Analysis of zz-www.sudokuwiki.org-0081-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=81
level: medium
position: ..4.3...22..1..9.........7.7.2..5....4.....9....7..5.6.8.........5..4..31...9.6.. initial
Autosolve
position: ..4.3...22..1..9.........7.7.2..5...54.....9....7..5.648......9..5..4..31...9.6.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 1,8 => CTR => H1: 5,6 * DIS # G3: 1,8 => CTR => G3: 3,4 * DIS # G4: 1,8 => CTR => G4: 3,4 * CNT 3 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # H1: 1,8 => CTR => H1: 5,6 * DIS H1: 5,6 # G3: 1,8 => CTR => G3: 3,4 * PRF H1: 5,6 + G3: 3,4 # I3: 4,5 => SOL * STA H1: 5,6 + G3: 3,4 + I3: 4,5 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..4.3...22..1..9.........7.7.2..5....4.....9....7..5.6.8.........5..4..31...9.6.. | initial |
| ..4.3...22..1..9.........7.7.2..5...54.....9....7..5.648......9..5..4..31...9.6.. | autosolve |
| 874539162253176948619428375762985431541263897398741526486357219925614783137892654 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) G1: 1,8 A8: 6,9 C9: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G5,H6: 2.. / G5 = 2 => 6 pairs (_) / H6 = 2 => 6 pairs (_) B8,B9: 2.. / B8 = 2 => 18 pairs (_) / B9 = 2 => 3 pairs (_) H2,G3: 3.. / H2 = 3 => 4 pairs (_) / G3 = 3 => 8 pairs (_) A3,A6: 3.. / A3 = 3 => 0 pairs (X) / A6 = 3 => 8 pairs (_) H9,I9: 4.. / H9 = 4 => 4 pairs (_) / I9 = 4 => 8 pairs (_) E6,H6: 4.. / E6 = 4 => 4 pairs (_) / H6 = 4 => 0 pairs (X) D3,D4: 4.. / D3 = 4 => 4 pairs (_) / D4 = 4 => 0 pairs (X) G3,G4: 4.. / G3 = 4 => 0 pairs (X) / G4 = 4 => 4 pairs (_) H1,H2: 6.. / H1 = 6 => 4 pairs (_) / H2 = 6 => 17 pairs (_) B4,C5: 6.. / B4 = 6 => 7 pairs (_) / C5 = 6 => 0 pairs (X) G5,I5: 7.. / G5 = 7 => 0 pairs (X) / I5 = 7 => 3 pairs (_) B1,F1: 7.. / B1 = 7 => 4 pairs (_) / F1 = 7 => 4 pairs (_) I5,I9: 7.. / I5 = 7 => 3 pairs (_) / I9 = 7 => 0 pairs (X) D4,F6: 9.. / D4 = 9 => 4 pairs (_) / F6 = 9 => 0 pairs (X) A8,B8: 9.. / A8 = 9 => 4 pairs (_) / B8 = 9 => 8 pairs (_) B4,D4: 9.. / B4 = 9 => 0 pairs (X) / D4 = 9 => 4 pairs (_) C3,C6: 9.. / C3 = 9 => 5 pairs (_) / C6 = 9 => 6 pairs (_) * DURATION: 0:00:18.864306 START: 04:53:27.698399 END: 04:53:46.562705 2017-05-01 * CP COUNT: (17) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C9,G1) * ..4.3...22..1..9.........7.7.2..5...54.....9....7..5.648......9..5..4..31...9.6.. * PAIR G1: 1,8 BLK 3 H1: 1,8,5,6 # reduction candidate for 1,8 H1: 1,8 => CTR * 6549371822..1589648..4263757.2..543154.....973..74.5.6486....59925..4.131..592648 H1: 5,6 # 4 pairs G3: 1,8,3,4 # reduction candidate for 1,8 G3: 1,8 => CTR * .54.37162278156934...4298757.2.65481546...397...74.5264836...59..5..4.131.7593648 G3: 3,4 # 4 pairs I3: 1,8,4,5 # reduction candidate for 1,8 I3: 1,8 # 7 pairs * PAIR G1: 1,8 COL G G4: 1,8,3,4 # reduction candidate for 1,8 G4: 1,8 => CTR * ..4.3...22..1..9........47.7.24.5...54....397...7..5.648......9..5..4..31...9.6.. G4: 