Analysis of zz-www.sudokuwiki.org-0285-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=285
level: hard
position: .2.3.....4...1......9..58..1...2......5..97...3.5...4.....5.6....6....7.....47.89 initial
Autosolve
position: .2.3.....4...1......9..58..1...2......5..97...3.5...4.....5.6....6....7....647.89 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 6,7 => CTR => I3: 1,2,3,4 * CNT 1 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I3: 6,7 => CTR => I3: 1,2,3,4 * STA I3: 1,2,3,4 * CNT 1 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: .2.3.....4...1......9..58..1...2......5..97...3.5...4.....5.6....6....7....647.89 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:20.961726
The following important HDP chains were detected:
* DIS # E1: 6,7 # A1: 6,7 => CTR => A1: 5,8 * DIS # E1: 6,7 + A1: 5,8 # I3: 1,3 => CTR => I3: 2,4 * DIS # E1: 6,7 + A1: 5,8 + I3: 2,4 # B4: 4,8 => CTR => B4: 6,9 * PRF # E1: 6,7 + A1: 5,8 + I3: 2,4 + B4: 6,9 # B5: 6 => SOL * STA # E1: 6,7 + A1: 5,8 + I3: 2,4 + B4: 6,9 + B5: 6 * CNT 4 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.3.....4...1......9..58..1...2......5..97...3.5...4.....5.6....6....7.....47.89 | initial |
| .2.3.....4...1......9..58..1...2......5..97...3.5...4.....5.6....6....7....647.89 | autosolve |
| .2.3.....4...1......9..58..1...2......5..97...3.5...4.....5.6....6....7....647.89 | pair_reduction |
| 528364197473918562619275834194726358865439721732581946947852613286193475351647289 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (2) E3: 6,7 B9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B3: 1.. / C1 = 1 => 8 pairs (_) / B3 = 1 => 3 pairs (_) D5,F6: 1.. / D5 = 1 => 4 pairs (_) / F6 = 1 => 4 pairs (_) C2,A3: 3.. / C2 = 3 => 7 pairs (_) / A3 = 3 => 4 pairs (_) F4,E5: 3.. / F4 = 3 => 10 pairs (_) / E5 = 3 => 3 pairs (_) E5,E8: 3.. / E5 = 3 => 3 pairs (_) / E8 = 3 => 10 pairs (_) F1,D3: 4.. / F1 = 4 => 3 pairs (_) / D3 = 4 => 8 pairs (_) D3,I3: 4.. / D3 = 4 => 8 pairs (_) / I3 = 4 => 3 pairs (_) B5,D5: 4.. / B5 = 4 => 4 pairs (_) / D5 = 4 => 6 pairs (_) C4,C7: 4.. / C4 = 4 => 6 pairs (_) / C7 = 4 => 3 pairs (_) F1,F4: 4.. / F1 = 4 => 3 pairs (_) / F4 = 4 => 8 pairs (_) G1,G8: 4.. / G1 = 4 => 15 pairs (_) / G8 = 4 => 2 pairs (_) A1,B2: 5.. / A1 = 5 => 3 pairs (_) / B2 = 5 => 7 pairs (_) D4,E6: 7.. / D4 = 7 => 5 pairs (_) / E6 = 7 => 14 pairs (_) E1,D2: 9.. / E1 = 9 => 3 pairs (_) / D2 = 9 => 2 pairs (_) B4,A6: 9.. / B4 = 9 => 3 pairs (_) / A6 = 9 => 3 pairs (_) A6,G6: 9.. / A6 = 9 => 3 pairs (_) / G6 = 9 => 3 pairs (_) E1,E8: 9.. / E1 = 9 => 3 pairs (_) / E8 = 9 => 2 pairs (_) * DURATION: 0:00:10.892779 START: 14:50:42.677285 END: 14:50:53.570064 2019-04-28 * CP COUNT: (17) * INCONCLUSIVE * DEEP PAIR REDUCTION * DURATION: 0:00:20.756813 START: 14:51:10.682154 END: 14:51:31.438967 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0285-base-pr-002.dot * REASONING * DIS # E1: 6,7 # A1: 6,7 => CTR => A1: 5,8 * DIS # E1: 6,7 + A1: 5,8 # I3: 1,3 => CTR => I3: 2,4 * DIS # E1: 6,7 + A1: 5,8 + I3: 2,4 # B4: 4,8 => CTR => B4: 6,9 * PRF # E1: 6,7 + A1: 5,8 + I3: 2,4 + B4: 6,9 # B5: 6 => SOL * STA # E1: 6,7 + A1: 5,8 + I3: 2,4 + B4: 6,9 + B5: 6 * CNT 4 HDP CHAINS / 25 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=285
