Analysis of zz-www.sudokuwiki.org-0096-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=96
level: medium
position: ....43..95.........7...8.5..5.7..8...9..2..6...2..5.3..3.6...9.........41..85.... initial
Autosolve
position: ...543..95.........7...8.5..5.7..8...9.321.6...248593..3.6...9.....3...41..85.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C4: 3,4 => CTR => C4: 1 * DIS # H4: 1,2 => CTR => H4: 4 * DIS # I2: 1,2 => CTR => I2: 3,6,8 * DIS # I3: 1,2 => CTR => I3: 3,6 * DIS # I7: 1,2 => CTR => I7: 5,7,8 * DIS # G5: 4 => CTR => G5: 5,7 * DIS # I7: 5,7 => CTR => I7: 1,2,8 * DIS # H8: 2,7 => CTR => H8: 1,8 * DIS # F9: 2,7 => CTR => F9: 4,9 * CNT 9 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C4: 3,4 => CTR => C4: 1 * DIS C4: 1 # E2: 6,9 => CTR => E2: 1,7 * DIS C4: 1 + E2: 1,7 # F2: 6,9 => CTR => F2: 2,7 * DIS C4: 1 + E2: 1,7 + F2: 2,7 # I7: 5,7 => CTR => I7: 8 * PRF C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8 => SOL * STA C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8 * CNT 5 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....43..95.........7...8.5..5.7..8...9..2..6...2..5.3..3.6...9.........41..85.... | initial |
| ...543..95.........7...8.5..5.7..8...9.321.6...248593..3.6...9.....3...41..85.... | autosolve |
| 628543179513972486479168253351796842894321765762485931237614598985237614146859327 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A4: 3,4 A6: 6,7 B6: 1,6 E4: 6,9 F4: 6,9 I4: 1,2 I5: 5,7 I6: 1,7 E7: 1,7 H9: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C4,B6: 1.. / C4 = 1 => 14 pairs (_) / B6 = 1 => 0 pairs (X) E7,D8: 1.. / E7 = 1 => 11 pairs (_) / D8 = 1 => 13 pairs (_) B6,I6: 1.. / B6 = 1 => 0 pairs (X) / I6 = 1 => 14 pairs (_) H4,I4: 2.. / H4 = 2 => 0 pairs (X) / I4 = 2 => 10 pairs (_) A4,C4: 3.. / A4 = 3 => 10 pairs (_) / C4 = 3 => 0 pairs (X) G9,I9: 3.. / G9 = 3 => 10 pairs (_) / I9 = 3 => 10 pairs (_) A3,A4: 3.. / A3 = 3 => 0 pairs (X) / A4 = 3 => 10 pairs (_) H4,G5: 4.. / H4 = 4 => 14 pairs (_) / G5 = 4 => 0 pairs (X) F7,F9: 4.. / F7 = 4 => 10 pairs (_) / F9 = 4 => 0 pairs (X) B2,B9: 4.. / B2 = 4 => 0 pairs (X) / B9 = 4 => 10 pairs (_) H2,H4: 4.. / H2 = 4 => 0 pairs (X) / H4 = 4 => 14 pairs (_) G5,I5: 5.. / G5 = 5 => 0 pairs (X) / I5 = 5 => 10 pairs (_) C7,C8: 5.. / C7 = 5 => 13 pairs (_) / C8 = 5 => 10 pairs (_) C8,G8: 5.. / C8 = 5 => 10 pairs (_) / G8 = 5 => 13 pairs (_) I5,I7: 5.. / I5 = 5 => 10 pairs (_) / I7 = 5 => 0 pairs (X) A6,B6: 6.. / A6 = 6 => 0 pairs (X) / B6 = 6 => 14 pairs (_) E4,F4: 6.. / E4 = 6 => 0 pairs (X) / F4 = 6 => 9 pairs (_) F2,F4: 6.. / F2 = 6 => 0 pairs (X) / F4 = 6 => 9 pairs (_) E2,F2: 7.. / E2 = 7 => 11 pairs (_) / F2 = 7 => 13 pairs (_) G1,H1: 7.. / G1 = 7 => 11 pairs (_) / H1 = 7 => 11 pairs (_) A6,I6: 7.. / A6 = 7 => 14 pairs (_) / I6 = 7 => 0 pairs (X) E2,E7: 7.. / E2 = 7 => 11 pairs (_) / E7 = 7 => 13 pairs (_) A5,C5: 8.. / A5 = 8 => 12 pairs (_) / C5 = 8 => 12 pairs (_) I7,H8: 8.. / I7 = 8 => 10 pairs (_) / H8 = 8 => 15 pairs (_) I2,I7: 8.. / I2 = 8 => 15 pairs (_) / I7 = 8 => 10 pairs (_) E4,F4: 9.. / E4 = 9 => 9 pairs (_) / F4 = 9 => 0 pairs (X) C9,F9: 9.. / C9 = 9 => 12 pairs (_) / F9 = 9 => 13 pairs (_) A3,A8: 9.. / A3 = 9 => 12 pairs (_) / A8 = 9 => 13 pairs (_) * DURATION: 0:00:36.943553 START: 05:12:36.715349 END: 