Analysis of zz-www.sudokuwiki.org-0105-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=105
level: medium
position: ..4..58..6.....9...8.2...1.....63.7...37.82...7.41.....4...7.2...9.....3..85..7.. initial
Autosolve
position: ..4..58..6.....9...8.2...1....963.7...37582...7.412....4...7.2.7.9.....3..85..7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G6: 5,6 => SOL * CNT 1 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G6: 5,6 => SOL * STA G6: 5,6 * CNT 1 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4..58..6.....9...8.2...1.....63.7...37.82...7.41.....4...7.2...9.....3..85..7.. | initial |
| ..4..58..6.....9...8.2...1....963.7...37582...7.412....4...7.2.7.9.....3..85..7.. | autosolve |
| 194375862632841957587296314821963475463758291975412638346187529759624183218539746 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) C3: 5,7 F2: 1,4 H1: 3,6 C6: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I2: 2.. / I1 = 2 => 5 pairs (_) / I2 = 2 => 6 pairs (_) E8,E9: 2.. / E8 = 2 => 4 pairs (_) / E9 = 2 => 11 pairs (_) B8,E8: 2.. / B8 = 2 => 11 pairs (_) / E8 = 2 => 4 pairs (_) C2,C4: 2.. / C2 = 2 => 5 pairs (_) / C4 = 2 => 5 pairs (_) G6,H6: 3.. / G6 = 3 => 4 pairs (_) / H6 = 3 => 0 pairs (*) G3,G6: 3.. / G3 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) A4,A5: 4.. / A4 = 4 => 9 pairs (_) / A5 = 4 => 5 pairs (_) D1,F3: 6.. / D1 = 6 => 8 pairs (_) / F3 = 6 => 13 pairs (_) B5,C6: 6.. / B5 = 6 => 16 pairs (_) / C6 = 6 => 6 pairs (_) C6,C7: 6.. / C6 = 6 => 6 pairs (_) / C7 = 6 => 16 pairs (_) C2,C3: 7.. / C2 = 7 => 9 pairs (_) / C3 = 7 => 5 pairs (_) E1,I1: 7.. / E1 = 7 => 6 pairs (_) / I1 = 7 => 6 pairs (_) D2,E2: 8.. / D2 = 8 => 7 pairs (_) / E2 = 8 => 7 pairs (_) A4,A6: 8.. / A4 = 8 => 6 pairs (_) / A6 = 8 => 7 pairs (_) I7,H8: 8.. / I7 = 8 => 13 pairs (_) / H8 = 8 => 6 pairs (_) A4,I4: 8.. / A4 = 8 => 6 pairs (_) / I4 = 8 => 7 pairs (_) H6,H8: 8.. / H6 = 8 => 13 pairs (_) / H8 = 8 => 6 pairs (_) E7,I7: 9.. / E7 = 9 => 9 pairs (_) / I7 = 9 => 10 pairs (_) B1,B5: 9.. / B1 = 9 => 10 pairs (_) / B5 = 9 => 8 pairs (_) F3,F9: 9.. / F3 = 9 => 9 pairs (_) / F9 = 9 => 11 pairs (_) * DURATION: 0:00:21.632143 START: 05:21:06.653067 END: 05:21:28.285210 2017-05-01 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C6,F2,H1) * ..4..58..6.....9...8.2...1....963.7...37582...7.412....4...7.2.7.9.....3..85..7.. * PAIR C3: 5,7 BLK 1 C2: 5,7,1,2 # reduction candidate for 5,7 C2: 5,7 # 11 pairs C2: 1,2 # 6 pairs * PAIR C3: 5,7 ROW 3 I3: 5,7,4,6 # reduction candidate for 5,7 I3: 4,6 # 7 pairs I3: 5,7 # 6 pairs * PAIR F2: 1,4 COL F F8: 1,4,6 # reduction candidate for 1,4 F8: 1,4 # 7 pairs F9: 1,4,6,9 # reduction candidate for 1,4 F9: 1,4 # 10 pairs * PAIR H1: 3,6 BLK 3 G3: 3,6,4,5 # reduction candidate for 3,6 G3: 3,6 # 7 pairs G3: 4,5 # 6 pairs * PAIR H1: 3,6 ROW 1 D1: 3,6,1 # reduction candidate for 3,6 D1: 1 # 16 pairs D1: 3,6 # 7 pairs * PAIR H1: 3,6 COL H H6: 3,6,5,8,9 # reduction candidate for 3,6 H6: 3,6 # 11 pairs H6: 5,8,9 # 4 pairs * PAIR C6: 5,6 ROW 6 G6: 5,6,3 # reduction candidate for 5,6 G6: 5,6 => SOLVED * 194375862632841957587296314821963475463758291975412638346187529759624183218539746 G6: 3 # 4 pairs H6: 5,6,3,8,9 # reduction candidate for 5,6 H6: 5,6 # 9 pairs I6: 5,6,8,9 # reduction candidate for 5,6 I6: 5,6 # 7 pairs * PAIR C6: 5,6 COL C C7: 5,6,1 # reduction candidate for 5,6 C7: 1 # 9 pairs C7: 5,6 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0105-base-pr-000.dot * REASONING * PRF # G6: 5,6 => SOL * CNT 1 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C6,F2,H1) * ..4..58..6.....9...8.2...1....963.7...37582...7.412....4...7.2.7.9.....3..85..7.. * PAIR C3: 5,7 BLK 1 C2: 5,7,1,2 # reduction candidate for 5,7 C2: 5,7 # 11 pairs C2: 1,2 # 6 pairs * PAIR C3: 5,7 ROW 3 I3: 5,7,4,6 # reduction candidate for 5,7 I3: 4,6 # 7 pairs I3: 5,7 # 6 pairs * PAIR F2: 1,4 COL F F8: 1,4,6 # reduction candidate for 1,4 F8: 1,4 # 7 pairs F9: 1,4,6,9 # reduction candidate for 1,4 F9: 1,4 # 10 pairs * PAIR H1: 3,6 BLK 3 G3: 3,6,4,5 # reduction candidate for 3,6 G3: 3,6 # 7 pairs G3: 4,5 # 6 pairs * PAIR H1: 3,6 ROW 1 D1: 3,6,1 # reduction candidate for 3,6 D1: 1 # 16 pairs D1: 3,6 # 7 pairs * PAIR H1: 3,6 COL H H6: 3,6,5,8,9 # reduction candidate for 3,6 H6: 3,6 # 11 pairs H6: 5,8,9 # 4 pairs * PAIR C6: 5,6 ROW 6 G6: 5,6,3 # reduction candidate for 5,6 G6: 5,6 => SOLVED * 194375862632841957587296314821963475463758291975412638346187529759624183218539746 * DURATION: 0:00:09.195396 START: 05:21:39.726085 END: 05:21:48.921481 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0105-base-pr-001.dot * REASONING * PRF # G6: 5,6 => SOL * STA G6: 5,6 * CNT 1 HDP CHAINS / 13 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=105
Solution
position: 194375862632841957587296314821963475463758291975412638346187529759624183218539746 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 # C2: 5,7 => UNS * INC # C2: 1,2 => UNS * INC # I3: 5,7 => UNS * INC # I3: 4,6 => UNS * INC # F8: 1,4 => UNS * INC # F9: 1,4 => UNS * INC # G3: 3,6 => UNS * INC # G3: 4,5 => UNS * INC # D1: 3,6 => UNS * INC # D1: 1 => UNS * INC # H6: 3,6 => UNS * INC # H6: 5,8,9 => UNS * PRF # G6: 5,6 => SOL * INC # G6: 3 => UNS * INC # H6: 5,6 => UNS * INC # I6: 5,6 => UNS * INC # C7: 5,6 => UNS * INC # C7: 1 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 5,7 => UNS * INC # C2: 1,2 => UNS * INC # I3: 5,7 => UNS * INC # I3: 4,6 => UNS * INC # F8: 1,4 => UNS * INC # F9: 1,4 => UNS * INC # G3: 3,6 => UNS * INC # G3: 4,5 => UNS * INC # D1: 3,6 => UNS * INC # D1: 1 => UNS * INC # H6: 3,6 => UNS * INC # H6: 5,8,9 => UNS * PRF # G6: 5,6 => SOL * STA G6: 5,6 * CNT 13 HDP CHAINS / 13 HYP OPENED