Analysis of zz-sudoku-de-620657-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 8..5.....79..8......3...17..4.9.8..66..1.5..31..6.7.2..68...9......6..37.....4..5 initial

Autosolve

position: 8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F1: 3 => CTR => F1: 1,2
* DIS # D2: 2,4 => CTR => D2: 3
* PRF # D2: 3 => SOL
* DIS # I1: 2,4 => CTR => I1: 9
* PRF # I1: 9 => SOL
* DIS # D2: 2,4 => CTR => D2: 3
* PRF # D2: 3 => SOL
* PRF # G5: 7,8 => SOL
* DIS # G5: 4 => CTR => G5: 7,8
* DIS # I1: 2 => CTR => I1: 4,9
* DIS # C2: 1,4 => CTR => C2: 6
* PRF # C5: 2,7 => SOL
* DIS # C5: 9 => CTR => C5: 2,7
* DIS # D9: 8 => CTR => D9: 2,3
* DIS # F2: 2,3 => CTR => F2: 1
* PRF # D9: 2,8 => SOL
* DIS # D9: 3 => CTR => D9: 2,8
* DIS # G9: 2,8 => CTR => G9: 6
* PRF # G9: 6 => SOL
* DIS # G9: 2 => CTR => G9: 6,8
* CNT  20 HDP CHAINS /  28 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # F1: 3 => CTR => F1: 1,2
* PRF F1: 1,2 # G5: 7,8 => SOL
* STA F1: 1,2 + G5: 7,8
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

8..5.....79..8......3...17..4.9.8..66..1.5..31..6.7.2..68...9......6..37.....4..5 initial
8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5 autosolve
814572369796381452523496178345928716672145893189637524268753941451869237937214685 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (27)
B1: 1,2
A3: 4,5
B3: 2,5
D3: 2,4
H1: 6,9
I2: 2,4
A4: 2,3
C4: 5,7
B5: 7,8
B6: 3,8
C6: 5,9
E4: 2,3
E5: 2,4
E6: 3,4
G4: 5,7
H5: 8,9
I6: 4,9
A7: 2,3
A8: 4,5
B8: 1,5
C8: 1,4
B9: 3,7
C9: 2,7
F7: 2,3
D8: 2,8
G8: 2,8
H9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F2: 1.. / F1 = 1  =>  0 pairs (X) / F2 = 1  => 29 pairs (_)
B8,C8: 1.. / B8 = 1  =>  0 pairs (X) / C8 = 1  => 24 pairs (_)
C2,F2: 1.. / C2 = 1  =>  0 pairs (X) / F2 = 1  => 29 pairs (_)
B1,B8: 1.. / B1 = 1  => 24 pairs (_) / B8 = 1  =>  0 pairs (X)
B1,B3: 2.. / B1 = 2  =>  0 pairs (X) / B3 = 2  => 24 pairs (_)
I1,I2: 2.. / I1 = 2  =>  0 pairs (X) / I2 = 2  => 29 pairs (_)
A4,C5: 2.. / A4 = 2  =>  0 pairs (X) / C5 = 2  =>  0 pairs (_)
E4,E5: 2.. / E4 = 2  =>  0 pairs (*) / E5 = 2  =>  0 pairs (X)
A7,C9: 2.. / A7 = 2  =>  0 pairs (*) / C9 = 2  =>  0 pairs (X)
G8,G9: 2.. / G8 = 2  => 27 pairs (_) / G9 = 2  =>  0 pairs (X)
B3,D3: 2.. / B3 = 2  => 24 pairs (_) / D3 = 2  =>  0 pairs (X)
A4,E4: 2.. / A4 = 2  =>  0 pairs (X) / E4 = 2  =>  0 pairs (_)
C5,E5: 2.. / C5 = 2  =>  0 pairs (*) / E5 = 2  =>  0 pairs (X)
A7,F7: 2.. / A7 = 2  =>  0 pairs (*) / F7 = 2  =>  0 pairs (X)
D8,G8: 2.. / D8 = 2  =>  0 pairs (X) / G8 = 2  => 27 pairs (_)
A4,A7: 2.. / A4 = 2  =>  0 pairs (X) / A7 = 2  =>  0 pairs (_)
C5,C9: 2.. / C5 = 2  =>  0 pairs (*) / C9 = 2  =>  0 pairs (X)
G1,G2: 3.. / G1 = 3  => 32 pairs (_) / G2 = 3  =>  0 pairs (X)
A4,B6: 3.. / A4 = 3  =>  0 pairs (*) / B6 = 3  =>  0 pairs (X)
E4,E6: 3.. / E4 = 3  =>  0 pairs (X) / E6 = 3  =>  0 pairs (_)
A7,B9: 3.. / A7 = 3  =>  0 pairs (X) / B9 = 3  =>  0 pairs (_)
F7,D9: 3.. / F7 = 3  =>  0 pairs (*) / D9 = 3  =>  0 pairs (X)
F1,G1: 3.. / F1 = 3  =>  0 pairs (X) / G1 = 3  => 32 pairs (_)
A4,E4: 3.. / A4 = 3  =>  0 pairs (*) / E4 = 3  =>  0 pairs (X)
B6,E6: 3.. / B6 = 3  =>  0 pairs (X) / E6 = 3  =>  0 pairs (_)
A7,F7: 3.. / A7 = 3  =>  0 pairs (X) / F7 = 3  =>  0 pairs (_)
B9,D9: 3.. / B9 = 3  =>  0 pairs (*) / D9 = 3  =>  0 pairs (X)
A4,A7: 3.. / A4 = 3  =>  0 pairs (*) / A7 = 3  =>  0 pairs (X)
B6,B9: 3.. / B6 = 3  =>  0 pairs (X) / B9 = 3  =>  0 pairs (_)
D2,D9: 3.. / D2 = 3  =>  0 pairs (*) / D9 = 3  =>  0 pairs (X)
D2,D3: 4.. / D2 = 4  =>  0 pairs (X) / D3 = 4  => 24 pairs (_)
E5,E6: 4.. / E5 = 4  =>  0 pairs (*) / E6 = 4  =>  0 pairs (X)
A8,C8: 4.. / A8 = 4  => 24 pairs (_) / C8 = 4  =>  0 pairs (X)
A3,D3: 4.. / A3 = 4  =>  0 pairs (X) / D3 = 4  => 24 pairs (_)
E5,G5: 4.. / E5 = 4  =>  0 pairs (*) / G5 = 4  =>  0 pairs (X)
A3,A8: 4.. / A3 = 4  =>  0 pairs (X) / A8 = 4  => 24 pairs (_)
A3,B3: 5.. / A3 = 5  => 24 pairs (_) / B3 = 5  =>  0 pairs (X)
C4,C6: 5.. / C4 = 5  =>  0 pairs (*) / C6 = 5  =>  0 pairs (X)
G4,G6: 5.. / G4 = 5  =>  0 pairs (X) / G6 = 5  =>  0 pairs (_)
A8,B8: 5.. / A8 = 5  =>  0 pairs (X) / B8 = 5  => 24 pairs (_)
C4,G4: 5.. / C4 = 5  =>  0 pairs (*) / G4 = 5  =>  0 pairs (X)
C6,G6: 5.. / C6 = 5  =>  0 pairs (X) / G6 = 5  =>  0 pairs (_)
A3,A8: 5.. / A3 = 5  => 24 pairs (_) / A8 = 5  =>  0 pairs (X)
B3,B8: 5.. / B3 = 5  =>  0 pairs (X) / B8 = 5  => 24 pairs (_)
C1,C2: 6.. / C1 = 6  =>  0 pairs (X) / C2 = 6  => 30 pairs (_)
