Analysis of zz-www.sudokuwiki.org-0137-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=137
level: medium
position: .4..8..1...95..2...7....5.61...3...2...6.8...4...1...89.1....2...7..24...2..9..3. initial
Autosolve
position: .4..8..1..195..2...7....5.61...3...27..6.8...4...1...89.1....2...7..24...24.9..3. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A3: 3,8 => SOL * PRF # D3: 2,4 => SOL * DIS # E5: 5 => CTR => E5: 2,4 * DIS # A8: 5,6 => CTR => A8: 3,8 * CNT 4 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:
* PRF # A3: 3,8 => SOL * STA A3: 3,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .4..8..1...95..2...7....5.61...3...2...6.8...4...1...89.1....2...7..24...2..9..3. | initial |
| .4..8..1..195..2...7....5.61...3...27..6.8...4...1...89.1....2...7..24...24.9..3. | autosolve |
| 245986713619573284378241596186435972793628145452719368961354827837162459524897631 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) C3: 3,8 E3: 2,4 E8: 5,6 I7: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D3,F3: 1.. / D3 = 1 => 17 pairs (_) / F3 = 1 => 4 pairs (_) G5,I5: 1.. / G5 = 1 => 4 pairs (_) / I5 = 1 => 19 pairs (_) D8,I8: 1.. / D8 = 1 => 10 pairs (_) / I8 = 1 => 17 pairs (_) F3,F9: 1.. / F3 = 1 => 4 pairs (_) / F9 = 1 => 17 pairs (_) G5,G9: 1.. / G5 = 1 => 4 pairs (_) / G9 = 1 => 19 pairs (_) A1,A3: 2.. / A1 = 2 => 0 pairs (*) / A3 = 2 => 0 pairs (X) C5,C6: 2.. / C5 = 2 => 0 pairs (X) / C6 = 2 => 7 pairs (_) E5,D6: 2.. / E5 = 2 => 7 pairs (_) / D6 = 2 => 0 pairs (X) A1,D1: 2.. / A1 = 2 => 0 pairs (*) / D1 = 2 => 0 pairs (X) C5,E5: 2.. / C5 = 2 => 0 pairs (X) / E5 = 2 => 7 pairs (_) C6,D6: 2.. / C6 = 2 => 7 pairs (_) / D6 = 2 => 0 pairs (X) E3,E5: 2.. / E3 = 2 => 0 pairs (X) / E5 = 2 => 7 pairs (_) I2,I5: 4.. / I2 = 4 => 8 pairs (_) / I5 = 4 => 16 pairs (_) A1,C1: 5.. / A1 = 5 => 21 pairs (_) / C1 = 5 => 7 pairs (_) E2,E7: 7.. / E2 = 7 => 7 pairs (_) / E7 = 7 => 9 pairs (_) H2,H3: 8.. / H2 = 8 => 7 pairs (_) / H3 = 8 => 0 pairs (X) B4,C4: 8.. / B4 = 8 => 8 pairs (_) / C4 = 8 => 9 pairs (_) G7,G9: 8.. / G7 = 8 => 4 pairs (_) / G9 = 8 => 7 pairs (_) A2,H2: 8.. / A2 = 8 => 0 pairs (X) / H2 = 8 => 7 pairs (_) C3,C4: 8.. / C3 = 8 => 8 pairs (_) / C4 = 8 => 9 pairs (_) H8,I8: 9.. / H8 = 9 => 16 pairs (_) / I8 = 9 => 11 pairs (_) * DURATION: 0:00:25.242316 START: 06:04:03.672762 END: 06:04:28.915078 2017-05-01 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,E3,E8,I7) * .4..8..1..195..2...7....5.61...3...27..6.8...4...1...89.1....2...7..24...24.9..3. * PAIR C3: 3,8 BLK 1 A2: 3,8,6 # reduction candidate for 3,8 A2: 3,8 # 10 pairs A3: 3,8,2 # reduction candidate for 3,8 A3: 3,8 => SOLVED * 245986713619573284378241596186435972793628145452719368961354827837162459524897631 