Analysis of zz-www.sudokuwiki.org-0074-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=74
level: medium
position: .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.7.....8..9...4...5.1...3.....5.2. initial
Autosolve
position: .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.79..5.8..9...45..5.1...3.....5.21 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C6: 1,6 => CTR => C6: 4,8 * DIS # G6: 4,8 => CTR => G6: 3,6 * DIS # C6: 1,6 => CTR => C6: 4,8 * CNT 3 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C6: 1,6 => CTR => C6: 4,8 * PRF C6: 4,8 # G9: 6,7 => SOL * STA C6: 4,8 + G9: 6,7 * CNT 2 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.7.....8..9...4...5.1...3.....5.2. | initial |
| .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.79..5.8..9...45..5.1...3.....5.21 | autosolve |
| 976354218431682579582179436154236897793548162628791354817923645265417983349865721 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) C3: 1,2 H1: 1,8 A4: 1,7 A6: 1,6 F5: 2,8 I6: 4,8 G7: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D4,F6: 1.. / D4 = 1 => 11 pairs (_) / F6 = 1 => 14 pairs (_) B7,C7: 1.. / B7 = 1 => 9 pairs (_) / C7 = 1 => 18 pairs (_) C7,A8: 2.. / C7 = 2 => 0 pairs (X) / A8 = 2 => 7 pairs (_) B2,A3: 3.. / B2 = 3 => 10 pairs (_) / A3 = 3 => 10 pairs (_) H2,H3: 3.. / H2 = 3 => 10 pairs (_) / H3 = 3 => 10 pairs (_) E4,F6: 3.. / E4 = 3 => 13 pairs (_) / F6 = 3 => 15 pairs (_) G4,G6: 3.. / G4 = 3 => 15 pairs (_) / G6 = 3 => 13 pairs (_) B2,H2: 3.. / B2 = 3 => 10 pairs (_) / H2 = 3 => 10 pairs (_) A3,H3: 3.. / A3 = 3 => 10 pairs (_) / H3 = 3 => 10 pairs (_) E4,G4: 3.. / E4 = 3 => 13 pairs (_) / G4 = 3 => 15 pairs (_) F6,G6: 3.. / F6 = 3 => 15 pairs (_) / G6 = 3 => 13 pairs (_) A3,A9: 3.. / A3 = 3 => 10 pairs (_) / A9 = 3 => 10 pairs (_) F6,F7: 3.. / F6 = 3 => 15 pairs (_) / F7 = 3 => 13 pairs (_) F1,D3: 4.. / F1 = 4 => 8 pairs (_) / D3 = 4 => 13 pairs (_) D3,G3: 4.. / D3 = 4 => 13 pairs (_) / G3 = 4 => 8 pairs (_) F1,F8: 4.. / F1 = 4 => 8 pairs (_) / F8 = 4 => 13 pairs (_) A1,A3: 5.. / A1 = 5 => 8 pairs (_) / A3 = 5 => 13 pairs (_) B4,B5: 5.. / B4 = 5 => 13 pairs (_) / B5 = 5 => 14 pairs (_) A1,E1: 5.. / A1 = 5 => 8 pairs (_) / E1 = 5 => 13 pairs (_) B5,D5: 5.. / B5 = 5 => 14 pairs (_) / D5 = 5 => 13 pairs (_) E1,D2: 6.. / E1 = 6 => 16 pairs (_) / D2 = 6 => 9 pairs (_) H5,G6: 6.. / H5 = 6 => 10 pairs (_) / G6 = 6 => 0 pairs (X) H5,H8: 6.. / H5 = 6 => 10 pairs (_) / H8 = 6 => 0 pairs (X) F2,E3: 7.. / F2 = 7 => 12 pairs (_) / E3 = 7 => 11 pairs (_) C4,C6: 8.. / C4 = 8 => 7 pairs (_) / C6 = 8 => 8 pairs (_) D9,G9: 8.. / D9 = 8 => 9 pairs (_) / G9 = 8 => 11 pairs (_) I1,I2: 9.. / I1 = 9 => 10 pairs (_) / I2 = 9 => 10 pairs (_) A5,B5: 9.. / A5 = 9 => 8 pairs (_) / B5 = 9 => 16 pairs (_) G8,G9: 9.. / G8 = 9 => 8 pairs (_) / G9 = 9 => 9 pairs (_) * DURATION: 0:00:31.573687 START: 04:44:43.939515 END: 04:45:15.513202 2017-05-01 * CP COUNT: (29) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C3,F5,G7,H1,I6) * .