Analysis of zz-www.sudokuwiki.org-0056-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=56
level: hard
position: 8.5.....6.1......2.26.1.5...6.4.1.....8...7.....5.8.6...2.4.13.5......8.9.....2.7 initial
Autosolve
position: 8.5....16.1......2.26.1.5...6.4.1....58.6.7.....5.8.6.6.2.4.13.5.....68.9.....2.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D7: 9 => CTR => D7: 7,8 * DIS # F7: 7 => CTR => F7: 5,9 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D7: 9 => CTR => D7: 7,8 * STA D7: 7,8 * CNT 1 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 8.5....16.1......2.26.1.5...6.4.1....58.6.7.....5.8.6.6.2.4.13.5.....68.9.....2.7 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:11.855977
The following important HDP chains were detected:
* DIS # D2: 7,8 # B1: 4,7 => CTR => B1: 3,9 * PRF # D2: 7,8 + B1: 3,9 => SOL * STA D2: 7,8 * CNT 2 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8.5.....6.1......2.26.1.5...6.4.1.....8...7.....5.8.6...2.4.13.5......8.9.....2.7 | initial |
| 8.5....16.1......2.26.1.5...6.4.1....58.6.7.....5.8.6.6.2.4.13.5.....68.9.....2.7 | autosolve |
| 8.5....16.1......2.26.1.5...6.4.1....58.6.7.....5.8.6.6.2.4.13.5.....68.9.....2.7 | pair_reduction |
| 895327416417856392326914578769431825158269743234578961682745139573192684941683257 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (6) E2: 5,8 B7: 7,8 E9: 5,8 I7: 5,9 I8: 4,9 H9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,A6: 1.. / A5 = 1 => 14 pairs (_) / A6 = 1 => 17 pairs (_) I5,I6: 1.. / I5 = 1 => 17 pairs (_) / I6 = 1 => 14 pairs (_) C8,C9: 1.. / C8 = 1 => 8 pairs (_) / C9 = 1 => 6 pairs (_) D8,D9: 1.. / D8 = 1 => 6 pairs (_) / D9 = 1 => 8 pairs (_) A5,I5: 1.. / A5 = 1 => 14 pairs (_) / I5 = 1 => 17 pairs (_) A6,I6: 1.. / A6 = 1 => 17 pairs (_) / I6 = 1 => 14 pairs (_) C8,D8: 1.. / C8 = 1 => 8 pairs (_) / D8 = 1 => 6 pairs (_) C9,D9: 1.. / C9 = 1 => 6 pairs (_) / D9 = 1 => 8 pairs (_) H4,H5: 2.. / H4 = 2 => 0 pairs (*) / H5 = 2 => 0 pairs (X) A6,E6: 2.. / A6 = 2 => 16 pairs (_) / E6 = 2 => 14 pairs (_) I8,H9: 4.. / I8 = 4 => 12 pairs (_) / H9 = 4 => 0 pairs (X) E2,F2: 5.. / E2 = 5 => 5 pairs (_) / F2 = 5 => 0 pairs (X) H4,I4: 5.. / H4 = 5 => 0 pairs (X) / I4 = 5 => 12 pairs (_) I7,H9: 5.. / I7 = 5 => 0 pairs (X) / H9 = 5 => 12 pairs (_) F7,I7: 5.. / F7 = 5 => 12 pairs (_) / I7 = 5 => 0 pairs (X) E2,E9: 5.. / E2 = 5 => 5 pairs (_) / E9 = 5 => 0 pairs (X) H4,H9: 5.. / H4 = 5 => 0 pairs (X) / H9 = 5 => 12 pairs (_) I4,I7: 5.. / I4 = 5 => 12 pairs (_) / I7 = 5 => 0 pairs (X) D2,F2: 6.. / D2 = 6 => 6 pairs (_) / F2 = 6 => 6 pairs (_) D9,F9: 6.. / D9 = 6 => 6 pairs (_) / F9 = 6 => 6 pairs (_) D2,D9: 6.. / D2 = 6 => 6 pairs (_) / D9 = 6 => 6 pairs (_) F2,F9: 6.. / F2 = 6 => 6 pairs (_) / F9 = 6 => 6 pairs (_) H2,H3: 7.. / H2 = 7 => 8 pairs (_) / H3 = 7 => 9 pairs (_) E4,E6: 7.. / E4 = 7 => 8 pairs (_) / E6 = 7 => 16 pairs (_) G2,I3: 8.. / G2 = 8 => 0 pairs (X) / I3 = 8 => 10 pairs (_) G4,I4: 8.. / G4 = 8 => 10 pairs (_) / I4 = 8 => 0 pairs (X) B7,B9: 8.. / B7 = 8 => 7 pairs (_) / B9 = 8 => 0 pairs (X) D3,I3: 8.. / D3 = 8 => 0 pairs (X) / I3 = 8 => 10 pairs (_) B7,D7: 8.. / B7 = 8 => 7 pairs (_) / D7 = 8 => 0 pairs (X) E2,E9: 8.. / E2 = 8 => 0 pairs (X) / E9 = 8 => 5 pairs (_) G2,G4: 8.. / G2 = 8 => 0 pairs (X) / G4 = 8 => 10 pairs (_) I3,I4: 8.. / I3 = 8 => 10 pairs (_) / I4 = 8 => 0 pairs (X) B1,C2: 9.. / B1 = 9 => 8 pairs (_) / C2 = 9 => 16 pairs (_) I7,I8: 9.. / I7 = 9 => 12 pairs (_) / I8 = 9 => 0 pairs (X) B1,B6: 9.. / B1 = 9 => 8 pairs (_) / B6 = 9 => 16 pairs (_) * DURATION: 0:00:58.147961 START: 18:37:41.019863 END: 18:38:39.167824 2017-04-30 * CP COUNT: (35) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:11.747147 START: 18:38:52.252031 END: 18:39:03.999178 2017-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0056-base-pr-002.dot * REASONING * DIS # D2: 7,8 # B1: 4,7 => CTR => B1: 3,9 * PRF # D2: 7,8 + B1: 3,9 => SOL * STA D2: 7,8 * CNT 2 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=56
Solution
position: 895327416417856392326914578769431825158269743234578961682745139573192684941683257 solved
See section Deep 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 # D7: 7,8 => UNS * DIS # D7: 9 => CTR => D7: 7,8 * INC # F7: 5,9 => UNS * DIS # F7: 7 => CTR => F7: 5,9 * CNT 4 HDP CHAINS / 4 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D7: 7,8 => UNS * DIS # D7: 9 => CTR => D7: 7,8 * INC D7: 7,8 # D2: 7,8 => UNS * INC D7: 7,8 # D3: 7,8 => UNS * INC D7: 7,8 # F2: 5,9 => UNS * INC D7: 7,8 # F2: 3,4,6,7 => UNS * STA D7: 7,8 * CNT 6 HDP CHAINS / 6 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 7,8 => UNS * INC # D3: 7,8 => UNS * INC # F2: 5,9 => UNS * INC # F2: 3,4,6,7 => UNS * DIS # D2: 7,8 # B1: 4,7 => CTR => B1: 3,9 * PRF # D2: 7,8 + B1: 3,9 => SOL * STA D2: 7,8 * CNT 6 HDP CHAINS / 6 HYP OPENED