Analysis of zz-sudoku-de-691604-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....2.4...9...7.383...9......3..6.819.......341.5..6......8...514.2...7...6.1.... initial

Autosolve

position: 6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C2: 2,5 => SOL
* DIS # C2: 1,4 => CTR => C2: 2,5
* PRF # A4: 7 => SOL
* DIS # D3: 4 => CTR => D3: 1,8
* PRF # F5: 1,8 => SOL
* DIS # F5: 2 => CTR => F5: 1,8
* PRF # D3: 1,4 => SOL
* DIS # D3: 8 => CTR => D3: 1,4
* DIS # C2: 1,4 => CTR => C2: 2,5
* PRF # C2: 2,5 => SOL
* DIS # G3: 1,2 => CTR => G3: 7
* PRF # G3: 7 => SOL
* PRF # C2: 1,2 => SOL
* PRF # G3: 2,7 => SOL
* DIS # G3: 1 => CTR => G3: 2,7
* PRF # A4: 2,7 => SOL
* DIS # A4: 5 => CTR => A4: 2,7
* DIS # C6: 2,7 => CTR => C6: 8
* PRF # C6: 8 => SOL
* DIS # G4: 2,7 => CTR => G4: 5
* PRF # G4: 5 => SOL
* PRF # F5: 1,8 => SOL
* DIS # F5: 2 => CTR => F5: 1,8
* DIS # D3: 4 => CTR => D3: 1,8
* DIS # F5: 2,8 => CTR => F5: 1
* PRF # F5: 1 => SOL
* PRF # C6: 2,8 => SOL
* DIS # C6: 7 => CTR => C6: 2,8
* PRF # G4: 2,5 => SOL
* DIS # G4: 7 => CTR => G4: 2,5
* PRF # C5: 2,5 => SOL
* DIS # C5: 8 => CTR => C5: 2,5
* DIS # G4: 2,7 => CTR => G4: 5
* PRF # G4: 5 => SOL
* DIS # C6: 2,7 => CTR => C6: 8
* PRF # C6: 8 => SOL
* PRF # A4: 2,7 => SOL
* DIS # A4: 5 => CTR => A4: 2,7
* DIS # C6: 2,7 => CTR => C6: 8
* PRF # C6: 8 => SOL
* CNT  40 HDP CHAINS /  44 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C2: 2,5 => SOL
* STA C2: 2,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

