Analysis of zz-www.sudokuwiki.org-0022-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=22
level: medium
position: ..9....6.....31..774..9...8..7..9...6...4...9...3..8..4...6..7.5..41.....2....3.. initial
Autosolve
position: ..9..4.6..6..31..774..9...8..7..9...6...4.7.9..43..8..4...6..7.57.41.....2....3.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 2,8 => CTR => A1: 1,3 * DIS # I4: 4,6 => CTR => I4: 1,2,3,5 * DIS # I4: 2,6 => CTR => I4: 1,3,4,5 * CNT 3 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 2,8 => CTR => A1: 1,3 * DIS A1: 1,3 # I4: 4,6 => CTR => I4: 1,2,3,5 * DIS A1: 1,3 + I4: 1,2,3,5 # A4: 1,3 => CTR => A4: 2,8 * DIS A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 # B7: 3,8 => CTR => B7: 1,9 * PRF A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 + B7: 1,9 # F8: 3,8 => SOL * STA A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 + B7: 1,9 + F8: 3,8 * CNT 5 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..9....6.....31..774..9...8..7..9...6...4...9...3..8..4...6..7.5..41.....2....3.. | initial |
| ..9..4.6..6..31..774..9...8..7..9...6...4.7.9..43..8..4...6..7.57.41.....2....3.. | autosolve |
| 359784261862531947741296538287659413635148729914327856493862175578413692126975384 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) A2: 2,8 G2: 4,9 H2: 4,9 G4: 4,6 G8: 6,9 I8: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,D5: 1.. / D4 = 1 => 8 pairs (_) / D5 = 1 => 6 pairs (_) I1,H3: 3.. / I1 = 3 => 0 pairs (X) / H3 = 3 => 7 pairs (_) F7,F8: 3.. / F7 = 3 => 8 pairs (_) / F8 = 3 => 13 pairs (_) C3,H3: 3.. / C3 = 3 => 0 pairs (X) / H3 = 3 => 7 pairs (_) C8,F8: 3.. / C8 = 3 => 8 pairs (_) / F8 = 3 => 13 pairs (_) A1,A4: 3.. / A1 = 3 => 7 pairs (_) / A4 = 3 => 0 pairs (X) I1,I4: 3.. / I1 = 3 => 0 pairs (X) / I4 = 3 => 7 pairs (_) G2,H2: 4.. / G2 = 4 => 5 pairs (_) / H2 = 4 => 0 pairs (*) H9,I9: 4.. / H9 = 4 => 0 pairs (X) / I9 = 4 => 7 pairs (_) G2,G4: 4.. / G2 = 4 => 5 pairs (_) / G4 = 4 => 0 pairs (*) I4,I9: 4.. / I4 = 4 => 0 pairs (X) / I9 = 4 => 7 pairs (_) C2,D2: 5.. / C2 = 5 => 7 pairs (_) / D2 = 5 => 15 pairs (_) D3,F3: 6.. / D3 = 6 => 8 pairs (_) / F3 = 6 => 0 pairs (*) D4,F6: 6.. / D4 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) C8,C9: 6.. / C8 = 6 => 0 pairs (X) / C9 = 6 => 7 pairs (_) F6,I6: 6.. / F6 = 6 => 8 pairs (_) / I6 = 6 => 0 pairs (*) C9,I9: 6.. / C9 = 6 => 7 pairs (_) / I9 = 6 => 0 pairs (X) D3,D4: 6.. / D3 = 6 => 8 pairs (_) / D4 = 6 => 0 pairs (*) F3,F6: 6.. / F3 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) G4,G8: 6.. / G4 = 6 => 5 pairs (_) / G8 = 6 => 0 pairs (*) D1,E1: 7.. / D1 = 7 => 6 pairs (_) / E1 = 7 => 0 pairs (X) E6,F6: 7.. / E6 = 7 => 7 pairs (_) / F6 = 7 => 0 pairs (*) D1,D9: 7.. / D1 = 7 => 6 pairs (_) / D9 = 7 => 0 pairs (X) F6,F9: 7.. / F6 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) H8,H9: 8.. / H8 = 8 => 6 pairs (_) / H9 = 8 => 0 pairs (*) G2,H2: 9.. / G2 = 9 => 0 pairs (*) / H2 = 9 => 0 pairs (X) A6,B6: 9.. / A6 = 9 => 9 pairs (_) / B6 = 9 => 16 pairs (_) B7,A9: 9.. / B7 = 9 => 9 pairs (_) / A9 = 9 => 16 pairs (_) D7,D9: 