Analysis of zz-www.sudokuwiki.org-0052-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=52
level: hard
position: ..12..8..75......2..4.3...1...56..3.3..4.9..8.9..83...1...5.7..8......56..9..62.. initial
Autosolve
position: ..12..8..75......2..4.3...1...56..3.3..4.9..8.9..83...1...5.7..8......565.9..62.. autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:28.712473
The following important HDP chains were detected:
* DIS # A3: 6,9 # H1: 6,9 => CTR => H1: 4,7 * DIS # A3: 6,9 + H1: 4,7 => CTR => A3: 2 * PRF A3: 2 # C2: 3 => SOL * STA A3: 2 + C2: 3 * CNT 3 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..12..8..75......2..4.3...1...56..3.3..4.9..8.9..83...1...5.7..8......56..9..62.. | initial |
| ..12..8..75......2..4.3...1...56..3.3..4.9..8.9..83...1...5.7..8......565.9..62.. | autosolve |
| 961245873753198462284637591418562937375419628692783145126354789847921356539876214 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A1: 6,9 B1: 3,6 A4: 2,4 D6: 1,7 I9: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,B5: 1.. / B4 = 1 => 0 pairs (*) / B5 = 1 => 0 pairs (X) G8,H9: 1.. / G8 = 1 => 15 pairs (_) / H9 = 1 => 9 pairs (_) A3,B3: 2.. / A3 = 2 => 7 pairs (_) / B3 = 2 => 22 pairs (_) F4,E5: 2.. / F4 = 2 => 13 pairs (_) / E5 = 2 => 7 pairs (_) H5,H6: 2.. / H5 = 2 => 13 pairs (_) / H6 = 2 => 6 pairs (_) E5,E8: 2.. / E5 = 2 => 7 pairs (_) / E8 = 2 => 13 pairs (_) B1,C2: 3.. / B1 = 3 => 6 pairs (_) / C2 = 3 => 0 pairs (*) I1,G2: 3.. / I1 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) B1,I1: 3.. / B1 = 3 => 6 pairs (_) / I1 = 3 => 0 pairs (*) C2,G2: 3.. / C2 = 3 => 0 pairs (*) / G2 = 3 => 0 pairs (X) G2,G8: 3.. / G2 = 3 => 6 pairs (_) / G8 = 3 => 0 pairs (*) A4,A6: 4.. / A4 = 4 => 7 pairs (_) / A6 = 4 => 0 pairs (X) F1,F3: 5.. / F1 = 5 => 7 pairs (_) / F3 = 5 => 11 pairs (_) I1,G3: 5.. / I1 = 5 => 11 pairs (_) / G3 = 5 => 7 pairs (_) C5,C6: 5.. / C5 = 5 => 6 pairs (_) / C6 = 5 => 11 pairs (_) F1,I1: 5.. / F1 = 5 => 7 pairs (_) / I1 = 5 => 11 pairs (_) F3,G3: 5.. / F3 = 5 => 11 pairs (_) / G3 = 5 => 7 pairs (_) C5,G5: 5.. / C5 = 5 => 6 pairs (_) / G5 = 5 => 11 pairs (_) I1,I6: 5.. / I1 = 5 => 11 pairs (_) / I6 = 5 => 7 pairs (_) D2,D3: 6.. / D2 = 6 => 7 pairs (_) / D3 = 6 => 9 pairs (_) B7,C7: 6.. / B7 = 6 => 8 pairs (_) / C7 = 6 => 6 pairs (_) C2,B3: 8.. / C2 = 8 => 11 pairs (_) / B3 = 8 => 8 pairs (_) B4,C4: 8.. / B4 = 8 => 11 pairs (_) / C4 = 8 => 8 pairs (_) H7,H9: 8.. / H7 = 8 => 9 pairs (_) / H9 = 8 => 15 pairs (_) D9,H9: 8.. / D9 = 8 => 9 pairs (_) / H9 = 8 => 15 pairs (_) B3,B4: 8.. / B3 = 8 => 8 pairs (_) / B4 = 8 => 11 pairs (_) C2,C4: 8.. / C2 = 8 => 11 pairs (_) / C4 = 8 => 8 pairs (_) A1,A3: 