....2.4...9...7.383...9......3..6.819.......341.5..6......8...514.2...7...6.1.... initial
6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324 autosolve
671328459592467138384195762723946581965871243418532697237684915149253876856719324 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B1: 7,8
C1: 1,7
A2: 2,5
B3: 2,8
F1: 1,8
D2: 1,4
G2: 1,2
I3: 2,7
B4: 2,7
D5: 1,8
F6: 2,8
G5: 2,5
I6: 2,7
A7: 2,7
C7: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,G3: 1.. / G2 = 1  =>  0 pairs (*) / G3 = 1  =>  0 pairs (X)
D5,F5: 1.. / D5 = 1  =>  0 pairs (X) / F5 = 1  =>  0 pairs (_)
C1,F1: 1.. / C1 = 1  =>  0 pairs (*) / F1 = 1  =>  0 pairs (X)
F1,F5: 1.. / F1 = 1  =>  0 pairs (X) / F5 = 1  =>  0 pairs (_)
F5,F6: 2.. / F5 = 2  =>  0 pairs (X) / F6 = 2  =>  0 pairs (_)
A7,C7: 2.. / A7 = 2  =>  0 pairs (*) / C7 = 2  =>  0 pairs (X)
B3,B4: 2.. / B3 = 2  =>  0 pairs (X) / B4 = 2  =>  0 pairs (_)
I3,I6: 2.. / I3 = 2  =>  0 pairs (*) / I6 = 2  =>  0 pairs (X)
C2,C3: 4.. / C2 = 4  =>  0 pairs (X) / C3 = 4  => 15 pairs (_)
D2,D3: 4.. / D2 = 4  => 15 pairs (_) / D3 = 4  =>  0 pairs (X)
C2,D2: 4.. / C2 = 4  =>  0 pairs (X) / D2 = 4  => 15 pairs (_)
C3,D3: 4.. / C3 = 4  => 15 pairs (_) / D3 = 4  =>  0 pairs (X)
A2,C2: 5.. / A2 = 5  =>  0 pairs (*) / C2 = 5  =>  0 pairs (X)
A4,C5: 5.. / A4 = 5  =>  0 pairs (X) / C5 = 5  =>  0 pairs (_)
G4,G5: 5.. / G4 = 5  =>  0 pairs (*) / G5 = 5  =>  0 pairs (X)
A4,G4: 5.. / A4 = 5  =>  0 pairs (X) / G4 = 5  =>  0 pairs (_)
C5,G5: 5.. / C5 = 5  =>  0 pairs (*) / G5 = 5  =>  0 pairs (X)
A2,A4: 5.. / A2 = 5  =>  0 pairs (*) / A4 = 5  =>  0 pairs (X)
C2,C5: 5.. / C2 = 5  =>  0 pairs (X) / C5 = 5  =>  0 pairs (_)
B1,C1: 7.. / B1 = 7  =>  0 pairs (*) / C1 = 7  =>  0 pairs (X)
G3,I3: 7.. / G3 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
G4,I6: 7.. / G4 = 7  =>  0 pairs (X) / I6 = 7  =>  0 pairs (_)
A7,C7: 7.. / A7 = 7  => 18 pairs (_) / C7 = 7  =>  0 pairs (*)
C6,I6: 7.. / C6 = 7  =>  0 pairs (X) / I6 = 7  =>  0 pairs (_)
A4,A7: 7.. / A4 = 7  =>  0 pairs (*) / A7 = 7  =>  0 pairs (X)
B1,B4: 7.. / B1 = 7  =>  0 pairs (*) / B4 = 7  =>  0 pairs (X)
G3,G4: 7.. / G3 = 7  =>  0 pairs (*) / G4 = 7  =>  0 pairs (X)
I3,I6: 7.. / I3 = 7  =>  0 pairs (X) / I6 = 7  =>  0 pairs (_)
B1,B3: 8.. / B1 = 8  =>  0 pairs (X) / B3 = 8  =>  0 pairs (_)
F1,D3: 8.. / F1 = 8  =>  0 pairs (*) / D3 = 8  =>  0 pairs (X)
C5,C6: 8.. / C5 = 8  =>  0 pairs (X) / C6 = 8  =>  0 pairs (_)
B1,F1: 8.. / B1 = 8  =>  0 pairs (X) / F1 = 8  =>  0 pairs (_)
B3,D3: 8.. / B3 = 8  =>  0 pairs (*) / D3 = 8  =>  0 pairs (X)
C6,F6: 8.. / C6 = 8  =>  0 pairs (*) / F6 = 8  =>  0 pairs (X)
D3,D5: 8.. / D3 = 8  =>  0 pairs (X) / D5 = 8  =>  0 pairs (_)
* DURATION: 0:01:04.812383  START: 07:51:02.736415  END: 07:52:07.548798 2017-05-01
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B1,B3,B4,C1,C7,D2,D5,F1,F6,G2,G5,I3,I6)
* 6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324
* PAIR A2: 2,5 BLK 1
C2: 2,5,1,4                              # reduction candidate for 2,5
C2: 2,5 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
C2: 1,4 => CTR
* 6..32.45959..672383...95167..3946.8196..7..4341.53.69..3.684915149253876856719324
* PAIR A2: 2,5 COL A
A4: 2,5,7                                # reduction candidate for 2,5
A4: 7 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
A4: 2,5                                  # 18 pairs
* PAIR F1: 1,8 BLK 2
D3: 1,8,4                                # reduction candidate for 1,8
D3: 4 => CTR
* 6..328459.9.167238382495167.23946.8196..7..4341.53.69..3.684915149253876856719324
D3: 1,8                                  # 15 pairs
* PAIR F1: 1,8 COL F
F5: 1,8,2                                # reduction candidate for 1,8
F5: 1,8 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
F5: 2 => CTR
* 6..321459.9.467.383.4895167..394678196817254341753.69..3.684915149253876856719324
* PAIR D2: 1,4 BLK 2
D3: 1,4,8                                # reduction candidate for 1,4
D3: 1,4 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
D3: 8 => CTR
* 6..32.459.9.467.383.4895167..394678196.17.54341753.69..3.684915149253876856719324
* PAIR D2: 1,4 ROW 2
C2: 1,4,2,5                              # reduction candidate for 1,4
C2: 1,4 => CTR
* 6..32.45959..672383...95167..3946.8196..7..4341.53.69..3.684915149253876856719324
C2: 2,5 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* PAIR G2: 1,2 BLK 3
G3: 1,2,7                                # reduction candidate for 1,2
G3: 1,2 => CTR
* 6..32.459.9..67.383...95.67..394678196..7.543417538692732684915149253876856719324
G3: 7 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* PAIR G2: 1,2 ROW 2
C2: 1,2,4,5                              # reduction candidate for 1,2
C2: 1,2 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
C2: 4,5                                  # 16 pairs
* PAIR I3: 2,7 BLK 3
G3: 2,7,1                                # reduction candidate for 2,7
G3: 2,7 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
G3: 1 => CTR
