Analysis of zz-www.sudokuwiki.org-0094-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=94
level: hard
position: .8.1..9...6...7.5.3...4...77....2....2..5..4....7....66...8...1.4.3...8...9..6.7. initial
Autosolve
position: .871..9...6...7.5.3...4...77....2....2..5.74....7....667..8...1.4.37.68.8.9..6.7. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 1,9 => CTR => A6: 4,5 * CNT 1 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 1,9 => CTR => A6: 4,5 * STA A6: 4,5 * CNT 1 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: .871..9...6...7.5.3...4...77....2....2..5.74....7....667..8...1.4.37.68.8.9..6.7. pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:23.565630
The following important HDP chains were detected:
* DIS # B4: 1,9 # E4: 1,9 => CTR => E4: 3,6 * DIS # B4: 1,9 + E4: 3,6 # H4: 3 => CTR => H4: 1,9 * DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 # B3: 5 => CTR => B3: 1,9 * DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 # F5: 1,9 => CTR => F5: 3,8 * PRF # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 + F5: 3,8 => SOL * STA B4: 1,9 * CNT 5 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.1..9...6...7.5.3...4...77....2....2..5..4....7....66...8...1.4.3...8...9..6.7. | initial |
| .871..9...6...7.5.3...4...77....2....2..5.74....7....667..8...1.4.37.68.8.9..6.7. | autosolve |
| .871..9...6...7.5.3...4...77....2....2..5.74....7....667..8...1.4.37.68.8.9..6.7. | pair_reduction |
| 587163924964827153312945867796432518123658749458791236675284391241379685839516472 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (3) F1: 3,5 A5: 1,9 E9: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F8,E9: 1.. / F8 = 1 => 18 pairs (_) / E9 = 1 => 6 pairs (_) B9,E9: 1.. / B9 = 1 => 18 pairs (_) / E9 = 1 => 6 pairs (_) G6,H6: 2.. / G6 = 2 => 4 pairs (_) / H6 = 2 => 6 pairs (_) C7,B9: 3.. / C7 = 3 => 6 pairs (_) / B9 = 3 => 11 pairs (_) D4,F6: 4.. / D4 = 4 => 4 pairs (_) / F6 = 4 => 9 pairs (_) A1,I1: 4.. / A1 = 4 => 13 pairs (_) / I1 = 4 => 4 pairs (_) C4,D4: 4.. / C4 = 4 => 9 pairs (_) / D4 = 4 => 4 pairs (_) F6,F7: 4.. / F6 = 4 => 9 pairs (_) / F7 = 4 => 4 pairs (_) A1,F1: 5.. / A1 = 5 => 8 pairs (_) / F1 = 5 => 7 pairs (_) E1,D3: 6.. / E1 = 6 => 7 pairs (_) / D3 = 6 => 8 pairs (_) H1,H3: 6.. / H1 = 6 => 8 pairs (_) / H3 = 6 => 7 pairs (_) C4,C5: 6.. / C4 = 6 => 7 pairs (_) / C5 = 6 => 4 pairs (_) E1,H1: 6.. / E1 = 6 => 7 pairs (_) / H1 = 6 => 8 pairs (_) D3,H3: 6.. / D3 = 6 => 8 pairs (_) / H3 = 6 => 7 pairs (_) C5,D5: 6.. / C5 = 6 => 4 pairs (_) / D5 = 6 => 7 pairs (_) E1,E4: 6.. / E1 = 6 => 7 pairs (_) / E4 = 6 => 8 pairs (_) A2,B3: 9.. / A2 = 9 => 0 pairs (*) / B3 = 9 => 0 pairs (X) H7,I8: 9.. / H7 = 9 => 9 pairs (_) / I8 = 9 => 7 pairs (_) F8,I8: 9.. / F8 = 9 => 9 pairs (_) / I8 = 9 => 7 pairs (_) * DURATION: 0:00:21.980311 START: 18:50:24.152625 END: 18:50:46.132936 2017-04-30 * CP COUNT: (19) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:23.433779 START: 18:51:09.917419 END: 18:51:33.351198 2017-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0094-base-pr-002.dot * REASONING * DIS # B4: 1,9 # E4: 1,9 => CTR => E4: 3,6 * DIS # B4: 1,9 + E4: 3,6 # H4: 3 => CTR => H4: 1,9 * DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 # B3: 5 => CTR => B3: 1,9 * DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 # F5: 1,9 => CTR => F5: 3,8 * PRF # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 + F5: 3,8 => SOL * STA B4: 1,9 * CNT 5 HDP CHAINS / 18 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=94
Solution
position: 587163924964827153312945867796432518123658749458791236675284391241379685839516472 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 # B4: 1,9 => UNS * DIS # A6: 1,9 => CTR => A6: 4,5 * INC # A6: 4,5 => UNS * INC # B6: 1,9 => UNS * INC # F5: 1,9 => UNS * INC # F5: 3,8 => UNS * INC # A2: 1,9 => UNS * INC # A2: 2,4 => UNS * CNT 8 HDP CHAINS / 8 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B4: 1,9 => UNS * DIS # A6: 1,9 => CTR => A6: 4,5 * INC A6: 4,5 # B6: 1,9 => UNS * INC A6: 4,5 # F5: 1,9 => UNS * INC A6: 4,5 # F5: 3,8 => UNS * INC A6: 4,5 # A2: 1,9 => UNS * INC A6: 4,5 # A2: 2,4 => UNS * INC A6: 4,5 # B4: 1,9 => UNS * INC A6: 4,5 # B6: 1,9 => UNS * INC A6: 4,5 # F5: 1,9 => UNS * INC A6: 4,5 # F5: 3,8 => UNS * INC A6: 4,5 # A2: 1,9 => UNS * INC A6: 4,5 # A2: 2,4 => UNS * INC A6: 4,5 # B4: 1,9 => UNS * INC A6: 4,5 # B6: 1,9 => UNS * INC A6: 4,5 # F5: 1,9 => UNS * INC A6: 4,5 # F5: 3,8 => UNS * INC A6: 4,5 # A2: 1,9 => UNS * INC A6: 4,5 # A2: 2,4 => UNS * INC A6: 4,5 # C4: 4,5 => UNS * INC A6: 4,5 # C6: 4,5 => UNS * INC A6: 4,5 # A1: 4,5 => UNS * INC A6: 4,5 # A1: 2 => UNS * STA A6: 4,5 * CNT 23 HDP CHAINS / 23 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # B4: 1,9 => UNS * INC # B6: 1,9 => UNS * INC # F5: 1,9 => UNS * INC # F5: 3,8 => UNS * INC # A2: 1,9 => UNS * INC # A2: 2,4 => UNS * INC # C4: 4,5 => UNS * INC # C6: 4,5 => UNS * INC # A1: 4,5 => UNS * INC # A1: 2 => UNS * DIS # B4: 1,9 # E4: 1,9 => CTR => E4: 3,6 * INC # B4: 1,9 + E4: 3,6 # H4: 1,9 => UNS * INC # B4: 1,9 + E4: 3,6 # H4: 1,9 => UNS * DIS # B4: 1,9 + E4: 3,6 # H4: 3 => CTR => H4: 1,9 * INC # B4: 1,9 + E4: 3,6 + H4: 1,9 # B3: 1,9 => UNS * DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 # B3: 5 => CTR => B3: 1,9 * DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 # F5: 1,9 => CTR => F5: 3,8 * PRF # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 + F5: 3,8 => SOL * STA B4: 1,9 * CNT 18 HDP CHAINS / 18 HYP OPENED