Analysis of zz-www.sudokuwiki.org-0043-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=43
level: medium
position: 62...4..51...6.4.2..8....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 initial
Autosolve
position: 62...4..51...6.4.2.48....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G5: 5,8 => CTR => G5: 1,9 * PRF # E9: 4 => SOL * DIS # C7: 6,9 => CTR => C7: 3,4,7 * PRF # C9: 6,9 => SOL * PRF # G9: 5,8 => SOL * DIS # B6: 6,9 => CTR => B6: 1,3,7,8 * PRF # E9: 4 => SOL * PRF # G9: 5,8 => SOL * CNT 8 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G5: 5,8 => CTR => G5: 1,9 * PRF G5: 1,9 # E9: 4 => SOL * STA G5: 1,9 + E9: 4 * CNT 2 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 62...4..51...6.4.2..8....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 | initial |
| 62...4..51...6.4.2.48....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 | autosolve |
| 629834175135967482748251396563419728412786953987523641354178269871692534296345817 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) I3: 1,6 E5: 5,8 B9: 6,9 F9: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,B6: 1.. / B5 = 1 => 4 pairs (_) / B6 = 1 => 0 pairs (X) D7,F7: 1.. / D7 = 1 => 14 pairs (_) / F7 = 1 => 5 pairs (_) D1,G1: 1.. / D1 = 1 => 12 pairs (_) / G1 = 1 => 16 pairs (_) B5,G5: 1.. / B5 = 1 => 4 pairs (_) / G5 = 1 => 0 pairs (X) F3,F7: 1.. / F3 = 1 => 14 pairs (_) / F7 = 1 => 5 pairs (_) I3,I6: 1.. / I3 = 1 => 12 pairs (_) / I6 = 1 => 5 pairs (_) D3,F3: 2.. / D3 = 2 => 8 pairs (_) / F3 = 2 => 10 pairs (_) C4,C5: 2.. / C4 = 2 => 5 pairs (_) / C5 = 2 => 10 pairs (_) H4,H5: 2.. / H4 = 2 => 10 pairs (_) / H5 = 2 => 5 pairs (_) D8,F8: 2.. / D8 = 2 => 10 pairs (_) / F8 = 2 => 8 pairs (_) C4,H4: 2.. / C4 = 2 => 5 pairs (_) / H4 = 2 => 10 pairs (_) C5,H5: 2.. / C5 = 2 => 10 pairs (_) / H5 = 2 => 5 pairs (_) D3,D8: 2.. / D3 = 2 => 8 pairs (_) / D8 = 2 => 10 pairs (_) F3,F8: 2.. / F3 = 2 => 10 pairs (_) / F8 = 2 => 8 pairs (_) E1,E3: 3.. / E1 = 3 => 7 pairs (_) / E3 = 3 => 6 pairs (_) F4,F6: 3.. / F4 = 3 => 4 pairs (_) / F6 = 3 => 4 pairs (_) D4,D6: 4.. / D4 = 4 => 4 pairs (_) / D6 = 4 => 5 pairs (_) H4,H6: 4.. / H4 = 4 => 5 pairs (_) / H6 = 4 => 4 pairs (_) C7,C9: 4.. / C7 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) E7,E9: 4.. / E7 = 4 => 13 pairs (_) / E9 = 4 => 0 pairs (*) D4,H4: 4.. / D4 = 4 => 4 pairs (_) / H4 = 4 => 5 pairs (_) D6,H6: 4.. / D6 = 4 => 5 pairs (_) / H6 = 4 => 4 pairs (_) C7,E7: 4.. / C7 = 4 => 0 pairs (*) / E7 = 4 => 0 pairs (X) C9,E9: 4.. / C9 = 4 => 13 pairs (_) / E9 = 4 => 0 pairs (*) C2,A3: 5.. / C2 = 5 => 7 pairs (_) / A3 = 5 => 6 pairs (_) G3,I3: 6.. / G3 = 6 => 12 pairs (_) / I3 = 6 => 5 pairs (_) D7,D8: 6.. / D7 = 6 => 9 pairs (_) / D8 = 6 => 10 pairs (_) B8,F8: 7.. / B8 = 7 => 8 pairs (_) / F8 = 7 => 13 pairs (_) I7,G9: 9.. / I7 = 9 => 10 pairs (_) / G9 = 9 => 14 pairs (_) C1,D1: 9.. / C1 = 9 => 10 pairs (_) / D1 = 9 => 19 pairs (_) * DURATION: 0:00:34.967288 START: 04:16:34.266264 END: 04:17:09.233552 2017-05-01 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,E5,F9,I3) * 62...4..51...6.4.2.48....