* 6..32.459.9..67.383...95167..394678196..7.543417538692732684915149253876856719324
* PAIR B4: 2,7 BLK 4
A4: 2,7,5                                # reduction candidate for 2,7
A4: 2,7 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
A4: 5 => CTR
* 6..32.459295467138384195.6.523946781968.7.54341.53.69.732684915149253876856719324
C6: 2,7,8                                # reduction candidate for 2,7
C6: 2,7 => CTR
* 687321459.9546713832..95.6...3946.8196817254341.53869..3.684915149253876856719324
C6: 8 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* PAIR B4: 2,7 ROW 4
G4: 2,7,5                                # reduction candidate for 2,7
G4: 2,7 => CTR
* 6..32.459295467138384195.6.523946781968.7.54341.53.69.732684915149253876856719324
G4: 5 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* PAIR D5: 1,8 BLK 5
F5: 1,8,2                                # reduction candidate for 1,8
F5: 1,8 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
F5: 2 => CTR
* 6..321459.9.467.383.4895167..394678196817254341753.69..3.684915149253876856719324
* PAIR D5: 1,8 COL D
D3: 1,8,4                                # reduction candidate for 1,8
D3: 4 => CTR
* 6..328459.9.167238382495167.23946.8196..7..4341.53.69..3.684915149253876856719324
D3: 1,8                                  # 15 pairs
* PAIR F6: 2,8 BLK 5
F5: 2,8,1                                # reduction candidate for 2,8
F5: 2,8 => CTR
* 6..321459.9.467.383.4895167..394678196.17.54341753.69..3.684915149253876856719324
F5: 1 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* PAIR F6: 2,8 ROW 6
C6: 2,8,7                                # reduction candidate for 2,8
C6: 2,8 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
C6: 7 => CTR
* 6..32.459.9..67.383...95.6...3946.81968172543417538692732684915149253876856719324
* PAIR G5: 2,5 BLK 6
G4: 2,5,7                                # reduction candidate for 2,5
G4: 2,5 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
G4: 7 => CTR
* 6..32.459.9..67.383...95.6.523946781968172543417538692732684915149253876856719324
* PAIR G5: 2,5 ROW 5
C5: 2,5,8                                # reduction candidate for 2,5
C5: 2,5 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
C5: 8 => CTR
* 6..32.459.954671383.4195.6.5.3946.81968.7..4341.53.69..3.684915149253876856719324
* PAIR I6: 2,7 BLK 6
G4: 2,7,5                                # reduction candidate for 2,7
G4: 2,7 => CTR
* 6..32.459295467138384195.6.523946781968.7.54341.53.69.732684915149253876856719324
G4: 5 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* PAIR I6: 2,7 ROW 6
C6: 2,7,8                                # reduction candidate for 2,7
C6: 2,7 => CTR
* 687321459.9546713832..95.6...3946.8196817254341.53869..3.684915149253876856719324
C6: 8 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* PAIR A7: 2,7 COL A
A4: 2,7,5                                # reduction candidate for 2,7
A4: 2,7 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
A4: 5 => CTR
* 6..32.459295467138384195.6.523946781968.7.54341.53.69.732684915149253876856719324
* PAIR C7: 2,7 COL C
C6: 2,7,8                                # reduction candidate for 2,7
C6: 2,7 => CTR
* 687321459.9546713832..95.6...3946.8196817254341.53869..3.684915149253876856719324
C6: 8 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-691604-base-pr-000.dot
* REASONING
* PRF # C2: 2,5 => SOL
* DIS # C2: 1,4 => CTR => C2: 2,5
* PRF # A4: 7 => SOL
* DIS # D3: 4 => CTR => D3: 1,8
* PRF # F5: 1,8 => SOL
* DIS # F5: 2 => CTR => F5: 1,8
* PRF # D3: 1,4 => SOL
* DIS # D3: 8 => CTR => D3: 1,4
* DIS # C2: 1,4 => CTR => C2: 2,5
* PRF # C2: 2,5 => SOL
* DIS # G3: 1,2 => CTR => G3: 7
* PRF # G3: 7 => SOL
* PRF # C2: 1,2 => SOL
* PRF # G3: 2,7 => SOL
* DIS # G3: 1 => CTR => G3: 2,7
* PRF # A4: 2,7 => SOL
* DIS # A4: 5 => CTR => A4: 2,7
* DIS # C6: 2,7 => CTR => C6: 8
* PRF # C6: 8 => SOL
* DIS # G4: 2,7 => CTR => G4: 5
* PRF # G4: 5 => SOL
* PRF # F5: 1,8 => SOL
* DIS # F5: 2 => CTR => F5: 1,8
* DIS # D3: 4 => CTR => D3: 1,8
* DIS # F5: 2,8 => CTR => F5: 1
* PRF # F5: 1 => SOL
* PRF # C6: 2,8 => SOL
* DIS # C6: 7 => CTR => C6: 2,8
* PRF # G4: 2,5 => SOL
* DIS # G4: 7 => CTR => G4: 2,5
* PRF # C5: 2,5 => SOL
* DIS # C5: 8 => CTR => C5: 2,5
* DIS # G4: 2,7 => CTR => G4: 5
* PRF # G4: 5 => SOL
* DIS # C6: 2,7 => CTR => C6: 8
* PRF # C6: 8 => SOL
* PRF # A4: 2,7 => SOL
* DIS # A4: 5 => CTR => A4: 2,7
* DIS # C6: 2,7 => CTR => C6: 8
* PRF # C6: 8 => SOL
* CNT  40 HDP CHAINS /  44 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A7,B1,B3,B4,C1,C7,D2,D5,F1,F6,G2,G5,I3,I6)
* 6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324
* PAIR A2: 2,5 BLK 1
C2: 2,5,1,4                              # reduction candidate for 2,5
C2: 2,5 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* DURATION: 0:00:02.169026  START: 07:53:02.941107  END: 07:53:05.110133 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-691604-base-pr-001.dot
* REASONING
* PRF # C2: 2,5 => SOL
* STA C2: 2,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokus.de/691604.html
sehr schwierig

