Analysis of zz-www.sudokuwiki.org-0273-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=273
level: hard
position: ...1..53.5...9...2.8..6..4...45.....2.......7.....68...3..2..6.8...5...3.75..4... initial
Autosolve
position: ...1..53.5...9...2.8..65.4...45.....2.8.....7.....68.4.3..2..658...5...3.75..4... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A7: 1,9 => CTR => A7: 4 * CNT 1 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A7: 1,9 => CTR => A7: 4 * STA A7: 4 * CNT 1 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: ...1..53.5...9...2.8..65.4...45.....2.8.....7.....68.443..2..658...5.4.3.75..4... pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:01:03.983832
The following important HDP chains were detected:
* DIS # G3: 1,9 # G9: 1,9 => CTR => G9: 2 * DIS # G3: 1,9 + G9: 2 # B8: 1,9 => CTR => B8: 2,6 * DIS # G3: 1,9 + G9: 2 + B8: 2,6 # C6: 1,9 => CTR => C6: 3,7 * DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # E5: 1,3 => CTR => E5: 4 * DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # C2: 3 => CTR => C2: 1,6 * PRF # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 # B4: 1,6 => SOL * STA # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 + B4: 1,6 * CNT 6 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...1..53.5...9...2.8..6..4...45.....2.......7.....68...3..2..6.8...5...3.75..4... | initial |
| ...1..53.5...9...2.8..65.4...45.....2.8.....7.....68.4.3..2..658...5...3.75..4... | autosolve |
| ...1..53.5...9...2.8..65.4...45.....2.8.....7.....68.443..2..658...5.4.3.75..4... | pair_reduction |
| 947182536561493782382765941614578329258349617793216854439827165826951473175634298 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (3) I3: 1,9 C7: 1,9 E9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,D3: 2.. / F1 = 2 => 4 pairs (_) / D3 = 2 => 9 pairs (_) F4,D6: 2.. / F4 = 2 => 9 pairs (_) / D6 = 2 => 4 pairs (_) B8,C8: 2.. / B8 = 2 => 3 pairs (_) / C8 = 2 => 11 pairs (_) G9,H9: 2.. / G9 = 2 => 3 pairs (_) / H9 = 2 => 0 pairs (X) C3,D3: 2.. / C3 = 2 => 4 pairs (_) / D3 = 2 => 9 pairs (_) D6,H6: 2.. / D6 = 2 => 4 pairs (_) / H6 = 2 => 9 pairs (_) B1,B8: 2.. / B1 = 2 => 11 pairs (_) / B8 = 2 => 3 pairs (_) D3,D6: 2.. / D3 = 2 => 9 pairs (_) / D6 = 2 => 4 pairs (_) F1,F4: 2.. / F1 = 2 => 4 pairs (_) / F4 = 2 => 9 pairs (_) G4,G9: 2.. / G4 = 2 => 0 pairs (X) / G9 = 2 => 3 pairs (_) G4,G5: 3.. / G4 = 3 => 4 pairs (_) / G5 = 3 => 13 pairs (_) D9,E9: 3.. / D9 = 3 => 12 pairs (_) / E9 = 3 => 6 pairs (_) E1,D2: 4.. / E1 = 4 => 7 pairs (_) / D2 = 4 => 10 pairs (_) D5,E5: 4.. / D5 = 4 => 7 pairs (_) / E5 = 4 => 10 pairs (_) A7,B8: 4.. / A7 = 4 => 3 pairs (_) / B8 = 4 => 0 pairs (X) G7,G8: 4.. / G7 = 4 => 0 pairs (X) / G8 = 4 => 3 pairs (_) B2,D2: 4.. / B2 = 4 => 7 pairs (_) / D2 = 4 => 10 pairs (_) A7,G7: 4.. / A7 = 4 => 3 pairs (_) / G7 = 4 => 0 pairs (X) B8,G8: 4.. / B8 = 4 => 0 pairs (X) / G8 = 4 => 3 pairs (_) A1,A7: 4.. / A1 = 4 => 0 pairs (X) / A7 = 4 => 3 pairs (_) D2,D5: 4.. / D2 = 4 => 10 pairs (_) / D5 = 4 => 7 pairs (_) E1,E5: 4.. / E1 = 4 => 7 pairs (_) / E5 = 4 => 10 pairs (_) B5,B6: 5.. / B5 = 5 => 0 pairs (*) / B6 = 5 => 0 pairs (X) H5,H6: 5.. / H5 = 5 => 3 pairs (_) / H6 = 5 => 0 pairs (*) B5,H5: 5.. / B5 = 5 => 0 pairs (*) / H5 = 5 => 0 pairs (X) B6,H6: 5.. / B6 = 5 => 3 pairs (_) / H6 = 5 => 0 pairs (*) I1,G2: 6.. / I1 = 6 => 15 pairs (_) / G2 = 6 => 6 pairs (_) D8,D9: 6.. / D8 = 6 => 5 pairs (_) / D9 = 6 => 9 pairs (_) B5,G5: 6.. / B5 = 6 => 5 pairs (_) / G5 = 6 => 16 pairs (_) A9,D9: 6.. / A9 = 6 => 5 pairs (_) / D9 = 6 => 9 pairs (_) I1,I4: 6.. / I1 = 6 => 15 pairs (_) / I4 = 6 => 6 pairs (_) H2,H8: 7.. / H2 = 7 => 15 pairs (_) / H8 = 7 => 8 pairs (_) I1,H2: 8.. / I1 = 8 => 9 pairs (_) / H2 = 8 => 11 pairs (_) E4,F4: 8.. / E4 = 8 => 4 pairs (_) / F4 = 8 => 21 pairs (_) D7,F7: 8.. / D7 = 8 => 3 pairs (_) / F7 = 8 => 14 pairs (_) H9,I9: 8.. / H9 = 8 => 9 pairs (_) / I9 = 8 => 11 pairs (_) D2,D7: 8.. / D2 = 8 => 14 pairs (_) / D7 = 8 => 3 pairs (_) E1,E4: 8.. / E1 = 8 => 21 pairs (_) / E4 = 8 => 4 pairs (_) H2,H9: 8.. / H2 = 8 => 11 pairs (_) / H9 = 8 => 9 pairs (_) I1,I9: 8.. / I1 = 8 => 9 pairs (_) / I9 = 8 => 11 pairs (_) * DURATION: 0:00:35.982938 START: 14:29:33.221092 END: 14:30:09.204030 2019-04-28 * CP COUNT: (40) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:01:03.720970 START: 14:30:39.703706 END: 14:31:43.424676 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0273-base-pr-002.dot * REASONING * DIS # G3: 1,9 # G9: 1,9 => CTR => G9: 2 * DIS # G3: 1,9 + G9: 2 # B8: 1,9 => CTR => B8: 2,6 * DIS # G3: 1,9 + G9: 2 + B8: 2,6 # C6: 1,9 => CTR => C6: 3,7 * DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # E5: 1,3 => CTR => E5: 4 * DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # C2: 3 => CTR => C2: 1,6 * PRF # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 # B4: 1,6 => SOL * STA # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 + B4: 1,6 * CNT 6 HDP CHAINS / 54 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=273
Solution
position: 947182536561493782382765941614578329258349617793216854439827165826951473175634298 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 # G3: 1,9 => UNS * INC # G3: 7 => UNS * INC # A3: 1,9 => UNS * INC # C3: 1,9 => UNS * INC # I4: 1,9 => UNS * INC # I9: 1,9 => UNS * DIS # A7: 1,9 => CTR => A7: 4 * INC # A7: 4 => UNS * INC # B8: 1,9 => UNS * INC # C8: 1,9 => UNS * INC # A9: 1,9 => UNS * INC # F7: 1,9 => UNS * INC # G7: 1,9 => UNS * INC # C3: 1,9 => UNS * INC # C6: 1,9 => UNS * INC # E4: 1,3 => UNS * INC # E5: 1,3 => UNS * INC # E6: 1,3 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 1,9 => UNS * INC # G3: 7 => UNS * INC # A3: 1,9 => UNS * INC # C3: 1,9 => UNS * INC # I4: 1,9 => UNS * INC # I9: 1,9 => UNS * DIS # A7: 1,9 => CTR => A7: 4 * INC A7: 4 # B8: 1,9 => UNS * INC A7: 4 # C8: 1,9 => UNS * INC A7: 4 # A9: 1,9 => UNS * INC A7: 4 # F7: 1,9 => UNS * INC A7: 4 # G7: 1,9 => UNS * INC A7: 4 # C3: 1,9 => UNS * INC A7: 4 # C6: 