Analysis of zz-sudoku-de-603428-base.sdk
Contents
Original Sudoku
level: medium
position: ...2...73.7.5...1...3..48..5...28....64...59....45...6..71..9...2...7.3.18...2... initial
Autosolve
position: .5.2..47347.5..2192.3..48655..628.4.864...5927.2459.86347165928.258.7.3.18...2.5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 6,9 => SOL * DIS # C1: 6,8 => CTR => C1: 1,9 * PRF # C1: 1,9 => SOL * PRF # C1: 1,9 => SOL * DIS # C1: 6,8 => CTR => C1: 1,9 * DIS # E3: 1,9 => CTR => E3: 7 * PRF # E3: 7 => SOL * PRF # B4: 1,9 => SOL * DIS # B4: 3 => CTR => B4: 1,9 * DIS # C1: 1,6 => CTR => C1: 8,9 * PRF # C1: 8,9 => SOL * PRF # E3: 7,9 => SOL * DIS # E3: 1 => CTR => E3: 7,9 * PRF # B4: 1,9 => SOL * DIS # B4: 3 => CTR => B4: 1,9 * PRF # C1: 1,9 => SOL * DIS # C1: 6,8 => CTR => C1: 1,9 * DIS # B4: 1,3 => CTR => B4: 9 * PRF # B4: 9 => SOL * DIS # E5: 3,7 => CTR => E5: 1 * PRF # E5: 1 => SOL * PRF # E5: 1,3 => SOL * DIS # E5: 7 => CTR => E5: 1,3 * DIS # G4: 1,7 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G4: 1,3 => SOL * DIS # G4: 7 => CTR => G4: 1,3 * PRF # C1: 6,9 => SOL * PRF # E9: 4,9 => SOL * DIS # E9: 3 => CTR => E9: 4,9 * PRF # E9: 3,9 => SOL * DIS # E9: 4 => CTR => E9: 3,9 * CNT 32 HDP CHAINS / 34 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 6,9 => SOL * STA C1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2...73.7.5...1...3..48..5...28....64...59....45...6..71..9...2...7.3.18...2... | initial |
| .5.2..47347.5..2192.3..48655..628.4.864...5927.2459.86347165928.258.7.3.18...2.5. | autosolve |
| 659281473478536219213974865591628347864713592732459186347165928925847631186392754 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (21) A1: 6,9 C2: 6,8 B3: 1,9 F1: 1,6 E2: 3,8 F2: 3,6 D3: 7,9 C4: 1,9 B6: 1,3 D5: 3,7 F5: 1,3 I4: 1,7 G6: 1,3 A8: 6,9 C9: 6,9 E8: 4,9 D9: 3,9 G8: 1,6 I8: 1,4 G9: 6,7 I9: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B3: 1.. / C1 = 1 => 0 pairs (X) / B3 = 1 => 0 pairs (_) E5,F5: 1.. / E5 = 1 => 0 pairs (*) / F5 = 1 => 0 pairs (X) G8,I8: 1.. / G8 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) B3,E3: 1.. / B3 = 1 => 0 pairs (*) / E3 = 1 => 0 pairs (X) B6,G6: 1.. / B6 = 1 => 0 pairs (X) / G6 = 1 => 0 pairs (_) C1,C4: 1.. / C1 = 1 => 0 pairs (X) / C4 = 1 => 0 pairs (_) F1,F5: 1.. / F1 = 1 => 0 pairs (*) / F5 = 1 => 0 pairs (X) I4,I8: 1.. / I4 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) E2,F2: 3.. / E2 = 3 => 0 pairs (*) / F2 = 3 => 0 pairs (X) B4,B6: 3.. / B4 = 3 => 0 pairs (X) / B6 = 3 => 0 pairs (_) G4,G6: 3.. / G4 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) D9,E9: 3.. / D9 = 3 => 0 pairs (*) / E9 = 3 => 0 pairs (X) B4,G4: 3.. / B4 = 3 => 0 pairs (X) / G4 = 3 => 0 pairs (_) B6,G6: 3.. / B6 = 3 => 0 pairs (*) / G6 = 3 => 0 pairs (X) D5,D9: 3.. / D5 = 3 => 0 pairs (X) / D9 = 3 => 0 pairs (_) F2,F5: 3.. / F2 = 3 => 0 pairs (X) / F5 = 3 => 0 pairs (_) E8,E9: 4.. / E8 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) I8,I9: 4.. / I8 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) E8,I8: 4.. / E8 = 4 => 0 pairs (*) / I8 = 4 => 0 pairs (X) E9,I9: 4.. / E9 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) F1,F2: 6.. / F1 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) A8,C9: 6.. / A8 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) G8,G9: 6.. / G8 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) C2,F2: 6.. / C2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) A8,G8: 6.. / A8 = 6 => 0 pairs (X) / G8 = 6 => 0 pairs (_) C9,G9: 6.. / C9 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) A1,A8: 6.. / A1 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 0 pairs (X) / E3 = 7 => 0 pairs (_) D5,E5: 7.. / D5 = 7 => 0 pairs (*) / E5 = 7 => 0 pairs (X) G4,I4: 7.. / G4 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) G9,I9: 7.. / G9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) D3,D5: 7.. / D3 = 7 => 0 pairs (X) / D5 = 7 => 0 pairs (_) E3,E5: 7.. / E3 = 7 => 0 pairs (*) / E5 = 7 => 0 pairs (X) G4,G9: 7.. / G4 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) I4,I9: 7.. / I4 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) C1,C2: 8.. / C1 = 8 => 0 pairs (X) / C2 = 8 => 0 pairs (_) E1,E2: 8.. / E1 = 8 => 0 pairs (*) / E2 = 8 => 0 pairs (X) C1,E1: 8.. / C1 = 8 => 0 pairs (X) / E1 = 8 => 0 pairs (_) C2,E2: 8.. / C2 = 8 => 0 pairs (*) / E2 = 8 => 0 pairs (X) B4,C4: 9.. / B4 = 9 => 0 pairs (*) / C4 = 9 => 0 pairs (X) A8,C9: 9.. / A8 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) A8,E8: 9.. / A8 = 9 => 0 pairs (*) / E8 = 9 => 0 pairs (X) A1,A8: 9.. / A1 = 9 => 0 pairs (X) / A8 = 9 => 0 pairs (_) B3,B4: 9.. / B3 = 9 => 0 pairs (X) / B4 = 9 => 0 pairs (_) D3,D9: 9.. / D3 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) * DURATION: 0:01:30.800319 START: 07:17:45.042979 END: 07:19:15.843298 2017-05-01 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B3,B6,C2,C4,C9,D3,D5,D9,E2,E8,F1,F2,F5,G6,G8,G9,I4,I8,I9) * .5.2..47347.5..2192.3..48655..628.4.864...5927.2459.86347165928.258.7.3.18...2.5. * PAIR A1: 6,9 BLK 1 C1: 6,9,1,8 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 C1: 1,8 # 22 pairs * PAIR C2: 6,8 BLK 1 C1: 6,8,1,9 # reduction candidate for 6,8 C1: 6,8 => CTR * .5.2..47347.5..219213..4865591628347864...592732459186347165928.258.763118...2.5. C1: 1,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 * PAIR B3: 1,9 BLK 1 C1: 1,9,6,8 # reduction candidate for 1,9 C1: 1,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 C1: 6,8 => CTR * .5.2..47347.5..219213..4865591628347864...592732459186347165928.258.763118...2.5. * PAIR B3: 1,9 ROW 3 E3: 1,9,7 # reduction candidate for 1,9 E3: 1,9 => CTR * .5.2.64734765..2192.37.48655..628.4.8643715927.2459.86347165928.258.7.3.18.932.54 E3: 7 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 * PAIR B3: 1,9 COL B B4: 1,9,3 # reduction candidate for 1,9 B4: 1,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 B4: 3 => CTR * .5.2..47347.5..219293714865539628.4.864371592712459386347165928925847631186932754 * PAIR F1: 1,6 ROW 1 C1: 1,6,8,9 # reduction candidate for 1,6 C1: 1,6 => CTR * 956281473478536219213974865591628347864713592732459186347165928.258.7.3.18.3.2.5. C1: 8,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 * PAIR D3: 7,9 BLK 2 E3: 7,9,1 # reduction candidate for 7,9 E3: 7,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 E3: 1 => CTR * .512..47347.5..2192.37148655..628.4.8643715927.2459.86347165928.258.7.3.18.932.54 * PAIR C4: 1,9 BLK 4 B4: 1,9,3 # reduction candidate for 1,9 B4: 1,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 B4: 3 => CTR * .5.2..47347.5..219293714865539628.4.864371592712459386347165928925847631186932754 * PAIR C4: 1,9 COL C C1: 1,9,6,8 # reduction candidate for 1,9 C1: 1,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 C1: 6,8 => CTR * .5.2..47347.5..219213..4865591628347864...592732459186347165928.258.763118...2.5. * PAIR B6: 1,3 BLK 4 B4: 1,3,9 # reduction candidate for 1,3 B4: 1,3 => CTR * .5.2..47347.5..2192937148655.9628.4.8643715927.2459.86347165928925847631186932754 B4: 9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 * PAIR D5: 3,7 BLK 5 E5: 3,7,1 # reduction candidate for 3,7 E5: 3,7 => CTR * .5.2.64734765832192.3..48655..628.4.864..15927.2459.86347165928625897134189342657 E5: 1 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 * PAIR F5: 1,3 BLK 5 E5: 1,3,7 # reduction candidate for 1,3 E5: 1,3 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 E5: 7 => CTR * .5.2.64734765832192.37.48655..628.4.8643715927.2459.86347165928625897.3.18...2.5. * PAIR I4: 1,7 BLK 6 G4: 1,7,3 # reduction candidate for 1,7 G4: 1,7 => CTR * 6512..47347.5..2192.3..4865539628.4.864...592712459386347165928925847631186..2754 G4: 3 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 * PAIR G6: 1,3 BLK 6 G4: 1,3,7 # reduction candidate for 1,3 G4: 1,3 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 G4: 7 => CTR * .5.2..47347.5..2192.3..4865539628741864...592712459386347165928925847.3.18...2.5. * PAIR C9: 6,9 COL C C1: 6,9,1,8 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 C1: 1,8 # 22 pairs * PAIR E8: 4,9 BLK 8 E9: 4,9,3 # reduction candidate for 4,9 E9: 4,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 E9: 3 => CTR * .5.2..47347.5832192.37.48655..628.478643715927.2459.86347165928925847631186932.54 * PAIR D9: 3,9 BLK 8 E9: 3,9,4 # reduction candidate for 3,9 E9: 3,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 E9: 4 => CTR * .5.2..47347.5..2192.3974865591628.4.864...5927.2459.86347165928.258.7.3.18.342.57 * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-603428-base-pr-000.dot * REASONING * PRF # C1: 6,9 => SOL * DIS # C1: 6,8 => CTR => C1: 1,9 * PRF # C1: 1,9 => SOL * PRF # C1: 1,9 => SOL * DIS # C1: 6,8 => CTR => C1: 1,9 * DIS # E3: 1,9 => CTR => E3: 7 * PRF # E3: 7 => SOL * PRF # B4: 1,9 => SOL * DIS # B4: 3 => CTR => B4: 1,9 * DIS # C1: 1,6 => CTR => C1: 8,9 * PRF # C1: 8,9 => SOL * PRF # E3: 7,9 => SOL * DIS # E3: 1 => CTR => E3: 7,9 * PRF # B4: 1,9 => SOL * DIS # B4: 3 => CTR => B4: 1,9 * PRF # C1: 1,9 => SOL * DIS # C1: 6,8 => CTR => C1: 1,9 * DIS # B4: 1,3 => CTR => B4: 9 * PRF # B4: 9 => SOL * DIS # E5: 3,7 => CTR => E5: 1 * PRF # E5: 1 => SOL * PRF # E5: 1,3 => SOL * DIS # E5: 7 => CTR => E5: 1,3 * DIS # G4: 1,7 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G4: 1,3 => SOL * DIS # G4: 7 => CTR => G4: 1,3 * PRF # C1: 6,9 => SOL * PRF # E9: 4,9 => SOL * DIS # E9: 3 => CTR => E9: 4,9 * PRF # E9: 3,9 => SOL * DIS # E9: 4 => CTR => E9: 3,9 * CNT 32 HDP CHAINS / 34 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A8,B3,B6,C2,C4,C9,D3,D5,D9,E2,E8,F1,F2,F5,G6,G8,G9,I4,I8,I9) * .5.2..47347.5..2192.3..48655..628.4.864...5927.2459.86347165928.258.7.3.18...2.5. * PAIR A1: 6,9 BLK 1 C1: 6,9,1,8 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 * DURATION: 0:00:02.250506 START: 07:20:01.117449 END: 07:20:03.367955 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-603428-base-pr-001.dot * REASONING * PRF # C1: 6,9 => SOL * STA