3,4 # 4 pairs G5: 1,8,2,3,7 # reduction candidate for 1,8 G5: 1,8 # 15 pairs G8: 1,8,2,7 # reduction candidate for 1,8 G8: 1,8 # 8 pairs * PAIR A8: 6,9 BLK 7 B8: 6,9,2,7 # reduction candidate for 6,9 B8: 2,7 # 15 pairs B8: 6,9 # 7 pairs * PAIR A8: 6,9 COL A A1: 6,9,8 # reduction candidate for 6,9 A1: 6,9 # 6 pairs A3: 6,9,3,8 # reduction candidate for 6,9 A3: 6,9 # 15 pairs * PAIR C9: 3,7 BLK 7 C7: 3,7,6 # reduction candidate for 3,7 C7: 3,7 # 7 pairs B9: 3,7,2 # reduction candidate for 3,7 B9: 3,7 # 18 pairs * PAIR C9: 3,7 ROW 9 F9: 3,7,2,8 # reduction candidate for 3,7 F9: 3,7 # 5 pairs F9: 2,8 # 4 pairs * PAIR C9: 3,7 COL C C2: 3,7,6,8 # reduction candidate for 3,7 C2: 3,7 # 15 pairs C2: 6,8 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0081-base-pr-000.dot * REASONING * DIS # H1: 1,8 => CTR => H1: 5,6 * DIS # G3: 1,8 => CTR => G3: 3,4 * DIS # G4: 1,8 => CTR => G4: 3,4 * CNT 3 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C9,G1) * ..4.3...22..1..9.........7.7.2..5...54.....9....7..5.648......9..5..4..31...9.6.. * PAIR G1: 1,8 BLK 3 H1: 1,8,5,6 # reduction candidate for 1,8 H1: 1,8 => CTR * 6549371822..1589648..4263757.2..543154.....973..74.5.6486....59925..4.131..592648 G3: 1,8,3,4 # reduction candidate for 1,8 G3: 1,8 => CTR * .54.37162278156934...4298757.2.65481546...397...74.5264836...59..5..4.131.7593648 I3: 1,8,4,5 # reduction candidate for 1,8 I3: 1,8 # 7 pairs * RESTART * PAIR G1: 1,8 BLK 3 I3: 1,8,4,5 # reduction candidate for 1,8 I3: 4,5 => SOLVED * 874539162253176948619428375762985431541263897398741526486357219925614783137892654 * DURATION: 0:00:05.954842 START: 04:53:58.587629 END: 04:54:04.542471 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0081-base-pr-001.dot * REASONING * DIS # H1: 1,8 => CTR => H1: 5,6 * DIS H1: 5,6 # G3: 1,8 => CTR => G3: 3,4 * PRF H1: 5,6 + G3: 3,4 # I3: 4,5 => SOL * STA H1: 5,6 + G3: 3,4 + I3: 4,5 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=81
Solution
position: 874539162253176948619428375762985431541263897398741526486357219925614783137892654 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # H1: 1,8 => CTR => H1: 5,6 * INC # H1: 5,6 => UNS * DIS # G3: 1,8 => CTR => G3: 3,4 * INC # G3: 3,4 => UNS * INC # I3: 1,8 => UNS * DIS # G4: 1,8 => CTR => G4: 3,4 * INC # G4: 3,4 => UNS * INC # G5: 1,8 => UNS * INC # G8: 1,8 => UNS * INC # B8: 6,9 => UNS * INC # B8: 2,7 => UNS * INC # A1: 6,9 => UNS * INC # A3: 6,9 => UNS * INC # C7: 3,7 => UNS * INC # B9: 3,7 => UNS * INC # F9: 3,7 => UNS * INC # F9: 2,8 => UNS * INC # C2: 3,7 => UNS * INC # C2: 6,8 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # H1: 1,8 => CTR => H1: 5,6 * DIS H1: 5,6 # G3: 1,8 => CTR => G3: 3,4 * INC H1: 5,6 + G3: 3,4 # I3: 1,8 => UNS * INC H1: 5,6 + G3: 3,4 # I3: 1,8 => UNS * PRF H1: 5,6 + G3: 3,4 # I3: 4,5 => SOL * STA H1: 5,6 + G3: 3,4 + I3: 4,5 * CNT 5 HDP CHAINS / 5 HYP OPENED