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.79..5.8..9...45..5.1...3.....5.21 * PAIR C3: 1,2 BLK 1 A1: 1,2,5,6,9 # reduction candidate for 1,2 A1: 1,2 # 18 pairs C1: 1,2,6,9 # reduction candidate for 1,2 C1: 1,2 # 20 pairs C2: 1,2,6,9 # reduction candidate for 1,2 C2: 1,2 # 15 pairs A3: 1,2,3,5 # reduction candidate for 1,2 A3: 1,2 # 18 pairs * PAIR C3: 1,2 ROW 3 D3: 1,2,4,5 # reduction candidate for 1,2 D3: 1,2 # 13 pairs D3: 4,5 # 8 pairs * PAIR C3: 1,2 COL C C7: 1,2,6,7 # reduction candidate for 1,2 C7: 1,2 # 15 pairs C7: 6,7 # 12 pairs * PAIR A4: 1,7 BLK 4 C4: 1,7,4,8 # reduction candidate for 1,7 C4: 1,7 # 19 pairs C4: 4,8 # 8 pairs * PAIR A6: 1,6 BLK 4 C6: 1,6,4,8 # reduction candidate for 1,6 C6: 1,6 => CTR * 57.3.....4...8.5.9.8.5.94.6748156392953248167.2.7938548179326452.5417983.94865721 C6: 4,8 # 10 pairs * PAIR A6: 1,6 COL A A1: 1,6,2,5,9 # reduction candidate for 1,6 A1: 1,6 # 22 pairs A1: 2,5,9 # 7 pairs * PAIR F5: 2,8 BLK 5 D4: 2,8,1,5 # reduction candidate for 2,8 D4: 2,8 # 17 pairs D5: 2,8,5 # reduction candidate for 2,8 D5: 2,8 # 14 pairs * PAIR F5: 2,8 ROW 5 I5: 2,8,7 # reduction candidate for 2,8 I5: 2,8 # 15 pairs I5: 7 # 11 pairs * PAIR F5: 2,8 COL F F8: 2,8,4,7 # reduction candidate for 2,8 F8: 2,8 # 12 pairs F8: 4,7 # 9 pairs * PAIR I6: 4,8 BLK 6 G4: 4,8,2,3,7 # reduction candidate for 4,8 G4: 4,8 # 30 pairs I4: 4,8,2,7 # reduction candidate for 4,8 I4: 4,8 # 14 pairs G6: 4,8,3,6 # reduction candidate for 4,8 G6: 4,8 => CTR * 57.3.42184...81579.8.579436748156392953248167.2.7938548179...45..5.1..83..48.5.21 G6: 3,6 # 8 pairs * PAIR I6: 4,8 ROW 6 C6: 4,8,1,6 # reduction candidate for 4,8 C6: 1,6 => CTR * 57.3.....4...8.5.9.8.5.94.6748156392953248167.2.7938548179326452.5417983.94865721 C6: 4,8 # 10 pairs * PAIR I6: 4,8 COL I I1: 4,8,2,9 # reduction candidate for 4,8 I1: 4,8 # 13 pairs I1: 2,9 # 10 pairs * PAIR G7: 6,7 BLK 9 G8: 6,7,8,9 # reduction candidate for 6,7 G8: 6,7 # 16 pairs H8: 6,7,8 # reduction candidate for 6,7 H8: 6,7 # 11 pairs G9: 6,7,8,9 # reduction candidate for 6,7 G9: 6,7 # 19 pairs * PAIR G7: 6,7 ROW 7 C7: 6,7,1,2 # reduction candidate for 6,7 C7: 6,7 # 12 pairs E7: 6,7,2,3 # reduction candidate for 6,7 E7: 6,7 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0074-base-pr-000.dot * REASONING * DIS # C6: 1,6 => CTR => C6: 4,8 * DIS # G6: 4,8 => CTR => G6: 3,6 * DIS # C6: 1,6 => CTR => C6: 4,8 * CNT 3 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,C3,F5,G7,H1,I6) * .7.3.....4...8.5...8...9..6.....6.9...3.4.1...2.79..5.8..9...45..5.1...3.....5.21 * PAIR C3: 1,2 BLK 1 A1: 1,2,5,6,9 # reduction candidate for 1,2 A1: 1,2 # 18 pairs C1: 1,2,6,9 # reduction candidate for 1,2 C1: 1,2 # 20 pairs C2: 1,2,6,9 # reduction candidate for 1,2 C2: 1,2 # 15 pairs A3: 1,2,3,5 # reduction candidate for 1,2 A3: 1,2 # 18 pairs * PAIR C3: 1,2 ROW 3 D3: 1,2,4,5 # reduction candidate for 1,2 D3: 1,2 # 13 pairs D3: 4,5 # 8 pairs * PAIR C3: 1,2 COL C C7: 1,2,6,7 # reduction candidate for 1,2 C7: 1,2 # 15 pairs C7: 6,7 # 12 pairs * PAIR A4: 1,7 BLK 4 C4: 1,7,4,8 # reduction candidate for 1,7 C4: 1,7 # 19 pairs C4: 4,8 # 8 pairs * PAIR A6: 1,6 BLK 4 C6: 1,6,4,8 # reduction candidate for 1,6 C6: 1,6 => CTR * 