C1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/603428.html sehr schwierig level: medium * PAIR REDUCTION .. * ROUND 1: .5.2..47347.5..2192.3..48655..628.4.864...5927.2459.86347165928.258.7.3.18...2.5. A1: 6,9 C1: 1,6,8,9 # reduction candidate for 6,9 C1: 6,9 => SOLVED * 659281473478536219213974865591628347864713592732459186347165928925847631186392754 * SOLVED! -------------------------------------------------- * AUTO .. D4 = 6 # set value H4 = 4 # set value F7 = 5 # set value D8 = 8 # set value F6: 9.. # hidden single F6 = 9 # set value Q3: 5.. = H3,I3: 5.. => B3 != 5 Q5: 1.. = E5,F5: 1.. => I5 != 1 Q5: 3.. = D5,E5,F5: 3.. => A5 != 3 Q5: 7.. = D5,E5: 7.. => A5,I5 != 7 Q7: 3.. = A7,B7: 3.. => E7 != 3 Q7: 5.. = C8,C9: 5.. => C1 != 5 Q8: 6.. = E7,E8,E9: 6.. => E1,E2,E3 != 6 B1: 5.. # hidden single A6: 7.. # hidden single B1 = 5 # set value A6 = 7 # set value A7: 3.. # hidden single B7: 4.. # hidden single A7 = 3 # set value B7: 4 # naked single B7 = 4 # set value E7: 6 # naked single E7 = 6 # set value A5,C6: 2,8.. => C6 != 1 # hidden pair I5,H6: 2,8.. => G6 != 2,8 # naked pair A3,H3,I3: 5,6,2.. => A3,I3 != 9 # hidden triple H3,H9: 5,6.. => H3 != 2 # hidden pair I3: 5 # naked single I5,I7: 2,8.. => I2,I3 != 2,8 # naked pair G2: 2.. # hidden single I2: 9.. # hidden single A3: 2.. # hidden single G2 = 2 # set value I2 = 9 # set value A3 = 2 # set value A5: 8 # naked single I3 = 5 # set value H3: 6 # naked single A5 = 8 # set value C6: 2 # naked single I5: 2 # naked single I5 = 2 # set value H6: 8 # naked single I7: 8 # naked single C6 = 2 # set value H6 = 8 # set value H7: 2 # naked single H7 = 2 # set value I7 = 8 # set value G1: 4.. # hidden single H9: 5.. # hidden single A2: 4.. # hidden single C8: 5.. # hidden single G1 = 4 # set value A2 = 4 # set value H3 = 6 # set value H9: 5 # naked single C8 = 5 # set value H9 = 5 # set value * UNSOLVED! |:step:| 00 -------------------------------------------------- pair quad * DISABLE VALUE:: B4 != 9 C4: 9.. # hidden single B3: 9.. # hidden single B4 = 9 * SOLVED! |:step:| 01 --------------------------------------------------
Solution
position: 659281473478536219213974865591628347864713592732459186347165928925847631186392754 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 # C1: 6,9 => SOL * INC # C1: 1,8 => UNS * DIS # C1: 6,8 => CTR => C1: 1,9 * PRF # C1: 1,9 => SOL * PRF # C1: 1,9 => SOL * DIS # C1: 6,8 => CTR => C1: 1,9 * DIS # E3: 1,9 => CTR => E3: 7 * PRF # E3: 7 => SOL * PRF # B4: 1,9 => SOL * DIS # B4: 3 => CTR => B4: 1,9 * DIS # C1: 1,6 => CTR => C1: 8,9 * PRF # C1: 8,9 => SOL * PRF # E3: 7,9 => SOL * DIS # E3: 1 => CTR => E3: 7,9 * PRF # B4: 1,9 => SOL * DIS # B4: 3 => CTR => B4: 1,9 * PRF # C1: 1,9 => SOL * DIS # C1: 6,8 => CTR => C1: 1,9 * DIS # B4: 1,3 => CTR => B4: 9 * PRF # B4: 9 => SOL * DIS # E5: 3,7 => CTR => E5: 1 * PRF # E5: 1 => SOL * PRF # E5: 1,3 => SOL * DIS # E5: 7 => CTR => E5: 1,3 * DIS # G4: 1,7 => CTR => G4: 3 * PRF # G4: 3 => SOL * PRF # G4: 1,3 => SOL * DIS # G4: 7 => CTR => G4: 1,3 * PRF # C1: 6,9 => SOL * INC # C1: 1,8 => UNS * PRF # E9: 4,9 => SOL * DIS # E9: 3 => CTR => E9: 4,9 * PRF # E9: 3,9 => SOL * DIS # E9: 4 => CTR => E9: 3,9 * CNT 34 HDP CHAINS / 34 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 6,9 => SOL * STA C1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED