Analysis of zz-www.sudokuwiki.org-0047-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=47
level: medium
position: .9.7.2.3...1...9..3.......1.....465..5.9.1.8..678.....5.......4..9...3...8.1.9.2. initial
Autosolve
position: .9.712.3...1...9..3...9...1....7465..5.961.8..678.....5......94..9...3...8.1.9.2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A6: 2,4 => CTR => A6: 9 * DIS # G5: 2,4 => CTR => G5: 7 * DIS # A2: 2,4 => CTR => A2: 6,7,8 * DIS # C4: 2,3 => CTR => C4: 8 * DIS # I4: 2,3 => CTR => I4: 9 * DIS # E6: 2 => CTR => E6: 3,5 * DIS # G6: 2 => CTR => G6: 1,4 * DIS # G3: 5,7 => CTR => G3: 2,4,8 * CNT 8 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A6: 2,4 => CTR => A6: 9 * DIS A6: 9 # C5: 3 => CTR => C5: 2,4 * DIS A6: 9 + C5: 2,4 # A2: 2,4 => CTR => A2: 6,7,8 * PRF A6: 9 + C5: 2,4 + A2: 6,7,8 # H3: 6 => SOL * STA A6: 9 + C5: 2,4 + A2: 6,7,8 + H3: 6 * CNT 4 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .9.7.2.3...1...9..3.......1.....465..5.9.1.8..678.....5.......4..9...3...8.1.9.2. | initial |
| .9.712.3...1...9..3...9...1....7465..5.961.8..678.....5......94..9...3...8.1.9.2. | autosolve |
| 695712438821436975374598261138274659452961783967853142516327894249685317783149526 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) A5: 2,4 D4: 2,3 F6: 3,5 H6: 1,4 G9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A4,B4: 1.. / A4 = 1 => 9 pairs (_) / B4 = 1 => 0 pairs (X) G6,H6: 1.. / G6 = 1 => 18 pairs (_) / H6 = 1 => 0 pairs (X) G7,H8: 1.. / G7 = 1 => 0 pairs (X) / H8 = 1 => 18 pairs (_) B7,G7: 1.. / B7 = 1 => 18 pairs (_) / G7 = 1 => 0 pairs (X) A4,A8: 1.. / A4 = 1 => 9 pairs (_) / A8 = 1 => 0 pairs (X) G6,G7: 1.. / G6 = 1 => 18 pairs (_) / G7 = 1 => 0 pairs (X) H6,H8: 1.. / H6 = 1 => 0 pairs (X) / H8 = 1 => 18 pairs (_) I2,G3: 2.. / I2 = 2 => 0 pairs (X) / G3 = 2 => 12 pairs (_) D4,E6: 2.. / D4 = 2 => 10 pairs (_) / E6 = 2 => 0 pairs (X) C5,I5: 3.. / C5 = 3 => 0 pairs (X) / I5 = 3 => 15 pairs (_) C9,E9: 3.. / C9 = 3 => 17 pairs (_) / E9 = 3 => 0 pairs (X) B4,B7: 3.. / B4 = 3 => 14 pairs (_) / B7 = 3 => 0 pairs (X) C1,C3: 5.. / C1 = 5 => 11 pairs (_) / C3 = 5 => 7 pairs (_) E6,F6: 5.. / E6 = 5 => 9 pairs (_) / F6 = 5 => 6 pairs (_) G5,I5: 7.. / G5 = 7 => 12 pairs (_) / I5 = 7 => 0 pairs (X) F7,F8: 7.. / F7 = 7 => 6 pairs (_) / F8 = 7 => 0 pairs (X) A4,C4: 8.. / A4 = 8 => 0 pairs (X) / C4 = 8 => 5 pairs (_) G7,I8: 8.. / G7 = 8 => 18 pairs (_) / I8 = 8 => 8 pairs (_) A4,A6: 9.. / A4 = 9 => 0 pairs (X) / A6 = 9 => 8 pairs (_) I4,I6: 9.. / I4 = 9 => 8 pairs (_) / I6 = 9 => 0 pairs (X) A4,I4: 9.. / A4 = 9 => 0 pairs (X) / I4 = 9 => 8 pairs (_) A6,I6: 9.. / A6 = 9 => 8 pairs (_) / I6 = 9 => 0 pairs (X) * DURATION: 0:00:30.808459 START: 04:21:19.016264 END: 04:21:49.824723 2017-05-01 * CP COUNT: (22) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,D4,F6,G9,H6) * .9.712.3...1...9..3...9...1....7465..5.961.8..678.....5......94..9...3...8.1.9.2. * PAIR