9.. / D7 = 9 => 16 pairs (_) / D9 = 9 => 9 pairs (_) G8,H8: 9.. / G8 = 9 => 5 pairs (_) / H8 = 9 => 0 pairs (*) B7,D7: 9.. / B7 = 9 => 9 pairs (_) / D7 = 9 => 16 pairs (_) A9,D9: 9.. / A9 = 9 => 16 pairs (_) / D9 = 9 => 9 pairs (_) A6,A9: 9.. / A6 = 9 => 9 pairs (_) / A9 = 9 => 16 pairs (_) B6,B7: 9.. / B6 = 9 => 16 pairs (_) / B7 = 9 => 9 pairs (_) G2,G8: 9.. / G2 = 9 => 0 pairs (*) / G8 = 9 => 0 pairs (X) H2,H8: 9.. / H2 = 9 => 5 pairs (_) / H8 = 9 => 0 pairs (*) * DURATION: 0:00:59.042953 START: 03:48:49.229231 END: 03:49:48.272184 2017-05-01 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,G2,G4,G8,H2,I8) * ..9..4.6..6..31..774..9...8..7..9...6...4.7.9..43..8..4...6..7.57.41.....2....3.. * PAIR A2: 2,8 BLK 1 A1: 2,8,1,3 # reduction candidate for 2,8 A1: 2,8 => CTR * .19754.63.65.31497743.9...83.7..96.46.214.7391943.68.5438962571576413982921..7346 A1: 1,3 # 7 pairs C2: 2,8,5 # reduction candidate for 2,8 C2: 2,8 # 15 pairs * PAIR A2: 2,8 ROW 2 D2: 2,8,5 # reduction candidate for 2,8 D2: 5 # 15 pairs D2: 2,8 # 7 pairs * PAIR A2: 2,8 COL A A4: 2,8,1,3 # reduction candidate for 2,8 A4: 2,8 # 10 pairs A4: 1,3 # 7 pairs * PAIR G4: 4,6 BLK 6 I4: 4,6,1,2,3,5 # reduction candidate for 4,6 I4: 4,6 => CTR * ..97.4563.65.314977436952183871.96.46...48739.943768..438962.7.576413982921..7346 I4: 1,2,3,5 # 7 pairs * PAIR I8: 2,6 COL I I4: 2,6,1,3,4,5 # reduction candidate for 2,6 I4: 2,6 => CTR * ..9..4.63.6..31..7743.9...83.7..9...6...4.739.943..8..43.962.7.57.413...926...314 I4: 1,3,4,5 # 6 pairs I6: 2,6,1,5 # reduction candidate for 2,6 I6: 2,6 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0022-base-pr-000.dot * REASONING * DIS # A1: 2,8 => CTR => A1: 1,3 * DIS # I4: 4,6 => CTR => I4: 1,2,3,5 * DIS # I4: 2,6 => CTR => I4: 1,3,4,5 * CNT 3 HDP CHAINS / 12 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,G2,G4,G8,H2,I8) * ..9..4.6..6..31..774..9...8..7..9...6...4.7.9..43..8..4...6..7.57.41.....2....3.. * PAIR A2: 2,8 BLK 1 A1: 2,8,1,3 # reduction candidate for 2,8 A1: 2,8 => CTR * .19754.63.65.31497743.9...83.7..96.46.214.7391943.68.5438962571576413982921..7346 C2: 2,8,5 # reduction candidate for 2,8 C2: 2,8 # 15 pairs * RESTART * PAIR A2: 2,8 BLK 1 C2: 2,8,5 # reduction candidate for 2,8 C2: 2,8 # 15 pairs C2: 5 # 8 pairs * PAIR A2: 2,8 ROW 2 D2: 2,8,5 # reduction candidate for 2,8 D2: 5 # 15 pairs D2: 2,8 # 8 pairs * PAIR A2: 2,8 COL A A4: 2,8,1,3 # reduction candidate for 2,8 A4: 1,3 # 12 pairs A4: 2,8 # 10 pairs * PAIR G4: 4,6 BLK 6 I4: 4,6,1,2,3,5 # reduction candidate for 4,6 I4: 4,6 => CTR * 159..4263862531..7743296..83.76294..6.5.4.7392943..8..43.962.7.57.413..292....3.. * PAIR I8: 2,6 COL I I6: 2,6,1,5 # reduction candidate for 2,6 I6: 2,6 # 10 pairs I6: 1,5 # 7 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,A2,C8,G2,G4,G8,H2,I8) * ..9..4.6..6..31..774..9...8..7..9...6...4.7.9..43..8..4...6..7.57.41.....26...3.4 * PAIR A1: 1,3 BLK 1 B1: 1,3,5,8 # reduction candidate for 1,3 B1: 1,3 # 17 pairs C3: 1,3,2,5 # reduction candidate for 1,3 C3: 1,3 # 14 pairs * PAIR A1: 1,3 ROW 1 I1: 1,3,2,5 # reduction candidate for 