Analysis of zz-sudoku-de-665801-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...9..5..29.....3...4..7.6..4783..2.1.......8.3..5417..6.7..4...2.....17..9..6... initial

Autosolve

position: 71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A7: 3,5 => SOL
* DIS # A7: 8 => CTR => A7: 3,5
* DIS # A8: 3,5 => CTR => A8: 4,8
* DIS # F7: 2,3 => CTR => F7: 5,8
* PRF # F7: 5,8 => SOL
* PRF # D8: 4,5 => SOL
* DIS # D8: 3 => CTR => D8: 4,5
* PRF # F7: 5,8 => SOL
* DIS # F7: 2,3 => CTR => F7: 5,8
* DIS # F8: 5,8 => CTR => F8: 3
* PRF # F8: 3 => SOL
* DIS # D8: 3,5 => CTR => D8: 4
* PRF # D8: 4 => SOL
* PRF # A7: 3,5 => SOL
* DIS # A7: 8 => CTR => A7: 3,5
* DIS # A8: 3,5 => CTR => A8: 4,8
* DIS # D8: 3,5 => CTR => D8: 4
* PRF # D8: 4 => SOL
* PRF # F8: 3,5 => SOL
* DIS # F8: 8 => CTR => F8: 3,5
* DIS # A8: 3,4 => CTR => A8: 5,8
* PRF # A8: 5,8 => SOL
* DIS # F7: 2,8 => CTR => F7: 3,5
* PRF # F7: 3,5 => SOL
* DIS # F7: 2,3 => CTR => F7: 5,8
* PRF # F7: 5,8 => SOL
* CNT  26 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:

