Analysis of zz-www.sudokuwiki.org-0055-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=55
level: hard
position: ...7..4.....49.21......1.78..5....6..7.8.2.5..3....1..45.6......16.34.....9..7... initial
Autosolve
position: ...7..4.....49.21......1.78..5....6..7.8.2.5..3....1..45.6......16.34.....9..7... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 3,9 => CTR => A1: 1,2,5,8 * CNT 1 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 3,9 => CTR => A1: 1,2,5,8 * STA A1: 1,2,5,8 * CNT 1 HDP CHAINS / 63 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: ...7..4.....49.21......1.78..5....6..7.8.2.5..3....1..45.6......16.34.....9..7... pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:35.269807
The following important HDP chains were detected:
* PRF # B1: 6,8 # C7: 8 => SOL * STA # B1: 6,8 + C7: 8 * CNT 1 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...7..4.....49.21......1.78..5....6..7.8.2.5..3....1..45.6......16.34.....9..7... | initial |
| ...7..4.....49.21......1.78..5....6..7.8.2.5..3....1..45.6......16.34.....9..7... | autosolve |
| ...7..4.....49.21......1.78..5....6..7.8.2.5..3....1..45.6......16.34.....9..7... | pair_reduction |
| 183725496567498213942361578295173864671842359834956127458619732716234985329587641 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (8) B2: 6,8 H1: 3,9 C5: 1,4 F4: 3,9 D6: 5,9 G5: 3,9 B9: 2,8 F7: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 1.. / A1 = 1 => 9 pairs (_) / C1 = 1 => 16 pairs (_) I7,I9: 1.. / I7 = 1 => 9 pairs (_) / I9 = 1 => 15 pairs (_) E7,I7: 1.. / E7 = 1 => 15 pairs (_) / I7 = 1 => 9 pairs (_) C1,C5: 1.. / C1 = 1 => 16 pairs (_) / C5 = 1 => 9 pairs (_) D4,D9: 1.. / D4 = 1 => 12 pairs (_) / D9 = 1 => 16 pairs (_) D4,F4: 3.. / D4 = 3 => 17 pairs (_) / F4 = 3 => 10 pairs (_) G5,I5: 3.. / G5 = 3 => 8 pairs (_) / I5 = 3 => 12 pairs (_) C7,A9: 3.. / C7 = 3 => 18 pairs (_) / A9 = 3 => 8 pairs (_) D3,D4: 3.. / D3 = 3 => 10 pairs (_) / D4 = 3 => 17 pairs (_) B3,C3: 4.. / B3 = 4 => 9 pairs (_) / C3 = 4 => 11 pairs (_) H9,I9: 4.. / H9 = 4 => 8 pairs (_) / I9 = 4 => 18 pairs (_) B3,B4: 4.. / B3 = 4 => 9 pairs (_) / B4 = 4 => 11 pairs (_) H6,H9: 4.. / H6 = 4 => 18 pairs (_) / H9 = 4 => 8 pairs (_) A5,A6: 6.. / A5 = 6 => 11 pairs (_) / A6 = 6 => 15 pairs (_) G9,I9: 6.. / G9 = 6 => 8 pairs (_) / I9 = 6 => 13 pairs (_) A5,E5: 6.. / A5 = 6 => 11 pairs (_) / E5 = 6 => 15 pairs (_) G3,G9: 6.. / G3 = 6 => 13 pairs (_) / G9 = 6 => 8 pairs (_) A2,C2: 7.. / A2 = 7 => 10 