Analysis of zz-sudoku-de-722388-base.sdk
Contents
Original Sudoku
level: medium
position: .8.32.....1.8...32..21..6........7568...1...4769........3..82..14...7.6.....31.9. initial
Autosolve
position: 68432.....1786..323.217.6..421983756835716924769..2.....36.82..148297.6.2.6.31.9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F2: 5,9 => SOL * DIS # F2: 4 => CTR => F2: 5,9 * DIS # F3: 5,9 => CTR => F3: 4 * PRF # F3: 4 => SOL * PRF # I3: 5,9 => SOL * DIS # I3: 8 => CTR => I3: 5,9 * DIS # B7: 5,9 => CTR => B7: 7 * PRF # B7: 7 => SOL * PRF # F2: 5,9 => SOL * DIS # F2: 4 => CTR => F2: 5,9 * DIS # F3: 5,9 => CTR => F3: 4 * PRF # F3: 4 => SOL * DIS # I1: 1,7 => CTR => I1: 5,9 * DIS # I1: 1,5 => CTR => I1: 7,9 * DIS # I1: 1,7 => CTR => I1: 5,9 * DIS # H7: 1,7 => CTR => H7: 4 * PRF # H7: 4 => SOL * DIS # F2: 4,5 => CTR => F2: 9 * PRF # F2: 9 => SOL * PRF # I6: 1,8 => SOL * DIS # B7: 5,9 => CTR => B7: 7 * PRF # B7: 7 => SOL * PRF # B7: 5,7 => SOL * DIS # B7: 9 => CTR => B7: 5,7 * DIS # H7: 1,7 => CTR => H7: 4 * PRF # H7: 4 => SOL * DIS # I1: 1,7 => CTR => I1: 5,9 * CNT 27 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:
* PRF # F2: 5,9 => SOL * STA F2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.32.....1.8...32..21..6........7568...1...4769........3..82..14...7.6.....31.9. | initial |
| 68432.....1786..323.217.6..421983756835716924769..2.....36.82..148297.6.2.6.31.9. | autosolve |
| 684325179517869432392174685421983756835716924769542318973658241148297563256431897 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A2: 5,9 B3: 5,9 F1: 5,9 G1: 1,5 H1: 1,7 G2: 4,5 H3: 4,8 D6: 4,5 E6: 4,5 H6: 1,8 A7: 5,9 B9: 5,7 E7: 4,5 D9: 4,5 I7: 1,7 G8: 3,5 I8: 3,5 G9: 4,8 I9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H7,I7: 1.. / H7 = 1 => 0 pairs (X) / I7 = 1 => 20 pairs (_) G1,G6: 1.. / G1 = 1 => 20 pairs (_) / G6 = 1 => 0 pairs (X) G6,I6: 3.. / G6 = 3 => 0 pairs (*) / I6 = 3 => 0 pairs (X) G8,I8: 3.. / G8 = 3 => 19 pairs (_) / I8 = 3 => 0 pairs (*) G6,G8: 3.. / G6 = 3 => 0 pairs (*) / G8 = 3 => 0 pairs (X) I6,I8: 3.. / I6 = 3 => 19 pairs (_) / I8 = 3 => 0 pairs (*) F2,F3: 4.. / F2 = 4 => 0 pairs (X) / F3 = 4 => 0 pairs (_) G2,H3: 4.. / G2 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) D6,E6: 4.. / D6 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) E7,D9: 4.. / E7 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) H7,G9: 4.. / H7 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) F2,G2: 4.. / F2 = 4 => 0 pairs (X) / G2 = 4 => 0 pairs (_) F3,H3: 4.. / F3 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) E7,H7: 4.. / E7 = 4 => 0 pairs (X) / H7 = 4 => 0 pairs (_) D9,G9: 4.. / D9 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) D6,D9: 4.. / D6 = 4 => 0 pairs (X) / D9 = 4 => 0 pairs (_) E6,E7: 4.. / E6 = 4 => 0 pairs (*) / E7 = 4 => 0 pairs (X) G2,G9: 4.. / G2 = 4 => 0 pairs (*) / G9 = 4 => 0 pairs (X) H3,H7: 4.. / H3 = 4 => 0 pairs (X) / H7 = 4 => 0 pairs (_) A2,B3: 5.. / A2 = 5 => 0 pairs (*) / B3 = 5 => 0 pairs (X) D6,E6: 5.. / D6 = 5 => 0 pairs (*) / E6 = 5 => 0 pairs (X) E7,D9: 5.. / E7 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) G8,I8: 5.. / G8 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) B9,D9: 5.. / B9 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) A2,A7: 5.. / A2 = 5 => 0 pairs (*) / A7 = 5 => 0 pairs (X) D6,D9: 5.. / D6 = 5 => 0 pairs (*) / D9 = 5 => 0 pairs (X) E6,E7: 5.. / E6 = 5 => 0 pairs (X) / E7 = 5 => 0 pairs (_) H1,I1: 7.. / H1 = 7 => 19 pairs (_) / I1 = 7 => 0 pairs (X) B7,B9: 7.. / B7 = 7 => 0 pairs (*) / B9 = 7 => 0 pairs (X) B9,I9: 7.. / B9 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) H1,H7: 7.. / H1 = 7 => 19 pairs (_) / H7 = 7 => 0 pairs (X) H3,I3: 8.. / H3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) G9,I9: 8.. / G9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) G6,G9: 8.. / G6 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) H3,H6: 8.. / H3 = 8 => 0 pairs (*) / H6 = 8 => 0 pairs (X) A2,B3: 9.. / A2 = 9 => 0 pairs (X) / B3 = 9 => 0 pairs (_) I1,I3: 9.. / I1 = 9 => 21 pairs (_) / I3 = 9 => 0 pairs (X) A7,B7: 9.. / A7 = 9 => 0 pairs (*) / B7 = 9 => 0 pairs (X) F1,I1: 9.. / F1 = 9 => 0 pairs (X) / I1 = 9 => 21 pairs (_) A2,F2: 9.. / A2 = 9 => 0 pairs (X) / F2 = 9 => 0 pairs (_) A2,A7: 9.. / A2 = 9 => 0 pairs (X) / A7 = 9 => 0 pairs (_) B3,B7: 9.. / B3 = 9 => 0 pairs (*) / B7 = 9 => 0 pairs (X) * DURATION: 0:01:10.333099 START: 08:19:18.118353 END: 08:20:28.451452 2017-05-01 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B3,B9,D6,D9,E6,E7,F1,G1,G2,G8,G9,H1,H3,H6,I7,I8,I9) * 68432.....1786..323.217.6..421983756835716924769..2.....36.82..148297.6.2.6.31.9. * PAIR A2: 5,9 ROW 2 F2: 5,9,4 # reduction candidate for 5,9 F2: 5,9 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 F2: 4 => CTR * 68432....917864532352179648421983756835716924769..2.8.5936482..14829736.2.6.31.9. * PAIR B3: 5,9 ROW 3 F3: 5,9,4 # reduction candidate for 5,9 F3: 5,9 => CTR * 68432.....17864532352179648421983756835716924769..2.8.5936482..14829736.2.6.31.9. F3: 4 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 I3: 5,9,8 # reduction candidate for 5,9 I3: 5,9 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 I3: 8 => CTR * 6843251.9.1786..323.217.6.8421983756835716924769..2.8...36.82..148297.652.6.31897 * PAIR B3: 5,9 COL B B7: 5,9,7 # reduction candidate for 5,9 B7: 5,9 => CTR * 68432.....1786..323.217.6..421983756835716924769..2.....36.82..148297.6.276531498 B7: 7 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 * PAIR F1: 5,9 BLK 2 F2: 5,9,4 # reduction candidate for 5,9 F2: 5,9 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 F2: 4 => CTR * 68432....917864532352179648421983756835716924769..2.8.5936482..14829736.2.6.31.9. F3: 5,9,4 # reduction candidate for 5,9 F3: 5,9 => CTR * 68432.....17864532352179648421983756835716924769..2.8.5936482..14829736.2.6.31.9. F3: 4 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 * PAIR F1: 5,9 ROW 1 I1: 5,9,1,7 # reduction candidate for 5,9 I1: 1,7 => CTR * 6843295..917865432352174689421983756835716924769..21....36.82..148297.6.2.6.31.9. I1: 5,9 # 20 pairs * PAIR G1: 1,5 BLK 3 I1: 1,5,7,9 # reduction candidate for 1,5 I1: 1,5 => CTR * 684329.7.91786..32352174689421983756835716924769..2.1.5936482..148297.6.2.6.31.9. I1: 7,9 # 20 pairs * PAIR H1: 1,7 BLK 3 I1: 1,7,5,9 # reduction candidate for 1,7 I1: 1,7 => CTR * 6843295..917865432352174689421983756835716924769..21....36.82..148297.6.2.6.31.9. I1: 5,9 # 20 pairs * PAIR H1: 1,7 COL H H7: 1,7,4 # reduction candidate for 1,7 H7: 1,7 => CTR * 68432.....1786..323.217.648421983756835716924769..2.8...36482..148297.6.2.6531.9. H7: 4 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 * PAIR G2: 4,5 ROW 2 F2: 4,5,9 # reduction candidate for 4,5 F2: 4,5 => CTR * 68432....91786..3235217.6..421983756835716924769..2...5936482..148297.6.276531498 F2: 9 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 * PAIR H6: 1,8 BLK 6 G6: 1,8,3 # reduction candidate for 1,8 G6: 1,8 # 19 pairs I6: 1,8,3 # reduction candidate for 1,8 I6: 1,8 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 I6: 3 # 19 pairs * PAIR A7: 5,9 BLK 7 B7: 5,9,7 # reduction candidate for 5,9 B7: 5,9 => CTR * 68432.....1786..323.217.6..421983756835716924769..2.....36.82..148297.6.276531498 B7: 7 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 * PAIR B9: 5,7 BLK 7 B7: 5,7,9 # reduction candidate for 5,7 B7: 5,7 