* PRF # A7: 3,5 => SOL
* STA A7: 3,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...9..5..29.....3...4..7.6..4783..2.1.......8.3..5417..6.7..4...2.....17..9..6... initial
71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685. autosolve
713962584296548731584317269647831925152679348938254176361785492825493617479126853 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
C1: 3,6
C2: 5,6
A3: 3,5
E1: 2,6
F1: 2,3
D2: 4,5
F2: 5,8
D3: 3,5
C8: 3,5
A9: 3,4
E7: 2,8
E9: 2,4
I7: 2,3
I9: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,F1: 2.. / E1 = 2  =>  0 pairs (X) / F1 = 2  =>  0 pairs (_)
I7,I9: 2.. / I7 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
E9,I9: 2.. / E9 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
F1,F7: 2.. / F1 = 2  =>  0 pairs (*) / F7 = 2  =>  0 pairs (X)
C1,A3: 3.. / C1 = 3  =>  0 pairs (*) / A3 = 3  =>  0 pairs (X)
F1,D3: 3.. / F1 = 3  =>  0 pairs (X) / D3 = 3  =>  0 pairs (_)
I7,I9: 3.. / I7 = 3  =>  0 pairs (X) / I9 = 3  =>  0 pairs (_)
C1,F1: 3.. / C1 = 3  =>  0 pairs (*) / F1 = 3  =>  0 pairs (X)
A3,D3: 3.. / A3 = 3  =>  0 pairs (X) / D3 = 3  =>  0 pairs (_)
A9,I9: 3.. / A9 = 3  =>  0 pairs (X) / I9 = 3  =>  0 pairs (_)
C1,C8: 3.. / C1 = 3  =>  0 pairs (*) / C8 = 3  =>  0 pairs (X)
D3,D8: 3.. / D3 = 3  =>  0 pairs (*) / D8 = 3  =>  0 pairs (X)
D2,E2: 4.. / D2 = 4  =>  0 pairs (X) / E2 = 4  =>  0 pairs (_)
A8,A9: 4.. / A8 = 4  =>  0 pairs (X) / A9 = 4  =>  0 pairs (_)
D8,E9: 4.. / D8 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
A8,D8: 4.. / A8 = 4  =>  0 pairs (X) / D8 = 4  =>  0 pairs (_)
A9,E9: 4.. / A9 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
D2,D8: 4.. / D2 = 4  =>  0 pairs (X) / D8 = 4  =>  0 pairs (_)
E2,E9: 4.. / E2 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
C2,A3: 5.. / C2 = 5  =>  0 pairs (X) / A3 = 5  =>  0 pairs (_)
A3,D3: 5.. / A3 = 5  =>  0 pairs (*) / D3 = 5  =>  0 pairs (X)
A7,F7: 5.. / A7 = 5  =>  0 pairs (X) / F7 = 5  =>  0 pairs (_)
C2,C8: 5.. / C2 = 5  =>  0 pairs (X) / C8 = 5  =>  0 pairs (_)
C1,C2: 6.. / C1 = 6  =>  0 pairs (X) / C2 = 6  =>  0 pairs (_)
E1,E2: 6.. / E1 = 6  =>  0 pairs (*) / E2 = 6  =>  0 pairs (X)
C1,E1: 6.. / C1 = 6  =>  0 pairs (X) / E1 = 6  =>  0 pairs (_)
C2,E2: 6.. / C2 = 6  =>  0 pairs (*) / E2 = 6  =>  0 pairs (X)
E2,F2: 8.. / E2 = 8  =>  0 pairs (X) / F2 = 8  =>  0 pairs (_)
A7,A8: 8.. / A7 = 8  =>  0 pairs (X) / A8 = 8  =>  0 pairs (_)
A8,F8: 8.. / A8 = 8  =>  0 pairs (*) / F8 = 8  =>  0 pairs (X)
E2,E7: 8.. / E2 = 8  =>  0 pairs (X) / E7 = 8  =>  0 pairs (_)
* DURATION: 0:00:54.318146  START: 07:41:54.800668  END: 07:42:49.118814 2017-05-01
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,C1,C2,C8,D2,D3,E1,E7,E9,F1,F2,I7,I9)
* 71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685.
* PAIR A3: 3,5 COL A
A7: 3,5,8                                # reduction candidate for 3,5
A7: 3,5 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
A7: 8 => CTR
* 71.9..58429....731.84.17269647831925152679348938254176861725493.2..98617.791.685.
A8: 3,5,4,8                              # reduction candidate for 3,5
A8: 3,5 => CTR
* 71.9..58429....731.84.17269647831925152679348938254176861725493.2.49.617.791.685.
A8: 4,8                                  # 15 pairs
* PAIR F1: 2,3 COL F
F7: 2,3,5,8                              # reduction candidate for 2,3
F7: 2,3 => CTR
* 71.9..58429....731.84.1726964783192515267934893825417656178.49.82349.617.791.685.
F7: 5,8 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
* PAIR D2: 4,5 COL D
D8: 4,5,3                                # reduction candidate for 4,5
D8: 4,5 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
D8: 3 => CTR
* 71.9..58429.4..731.84517269647831925152679348938254176.617..49.42.398617.791.685.
* PAIR F2: 5,8 COL F
F7: 5,8,2,3                              # reduction candidate for 5,8
F7: 5,8 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
F7: 2,3 => CTR
* 71.9..58429....731.84.1726964783192515267934893825417656178.49.82349.617.791.685.
F8: 5,8,3                                # reduction candidate for 5,8
F8: 5,8 => CTR
* 71.9..58429....731.84.1726964783192515267934893825417656178.49.82349.617.791.685.
F8: 3 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
* PAIR D3: 3,5 COL D
D8: 3,5,4                                # reduction candidate for 3,5
D8: 3,5 => CTR
* 713962584296485731584.17269647831925152679348938254176.617..49.42..98617379146852
D8: 4 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
* PAIR C8: 3,5 BLK 7
A7: 3,5,8                                # reduction candidate for 3,5
A7: 3,5 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
A7: 8 => CTR
* 71.9..58429....731.84.17269647831925152679348938254176861725493.2..98617.791.685.
A8: 3,5,4,8                              # reduction candidate for 3,5
A8: 3,5 => CTR
* 71.9..58429....731.84.17269647831925152679348938254176861725493.2.49.617.791.685.
A8: 4,8                                  # 15 pairs
* PAIR C8: 3,5 ROW 8
D8: 3,5,4                                # reduction candidate for 3,5
D8: 3,5 => CTR
* 713962584296485731584.17269647831925152679348938254176.617..49.42..98617379146852
D8: 4 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
F8: 3,5,8                                # reduction candidate for 3,5
F8: 3,5 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
F8: 8 => CTR
* 71.9..58429..85731584.17269647831925152679348938254176.617..49..2..98617.791.685.
* PAIR A9: 3,4 BLK 7
A8: 3,4,5,8                              # reduction candidate for 3,4
A8: 3,4 => CTR
* 71.9..58429....731.84.17269647831925152679348938254176861725493.25.98617.791.685.
A8: 5,8 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
* PAIR E7: 2,8 BLK 8
F7: 2,8,3,5                              # reduction candidate for 2,8
F7: 2,8 => CTR
* 71.9..58429....731.84.172696478319251526793489382541765617..493823.9.617.791.685.
F7: 3,5 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
* PAIR I7: 2,3 ROW 7
F7: 2,3,5,8                              # reduction candidate for 2,3
F7: 2,3 => CTR
* 71.9..58429....731.84.1726964783192515267934893825417656178.49.82349.617.791.685.
F7: 5,8 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-665801-base-pr-000.dot
* REASONING
* PRF # A7: 3,5 => SOL
* DIS # A7: 8 => CTR => A7: 3,5
* DIS # A8: 3,5 => CTR => A8: 4,8
* DIS # F7: 2,3 => CTR => F7: 5,8
* PRF # F7: 5,8 => SOL
* PRF # D8: 4,5 => SOL
* DIS # D8: 3 => CTR => D8: 4,5
* PRF # F7: 5,8 => SOL
* DIS # F7: 2,3 => CTR => F7: 5,8
* DIS # F8: 5,8 => CTR => F8: 3
* PRF # F8: 3 => SOL
* DIS # D8: 3,5 => CTR => D8: 4
* PRF # D8: 4 => SOL
* PRF # A7: 3,5 => SOL
* DIS # A7: 8 => CTR => A7: 3,5
* DIS # A8: 3,5 => CTR => A8: 4,8
* DIS # D8: 3,5 => CTR => D8: 4
* PRF # D8: 4 => SOL
* PRF # F8: 3,5 => SOL
* DIS # F8: 8 => CTR => F8: 3,5
* DIS # A8: 3,4 => CTR => A8: 5,8
* PRF # A8: 5,8 => SOL
* DIS # F7: 2,8 => CTR => F7: 3,5
* PRF # F7: 3,5 => SOL
* DIS # F7: 2,3 => CTR => F7: 5,8
* PRF # F7: 5,8 => SOL
* CNT  26 HDP CHAINS /  28 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,C1,C2,C8,D2,D3,E1,E7,E9,F1,F2,I7,I9)
* 71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685.
* PAIR A3: 3,5 COL A
A7: 3,5,8                                # reduction candidate for 3,5
A7: 3,5 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
* DURATION: 0:00:01.975912  START: 07:43:21.515885  END: 07:43:23.491797 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-665801-base-pr-001.dot
* REASONING
* PRF # A7: 3,5 => SOL
* STA A7: 3,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokus.de/665801.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: 71.9..58429....731.84.17269647831925152679348938254176.617..49..2..9.617.791.685.
C1: 3,6
C2: 5,6
A3: 3,5
A7: 3,5,8                                # reduction candidate for 3,5
A7: 3,5 => SOLVED
* 713962584296548731584317269647831925152679348938254176361785492825493617479126853
* SOLVED!

