Analysis of zz-sudoku-de-640978-base.sdk
Contents
Original Sudoku
level: medium
position: ...8..6..9.8.5..3.2..4..5....4.31..6.2.....1.1..69.7....2..4..7.4..1.2.8..6..5... initial
Autosolve
position: 4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 6,7 => SOL * DIS # B3: 3 => CTR => B3: 6,7 * PRF # B3: 6,7 => SOL * DIS # B3: 3 => CTR => B3: 6,7 * DIS # C5: 3 => CTR => C5: 5,7 * DIS # C5: 3,5 => CTR => C5: 7 * PRF # C5: 7 => SOL * DIS # C5: 3 => CTR => C5: 5,7 * DIS # C5: 3,5 => CTR => C5: 7 * PRF # C5: 7 => SOL * CNT 10 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 6,7 => SOL * STA B3: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8..6..9.8.5..3.2..4..5....4.31..6.2.....1.1..69.7....2..4..7.4..1.2.8..6..5... | initial |
| 4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94 | autosolve |
| 435829671968157432271463589594731826627548913183692745352984167749316258816275394 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (28) B1: 3,5 C1: 1,5 B2: 6,7 C3: 1,7 F1: 3,9 F2: 6,7 E3: 6,7 F3: 3,9 I1: 1,9 I3: 1,9 A4: 5,7 C6: 3,5 D4: 5,7 D5: 5,7 I5: 3,5 I6: 3,5 A7: 3,8 B7: 1,5 A8: 5,7 A9: 3,8 B9: 1,7 E7: 6,8 F8: 6,7 E9: 7,8 G7: 1,3 H7: 5,6 H8: 5,6 G9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C3: 1.. / C1 = 1 => 0 pairs (X) / C3 = 1 => 0 pairs (_) I1,I3: 1.. / I1 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) B7,B9: 1.. / B7 = 1 => 0 pairs (X) / B9 = 1 => 0 pairs (_) G7,G9: 1.. / G7 = 1 => 0 pairs (*) / G9 = 1 => 0 pairs (X) C1,I1: 1.. / C1 = 1 => 0 pairs (X) / I1 = 1 => 0 pairs (_) C3,I3: 1.. / C3 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) B7,G7: 1.. / B7 = 1 => 0 pairs (X) / G7 = 1 => 0 pairs (_) B9,G9: 1.. / B9 = 1 => 0 pairs (*) / G9 = 1 => 0 pairs (X) B1,B3: 3.. / B1 = 3 => 0 pairs (*) / B3 = 3 => 0 pairs (X) F1,F3: 3.. / F1 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) C5,C6: 3.. / C5 = 3 => 0 pairs (X) / C6 = 3 => 26 pairs (_) I5,I6: 3.. / I5 = 3 => 26 pairs (_) / I6 = 3 => 0 pairs (X) A7,A9: 3.. / A7 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) G7,G9: 3.. / G7 = 3 => 0 pairs (X) / G9 = 3 => 0 pairs (_) B1,F1: 3.. / B1 = 3 => 0 pairs (*) / F1 = 3 => 0 pairs (X) B3,F3: 3.. / B3 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) C5,I5: 3.. / C5 = 3 => 0 pairs (X) / I5 = 3 => 26 pairs (_) C6,I6: 3.. / C6 = 3 => 26 pairs (_) / I6 = 3 => 0 pairs (X) A7,G7: 3.. / A7 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) A9,G9: 3.. / A9 = 3 => 0 pairs (X) / G9 = 3 => 0 pairs (_) B1,C1: 5.. / B1 = 5 => 0 pairs (X) / C1 = 5 => 0 pairs (_) D4,D5: 5.. / D4 = 5 => 0 pairs (X) / D5 = 5 => 0 pairs (_) I5,I6: 5.. / I5 = 5 => 0 pairs (X) / I6 = 5 => 26 pairs (_) B7,A8: 5.. / B7 = 5 => 0 pairs (*) / A8 = 5 => 0 pairs (X) H7,H8: 5.. / H7 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) A4,D4: 5.. / A4 = 5 => 0 pairs (*) / D4 = 5 => 0 pairs (X) C6,I6: 5.. / C6 = 5 => 0 pairs (X) / I6 = 5 => 26 pairs (_) B7,H7: 5.. / B7 = 5 => 0 pairs (*) / H7 = 5 => 0 pairs (X) A8,H8: 5.. / A8 = 5 => 0 pairs (X) / H8 = 5 => 0 pairs (_) A4,A8: 5.. / A4 = 5 => 0 pairs (*) / A8 = 5 => 0 pairs (X) B1,B7: 5.. / B1 = 5 => 0 pairs (X) / B7 = 5 => 0 pairs (_) B2,B3: 6.. / B2 = 6 => 0 pairs (*) / B3 = 6 => 0 pairs (X) F2,E3: 6.. / F2 = 6 => 0 pairs (X) / E3 = 6 => 0 pairs (_) E7,F8: 6.. / E7 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) H7,H8: 6.. / H7 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) B2,F2: 6.. / B2 = 6 => 0 pairs (*) / F2 = 6 => 0 pairs (X) B3,E3: 6.. / B3 = 6 => 0 pairs (X) / E3 = 6 => 0 pairs (_) E7,H7: 6.. / E7 = 6 => 0 pairs (X) / H7 = 6 => 0 pairs (_) F8,H8: 6.. / F8 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) E3,E7: 6.. / E3 = 6 => 0 pairs (*) / E7 = 6 => 0 pairs (X) F2,F8: 6.. / F2 = 6 => 0 pairs (X) / F8 = 6 => 0 pairs (_) F2,E3: 7.. / F2 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) A4,C5: 7.. / A4 = 7 => 0 pairs (X) / C5 = 7 => 0 pairs (_) D4,D5: 7.. / D4 = 7 => 0 pairs (*) / D5 = 7 => 0 pairs (X) A8,B9: 7.. / A8 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) F8,E9: 7.. / F8 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) B2,F2: 7.. / B2 = 7 => 0 pairs (X) / F2 = 7 => 0 pairs (_) A4,D4: 7.. / A4 = 7 => 0 pairs (X) / D4 = 7 => 0 pairs (_) C5,D5: 7.. / C5 = 7 => 0 pairs (*) / D5 = 7 => 0 pairs (X) A8,F8: 7.. / A8 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) B9,E9: 7.. / B9 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) A4,A8: 7.. / A4 = 7 => 0 pairs (X) / A8 = 7 => 0 pairs (_) C3,C5: 7.. / C3 = 7 => 0 pairs (X) / C5 = 7 => 0 pairs (_) E3,E9: 7.. / E3 = 7 => 0 pairs (X) / E9 = 7 => 0 pairs (_) F2,F8: 7.. / F2 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) A7,A9: 8.. / A7 = 8 => 0 pairs (X) / A9 = 8 => 0 pairs (_) E7,E9: 8.. / E7 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) A7,E7: 8.. / A7 = 8 => 0 pairs (X) / E7 = 8 => 0 pairs (_) A9,E9: 8.. / A9 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) F1,F3: 9.. / F1 = 9 => 0 pairs (*) / F3 = 9 => 0 pairs (X) I1,I3: 9.. / I1 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) F1,I1: 9.. / F1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) F3,I3: 9.. / F3 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) * DURATION: 0:01:55.770851 START: 07:33:35.054631 END: 07:35:30.825482 2017-05-01 * CP COUNT: (63) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,A8,A9,B1,B2,B7,B9,C1,C3,C6,D4,D5,E3,E7,E9,F1,F2,F3,F8,G7,G9,H7,H8,I1,I3,I5,I6) * 4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94 * PAIR B2: 6,7 BLK 1 B3: 6,7,3 # reduction candidate for 6,7 B3: 6,7 => SOLVED * 435829671968157432271463589594731826627548913183692745352984167749316258816275394 B3: 3 => CTR * 4..82.67.96815743223746958179453182662.74891.18.69274...2984.6754931.2.8..62.5.94 * PAIR E3: 6,7 ROW 3 B3: 6,7,3 # reduction candidate for 6,7 B3: 6,7 => SOLVED * 435829671968157432271463589594731826627548913183692745352984167749316258816275394 B3: 3 => CTR * 4..82.67.96815743223746958179453182662.74891.18.69274...2984.6754931.2.8..62.5.94 * PAIR A4: 5,7 BLK 4 C5: 5,7,3 # reduction candidate for 5,7 C5: 3 => CTR * 4..82.67.9.815.4322.746.581794531826623748915185692743..2984..7.4931.2.8..62.5.94 C5: 5,7 # 26 pairs * PAIR C6: 3,5 BLK 4 C5: 3,5,7 # reduction candidate for 3,5 C5: 3,5 => CTR * 4..82.67.9.815.4322.746.58179453182662.74891.18.69274...2984..7.4931.2.8..62.5.94 C5: 7 => SOLVED * 435829671968157432271463589594731826627548913183692745352984167749316258816275394 * PAIR D5: 5,7 ROW 5 C5: 5,7,3 # reduction candidate for 5,7 C5: 3 => CTR * 4..82.67.9.815.4322.746.581794531826623748915185692743..2984..7.4931.2.8..62.5.94 C5: 5,7 # 26 pairs * PAIR I5: 3,5 ROW 5 C5: 3,5,7 # reduction candidate for 3,5 C5: 3,5 => CTR * 4..82.67.9.815.4322.746.58179453182662.74891.18.69274...2984..7.4931.2.8..62.5.94 C5: 7 => SOLVED * 