1,3 I1: 1,3 # 16 pairs I1: 2,5 # 9 pairs * PAIR A1: 1,3 COL A A4: 1,3,2,8 # reduction candidate for 1,3 A4: 1,3 => CTR * 3.97.4.6..65.3149774.695.38187..96436321487599.43768.14...63.7.573412986.26..7314 * PAIR RESTART * PAIR A2: 2,8 BLK 1 C2: 2,8,5 # reduction candidate for 2,8 C2: 2,8 # 20 pairs C2: 5 # 13 pairs * PAIR A2: 2,8 ROW 2 D2: 2,8,5 # reduction candidate for 2,8 D2: 5 # 20 pairs D2: 2,8 # 13 pairs * PAIR C8: 3,8 BLK 7 B7: 3,8,1,9 # reduction candidate for 3,8 B7: 3,8 => CTR * 3.9..4.6..6..31..774..9..38..7..9..36...4.7.91943..8..4.196..7.57.41..8.926...314 * RESTART * PAIR C8: 3,8 ROW 8 F8: 3,8,2 # reduction candidate for 3,8 F8: 3,8 => SOLVED * 359784261862531947741296538287659413635148729914327856493862175578413692126975384 * DURATION: 0:00:21.292007 START: 03:49:57.442381 END: 03:50:18.734388 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0022-base-pr-001.dot * REASONING * DIS # A1: 2,8 => CTR => A1: 1,3 * DIS A1: 1,3 # I4: 4,6 => CTR => I4: 1,2,3,5 * DIS A1: 1,3 + I4: 1,2,3,5 # A4: 1,3 => CTR => A4: 2,8 * DIS A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 # B7: 3,8 => CTR => B7: 1,9 * PRF A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 + B7: 1,9 # F8: 3,8 => SOL * STA A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 + B7: 1,9 + F8: 3,8 * CNT 5 HDP CHAINS / 22 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=22
Solution
position: 359784261862531947741296538287659413635148729914327856493862175578413692126975384 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 # A1: 2,8 => CTR => A1: 1,3 * INC # A1: 1,3 => UNS * INC # C2: 2,8 => UNS * INC # D2: 2,8 => UNS * INC # D2: 5 => UNS * INC # A4: 2,8 => UNS * INC # A4: 1,3 => UNS * DIS # I4: 4,6 => CTR => I4: 1,2,3,5 * INC # I4: 1,2,3,5 => UNS * DIS # I4: 2,6 => CTR => I4: 1,3,4,5 * INC # I4: 1,3,4,5 => UNS * INC # I6: 2,6 => UNS * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 2,8 => CTR => A1: 1,3 * INC A1: 1,3 # C2: 2,8 => UNS * INC A1: 1,3 # C2: 2,8 => UNS * INC A1: 1,3 # C2: 5 => UNS * INC A1: 1,3 # D2: 2,8 => UNS * INC A1: 1,3 # D2: 5 => UNS * INC A1: 1,3 # A4: 2,8 => UNS * INC A1: 1,3 # A4: 1,3 => UNS * DIS A1: 1,3 # I4: 4,6 => CTR => I4: 1,2,3,5 * INC A1: 1,3 + I4: 1,2,3,5 # I6: 2,6 => UNS * INC A1: 1,3 + I4: 1,2,3,5 # I6: 1,5 => UNS * INC A1: 1,3 + I4: 1,2,3,5 # B1: 1,3 => UNS * INC A1: 1,3 + I4: 1,2,3,5 # C3: 1,3 => UNS * INC A1: 1,3 + I4: 1,2,3,5 # I1: 1,3 => UNS * INC A1: 1,3 + I4: 1,2,3,5 # I1: 2,5 => UNS * DIS A1: 1,3 + I4: 1,2,3,5 # A4: 1,3 => CTR => A4: 2,8 * INC A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 # C2: 2,8 => UNS * INC A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 # C2: 5 => UNS * INC A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 # D2: 2,8 => UNS * INC A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 # D2: 5 => UNS * DIS A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 # B7: 3,8 => CTR => B7: 1,9 * PRF A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 + B7: 1,9 # F8: 3,8 => SOL * STA A1: 1,3 + I4: 1,2,3,5 + A4: 2,8 + B7: 1,9 + F8: 3,8 * CNT 22 HDP CHAINS / 22 HYP OPENED