Analysis of zz-sudoku-de-640978-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...8..6..9.8.5..3.2..4..5....4.31..6.2.....1.1..69.7....2..4..7.4..1.2.8..6..5... initial

Autosolve

position: 4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B3: 6,7 => SOL
* DIS # B3: 3 => CTR => B3: 6,7
* PRF # B3: 6,7 => SOL
* DIS # B3: 3 => CTR => B3: 6,7
* DIS # C5: 3 => CTR => C5: 5,7
* DIS # C5: 3,5 => CTR => C5: 7
* PRF # C5: 7 => SOL
* DIS # C5: 3 => CTR => C5: 5,7
* DIS # C5: 3,5 => CTR => C5: 7
* PRF # C5: 7 => SOL
* CNT  10 HDP CHAINS /  12 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 # B3: 6,7 => SOL
* STA B3: 6,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...8..6..9.8.5..3.2..4..5....4.31..6.2.....1.1..69.7....2..4..7.4..1.2.8..6..5... initial
4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94 autosolve
435829671968157432271463589594731826627548913183692745352984167749316258816275394 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (28)
B1: 3,5
C1: 1,5
B2: 6,7
C3: 1,7
F1: 3,9
F2: 6,7
E3: 6,7
F3: 3,9
I1: 1,9
I3: 1,9
A4: 5,7
C6: 3,5
D4: 5,7
D5: 5,7
I5: 3,5
I6: 3,5
A7: 3,8
B7: 1,5
A8: 5,7
A9: 3,8
B9: 1,7
E7: 6,8
F8: 6,7
E9: 7,8
G7: 1,3
H7: 5,6
H8: 5,6
G9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,C3: 1.. / C1 = 1  =>  0 pairs (X) / C3 = 1  =>  0 pairs (_)
I1,I3: 1.. / I1 = 1  =>  0 pairs (*) / I3 = 1  =>  0 pairs (X)
B7,B9: 1.. / B7 = 1  =>  0 pairs (X) / B9 = 1  =>  0 pairs (_)
G7,G9: 1.. / G7 = 1  =>  0 pairs (*) / G9 = 1  =>  0 pairs (X)
C1,I1: 1.. / C1 = 1  =>  0 pairs (X) / I1 = 1  =>  0 pairs (_)
C3,I3: 1.. / C3 = 1  =>  0 pairs (*) / I3 = 1  =>  0 pairs (X)
B7,G7: 1.. / B7 = 1  =>  0 pairs (X) / G7 = 1  =>  0 pairs (_)
B9,G9: 1.. / B9 = 1  =>  0 pairs (*) / G9 = 1  =>  0 pairs (X)
B1,B3: 3.. / B1 = 3  =>  0 pairs (*) / B3 = 3  =>  0 pairs (X)
F1,F3: 3.. / F1 = 3  =>  0 pairs (X) / F3 = 3  =>  0 pairs (_)
C5,C6: 3.. / C5 = 3  =>  0 pairs (X) / C6 = 3  => 26 pairs (_)
I5,I6: 3.. / I5 = 3  => 26 pairs (_) / I6 = 3  =>  0 pairs (X)
A7,A9: 3.. / A7 = 3  =>  0 pairs (*) / A9 = 3  =>  0 pairs (X)
G7,G9: 3.. / G7 = 3  =>  0 pairs (X) / G9 = 3  =>  0 pairs (_)
B1,F1: 3.. / B1 = 3  =>  0 pairs (*) / F1 = 3  =>  0 pairs (X)
B3,F3: 3.. / B3 = 3  =>  0 pairs (X) / F3 = 3  =>  0 pairs (_)
C5,I5: 3.. / C5 = 3  =>  0 pairs (X) / I5 = 3  => 26 pairs (_)
C6,I6: 3.. / C6 = 3  => 26 pairs (_) / I6 = 3  =>  0 pairs (X)
A7,G7: 3.. / A7 = 3  =>  0 pairs (*) / G7 = 3  =>  0 pairs (X)
A9,G9: 3.. / A9 = 3  =>  0 pairs (X) / G9 = 3  =>  0 pairs (_)
B1,C1: 5.. / B1 = 5  =>  0 pairs (X) / C1 = 5  =>  0 pairs (_)
D4,D5: 5.. / D4 = 5  =>  0 pairs (X) / D5 = 5  =>  0 pairs (_)
I5,I6: 5.. / I5 = 5  =>  0 pairs (X) / I6 = 5  => 26 pairs (_)
B7,A8: 5.. / B7 = 5  =>  0 pairs (*) / A8 = 5  =>  0 pairs (X)
H7,H8: 5.. / H7 = 5  =>  0 pairs (X) / H8 = 5  =>  0 pairs (_)
A4,D4: 5.. / A4 = 5  =>  0 pairs (*) / D4 = 5  =>  0 pairs (X)
C6,I6: 5.. / C6 = 5  =>  0 pairs (X) / I6 = 5  => 26 pairs (_)
B7,H7: 5.. / B7 = 5  =>  0 pairs (*) / H7 = 5  =>  0 pairs (X)
A8,H8: 5.. / A8 = 5  =>  0 pairs (X) / H8 = 5  =>  0 pairs (_)
A4,A8: 5.. / A4 = 5  =>  0 pairs (*) / A8 = 5  =>  0 pairs (X)
B1,B7: 5.. / B1 = 5  =>  0 pairs (X) / B7 = 5  =>  0 pairs (_)
B2,B3: 6.. / B2 = 6  =>  0 pairs (*) / B3 = 6  =>  0 pairs (X)
F2,E3: 6.. / F2 = 6  =>  0 pairs (X) / E3 = 6  =>  0 pairs (_)
E7,F8: 6.. / E7 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
H7,H8: 6.. / H7 = 6  =>  0 pairs (*) / H8 = 6  =>  0 pairs (X)
B2,F2: 6.. / B2 = 6  =>  0 pairs (*) / F2 = 6  =>  0 pairs (X)
B3,E3: 6.. / B3 = 6  =>  0 pairs (X) / E3 = 6  =>  0 pairs (_)
E7,H7: 6.. / E7 = 6  =>  0 pairs (X) / H7 = 6  =>  0 pairs (_)
F8,H8: 6.. / F8 = 6  =>  0 pairs (*) / H8 = 6  =>  0 pairs (X)
E3,E7: 6.. / E3 = 6  =>  0 pairs (*) / E7 = 6  =>  0 pairs (X)
F2,F8: 6.. / F2 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
F2,E3: 7.. / F2 = 7  =>  0 pairs (*) / E3 = 7  =>  0 pairs (X)
A4,C5: 7.. / A4 = 7  =>  0 pairs (X) / C5 = 7  =>  0 pairs (_)
D4,D5: 7.. / D4 = 7  =>  0 pairs (*) / D5 = 7  =>  0 pairs (X)
A8,B9: 7.. / A8 = 7  =>  0 pairs (*) / B9 = 7  =>  0 pairs (X)
F8,E9: 7.. / F8 = 7  =>  0 pairs (X) / E9 = 7  =>  0 pairs (_)
B2,F2: 7.. / B2 = 7  =>  0 pairs (X) / F2 = 7  =>  0 pairs (_)
A4,D4: 7.. / A4 = 7  =>  0 pairs (X) / D4 = 7  =>  0 pairs (_)
