INC # E9: 4,6 => UNS * INC # F9: 7,9 => UNS * DIS # A7: 7,9 => CTR => A7: 1,2,3 * INC # A7: 1,2,3 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 3,4 => CTR => D1: 7,8 * DIS D1: 7,8 # F2: 3,4 => CTR => F2: 2,7,8 * DIS D1: 7,8 + F2: 2,7,8 # F3: 3,4 => CTR => F3: 2,9 * DIS D1: 7,8 + F2: 2,7,8 + F3: 2,9 # F4: 7,8 => CTR => F4: 4 * PRF D1: 7,8 + F2: 2,7,8 + F3: 2,9 + F4: 4 => SOL * STA D1: 7,8 + F2: 2,7,8 + F3: 2,9 + F4: 4 * CNT 5 HDP CHAINS / 4 HYP OPENED