G9,H9: 6.. / G9 = 6  =>  0 pairs (*) / H9 = 6  =>  0 pairs (X)
C2,G2: 6.. / C2 = 6  => 30 pairs (_) / G2 = 6  =>  0 pairs (X)
H1,H9: 6.. / H1 = 6  =>  0 pairs (*) / H9 = 6  =>  0 pairs (X)
G4,G5: 7.. / G4 = 7  =>  0 pairs (*) / G5 = 7  =>  0 pairs (X)
B9,C9: 7.. / B9 = 7  =>  0 pairs (X) / C9 = 7  =>  0 pairs (_)
C4,G4: 7.. / C4 = 7  =>  0 pairs (X) / G4 = 7  =>  0 pairs (_)
B5,B9: 7.. / B5 = 7  =>  0 pairs (*) / B9 = 7  =>  0 pairs (X)
B5,B6: 8.. / B5 = 8  =>  0 pairs (X) / B6 = 8  =>  0 pairs (_)
D8,D9: 8.. / D8 = 8  => 27 pairs (_) / D9 = 8  =>  0 pairs (X)
B6,G6: 8.. / B6 = 8  =>  0 pairs (*) / G6 = 8  =>  0 pairs (X)
D8,G8: 8.. / D8 = 8  => 27 pairs (_) / G8 = 8  =>  0 pairs (X)
H5,H9: 8.. / H5 = 8  =>  0 pairs (X) / H9 = 8  =>  0 pairs (_)
H1,I1: 9.. / H1 = 9  =>  0 pairs (X) / I1 = 9  =>  0 pairs (_)
C5,C6: 9.. / C5 = 9  =>  0 pairs (X) / C6 = 9  =>  0 pairs (_)
H5,I6: 9.. / H5 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
C5,H5: 9.. / C5 = 9  =>  0 pairs (X) / H5 = 9  =>  0 pairs (_)
C6,I6: 9.. / C6 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
H1,H5: 9.. / H1 = 9  =>  0 pairs (X) / H5 = 9  =>  0 pairs (_)
I1,I6: 9.. / I1 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
* DURATION: 0:01:52.576056  START: 07:20:18.546856  END: 07:22:11.122912 2017-05-01
* CP COUNT: (64)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,A8,B1,B3,B5,B6,B8,B9,C4,C6,C8,C9,D3,D8,E4,E5,E6,F7,G4,G8,H1,H5,H9,I2,I6)
* 8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5
* PAIR B1: 1,2 ROW 1
F1: 1,2,3                                # reduction candidate for 1,2
F1: 3 => CTR
* 8..573...796.8135...3.9617824.938.1668.1254931..6.7.2.368752941...869237972314..5
F1: 1,2                                  # 32 pairs
* PAIR D3: 2,4 BLK 2
D2: 2,4,3                                # reduction candidate for 2,4
D2: 2,4 => CTR
* 8..57....79..8..5...3.96178.4.9.8.166..1.5..313.647829.6875.941....69.379..314..5
D2: 3 => SOLVED
* 814572369796381452523496178345928716672145893189637524268753941451869237937214685
* PAIR I2: 2,4 BLK 3
I1: 2,4,9                                # reduction candidate for 2,4
I1: 2,4 => CTR
* 8..57..9.79..8..5...3.96178.4.9.8.166.91254831856.7.2..6875.941....69.379...14..5
I1: 9 => SOLVED
* 814572369796381452523496178345928716672145893189637524268753941451869237937214685
* PAIR I2: 2,4 ROW 2
D2: 2,4,3                                # reduction candidate for 2,4
D2: 2,4 => CTR
* 8..57....79..8..5...3.96178.4.9.8.166..1.5..313.647829.6875.941....69.379..314..5
D2: 3 => SOLVED
* 814572369796381452523496178345928716672145893189637524268753941451869237937214685
* PAIR B5: 7,8 ROW 5
G5: 7,8,4                                # reduction candidate for 7,8
G5: 7,8 => SOLVED
* 814572369796381452523496178345928716672145893189637524268753941451869237937214685
G5: 4 => CTR
* 8..57....79..8..5...3.96178.4.9.87166..1.54.31..647529.6875.941....69.379...14..5
* PAIR I6: 4,9 COL I
I1: 4,9,2                                # reduction candidate for 4,9
I1: 2 => CTR
* 8..57..9279..8..54.23496178.4.9.8.166.91254831856.7.2..6875.941....69.379...14..5
I1: 4,9                                  # 29 pairs
* PAIR C8: 1,4 COL C
C1: 1,4,6                                # reduction candidate for 1,4
C1: 1,4                                  # 30 pairs
C2: 1,4,6                                # reduction candidate for 1,4
C2: 1,4 => CTR
* 8.657..9.79..8.65...3.96178.4.9.8.166.91254831856.7.2..6875.941....69.379...14..5
C2: 6                                    # 30 pairs
* PAIR C9: 2,7 COL C
C5: 2,7,9                                # reduction candidate for 2,7
C5: 2,7 => SOLVED
* 814572369796381452523496178345928716672145893189637524268753941451869237937214685
C5: 9 => CTR
* 8..57....79..8..5...3.9617824.938.166.91254831..6.7.2..6875.941....69.379...14..5
* PAIR F7: 2,3 BLK 8
D9: 2,3,8                                # reduction candidate for 2,3
D9: 8 => CTR
* 81.57239479438..5...3496178.4.9.8.166..1.5..31..6.7.2..68753941451269837937814265
D9: 2,3                                  # 27 pairs
* PAIR F7: 2,3 COL F
F1: 2,3,1                                # reduction candidate for 2,3
F1: 2,3                                  # 29 pairs
F2: 2,3,1                                # reduction candidate for 2,3
F2: 2,3 => CTR
* 826571394791483652453296178.4.9.8.166.91254831856.7.2..6875.941.14.69.379...14.65
F2: 1                                    # 29 pairs
* PAIR D8: 2,8 BLK 8
D9: 2,8,3                                # reduction candidate for 2,8
D9: 2,8 => SOLVED
* 814572369796381452523496178345928716672145893189637524268753941451869237937214685
D9: 3 => CTR
* 8..57....79..8..5...3.9617824.938.166..1254.313.647829.6875.941...8692379.2314..5
* PAIR G8: 2,8 BLK 9
G9: 2,8,6                                # reduction candidate for 2,8
G9: 2,8 => CTR
* 8..57..9.79..8..5...3.96178.4.9.8.166.91254831856.7.2..6875.941....69.379...14.65
G9: 6 => SOLVED
* 814572369796381452523496178345928716672145893189637524268753941451869237937214685
* PAIR H9: 6,8 BLK 9
G9: 6,8,2                                # reduction candidate for 6,8
G9: 2 => CTR
* 8..57..9.79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14265
G9: 6,8                                  # 27 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-620657-base-pr-000.dot
* REASONING
* DIS # F1: 3 => CTR => F1: 1,2
* DIS # D2: 2,4 => CTR => D2: 3
* PRF # D2: 3 => SOL
* DIS # I1: 2,4 => CTR => I1: 9
* PRF # I1: 9 => SOL
* DIS # D2: 2,4 => CTR => D2: 3
* PRF # D2: 3 => SOL
* PRF # G5: 7,8 => SOL
* DIS # G5: 4 => CTR => G5: 7,8
* DIS # I1: 2 => CTR => I1: 4,9
* DIS # C2: 1,4 => CTR => C2: 6
* PRF # C5: 2,7 => SOL
* DIS # C5: 9 => CTR => C5: 2,7
* DIS # D9: 8 => CTR => D9: 2,3
* DIS # F2: 2,3 => CTR => F2: 1
* PRF # D9: 2,8 => SOL
* DIS # D9: 3 => CTR => D9: 2,8
* DIS # G9: 2,8 => CTR => G9: 6
* PRF # G9: 6 => SOL
* DIS # G9: 2 => CTR => G9: 6,8
* CNT  20 HDP CHAINS /  28 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A7,A8,B1,B3,B5,B6,B8,B9,C4,C6,C8,C9,D3,D8,E4,E5,E6,F7,G4,G8,H1,H5,H9,I2,I6)
* 8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5
* PAIR B1: 1,2 ROW 1
F1: 1,2,3                                # reduction candidate for 1,2
F1: 3 => CTR
* 8..573...796.8135...3.9617824.938.1668.1254931..6.7.2.368752941...869237972314..5
* PAIR RESTART
* PAIR B5: 7,8 ROW 5
G5: 7,8,4                                # reduction candidate for 7,8
G5: 7,8 => SOLVED
* 814572369796381452523496178345928716672145893189637524268753941451869237937214685
* DURATION: 0:00:04.638167  START: 07:22:40.791678  END: 07:22:45.429845 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-620657-base-pr-001.dot
* REASONING
* DIS # F1: 3 => CTR => F1: 1,2
* PRF F1: 1,2 # G5: 7,8 => SOL
* STA F1: 1,2 + G5: 7,8
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokus.de/620657.html
sehr schwierig