C5,D5: 7.. / C5 = 7  =>  0 pairs (*) / D5 = 7  =>  0 pairs (X)
A8,F8: 7.. / A8 = 7  =>  0 pairs (*) / F8 = 7  =>  0 pairs (X)
B9,E9: 7.. / B9 = 7  =>  0 pairs (X) / E9 = 7  =>  0 pairs (_)
A4,A8: 7.. / A4 = 7  =>  0 pairs (X) / A8 = 7  =>  0 pairs (_)
C3,C5: 7.. / C3 = 7  =>  0 pairs (X) / C5 = 7  =>  0 pairs (_)
E3,E9: 7.. / E3 = 7  =>  0 pairs (X) / E9 = 7  =>  0 pairs (_)
F2,F8: 7.. / F2 = 7  =>  0 pairs (*) / F8 = 7  =>  0 pairs (X)
A7,A9: 8.. / A7 = 8  =>  0 pairs (X) / A9 = 8  =>  0 pairs (_)
E7,E9: 8.. / E7 = 8  =>  0 pairs (*) / E9 = 8  =>  0 pairs (X)
A7,E7: 8.. / A7 = 8  =>  0 pairs (X) / E7 = 8  =>  0 pairs (_)
A9,E9: 8.. / A9 = 8  =>  0 pairs (*) / E9 = 8  =>  0 pairs (X)
F1,F3: 9.. / F1 = 9  =>  0 pairs (*) / F3 = 9  =>  0 pairs (X)
I1,I3: 9.. / I1 = 9  =>  0 pairs (X) / I3 = 9  =>  0 pairs (_)
F1,I1: 9.. / F1 = 9  =>  0 pairs (*) / I1 = 9  =>  0 pairs (X)
F3,I3: 9.. / F3 = 9  =>  0 pairs (X) / I3 = 9  =>  0 pairs (_)
* DURATION: 0:01:55.770851  START: 07:33:35.054631  END: 07:35:30.825482 2017-05-01
* CP COUNT: (63)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,A8,A9,B1,B2,B7,B9,C1,C3,C6,D4,D5,E3,E7,E9,F1,F2,F3,F8,G7,G9,H7,H8,I1,I3,I5,I6)
* 4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94
* PAIR B2: 6,7 BLK 1
B3: 6,7,3                                # reduction candidate for 6,7
B3: 6,7 => SOLVED
* 435829671968157432271463589594731826627548913183692745352984167749316258816275394
B3: 3 => CTR
* 4..82.67.96815743223746958179453182662.74891.18.69274...2984.6754931.2.8..62.5.94
* PAIR E3: 6,7 ROW 3
B3: 6,7,3                                # reduction candidate for 6,7
B3: 6,7 => SOLVED
* 435829671968157432271463589594731826627548913183692745352984167749316258816275394
B3: 3 => CTR
* 4..82.67.96815743223746958179453182662.74891.18.69274...2984.6754931.2.8..62.5.94
* PAIR A4: 5,7 BLK 4
C5: 5,7,3                                # reduction candidate for 5,7
C5: 3 => CTR
* 4..82.67.9.815.4322.746.581794531826623748915185692743..2984..7.4931.2.8..62.5.94
C5: 5,7                                  # 26 pairs
* PAIR C6: 3,5 BLK 4
C5: 3,5,7                                # reduction candidate for 3,5
C5: 3,5 => CTR
* 4..82.67.9.815.4322.746.58179453182662.74891.18.69274...2984..7.4931.2.8..62.5.94
C5: 7 => SOLVED
* 435829671968157432271463589594731826627548913183692745352984167749316258816275394
* PAIR D5: 5,7 ROW 5
C5: 5,7,3                                # reduction candidate for 5,7
C5: 3 => CTR
* 4..82.67.9.815.4322.746.581794531826623748915185692743..2984..7.4931.2.8..62.5.94
C5: 5,7                                  # 26 pairs
* PAIR I5: 3,5 ROW 5
C5: 3,5,7                                # reduction candidate for 3,5
C5: 3,5 => CTR
* 4..82.67.9.815.4322.746.58179453182662.74891.18.69274...2984..7.4931.2.8..62.5.94
C5: 7 => SOLVED
* 435829671968157432271463589594731826627548913183692745352984167749316258816275394
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-640978-base-pr-000.dot
* REASONING
* PRF # B3: 6,7 => SOL
* DIS # B3: 3 => CTR => B3: 6,7
* PRF # B3: 6,7 => SOL
* DIS # B3: 3 => CTR => B3: 6,7
* DIS # C5: 3 => CTR => C5: 5,7
* DIS # C5: 3,5 => CTR => C5: 7
* PRF # C5: 7 => SOL
* DIS # C5: 3 => CTR => C5: 5,7
* DIS # C5: 3,5 => CTR => C5: 7
* PRF # C5: 7 => SOL
* CNT  10 HDP CHAINS /  12 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A7,A8,A9,B1,B2,B7,B9,C1,C3,C6,D4,D5,E3,E7,E9,F1,F2,F3,F8,G7,G9,H7,H8,I1,I3,I5,I6)
* 4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94
* PAIR B2: 6,7 BLK 1
B3: 6,7,3                                # reduction candidate for 6,7
B3: 6,7 => SOLVED
* 435829671968157432271463589594731826627548913183692745352984167749316258816275394
* DURATION: 0:00:02.172945  START: 07:35:45.795818  END: 07:35:47.968763 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-640978-base-pr-001.dot
* REASONING
* PRF # B3: 6,7 => SOL
* STA B3: 6,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokus.de/640978.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: 4..82.67.9.815.4322..4..58..94.3182662..4891.18.69274...29.4..7.4931.2.8..62.5.94
B1: 3,5
C1: 1,5
B2: 6,7
B3: 3,6,7                                # reduction candidate for 6,7
B3: 6,7 => SOLVED
* 435829671968157432271463589594731826627548913183692745352984167749316258816275394
* SOLVED!