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 B7: 9 => CTR * 68432.....1786..323.217.6..421983756835716924769..2....936.82..148297.6.276531498 * PAIR I7: 1,7 BLK 9 H7: 1,7,4 # reduction candidate for 1,7 H7: 1,7 => CTR * 68432.....1786..323.217.648421983756835716924769..2.8...36482..148297.6.2.6531.9. H7: 4 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 * PAIR I7: 1,7 COL I I1: 1,7,5,9 # reduction candidate for 1,7 I1: 1,7 => CTR * 6843295..917865432352174689421983756835716924769..21....36.82..148297.6.2.6.31.9. I1: 5,9 # 20 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-722388-base-pr-000.dot * REASONING * PRF # F2: 5,9 => SOL * DIS # F2: 4 => CTR => F2: 5,9 * DIS # F3: 5,9 => CTR => F3: 4 * PRF # F3: 4 => SOL * PRF # I3: 5,9 => SOL * DIS # I3: 8 => CTR => I3: 5,9 * DIS # B7: 5,9 => CTR => B7: 7 * PRF # B7: 7 => SOL * PRF # F2: 5,9 => SOL * DIS # F2: 4 => CTR => F2: 5,9 * DIS # F3: 5,9 => CTR => F3: 4 * PRF # F3: 4 => SOL * DIS # I1: 1,7 => CTR => I1: 5,9 * DIS # I1: 1,5 => CTR => I1: 7,9 * DIS # I1: 1,7 => CTR => I1: 5,9 * DIS # H7: 1,7 => CTR => H7: 4 * PRF # H7: 4 => SOL * DIS # F2: 4,5 => CTR => F2: 9 * PRF # F2: 9 => SOL * PRF # I6: 1,8 => SOL * DIS # B7: 5,9 => CTR => B7: 7 * PRF # B7: 7 => SOL * PRF # B7: 5,7 => SOL * DIS # B7: 9 => CTR => B7: 5,7 * DIS # H7: 1,7 => CTR => H7: 4 * PRF # H7: 4 => SOL * DIS # I1: 1,7 => CTR => I1: 5,9 * CNT 27 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B3,B9,D6,D9,E6,E7,F1,G1,G2,G8,G9,H1,H3,H6,I7,I8,I9) * 68432.....1786..323.217.6..421983756835716924769..2.....36.82..148297.6.2.6.31.9. * PAIR A2: 5,9 ROW 2 F2: 5,9,4 # reduction candidate for 5,9 F2: 5,9 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 * DURATION: 0:00:02.155161 START: 08:21:05.922231 END: 08:21:08.077392 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-722388-base-pr-001.dot * REASONING * PRF # F2: 5,9 => SOL * STA F2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/722388.html sehr schwierig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 68432.....1786..323.217.6..421983756835716924769..2.....36.82..148297.6.2.6.31.9. A2: 5,9 F2: 4,5,9 # reduction candidate for 5,9 F2: 5,9 => SOLVED * 684325179517869432392174685421983756835716924769542318973658241148297563256431897 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- pair quad |:guess:| highlight 1,7 H1,I7,H7,I1: 1,7.. => H7 = 4 or I1 = 5,9 # pair quad H7 != 4 => CTR I1 != 5,9 => CTR # |:info:||:check:| oops H7 = 4 * SOLVED! |:step:| 01 --------------------------------------------------
Solution
position: 684325179517869432392174685421983756835716924769542318973658241148297563256431897 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 # F2: 5,9 => SOL * DIS # F2: 4 => CTR => F2: 5,9 * DIS # F3: 5,9 => CTR => F3: 4 * PRF # F3: 4 => SOL * PRF # I3: 5,9 => SOL * DIS # I3: 8 => CTR => I3: 5,9 * DIS # B7: 5,9 => CTR => B7: 7 * PRF # B7: 7 => SOL * PRF # F2: 5,9 => SOL * DIS # F2: 4 => CTR => F2: 5,9 * DIS # F3: 5,9 => CTR => F3: 4 * PRF # F3: 4 => SOL * INC # I1: 5,9 => UNS * DIS # I1: 1,7 => CTR => I1: 5,9 * DIS # I1: 1,5 => CTR => I1: 7,9 * INC # I1: 7,9 => UNS * DIS # I1: 1,7 => CTR => I1: 5,9 * INC # I1: 5,9 => UNS * DIS # H7: 1,7 => CTR => H7: 4 * PRF # H7: 4 => SOL * DIS # F2: 4,5 => CTR => F2: 9 * PRF # F2: 9 => SOL * INC # G6: 1,8 => UNS * PRF # I6: 1,8 => SOL * INC # I6: 3 => UNS * DIS # B7: 5,9 => CTR => B7: 7 * PRF # B7: 7 => SOL * PRF # B7: 5,7 => SOL * DIS # B7: 9 => CTR => B7: 5,7 * DIS # H7: 1,7 => CTR => H7: 4 * PRF # H7: 4 => SOL * DIS # I1: 1,7 => CTR => I1: 5,9 * INC # I1: 5,9 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F2: 5,9 => SOL * STA F2: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED