Analysis of zz-sudoku-de-603428-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

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
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

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
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 # 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