9.. / A1 = 9 => 6 pairs (_) / A3 = 9 => 0 pairs (X) G4,I4: 9.. / G4 = 9 => 8 pairs (_) / I4 = 9 => 13 pairs (_) * DURATION: 0:00:34.062659 START: 18:31:21.091504 END: 18:31:55.154163 2017-04-30 * CP COUNT: (29) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:28.463482 START: 18:32:22.898077 END: 18:32:51.361559 2017-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0052-base-pr-002.dot * REASONING * DIS # A3: 6,9 # H1: 6,9 => CTR => H1: 4,7 * DIS # A3: 6,9 + H1: 4,7 => CTR => A3: 2 * PRF A3: 2 # C2: 3 => SOL * STA A3: 2 + C2: 3 * CNT 3 HDP CHAINS / 30 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=52
Solution
position: 961245873753198462284637591418562937375419628692783145126354789847921356539876214 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 # A3: 6,9 => UNS * INC # A3: 2 => UNS * INC # H1: 6,9 => UNS * INC # H1: 4,7 => UNS * INC # C2: 3,6 => UNS * INC # C2: 8 => UNS * INC # B7: 3,6 => UNS * INC # B7: 2,4 => UNS * INC # A6: 2,4 => UNS * INC # A6: 6 => UNS * INC # F4: 1,7 => UNS * INC # E5: 1,7 => UNS * INC # H6: 1,7 => UNS * INC # H6: 2,4,6 => UNS * INC # D8: 1,7 => UNS * INC # D9: 1,7 => UNS * INC # I7: 3,4 => UNS * INC # G8: 3,4 => UNS * INC # B9: 3,4 => UNS * INC # B9: 7 => UNS * INC # I1: 3,4 => UNS * INC # I1: 5,7,9 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 6,9 => UNS * INC # A3: 2 => UNS * INC # H1: 6,9 => UNS * INC # H1: 4,7 => UNS * INC # C2: 3,6 => UNS * INC # C2: 8 => UNS * INC # B7: 3,6 => UNS * INC # B7: 2,4 => UNS * INC # A6: 2,4 => UNS * INC # A6: 6 => UNS * INC # F4: 1,7 => UNS * INC # E5: 1,7 => UNS * INC # H6: 1,7 => UNS * INC # H6: 2,4,6 => UNS * INC # D8: 1,7 => UNS * INC # D9: 1,7 => UNS * INC # I7: 3,4 => UNS * INC # G8: 3,4 => UNS * INC # B9: 3,4 => UNS * INC # B9: 7 => UNS * INC # I1: 3,4 => UNS * INC # I1: 5,7,9 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 6,9 => UNS * INC # A3: 2 => UNS * INC # H1: 6,9 => UNS * INC # H1: 4,7 => UNS * INC # C2: 3,6 => UNS * INC # C2: 8 => UNS * INC # B7: 3,6 => UNS * INC # B7: 2,4 => UNS * INC # A6: 2,4 => UNS * INC # A6: 6 => UNS * INC # F4: 1,7 => UNS * INC # E5: 1,7 => UNS * INC # H6: 1,7 => UNS * INC # H6: 2,4,6 => UNS * INC # D8: 1,7 => UNS * INC # D9: 1,7 => UNS * INC # I7: 3,4 => UNS * INC # G8: 3,4 => UNS * INC # B9: 3,4 => UNS * INC # B9: 7 => UNS * INC # I1: 3,4 => UNS * INC # I1: 5,7,9 => UNS * DIS # A3: 6,9 # H1: 6,9 => CTR => H1: 4,7 * DIS # A3: 6,9 + H1: 4,7 => CTR => A3: 2 * INC A3: 2 # C2: 3,6 => UNS * INC A3: 2 # C2: 8 => UNS * INC A3: 2 # B7: 3,6 => UNS * INC A3: 2 # B7: 2,4 => UNS * INC A3: 2 # C2: 6,8 => UNS * PRF A3: 2 # C2: 3 => SOL * STA A3: 2 + C2: 3 * CNT 30 HDP CHAINS / 30 HYP OPENED