--------------------------------------------------
* AUTO ..
A1 = 4                # set value
D2 = 1                # set value
G2: 4                 # naked single
G2 = 4                # set value
I2: 2                 # naked single
I2 = 2                # set value
H3 = 8                # set value
A5 = 6                # set value
E5 = 4                # set value
H1: 7..               # hidden single
H1 = 7                # set value
E1: 2                 # naked single
E1 = 2                # set value
D9: 2..               # hidden single
F6: 2..               # hidden single
F6 = 2                # set value
D9 = 2                # set value
F5: 8..               # hidden single
H4: 2..               # hidden single
B6: 8..               # hidden single
H4 = 2                # set value
F5 = 8                # set value
B6 = 8                # set value
G4: 8..               # hidden single
G4 = 8                # set value
B4: 9..               # hidden single
B4 = 9                # set value
C8: 9..               # hidden single
C8 = 9                # set value
D7: 9..               # hidden single
D7 = 9                # set value
D8: 3..               # hidden single
H9: 9..               # hidden single
D8 = 3                # set value
H9 = 9                # set value
I9: 4..               # hidden single
G5: 9..               # hidden single
H6: 4..               # hidden single
G5 = 9                # set value
H6 = 4                # set value
I9 = 4                # set value
Q7: 1.. = B7,B9: 1.. => B1,B3 != 1
Q4: 3.. = C5,C6: 3.. => C1,C3 != 3
Q1: 3.. = B1,B3: 3.. => B7,B9 != 3
F1,F3: 3,9.. => F3 != 6,7 # hidden pair
A7,A9: 3,8.. => A7,A9 != 5,7 # hidden pair
* UNSOLVED!