A5: 2,4 BLK 4 C5: 2,4,3 # reduction candidate for 2,4 C5: 2,4 # 15 pairs A6: 2,4,9 # reduction candidate for 2,4 A6: 2,4 => CTR * .9.712.3...134.97537.59.241918274653.53961.82267853419532687194149.25368.8.139.2. A6: 9 # 8 pairs * PAIR A5: 2,4 ROW 5 G5: 2,4,7 # reduction candidate for 2,4 G5: 2,4 => CTR * .94712.3...1...9..3.5.9...1..8.7465..53961.87.678...1.532687194..9..53.8.86139.25 G5: 7 # 12 pairs * PAIR A5: 2,4 COL A A2: 2,4,6,7,8 # reduction candidate for 2,4 A2: 2,4 => CTR * 89.712435..1...9.83.5.982.1138274659.5.9617839678..14251..27894.2948531..8413952. A2: 6,7,8 # 5 pairs A8: 2,4,1,6,7 # reduction candidate for 2,4 A8: 2,4 # 14 pairs * PAIR D4: 2,3 BLK 5 E6: 2,3,5 # reduction candidate for 2,3 E6: 5 # 9 pairs E6: 2,3 # 6 pairs * PAIR D4: 2,3 ROW 4 B4: 2,3,1 # reduction candidate for 2,3 B4: 2,3 # 9 pairs C4: 2,3,8 # reduction candidate for 2,3 C4: 2,3 => CTR * .9.712.3...13489.53...9.241813274659.5.96178396785341253268719414952.3.8.8.139.2. C4: 8 # 5 pairs I4: 2,3,9 # reduction candidate for 2,3 I4: 2,3 => CTR * .9.712.3...134.97537.59.241918274653.53961.82267853419532687194149.25368.8.139.2. I4: 9 # 8 pairs * PAIR D4: 2,3 COL D D7: 2,3,6 # reduction candidate for 2,3 D7: 6 # 7 pairs D7: 2,3 # 6 pairs * PAIR F6: 3,5 BLK 5 E6: 3,5,2 # reduction candidate for 3,5 E6: 2 => CTR * .9.712.3...1..39..3...98..1...374659453961.8.96782541353..87194..9..6378784139526 E6: 3,5 # 10 pairs * PAIR F6: 3,5 COL F F2: 3,5,6,8 # reduction candidate for 3,5 F2: 3,5 # 7 pairs F2: 6,8 # 6 pairs * PAIR H6: 1,4 BLK 6 G6: 1,4,2 # reduction candidate for 1,4 G6: 2 => CTR * .94712.3..71...9.2325.9...19182746532539614874678..2195326..194..9...3.8.8.1.9.2. G6: 1,4 # 8 pairs * PAIR G9: 5,7 BLK 9 I8: 5,7,6,8 # reduction candidate for 5,7 I8: 5,7 # 18 pairs I9: 5,7,6 # reduction candidate for 5,7 I9: 5,7 # 12 pairs * PAIR G9: 5,7 COL G G3: 5,7,2,4,8 # reduction candidate for 5,7 G3: 5,7 => CTR * .9.71283...1...9.23...9...1....7465..53961.87.678...1.53..87194..9...3.8.8.139.2. G3: 2,4,8 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0047-base-pr-000.dot * REASONING * DIS # A6: 2,4 => CTR => A6: 9 * DIS # G5: 2,4 => CTR => G5: 7 * DIS # A2: 2,4 => CTR => A2: 6,7,8 * DIS # C4: 2,3 => CTR => C4: 8 * DIS # I4: 2,3 => CTR => I4: 9 * DIS # E6: 2 => CTR => E6: 3,5 * DIS # G6: 2 => CTR => G6: 1,4 * DIS # G3: 5,7 => CTR => G3: 2,4,8 * CNT 8 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,D4,F6,G9,H6) * .9.712.3...1...9..3...9...1....7465..5.961.8..678.....5......94..9...3...8.1.9.2. * PAIR A5: 2,4 BLK 4 C5: 2,4,3 # reduction candidate for 2,4 C5: 2,4 # 15 pairs A6: 2,4,9 # reduction candidate for 2,4 A6: 2,4 => CTR * .9.712.3...134.97537.59.241918274653.53961.82267853419532687194149.25368.8.139.2. * RESTART * PAIR A5: 2,4 BLK 4 C5: 2,4,3 # reduction candidate for 2,4 C5: 3 => CTR * .9.712.3...1..39..3...9...1...374659453961.8.96782541353..87194..9..6378784139526 * PAIR A5: 2,4 COL