Solution
position: 528364197473918562619275834194726358865439721732581946947852613286193475351647289 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 # E1: 6,7 => UNS * INC # E1: 8,9 => UNS * INC # A3: 6,7 => UNS * INC # B3: 6,7 => UNS * DIS # I3: 6,7 => CTR => I3: 1,2,3,4 * INC # I3: 1,2,3,4 => UNS * INC # E6: 6,7 => UNS * INC # E6: 8 => UNS * INC # B8: 1,5 => UNS * INC # B8: 4,8,9 => UNS * INC # G9: 1,5 => UNS * INC # G9: 2,3 => UNS * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 6,7 => UNS * INC # E1: 8,9 => UNS * INC # A3: 6,7 => UNS * INC # B3: 6,7 => UNS * DIS # I3: 6,7 => CTR => I3: 1,2,3,4 * INC I3: 1,2,3,4 # E6: 6,7 => UNS * INC I3: 1,2,3,4 # E6: 8 => UNS * INC I3: 1,2,3,4 # E1: 6,7 => UNS * INC I3: 1,2,3,4 # E1: 8,9 => UNS * INC I3: 1,2,3,4 # A3: 6,7 => UNS * INC I3: 1,2,3,4 # B3: 6,7 => UNS * INC I3: 1,2,3,4 # E6: 6,7 => UNS * INC I3: 1,2,3,4 # E6: 8 => UNS * INC I3: 1,2,3,4 # B8: 1,5 => UNS * INC I3: 1,2,3,4 # B8: 4,8,9 => UNS * INC I3: 1,2,3,4 # G9: 1,5 => UNS * INC I3: 1,2,3,4 # G9: 2,3 => UNS * INC I3: 1,2,3,4 # E1: 6,7 => UNS * INC I3: 1,2,3,4 # E1: 8,9 => UNS * INC I3: 1,2,3,4 # A3: 6,7 => UNS * INC I3: 1,2,3,4 # B3: 6,7 => UNS * INC I3: 1,2,3,4 # E6: 6,7 => UNS * INC I3: 1,2,3,4 # E6: 8 => UNS * INC I3: 1,2,3,4 # B8: 1,5 => UNS * INC I3: 1,2,3,4 # B8: 4,8,9 => UNS * INC I3: 1,2,3,4 # G9: 1,5 => UNS * INC I3: 1,2,3,4 # G9: 2,3 => UNS * STA I3: 1,2,3,4 * CNT 27 HDP CHAINS / 27 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 6,7 => UNS * INC # E1: 8,9 => UNS * INC # A3: 6,7 => UNS * INC # B3: 6,7 => UNS * INC # E6: 6,7 => UNS * INC # E6: 8 => UNS * INC # B8: 1,5 => UNS * INC # B8: 4,8,9 => UNS * INC # G9: 1,5 => UNS * INC # G9: 2,3 => UNS * DIS # E1: 6,7 # A1: 6,7 => CTR => A1: 5,8 * INC # E1: 6,7 + A1: 5,8 # I1: 6,7 => UNS * INC # E1: 6,7 + A1: 5,8 # I1: 6,7 => UNS * INC # E1: 6,7 + A1: 5,8 # I1: 1,4,5 => UNS * INC # E1: 6,7 + A1: 5,8 # I1: 6,7 => UNS * INC # E1: 6,7 + A1: 5,8 # I1: 1,4,5 => UNS * INC # E1: 6,7 + A1: 5,8 # I3: 2,4 => UNS * DIS # E1: 6,7 + A1: 5,8 # I3: 1,3 => CTR => I3: 2,4 * INC # E1: 6,7 + A1: 5,8 + I3: 2,4 # A3: 6,7 => UNS * INC # E1: 6,7 + A1: 5,8 + I3: 2,4 # B3: 6,7 => UNS * DIS # E1: 6,7 + A1: 5,8 + I3: 2,4 # B4: 4,8 => CTR => B4: 6,9 * INC # E1: 6,7 + A1: 5,8 + I3: 2,4 + B4: 6,9 # B5: 4,8 => UNS * INC # E1: 6,7 + A1: 5,8 + I3: 2,4 + B4: 6,9 # B5: 4,8 => UNS * PRF # E1: 6,7 + A1: 5,8 + I3: 2,4 + B4: 6,9 # B5: 6 => SOL * STA # E1: 6,7 + A1: 5,8 + I3: 2,4 + B4: 6,9 + B5: 6 * CNT 24 HDP CHAINS / 25 HYP OPENED