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

highlight 3
C5: 3,5,7
I5: 3,5
I6: 3,5
C6: 3,5
=> C5 = 7

* FORCE VALUE:: C5 = 7
C5 = 7                # set value
A4: 5                 # naked single
C3: 1                 # naked single
D5: 5                 # naked single
C6: 3..               # hidden single
D4: 7..               # hidden single
I5: 3..               # hidden single
A8: 7..               # hidden single

* AUTO ..
* SOLVED!

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

Solution

position: 435829671968157432271463589594731826627548913183692745352984167749316258816275394 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 # B3: 6,7 => SOL
* DIS # B3: 3 => CTR => B3: 6,7
* PRF # B3: 6,7 => SOL
* DIS # B3: 3 => CTR => B3: 6,7
* INC # C5: 5,7 => UNS
* DIS # C5: 3 => CTR => C5: 5,7
* DIS # C5: 3,5 => CTR => C5: 7
* PRF # C5: 7 => SOL
* INC # C5: 5,7 => UNS
* DIS # C5: 3 => CTR => C5: 5,7
* DIS # C5: 3,5 => CTR => C5: 7
* PRF # C5: 7 => SOL
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # B3: 6,7 => SOL
* STA B3: 6,7
* CNT   1 HDP CHAINS /   1 HYP OPENED