435829671968157432271463589594731826627548913183692745352984167749316258816275394 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-640978-base-pr-000.dot * REASONING * PRF # B3: 6,7 => SOL * DIS # B3: 3 => CTR => B3: 6,7 * PRF # B3: 6,7 => SOL * DIS # B3: 3 => CTR => B3: 6,7 * DIS # C5: 3 => CTR => C5: 5,7 * DIS # C5: 3,5 => CTR => C5: 7 * PRF # C5: 7 => SOL * DIS # C5: 3 => CTR => C5: 5,7 * DIS # C5: 3,5 => CTR => C5: 7 * PRF # C5: 7 => SOL * CNT 10 HDP CHAINS / 12 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,A8,A9,B1,B2,B7,B9,C1,C3,C6,D4,D5,E3,E7,E9,F1,F2,F3,F8,G7,G9,H7,H8,I1,I3,I5,I6) * 4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94 * PAIR B2: 6,7 BLK 1 B3: 6,7,3 # reduction candidate for 6,7 B3: 6,7 => SOLVED * 435829671968157432271463589594731826627548913183692745352984167749316258816275394 * DURATION: 0:00:02.172945 START: 07:35:45.795818 END: 07:35:47.968763 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-640978-base-pr-001.dot * REASONING * PRF # B3: 6,7 => SOL * STA B3: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/640978.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94 B1: 3,5 C1: 1,5 B2: 6,7 B3: 3,6,7 # reduction candidate for 6,7 B3: 6,7 => SOLVED * 435829671968157432271463589594731826627548913183692745352984167749316258816275394 * SOLVED! -------------------------------------------------- * AUTO .. A1 = 4 # set value D2 = 1 # set value G2: 4 # naked single G2 = 4 # set value I2: 2 # naked single I2 = 2 # set value H3 = 8 # set value A5 = 6 # set value E5 = 4 # set value H1: 7.. # hidden single H1 = 7 # set value E1: 2 # naked single E1 = 2 # set value D9: 2.. # hidden single F6: 2.. # hidden single F6 = 2 # set value D9 = 2 # set value F5: 8.. # hidden single H4: 2.. # hidden single B6: 8.. # hidden single H4 = 2 # set value F5 = 8 # set value B6 = 8 # set value G4: 8.. # hidden single G4 = 8 # set value B4: 9.. # hidden single B4 = 9 # set value C8: 9.. # hidden single C8 = 9 # set value D7: 9.. # hidden single D7 = 9 # set value D8: 3.. # hidden single H9: 9.. # hidden single D8 = 3 # set value H9 = 9 # set value I9: 4.. # hidden single G5: 9.. # hidden single H6: 4.. # hidden single G5 = 9 # set value H6 = 4 # set value I9 = 4 # set value Q7: 1.. = B7,B9: 1.. => B1,B3 != 1 Q4: 3.. = C5,C6: 3.. => C1,C3 != 3 Q1: 3.. = B1,B3: 3.. => B7,B9 != 3 F1,F3: 3,9.. => F3 != 6,7 # hidden pair A7,A9: 3,8.. => A7,A9 != 5,7 # hidden pair * UNSOLVED! |:step:| 00 -------------------------------------------------- highlight 3 C5: 3,5,7 I5: 3,5 I6: 3,5 C6: 3,5 => C5 = 7 * FORCE VALUE:: C5 = 7 C5 = 7 # set value A4: 5 # naked single C3: 1 # naked single D5: 5 # naked single C6: 3.. # hidden single D4: 7.. # hidden single I5: 3.. # hidden single A8: 7.. # hidden single * AUTO .. * SOLVED! |:step:| 01 --------------------------------------------------
Solution
position: 435829671968157432271463589594731826627548913183692745352984167749316258816275394 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:
* PRF # B3: 6,7 => SOL * DIS # B3: 3 => CTR => B3: 6,7 * PRF # B3: 6,7 => SOL * DIS # B3: 3 => CTR => B3: 6,7 * INC # C5: 5,7 => UNS * DIS # C5: 3 => CTR => C5: 5,7 * DIS # C5: 3,5 => CTR => C5: 7 * PRF # C5: 7 => SOL * INC # C5: 5,7 => UNS * DIS # C5: 3 => CTR => C5: 5,7 * DIS # C5: 3,5 => CTR => C5: 7 * PRF # C5: 7 => SOL * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B3: 6,7 => SOL * STA B3: 6,7 * CNT 1 HDP CHAINS / 1 HYP OPENED