--------------------------------------------------
level: medium

* PAIR REDUCTION ..
* ROUND 1: 6..32.459.9..67.383...95.6...3946.8196..7..4341.53.69..3.684915149253876856719324
B1: 7,8
C1: 1,7
A2: 2,5
C2: 1,2,4,5                              # reduction candidate for 2,5
C2: 2,5 => SOLVED
* 671328459592467138384195762723946581965871243418532697237684915149253876856719324
* SOLVED!
--------------------------------------------------

Solution

position: 671328459592467138384195762723946581965871243418532697237684915149253876856719324 solved
Solution

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 # C2: 2,5 => SOL
* DIS # C2: 1,4 => CTR => C2: 2,5
* INC # A4: 2,5 => UNS
* PRF # A4: 7 => SOL
* INC # D3: 1,8 => UNS
* DIS # D3: 4 => CTR => D3: 1,8
* PRF # F5: 1,8 => SOL
* DIS # F5: 2 => CTR => F5: 1,8
* PRF # D3: 1,4 => SOL
* DIS # D3: 8 => CTR => D3: 1,4
* DIS # C2: 1,4 => CTR => C2: 2,5
* PRF # C2: 2,5 => SOL
* DIS # G3: 1,2 => CTR => G3: 7
* PRF # G3: 7 => SOL
* PRF # C2: 1,2 => SOL
* INC # C2: 4,5 => UNS
* PRF # G3: 2,7 => SOL
* DIS # G3: 1 => CTR => G3: 2,7
* PRF # A4: 2,7 => SOL
* DIS # A4: 5 => CTR => A4: 2,7
* DIS # C6: 2,7 => CTR => C6: 8
* PRF # C6: 8 => SOL
* DIS # G4: 2,7 => CTR => G4: 5
* PRF # G4: 5 => SOL
* PRF # F5: 1,8 => SOL
* DIS # F5: 2 => CTR => F5: 1,8
* INC # D3: 1,8 => UNS
* DIS # D3: 4 => CTR => D3: 1,8
* DIS # F5: 2,8 => CTR => F5: 1
* PRF # F5: 1 => SOL
* PRF # C6: 2,8 => SOL
* DIS # C6: 7 => CTR => C6: 2,8
* PRF # G4: 2,5 => SOL
* DIS # G4: 7 => CTR => G4: 2,5
* PRF # C5: 2,5 => SOL
* DIS # C5: 8 => CTR => C5: 2,5
* DIS # G4: 2,7 => CTR => G4: 5
* PRF # G4: 5 => SOL
* DIS # C6: 2,7 => CTR => C6: 8
* PRF # C6: 8 => SOL
* PRF # A4: 2,7 => SOL
* DIS # A4: 5 => CTR => A4: 2,7
* DIS # C6: 2,7 => CTR => C6: 8
* PRF # C6: 8 => SOL
* CNT  44 HDP CHAINS /  44 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C2: 2,5 => SOL
* STA C2: 2,5
* CNT   1 HDP CHAINS /   1 HYP OPENED