05:13:13.658902 2017-05-01 * CP COUNT: (28) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,E4,E7,F4,H9,I4,I5,I6) * ...543..95.........7...8.5..5.7..8...9.321.6...248593..3.6...9.....3...41..85.... * PAIR A4: 3,4 BLK 4 C4: 3,4,1 # reduction candidate for 3,4 C4: 3,4 => CTR * 8.1543..95......48.7...8.5..5.7968..79832146561248593723.6.4.9198.132.74147859.2. C4: 1 # 14 pairs * PAIR A4: 3,4 COL A A3: 3,4,2,6,9 # reduction candidate for 3,4 A3: 3,4 # 15 pairs A3: 2,6,9 # 10 pairs * PAIR A6: 6,7 COL A A8: 6,7,2,8,9 # reduction candidate for 6,7 A8: 6,7 # 15 pairs A8: 2,8,9 # 10 pairs * PAIR B6: 1,6 COL B B1: 1,6,2,8 # reduction candidate for 1,6 B1: 1,6 # 13 pairs B2: 1,6,2,4,8 # reduction candidate for 1,6 B2: 1,6 # 14 pairs * PAIR E4: 6,9 COL E E2: 6,9,1,7 # reduction candidate for 6,9 E2: 6,9 # 11 pairs E3: 6,9,1 # reduction candidate for 6,9 E3: 6,9 # 12 pairs * PAIR F4: 6,9 COL F F2: 6,9,2,7 # reduction candidate for 6,9 F2: 2,7 # 11 pairs F2: 6,9 # 10 pairs * PAIR I4: 1,2 BLK 6 H4: 1,2,4 # reduction candidate for 1,2 H4: 1,2 => CTR * 8.1543..95......48.7...8.5..5.7968..79832146561248593723.6.4.9198.132.74147859.2. H4: 4 # 14 pairs * PAIR I4: 1,2 COL I I2: 1,2,3,6,8 # reduction candidate for 1,2 I2: 1,2 => CTR * 26154378958.....4..7...8.5..5.7..8...9.321465612485937735614298.2.937514149852.7. I2: 3,6,8 # 10 pairs I3: 1,2,3,6 # reduction candidate for 1,2 I3: 1,2 => CTR * 26154378958.....4..7...8.5..5.7..8...9.321465612485937735614298.2.937514149852.7. I3: 3,6 # 11 pairs I7: 1,2,5,7,8 # reduction candidate for 1,2 I7: 1,2 => CTR * 28.543..956.....48.7..68.533547968...9.321465612485937.3.6.4.9..2..3..8414.852376 I7: 5,7,8 # 10 pairs * PAIR I5: 5,7 BLK 6 G5: 5,7,4 # reduction candidate for 5,7 G5: 4 => CTR * 8.1543..95......48.7...8.5..5.7968..79832146561248593723.6.4.9198.132.74147859.2. G5: 5,7 # 14 pairs * PAIR I5: 5,7 COL I I7: 5,7,1,2,8 # reduction candidate for 5,7 I7: 5,7 => CTR * .8654371951.....28.7...8.5..517..842.9.321.6.76248593183.6.429..2..3.18414.852.7. I7: 1,2,8 # 10 pairs * PAIR I6: 1,7 COL I I7: 1,7,2,5,8 # reduction candidate for 1,7 I7: 1,7 # 18 pairs I7: 2,5,8 # 10 pairs * PAIR E7: 1,7 ROW 7 G7: 1,7,2,5 # reduction candidate for 1,7 G7: 1,7 # 12 pairs I7: 1,7,2,5,8 # reduction candidate for 1,7 I7: 1,7 # 18 pairs * PAIR E7: 1,7 COL E E2: 1,7,6,9 # reduction candidate for 1,7 E2: 1,7 # 12 pairs E2: 6,9 # 11 pairs * PAIR H9: 2,7 BLK 9 G7: 2,7,1,5 # reduction candidate for 2,7 G7: 2,7 # 17 pairs I7: 2,7,1,5,8 # reduction candidate for 2,7 I7: 2,7 # 23 pairs G8: 2,7,1,5,6 # reduction candidate for 2,7 G8: 2,7 # 18 pairs H8: 2,7,1,8 # reduction candidate for 2,7 H8: 2,7 => CTR * 26154378958.....4..7...8.5..5.7..812.9.321465612485937735614.98....3...414.85.... H8: 1,8 # 11 pairs G9: 2,7,3,6 # reduction candidate for 2,7 G9: 2,7 # 17 pairs I9: 2,7,3,6 # reduction candidate for 2,7 I9: 2,7 # 21 pairs * PAIR H9: 2,7 ROW 9 F9: 2,7,4,9 # reduction candidate for 2,7 F9: 2,7 => CTR * ..6543..95.......897.218.5.3517..842498321.6.76248593183.674.9.6...3...414985.... F9: 4,9 # 11 pairs * PAIR H9: 2,7 COL H H1: 2,7,1,8 # reduction candidate for 2,7 H1: 2,7 # 12 pairs H1: 1,8 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0096-base-pr-000.dot * REASONING * DIS # C4: 3,4 => CTR => C4: 1 * DIS # H4: 1,2 => CTR => H4: 4 * DIS # I2: 1,2 => CTR => I2: 3,6,8 * DIS # I3: 1,2 => CTR => I3: 3,6 * DIS # I7: 1,2 => CTR => I7: 5,7,8 * DIS # G5: 4 => CTR => G5: 5,7 * DIS # I7: 5,7 => CTR => I7: 1,2,8 * DIS # H8: 2,7 => CTR => H8: 1,8 * DIS # F9: 2,7 => CTR => F9: 4,9 * CNT 9 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,E4,E7,F4,H9,I4,I5,I6) * ...543..95.........7...8.5..5.7..8...9.321.6...248593..3.6...9.....3...41..85.... * PAIR A4: 3,4 BLK 4 C4: 3,4,1 # reduction candidate for 3,4 C4: 3,4 => CTR * 8.1543..95......48.7...8.5..5.7968..79832146561248593723.6.4.9198.132.74147859.2. * PAIR E4: 6,9 COL E E2: 6,9,1,7 # reduction candidate for 6,9 E2: 6,9 => CTR * ...543..95...67..3.73.18.56351796842.9.32176.762485931.3567.198.8.13.5.41..85.... * RESTART * PAIR RESTART * PAIR F4: 6,9 COL F F2: 6,9,2,7 # reduction candidate for 6,9 F2: 6,9 => CTR * ...543..95.3.796.8974.68.53351796842498321.6.76248593183.61429.62.937.84149852376 * PAIR RESTART * PAIR I5: 5,7 COL I I7: 5,7,8 # reduction candidate for 5,7 I7: 5,7 => CTR * ...543..95.39....8.7..68.53351796842.9.321.6.76248593183.6.429..2.13..8414.852376 I7: 8 => SOLVED * 628543179513972486479168253351796842894321765762485931237614598985237614146859327 * DURATION: 0:00:08.987418 START: 05:13:44.071125 END: 05:13:53.058543 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0096-base-pr-001.dot * REASONING * DIS # C4: 3,4 => CTR => C4: 1 * DIS C4: 1 # E2: 6,9 => CTR => E2: 1,7 * DIS C4: 1 + E2: 1,7 # F2: 6,9 => CTR => F2: 2,7 * DIS C4: 1 + E2: 1,7 + F2: 2,7 # I7: 5,7 => CTR => I7: 8 * PRF C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8 => SOL * STA C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8 * CNT 5 HDP CHAINS / 4 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=96
Solution
position: 628543179513972486479168253351796842894321765762485931237614598985237614146859327 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 # C4: 3,4 => CTR => C4: 1 * INC # C4: 1 => UNS * INC # A3: 3,4 => UNS * INC # A3: 2,6,9 => UNS * INC # A8: 6,7 => UNS * INC # A8: 2,8,9 => UNS * INC # B1: 1,6 => UNS * INC # B2: 1,6 => UNS * INC # E2: 6,9 => UNS * INC # E3: 6,9 => UNS * INC # F2: 6,9 => UNS * INC # F2: 2,7 => UNS * DIS # H4: 1,2 => CTR => H4: 4 * INC # H4: 4 => UNS * DIS # I2: 1,2 => CTR => I2: 3,6,8 * INC # I2: 3,6,8 => UNS * DIS # I3: 1,2 => CTR => I3: 3,6 * INC # I3: 3,6 => UNS * DIS # I7: 1,2 => CTR => I7: 5,7,8 * INC # I7: 5,7,8 => UNS * INC # G5: 5,7 => UNS * DIS # G5: 4 => CTR => G5: 5,7 * DIS # I7: 5,7 => CTR => I7: 1,2,8 * INC # I7: 1,2,8 => UNS * INC # I7: 1,7 => UNS * INC # I7: 2,5,8 => UNS * INC # G7: 1,7 => UNS * INC # I7: 1,7 => UNS * INC # E2: 1,7 => UNS * INC # E2: 6,9 => UNS * INC # G7: 2,7 => UNS * INC # I7: 2,7 => UNS * INC # G8: 2,7 => UNS * DIS # H8: 2,7 => CTR => H8: 1,8 * INC # H8: 1,8 => UNS * INC # G9: 2,7 => UNS * INC # I9: 2,7 => UNS * DIS # F9: 2,7 => CTR => F9: 4,9 * INC # F9: 4,9 => UNS * INC # H1: 2,7 => UNS * INC # H1: 1,8 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C4: 3,4 => CTR => C4: 1 * DIS C4: 1 # E2: 6,9 => CTR => E2: 1,7 * DIS C4: 1 + E2: 1,7 # F2: 6,9 => CTR => F2: 2,7 * DIS C4: 1 + E2: 1,7 + F2: 2,7 # I7: 5,7 => CTR => I7: 8 * PRF C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8 => SOL * STA C4: 1 + E2: 1,7 + F2: 2,7 + I7: 8 * CNT 5 HDP CHAINS / 4 HYP OPENED