A A2: 2,4,6,7,8 # reduction candidate for 2,4 A2: 2,4 => CTR * 89.712435..1...9.83.5.982.1138274659.5.9617839678..14251..27894.2948531..8413952. A8: 2,4,1,6,7 # reduction candidate for 2,4 A8: 2,4 # 19 pairs * RESTART * PAIR A5: 2,4 COL A A8: 2,4,1,6,7 # reduction candidate for 2,4 A8: 2,4 # 19 pairs A8: 1,6,7 # 16 pairs * PAIR RESTART * PAIR A5: 2,4 COL A A8: 2,4,1,6,7 # reduction candidate for 2,4 A8: 2,4 # 19 pairs A8: 1,6,7 # 16 pairs * PAIR F6: 3,5 COL F F2: 3,5,6,8 # reduction candidate for 3,5 F2: 3,5 # 17 pairs F2: 6,8 # 16 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,A5,B3,B4,C4,C5,D7,E6,E9,F6,G1,G6,G7,H6,I9) * .9.712.3..21...9..3...9.2.1...274659.5.9617839678....25......94..9...3...8.1.952. * PAIR B3: 4,7 ROW 3 H3: 4,7,6 # reduction candidate for 4,7 H3: 6 => SOLVED * 695712438821436975374598261138274659452961783967853142516327894249685317783149526 * DURATION: 0:00:13.325712 START: 04:22:08.756941 END: 04:22:22.082653 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0047-base-pr-001.dot * REASONING * DIS # A6: 2,4 => CTR => A6: 9 * DIS A6: 9 # C5: 3 => CTR => C5: 2,4 * DIS A6: 9 + C5: 2,4 # A2: 2,4 => CTR => A2: 6,7,8 * PRF A6: 9 + C5: 2,4 + A2: 6,7,8 # H3: 6 => SOL * STA A6: 9 + C5: 2,4 + A2: 6,7,8 + H3: 6 * CNT 4 HDP CHAINS / 14 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=47
Solution
position: 695712438821436975374598261138274659452961783967853142516327894249685317783149526 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 # C5: 2,4 => UNS * DIS # A6: 2,4 => CTR => A6: 9 * INC # A6: 9 => UNS * DIS # G5: 2,4 => CTR => G5: 7 * INC # G5: 7 => UNS * DIS # A2: 2,4 => CTR => A2: 6,7,8 * INC # A2: 6,7,8 => UNS * INC # A8: 2,4 => UNS * INC # E6: 2,3 => UNS * INC # E6: 5 => UNS * INC # B4: 2,3 => UNS * DIS # C4: 2,3 => CTR => C4: 8 * INC # C4: 8 => UNS * DIS # I4: 2,3 => CTR => I4: 9 * INC # I4: 9 => UNS * INC # D7: 2,3 => UNS * INC # D7: 6 => UNS * INC # E6: 3,5 => UNS * DIS # E6: 2 => CTR => E6: 3,5 * INC # F2: 3,5 => UNS * INC # F2: 6,8 => UNS * INC # G6: 1,4 => UNS * DIS # G6: 2 => CTR => G6: 1,4 * INC # I8: 5,7 => UNS * INC # I9: 5,7 => UNS * DIS # G3: 5,7 => CTR => G3: 2,4,8 * INC # G3: 2,4,8 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C5: 2,4 => UNS * DIS # A6: 2,4 => CTR => A6: 9 * INC A6: 9 # C5: 2,4 => UNS * DIS A6: 9 # C5: 3 => CTR => C5: 2,4 * DIS A6: 9 + C5: 2,4 # A2: 2,4 => CTR => A2: 6,7,8 * INC A6: 9 + C5: 2,4 + A2: 6,7,8 # A8: 2,4 => UNS * INC A6: 9 + C5: 2,4 + A2: 6,7,8 # A8: 2,4 => UNS * INC A6: 9 + C5: 2,4 + A2: 6,7,8 # A8: 1,6,7 => UNS * INC A6: 9 + C5: 2,4 + A2: 6,7,8 # A8: 2,4 => UNS * INC A6: 9 + C5: 2,4 + A2: 6,7,8 # A8: 1,6,7 => UNS * INC A6: 9 + C5: 2,4 + A2: 6,7,8 # F2: 3,5 => UNS * INC A6: 9 + C5: 2,4 + A2: 6,7,8 # F2: 6,8 => UNS * INC A6: 9 + C5: 2,4 + A2: 6,7,8 # H3: 4,7 => UNS * PRF A6: 9 + C5: 2,4 + A2: 6,7,8 # H3: 6 => SOL * STA A6: 9 + C5: 2,4 + A2: 6,7,8 + H3: 6 * CNT 14 HDP CHAINS / 14 HYP OPENED