level: medium

* PAIR REDUCTION ..
* ROUND 1: 8..57....79..8..5...3.96178.4.9.8.166..1.5..31..6.7.2..6875.941....69.379...14..5
B1: 1,2
F1: 1,2,3                                # reduction candidate for 1,2
F1: 3 => CTR
* 8..573...796.8135...3.9617824.938.1668.1254931..6.7.2.368752941...869237972314..5
A3: 4,5
B3: 2,5
D3: 2,4
H1: 6,9
A4: 2,3
C4: 5,7
B5: 7,8
G5: 4,7,8                                # reduction candidate for 7,8
G5: 7,8 => SOLVED
* 814572369796381452523496178345928716672145893189637524268753941451869237937214685
* SOLVED!

--------------------------------------------------
* AUTO ..
E1 = 7                # set value
F3 = 6                # set value
I3 = 8                # set value
H4 = 1                # set value
H7: 4                 # naked single
E7 = 5                # set value
H7 = 4                # set value
I7 = 1                # set value
E3: 9..               # hidden single
D7: 7..               # hidden single
E9: 1..               # hidden single
H2: 5..               # hidden single
H2 = 5                # set value
E3 = 9                # set value
D7 = 7                # set value
E9 = 1                # set value
F8: 9..               # hidden single
F8 = 9                # set value
A9: 9..               # hidden single
A9 = 9                # set value
Q9: 2.. = G8,G9: 2.. => G1,G2 != 2
A8,B8,C8: 1,4,5.. => A8,B8,C8 != 2 # hidden triple
B5,B6,B9: 3,7,8.. => B5,B6,B9 != 2,5 # hidden triple
C1,C2,C8: 6,1,4.. => C1,C2,C8 != 2,5 # hidden triple
Q4,Q7: 2.. => A3 != 2
Q1,Q7: 5.. => A4 != 5
C4,G4: 5,7.. => C4 != 2 # hidden pair
* UNSOLVED!

|:step:| 00
--------------------------------------------------

pair quad
D8: 2,8
G8: 2,8
D9: 2,3,8
G9: 2,6,8

* FORCE VALUE:: D9 = 3
D9 = 3                # set value
=> CTR

* FORCE VALUE:: G9 = 6
G9 = 6                # set value
* SOLVED!

|:step:| 01
--------------------------------------------------

Solution

position: 814572369796381452523496178345928716672145893189637524268753941451869237937214685 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:

* INC # F1: 1,2 => UNS
* DIS # F1: 3 => CTR => F1: 1,2
* DIS # D2: 2,4 => CTR => D2: 3
* PRF # D2: 3 => SOL
* DIS # I1: 2,4 => CTR => I1: 9
* PRF # I1: 9 => SOL
* DIS # D2: 2,4 => CTR => D2: 3
* PRF # D2: 3 => SOL
* PRF # G5: 7,8 => SOL
* DIS # G5: 4 => CTR => G5: 7,8
* INC # I1: 4,9 => UNS
* DIS # I1: 2 => CTR => I1: 4,9
* INC # C1: 1,4 => UNS
* DIS # C2: 1,4 => CTR => C2: 6
* INC # C2: 6 => UNS
* PRF # C5: 2,7 => SOL
* DIS # C5: 9 => CTR => C5: 2,7
* INC # D9: 2,3 => UNS
* DIS # D9: 8 => CTR => D9: 2,3
* INC # F1: 2,3 => UNS
* DIS # F2: 2,3 => CTR => F2: 1
* INC # F2: 1 => UNS
* PRF # D9: 2,8 => SOL
* DIS # D9: 3 => CTR => D9: 2,8
* DIS # G9: 2,8 => CTR => G9: 6
* PRF # G9: 6 => SOL
* INC # G9: 6,8 => UNS
* DIS # G9: 2 => CTR => G9: 6,8
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 1,2 => UNS
* DIS # F1: 3 => CTR => F1: 1,2
* PRF F1: 1,2 # G5: 7,8 => SOL
* STA F1: 1,2 + G5: 7,8
* CNT   3 HDP CHAINS /   3 HYP OPENED