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 * PAIR I3: 1,6 BLK 3 G3: 1,6,3,7 # reduction candidate for 1,6 G3: 3,7 # 16 pairs G3: 1,6 # 12 pairs * PAIR I3: 1,6 COL I I6: 1,6,8,9 # reduction candidate for 1,6 I6: 8,9 # 13 pairs I6: 1,6 # 7 pairs * PAIR E5: 5,8 BLK 5 D4: 5,8,4,9 # reduction candidate for 5,8 D4: 5,8 # 8 pairs F4: 5,8,3,9 # reduction candidate for 5,8 F4: 5,8 # 16 pairs D6: 5,8,4,9 # reduction candidate for 5,8 D6: 5,8 # 7 pairs F6: 5,8,3,9 # reduction candidate for 5,8 F6: 5,8 # 16 pairs * PAIR E5: 5,8 ROW 5 G5: 5,8,1,9 # reduction candidate for 5,8 G5: 5,8 => CTR * 62.9.41.5195867432.48...796..2.1...94197.6.23..6.29..195..4.2.88.1.9...42643..917 G5: 1,9 # 5 pairs H5: 5,8,2 # reduction candidate for 5,8 H5: 5,8 # 10 pairs * PAIR E5: 5,8 COL E E9: 5,8,4 # reduction candidate for 5,8 E9: 4 => SOLVED * 629834175135967482748251396563419728412786953987523641354178269871692534296345817 E9: 5,8 # 13 pairs * PAIR B9: 6,9 BLK 7 C7: 6,9,3,4,7 # reduction candidate for 6,9 C7: 6,9 => CTR * 62...4..51...6.4.2.48....96....1...841.7869.3.8..2...1.56147289871692..4294358617 C7: 3,4,7 # 4 pairs C9: 6,9,4 # reduction candidate for 6,9 C9: 6,9 => SOLVED * 629834175135967482748251396563419728412786953987523641354178269871692534296345817 C9: 4 # 13 pairs * PAIR B9: 6,9 ROW 9 G9: 6,9,5,8 # reduction candidate for 6,9 G9: 5,8 => SOLVED * 629834175135967482748251396563419728412786953987523641354178269871692534296345817 G9: 6,9 # 13 pairs * PAIR B9: 6,9 COL B B4: 6,9,3,7,8 # reduction candidate for 6,9 B4: 6,9 # 14 pairs B6: 6,9,1,3,7,8 # reduction candidate for 6,9 B6: 6,9 => CTR * 629134..5135.6.4.274825.691.8..1...641.7869.3.6..2.1.8.54.712.9871.9...429634..17 B6: 1,3,7,8 # 4 pairs * PAIR F9: 5,8 BLK 8 E9: 5,8,4 # reduction candidate for 5,8 E9: 4 => SOLVED * 629834175135967482748251396563419728412786953987523641354178269871692534296345817 E9: 5,8 # 13 pairs * PAIR F9: 5,8 ROW 9 G9: 5,8,6,9 # reduction candidate for 5,8 G9: 5,8 => SOLVED * 629834175135967482748251396563419728412786953987523641354178269871692534296345817 G9: 6,9 # 13 pairs * PAIR F9: 5,8 COL F F2: 5,8,7,9 # reduction candidate for 5,8 F2: 5,8 # 9 pairs F4: 5,8,3,9 # reduction candidate for 5,8 F4: 5,8 # 16 pairs F6: 5,8,3,9 # reduction candidate for 5,8 F6: 5,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0043-base-pr-000.dot * REASONING * DIS # G5: 5,8 => CTR => G5: 1,9 * PRF # E9: 4 => SOL * DIS # C7: 6,9 => CTR => C7: 3,4,7 * PRF # C9: 6,9 => SOL * PRF # G9: 5,8 => SOL * DIS # B6: 6,9 => CTR => B6: 1,3,7,8 * PRF # E9: 4 => SOL * PRF # G9: 5,8 => SOL * CNT 8 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,E5,F9,I3) * 62...4..51...6.4.2.48....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 * PAIR I3: 1,6 BLK 3 G3: 1,6,3,7 # reduction candidate for 1,6 G3: 3,7 # 16 pairs G3: 1,6 # 12 pairs * PAIR I3: 1,6 COL I I6: 1,6,8,9 # reduction candidate for 1,6 I6: 8,9 # 13 pairs I6: 1,6 # 7 pairs * PAIR E5: 5,8 BLK 5 D4: 5,8,4,9 # reduction candidate for 5,8 D4: 5,8 # 8 pairs F4: 5,8,3,9 # reduction candidate for 5,8 F4: 5,8 # 16 pairs D6: 5,8,4,9 # reduction candidate for 5,8 D6: 5,8 # 7 pairs F6: 5,8,3,9 # reduction candidate for 5,8 F6: 5,8 # 16 pairs * PAIR E5: 5,8 ROW 5 G5: 5,8,1,9 # reduction candidate for 5,8 G5: 5,8 => CTR * 62.9.41.5195867432.48...796..2.1...94197.6.23..6.29..195..4.2.88.1.9...42643..917 H5: 5,8,2 # reduction candidate for 5,8 H5: 5,8 # 10 pairs * RESTART * PAIR E5: 5,8 ROW 5 H5: 5,8,2 # reduction candidate for 5,8 H5: 5,8 # 10 pairs H5: 2 # 6 pairs * PAIR E5: 5,8 COL E E9: 5,8,4 # reduction candidate for 5,8 E9: 4 => SOLVED * 629834175135967482748251396563419728412786953987523641354178269871692534296345817 * DURATION: 0:00:10.758458 START: 04:17:31.669507 END: 04:17:42.427965 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0043-base-pr-001.dot * REASONING * DIS # G5: 5,8 => CTR => G5: 1,9 * PRF G5: 1,9 # E9: 4 => SOL * STA G5: 1,9 + E9: 4 * CNT 2 HDP CHAINS / 14 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=43
Solution
position: 629834175135967482748251396563419728412786953987523641354178269871692534296345817 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 # G3: 1,6 => UNS * INC # G3: 3,7 => UNS * INC # I6: 1,6 => UNS * INC # I6: 8,9 => UNS * INC # D4: 5,8 => UNS * INC # F4: 5,8 => UNS * INC # D6: 5,8 => UNS * INC # F6: 5,8 => UNS * DIS # G5: 5,8 => CTR => G5: 1,9 * INC # G5: 1,9 => UNS * INC # H5: 5,8 => UNS * INC # E9: 5,8 => UNS * PRF # E9: 4 => SOL * DIS # C7: 6,9 => CTR => C7: 3,4,7 * INC # C7: 3,4,7 => UNS * PRF # C9: 6,9 => SOL * INC # C9: 4 => UNS * INC # G9: 6,9 => UNS * PRF # G9: 5,8 => SOL * INC # B4: 6,9 => UNS * DIS # B6: 6,9 => CTR => B6: 1,3,7,8 * INC # B6: 1,3,7,8 => UNS * INC # E9: 5,8 => UNS * PRF # E9: 4 => SOL * PRF # G9: 5,8 => SOL * INC # G9: 6,9 => UNS * INC # F2: 5,8 => UNS * INC # F4: 5,8 => UNS * INC # F6: 5,8 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 1,6 => UNS * INC # G3: 3,7 => UNS * INC # I6: 1,6 => UNS * INC # I6: 8,9 => UNS * INC # D4: 5,8 => UNS * INC # F4: 5,8 => UNS * INC # D6: 5,8 => UNS * INC # F6: 5,8 => UNS * DIS # G5: 5,8 => CTR => G5: 1,9 * INC G5: 1,9 # H5: 5,8 => UNS * INC G5: 1,9 # H5: 5,8 => UNS * INC G5: 1,9 # H5: 2 => UNS * INC G5: 1,9 # E9: 5,8 => UNS * PRF G5: 1,9 # E9: 4 => SOL * STA G5: 1,9 + E9: 4 * CNT 14 HDP CHAINS / 14 HYP OPENED