--------------------------------------------------
* AUTO ..
G2 = 7                # set value
F4 = 1                # set value
B5 = 5                # set value
E5 = 7                # set value
G5 = 3                # set value
H5 = 4                # set value
H1: 8                 # naked single
G8 = 6                # set value
G4: 9                 # naked single
F5: 9..               # hidden single
I4: 5..               # hidden single
H7: 9..               # hidden single
H1 = 8                # set value
H9: 5                 # naked single
G4 = 9                # set value
I6: 6                 # naked single
G3: 2                 # naked single
A4: 6                 # naked single
I4 = 5                # set value
F5 = 9                # set value
I6 = 6                # set value
D6: 2                 # naked single
H7 = 9                # set value
H9 = 5                # set value
I3: 9..               # hidden single
A6: 9..               # hidden single
D5: 6..               # hidden single
E8: 9..               # hidden single
G9: 8..               # hidden single
G3 = 2                # set value
G9: 8                 # naked single
I3 = 9                # set value
A4 = 6                # set value
C5: 2                 # naked single
C5 = 2                # set value
C6: 8                 # naked single
D5: 6                 # naked single
D5 = 6                # set value
A6 = 9                # set value
C6 = 8                # set value
D6 = 2                # set value
E8 = 9                # set value
G9 = 8                # set value
B3: 8..               # hidden single
B3 = 8                # set value
E3: 1                 # naked single
E3 = 1                # set value
D9: 1..               # hidden single
C7: 1..               # hidden single
C7 = 1                # set value
B9: 7                 # naked single
B9 = 7                # set value
B1: 1                 # naked single
D9 = 1                # set value
A1: 7..               # hidden single
I2: 1..               # hidden single
A1 = 7                # set value
B1 = 1                # set value
I1: 4                 # naked single
I1 = 4                # set value
I2: 1                 # naked single
I2 = 1                # set value
* UNSOLVED!

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

* DISABLE VALUE:: A7 != 8

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

Solution

position: 713962584296548731584317269647831925152679348938254176361785492825493617479126853 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 # A7: 3,5 => SOL
* DIS # A7: 8 => CTR => A7: 3,5
* DIS # A8: 3,5 => CTR => A8: 4,8
* INC # A8: 4,8 => UNS
* DIS # F7: 2,3 => CTR => F7: 5,8
* PRF # F7: 5,8 => SOL
* PRF # D8: 4,5 => SOL
* DIS # D8: 3 => CTR => D8: 4,5
* PRF # F7: 5,8 => SOL
* DIS # F7: 2,3 => CTR => F7: 5,8
* DIS # F8: 5,8 => CTR => F8: 3
* PRF # F8: 3 => SOL
* DIS # D8: 3,5 => CTR => D8: 4
* PRF # D8: 4 => SOL
* PRF # A7: 3,5 => SOL
* DIS # A7: 8 => CTR => A7: 3,5
* DIS # A8: 3,5 => CTR => A8: 4,8
* INC # A8: 4,8 => UNS
* DIS # D8: 3,5 => CTR => D8: 4
* PRF # D8: 4 => SOL
* PRF # F8: 3,5 => SOL
* DIS # F8: 8 => CTR => F8: 3,5
* DIS # A8: 3,4 => CTR => A8: 5,8
* PRF # A8: 5,8 => SOL
* DIS # F7: 2,8 => CTR => F7: 3,5
* PRF # F7: 3,5 => SOL
* DIS # F7: 2,3 => CTR => F7: 5,8
* PRF # F7: 5,8 => SOL
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A7: 3,5 => SOL
* STA A7: 3,5
* CNT   1 HDP CHAINS /   1 HYP OPENED