1,9 => UNS * INC A7: 4 # E4: 1,3 => UNS * INC A7: 4 # E5: 1,3 => UNS * INC A7: 4 # E6: 1,3 => UNS * INC A7: 4 # G3: 1,9 => UNS * INC A7: 4 # G3: 7 => UNS * INC A7: 4 # A3: 1,9 => UNS * INC A7: 4 # C3: 1,9 => UNS * INC A7: 4 # I4: 1,9 => UNS * INC A7: 4 # I9: 1,9 => UNS * INC A7: 4 # B8: 1,9 => UNS * INC A7: 4 # C8: 1,9 => UNS * INC A7: 4 # A9: 1,9 => UNS * INC A7: 4 # F7: 1,9 => UNS * INC A7: 4 # G7: 1,9 => UNS * INC A7: 4 # C3: 1,9 => UNS * INC A7: 4 # C6: 1,9 => UNS * INC A7: 4 # E4: 1,3 => UNS * INC A7: 4 # E5: 1,3 => UNS * INC A7: 4 # E6: 1,3 => UNS * STA A7: 4 * CNT 33 HDP CHAINS / 33 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 1,9 => UNS * INC # G3: 7 => UNS * INC # A3: 1,9 => UNS * INC # C3: 1,9 => UNS * INC # I4: 1,9 => UNS * INC # I9: 1,9 => UNS * INC # B8: 1,9 => UNS * INC # C8: 1,9 => UNS * INC # A9: 1,9 => UNS * INC # F7: 1,9 => UNS * INC # G7: 1,9 => UNS * INC # C3: 1,9 => UNS * INC # C6: 1,9 => UNS * INC # E4: 1,3 => UNS * INC # E5: 1,3 => UNS * INC # E6: 1,3 => UNS * INC # G3: 1,9 # C3: 3,7 => UNS * INC # G3: 1,9 # C3: 2 => UNS * INC # G3: 1,9 # D3: 3,7 => UNS * INC # G3: 1,9 # D3: 2 => UNS * INC # G3: 1,9 # A4: 3,7 => UNS * INC # G3: 1,9 # A6: 3,7 => UNS * INC # G3: 1,9 # D2: 3,8 => UNS * INC # G3: 1,9 # D2: 4 => UNS * INC # G3: 1,9 # F4: 3,8 => UNS * INC # G3: 1,9 # F4: 1,2,7,9 => UNS * INC # G3: 1,9 # G4: 1,9 => UNS * INC # G3: 1,9 # G5: 1,9 => UNS * INC # G3: 1,9 # G7: 1,9 => UNS * DIS # G3: 1,9 # G9: 1,9 => CTR => G9: 2 * INC # G3: 1,9 + G9: 2 # G4: 1,9 => UNS * INC # G3: 1,9 + G9: 2 # G5: 1,9 => UNS * INC # G3: 1,9 + G9: 2 # G7: 1,9 => UNS * INC # G3: 1,9 + G9: 2 # I4: 1,9 => UNS * INC # G3: 1,9 + G9: 2 # I9: 1,9 => UNS * DIS # G3: 1,9 + G9: 2 # B8: 1,9 => CTR => B8: 2,6 * INC # G3: 1,9 + G9: 2 + B8: 2,6 # C8: 1,9 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 # A9: 1,9 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 # F7: 1,9 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 # G7: 1,9 => UNS * DIS # G3: 1,9 + G9: 2 + B8: 2,6 # C6: 1,9 => CTR => C6: 3,7 * INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # C8: 1,9 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # A9: 1,9 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # F7: 1,9 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # G7: 1,9 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # E4: 1,3 => UNS * DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # E5: 1,3 => CTR => E5: 4 * INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # E6: 1,3 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # E4: 1,3 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # E6: 1,3 => UNS * INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # C2: 1,6 => UNS * DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # C2: 3 => CTR => C2: 1,6 * PRF # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 # B4: 1,6 => SOL * STA # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 + B4: 1,6 * CNT 53 HDP CHAINS / 54 HYP OPENED