57.3.....4...8.5.9.8.5.94.6748156392953248167.2.7938548179326452.5417983.94865721 * PAIR A6: 1,6 COL A A1: 1,6,2,5,9 # reduction candidate for 1,6 A1: 1,6 # 26 pairs A1: 2,5,9 # 10 pairs * PAIR F5: 2,8 BLK 5 D4: 2,8,1,5 # reduction candidate for 2,8 D4: 2,8 # 17 pairs D5: 2,8,5 # reduction candidate for 2,8 D5: 2,8 # 17 pairs * PAIR F5: 2,8 ROW 5 I5: 2,8,7 # reduction candidate for 2,8 I5: 2,8 # 15 pairs I5: 7 # 14 pairs * PAIR F5: 2,8 COL F F8: 2,8,4,7 # reduction candidate for 2,8 F8: 2,8 # 14 pairs F8: 4,7 # 13 pairs * PAIR I6: 4,8 BLK 6 G4: 4,8,2,3,7 # reduction candidate for 4,8 G4: 4,8 # 30 pairs I4: 4,8,2,7 # reduction candidate for 4,8 I4: 4,8 # 14 pairs * PAIR I6: 4,8 COL I I1: 4,8,2,9 # reduction candidate for 4,8 I1: 4,8 # 16 pairs I1: 2,9 # 12 pairs * PAIR G7: 6,7 BLK 9 G8: 6,7,8,9 # reduction candidate for 6,7 G8: 6,7 # 27 pairs H8: 6,7,8 # reduction candidate for 6,7 H8: 6,7 # 14 pairs G9: 6,7,8,9 # reduction candidate for 6,7 G9: 6,7 => SOLVED * 976354218431682579582179436154236897793548162628791354817923645265417983349865721 * DURATION: 0:00:20.121010 START: 04:45:37.640233 END: 04:45:57.761243 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0074-base-pr-001.dot * REASONING * DIS # C6: 1,6 => CTR => C6: 4,8 * PRF C6: 4,8 # G9: 6,7 => SOL * STA C6: 4,8 + G9: 6,7 * CNT 2 HDP CHAINS / 26 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=74
Solution
position: 976354218431682579582179436154236897793548162628791354817923645265417983349865721 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:
* INC # A1: 1,2 => UNS * INC # C1: 1,2 => UNS * INC # C2: 1,2 => UNS * INC # A3: 1,2 => UNS * INC # D3: 1,2 => UNS * INC # D3: 4,5 => UNS * INC # C7: 1,2 => UNS * INC # C7: 6,7 => UNS * INC # C4: 1,7 => UNS * INC # C4: 4,8 => UNS * DIS # C6: 1,6 => CTR => C6: 4,8 * INC # C6: 4,8 => UNS * INC # A1: 1,6 => UNS * INC # A1: 2,5,9 => UNS * INC # D4: 2,8 => UNS * INC # D5: 2,8 => UNS * INC # I5: 2,8 => UNS * INC # I5: 7 => UNS * INC # F8: 2,8 => UNS * INC # F8: 4,7 => UNS * INC # G4: 4,8 => UNS * INC # I4: 4,8 => UNS * DIS # G6: 4,8 => CTR => G6: 3,6 * INC # G6: 3,6 => UNS * INC # C6: 4,8 => UNS * DIS # C6: 1,6 => CTR => C6: 4,8 * INC # I1: 4,8 => UNS * INC # I1: 2,9 => UNS * INC # G8: 6,7 => UNS * INC # H8: 6,7 => UNS * INC # G9: 6,7 => UNS * INC # C7: 6,7 => UNS * INC # E7: 6,7 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 1,2 => UNS * INC # C1: 1,2 => UNS * INC # C2: 1,2 => UNS * INC # A3: 1,2 => UNS * INC # D3: 1,2 => UNS * INC # D3: 4,5 => UNS * INC # C7: 1,2 => UNS * INC # C7: 6,7 => UNS * INC # C4: 1,7 => UNS * INC # C4: 4,8 => UNS * DIS # C6: 1,6 => CTR => C6: 4,8 * INC C6: 4,8 # A1: 1,6 => UNS * INC C6: 4,8 # A1: 2,5,9 => UNS * INC C6: 4,8 # D4: 2,8 => UNS * INC C6: 4,8 # D5: 2,8 => UNS * INC C6: 4,8 # I5: 2,8 => UNS * INC C6: 4,8 # I5: 7 => UNS * INC C6: 4,8 # F8: 2,8 => UNS * INC C6: 4,8 # F8: 4,7 => UNS * INC C6: 4,8 # G4: 4,8 => UNS * INC C6: 4,8 # I4: 4,8 => UNS * INC C6: 4,8 # I1: 4,8 => UNS * INC C6: 4,8 # I1: 2,9 => UNS * INC C6: 4,8 # G8: 6,7 => UNS * INC C6: 4,8 # H8: 6,7 => UNS * PRF C6: 4,8 # G9: 6,7 => SOL * STA C6: 4,8 + G9: 6,7 * CNT 26 HDP CHAINS / 26 HYP OPENED