A3: 2 # 7 pairs * PAIR E3: 2,4 BLK 2 D3: 2,4,1,3,9 # reduction candidate for 2,4 D3: 2,4 => SOLVED * 245986713619573284378241596186435972793628145452719368961354827837162459524897631 D3: 1,3,9 # 4 pairs * PAIR E3: 2,4 COL E E5: 2,4,5 # reduction candidate for 2,4 E5: 5 => CTR * 245.8671.6195..28..7..2.5.61...3.9.27926581434..21...8961...82...7.624...24.9.63. E5: 2,4 # 6 pairs * PAIR E8: 5,6 BLK 8 E7: 5,6,4,7 # reduction candidate for 5,6 E7: 5,6 # 10 pairs F7: 5,6,3,4,7 # reduction candidate for 5,6 F7: 5,6 # 7 pairs F9: 5,6,1,7 # reduction candidate for 5,6 F9: 5,6 # 6 pairs * PAIR E8: 5,6 ROW 8 A8: 5,6,3,8 # reduction candidate for 5,6 A8: 5,6 => CTR * .4..8..1..195..28..78...54618..3...27..6.81544...1.3.89.1...82..378.2491824.9.63. A8: 3,8 # 5 pairs B8: 5,6,3,8 # reduction candidate for 5,6 B8: 5,6 # 19 pairs H8: 5,6,9 # reduction candidate for 5,6 H8: 5,6 # 11 pairs * PAIR I7: 5,7 BLK 9 I9: 5,7,1 # reduction candidate for 5,7 I9: 5,7 # 10 pairs I9: 1 # 10 pairs * PAIR I7: 5,7 ROW 7 E7: 5,7,4,6 # reduction candidate for 5,7 E7: 5,7 # 6 pairs F7: 5,7,3,4,6 # reduction candidate for 5,7 F7: 5,7 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0137-base-pr-000.dot * REASONING * PRF # A3: 3,8 => SOL * PRF # D3: 2,4 => SOL * DIS # E5: 5 => CTR => E5: 2,4 * DIS # A8: 5,6 => CTR => A8: 3,8 * CNT 4 HDP CHAINS / 18 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,E3,E8,I7) * .4..8..1..195..2...7....5.61...3...27..6.8...4...1...89.1....2...7..24...24.9..3. * PAIR C3: 3,8 BLK 1 A2: 3,8,6 # reduction candidate for 3,8 A2: 3,8 # 10 pairs A3: 3,8,2 # reduction candidate for 3,8 A3: 3,8 => SOLVED * 245986713619573284378241596186435972793628145452719368961354827837162459524897631 * DURATION: 0:00:03.127477 START: 06:04:42.989159 END: 06:04:46.116636 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0137-base-pr-001.dot * REASONING * PRF # A3: 3,8 => SOL * STA A3: 3,8 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=137
Solution
position: 245986713619573284378241596186435972793628145452719368961354827837162459524897631 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 # A2: 3,8 => UNS * PRF # A3: 3,8 => SOL * INC # A3: 2 => UNS * PRF # D3: 2,4 => SOL * INC # D3: 1,3,9 => UNS * INC # E5: 2,4 => UNS * DIS # E5: 5 => CTR => E5: 2,4 * INC # E7: 5,6 => UNS * INC # F7: 5,6 => UNS * INC # F9: 5,6 => UNS * DIS # A8: 5,6 => CTR => A8: 3,8 * INC # A8: 3,8 => UNS * INC # B8: 5,6 => UNS * INC # H8: 5,6 => UNS * INC # I9: 5,7 => UNS * INC # I9: 1 => UNS * INC # E7: 5,7 => UNS * INC # F7: 5,7 => UNS * CNT 18 HDP CHAINS / 18 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 3,8 => UNS * PRF # A3: 3,8 => SOL * STA A3: 3,8 * CNT 2 HDP CHAINS / 2 HYP OPENED