pairs (_) / C2 = 7 => 8 pairs (_) E4,E6: 7.. / E4 = 7 => 9 pairs (_) / E6 = 7 => 9 pairs (_) C7,A8: 7.. / C7 = 7 => 10 pairs (_) / A8 = 7 => 8 pairs (_) E6,I6: 7.. / E6 = 7 => 9 pairs (_) / I6 = 7 => 9 pairs (_) A2,A8: 7.. / A2 = 7 => 10 pairs (_) / A8 = 7 => 8 pairs (_) C2,C7: 7.. / C2 = 7 => 8 pairs (_) / C7 = 7 => 10 pairs (_) G4,H6: 8.. / G4 = 8 => 8 pairs (_) / H6 = 8 => 11 pairs (_) F7,D8: 9.. / F7 = 9 => 11 pairs (_) / D8 = 9 => 14 pairs (_) * DURATION: 0:00:26.874199 START: 18:35:20.484109 END: 18:35:47.358308 2017-04-30 * CP COUNT: (25) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:34.968405 START: 18:36:50.479162 END: 18:37:25.447567 2017-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0055-base-pr-002.dot * REASONING * PRF # B1: 6,8 # C7: 8 => SOL * STA # B1: 6,8 + C7: 8 * CNT 1 HDP CHAINS / 38 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=55
Solution
position: 183725496567498213942361578295173864671842359834956127458619732716234985329587641 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 # B1: 6,8 => UNS * INC # B1: 2,9 => UNS * INC # F2: 6,8 => UNS * INC # F2: 3,5 => UNS * INC # I1: 3,9 => UNS * INC # G3: 3,9 => UNS * DIS # A1: 3,9 => CTR => A1: 1,2,5,8 * INC # A1: 1,2,5,8 => UNS * INC # H7: 3,9 => UNS * INC # H7: 2,8 => UNS * INC # E5: 1,4 => UNS * INC # E5: 6 => UNS * INC # D4: 3,9 => UNS * INC # D4: 1 => UNS * INC # F6: 5,9 => UNS * INC # F6: 6 => UNS * INC # D8: 5,9 => UNS * INC # D8: 2 => UNS * INC # I5: 3,9 => UNS * INC # I5: 4 => UNS * INC # G3: 3,9 => UNS * INC # G7: 3,9 => UNS * INC # C7: 2,8 => UNS * INC # A8: 2,8 => UNS * INC # A9: 2,8 => UNS * INC # E9: 2,8 => UNS * INC # H9: 2,8 => UNS * INC # B1: 2,8 => UNS * INC # B4: 2,8 => UNS * INC # G7: 8,9 => UNS * INC # H7: 8,9 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 6,8 => UNS * INC # B1: 2,9 => UNS * INC # F2: 6,8 => UNS * INC # F2: 3,5 => UNS * INC # I1: 3,9 => UNS * INC # G3: 3,9 => UNS * DIS # A1: 3,9 => CTR => A1: 1,2,5,8 * INC A1: 1,2,5,8 # H7: 3,9 => UNS * INC A1: 1,2,5,8 # H7: 2,8 => UNS * INC A1: 1,2,5,8 # I1: 3,9 => UNS * INC A1: 1,2,5,8 # G3: 3,9 => UNS * INC A1: 1,2,5,8 # H7: 3,9 => UNS * INC A1: 1,2,5,8 # H7: 2,8 => UNS * INC A1: 1,2,5,8 # E5: 1,4 => UNS * INC A1: 1,2,5,8 # E5: 6 => UNS * INC A1: 1,2,5,8 # D4: 3,9 => UNS * INC A1: 1,2,5,8 # D4: 1 => UNS * INC A1: 1,2,5,8 # F6: 5,9 => UNS * INC A1: 1,2,5,8 # F6: 6 => UNS * INC A1: 1,2,5,8 # D8: 5,9 => UNS * INC A1: 1,2,5,8 # D8: 2 => UNS * INC A1: 1,2,5,8 # I5: 3,9 => UNS * INC A1: 1,2,5,8 # I5: 4 => UNS * INC A1: 1,2,5,8 # G3: 3,9 => UNS * INC A1: 1,2,5,8 # G7: 3,9 => UNS * INC A1: 1,2,5,8 # C7: 2,8 => UNS * INC A1: 1,2,5,8 # A8: 2,8 => UNS * INC A1: 1,2,5,8 # A9: 2,8 => UNS * INC A1: 1,2,5,8 # E9: 2,8 => UNS * INC A1: 1,2,5,8 # H9: 2,8 => UNS * INC A1: 1,2,5,8 # B1: 2,8 => UNS * INC A1: 1,2,5,8 # B4: 2,8 => UNS * INC A1: 1,2,5,8 # G7: 8,9 => UNS * INC A1: 1,2,5,8 # H7: 8,9 => UNS * INC A1: 1,2,5,8 # B1: 6,8 => UNS * INC A1: 1,2,5,8 # B1: 2,9 => UNS * INC A1: 1,2,5,8 # F2: 6,8 => UNS * INC A1: 1,2,5,8 # F2: 3,5 => UNS * INC A1: 1,2,5,8 # I1: 3,9 => UNS * INC A1: 1,2,5,8 # G3: 3,9 => UNS * INC A1: 1,2,5,8 # H7: 3,9 => UNS * INC A1: 1,2,5,8 # H7: 2,8 => UNS * INC A1: 1,2,5,8 # E5: 1,4 => UNS * INC A1: 1,2,5,8 # E5: 6 => UNS * INC A1: 1,2,5,8 # D4: 3,9 => UNS * INC A1: 1,2,5,8 # D4: 1 => UNS * INC A1: 1,2,5,8 # F6: 5,9 => UNS * INC A1: 1,2,5,8 # F6: 6 => UNS * INC A1: 1,2,5,8 # D8: 5,9 => UNS * INC A1: 1,2,5,8 # D8: 2 => UNS * INC A1: 1,2,5,8 # I5: 3,9 => UNS * INC A1: 1,2,5,8 # I5: 4 => UNS * INC A1: 1,2,5,8 # G3: 3,9 => UNS * INC A1: 1,2,5,8 # G7: 3,9 => UNS * INC A1: 1,2,5,8 # C7: 2,8 => UNS * INC A1: 1,2,5,8 # A8: 2,8 => UNS * INC A1: 1,2,5,8 # A9: 2,8 => UNS * INC A1: 1,2,5,8 # E9: 2,8 => UNS * INC A1: 1,2,5,8 # H9: 2,8 => UNS * INC A1: 1,2,5,8 # B1: 2,8 => UNS * INC A1: 1,2,5,8 # B4: 2,8 => UNS * INC A1: 1,2,5,8 # G7: 8,9 => UNS * INC A1: 1,2,5,8 # H7: 8,9 => UNS * STA A1: 1,2,5,8 * CNT 63 HDP CHAINS / 63 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 6,8 => UNS * INC # B1: 2,9 => UNS * INC # F2: 6,8 => UNS * INC # F2: 3,5 => UNS * INC # I1: 3,9 => UNS * INC # G3: 3,9 => UNS * INC # H7: 3,9 => UNS * INC # H7: 2,8 => UNS * INC # E5: 1,4 => UNS * INC # E5: 6 => UNS * INC # D4: 3,9 => UNS * INC # D4: 1 => UNS * INC # F6: 5,9 => UNS * INC # F6: 6 => UNS * INC # D8: 5,9 => UNS * INC # D8: 2 => UNS * INC # I5: 3,9 => UNS * INC # I5: 4 => UNS * INC # G3: 3,9 => UNS * INC # G7: 3,9 => UNS * INC # C7: 2,8 => UNS * INC # A8: 2,8 => UNS * INC # A9: 2,8 => UNS * INC # E9: 2,8 => UNS * INC # H9: 2,8 => UNS * INC # B1: 2,8 => UNS * INC # B4: 2,8 => UNS * INC # G7: 8,9 => UNS * INC # H7: 8,9 => UNS * INC # B1: 6,8 # E1: 6,8 => UNS * INC # B1: 6,8 # F1: 6,8 => UNS * INC # B1: 6,8 # F2: 6,8 => UNS * INC # B1: 6,8 # F2: 3,5 => UNS * INC # B1: 6,8 # A2: 3,7 => UNS * INC # B1: 6,8 # A2: 5 => UNS * INC # B1: 6,8 # C7: 3,7 => UNS * PRF # B1: 6,8 # C7: 8 => SOL * STA # B1: 6,8 + C7: 8 * CNT 37 HDP CHAINS / 38 HYP OPENED