Analysis of zz-sudoku-de-626776-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .2.....3...9...2..48.276.91.9.8.7.2.1.......3.7.6.4.5.65.489.12..8...7...3.....8. initial

Autosolve

position: .2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E1: 9 => CTR => E1: 4,5
* DIS # E5: 2 => CTR => E5: 5,9
* DIS # D1: 1 => CTR => D1: 5,9
* DIS # E5: 2,5 => CTR => E5: 9
* PRF # F8: 2,5 => SOL
* PRF # I8: 4,6 => SOL
* DIS # E8: 5,6 => CTR => E8: 2
* PRF # I9: 5,6 => SOL
* DIS # I9: 4 => CTR => I9: 5,6
* DIS # F1: 1,5 => CTR => F1: 8
* PRF # I8: 4,6 => SOL
* CNT  11 HDP CHAINS /  25 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 # E1: 9 => CTR => E1: 4,5
* PRF E1: 4,5 # I8: 4,6 => SOL
* STA E1: 4,5 + I8: 4,6
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

.2.....3...9...2..48.276.91.9.8.7.2.1.......3.7.6.4.5.65.489.12..8...7...3.....8. initial
.2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98. autosolve
521948637769153248483276591395817426146592873872634159657489312918325764234761985 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
A1: 5,7
C1: 1,6
A2: 5,7
B2: 1,6
E2: 4,5
G1: 4,6
I1: 7,8
H2: 4,6
I2: 7,8
B5: 4,6
C5: 4,6
D5: 5,9
F5: 2,5
G4: 4,6
I4: 4,6
B8: 1,4
C9: 1,4
E9: 5,6
F9: 1,5
H8: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,B2: 1.. / C1 = 1  =>  0 pairs (*) / B2 = 1  =>  0 pairs (X)
B8,C9: 1.. / B8 = 1  =>  0 pairs (*) / C9 = 1  =>  0 pairs (X)
C9,F9: 1.. / C9 = 1  =>  0 pairs (X) / F9 = 1  =>  0 pairs (_)
B2,B8: 1.. / B2 = 1  =>  0 pairs (X) / B8 = 1  =>  0 pairs (_)
C1,C9: 1.. / C1 = 1  =>  0 pairs (*) / C9 = 1  =>  0 pairs (X)
E5,F5: 2.. / E5 = 2  =>  0 pairs (X) / F5 = 2  => 20 pairs (_)
E8,F8: 2.. / E8 = 2  => 20 pairs (_) / F8 = 2  =>  0 pairs (X)
E5,E8: 2.. / E5 = 2  =>  0 pairs (X) / E8 = 2  => 20 pairs (_)
F5,F8: 2.. / F5 = 2  => 20 pairs (_) / F8 = 2  =>  0 pairs (X)
D2,F2: 3.. / D2 = 3  => 21 pairs (_) / F2 = 3  => 19 pairs (_)
D8,F8: 3.. / D8 = 3  => 19 pairs (_) / F8 = 3  => 21 pairs (_)
D2,D8: 3.. / D2 = 3  => 21 pairs (_) / D8 = 3  => 19 pairs (_)
F2,F8: 3.. / F2 = 3  => 19 pairs (_) / F8 = 3  => 21 pairs (_)
E1,E2: 4.. / E1 = 4  =>  0 pairs (*) / E2 = 4  =>  0 pairs (X)
G1,H2: 4.. / G1 = 4  =>  0 pairs (X) / H2 = 4  =>  0 pairs (_)
B5,C5: 4.. / B5 = 4  =>  0 pairs (*) / C5 = 4  =>  0 pairs (X)
G4,I4: 4.. / G4 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
B8,C9: 4.. / B8 = 4  =>  0 pairs (X) / C9 = 4  =>  0 pairs (_)
E1,G1: 4.. / E1 = 4  =>  0 pairs (*) / G1 = 4  =>  0 pairs (X)
E2,H2: 4.. / E2 = 4  =>  0 pairs (X) / H2 = 4  =>  0 pairs (_)
C9,I9: 4.. / C9 = 4  =>  0 pairs (*) / I9 = 4  =>  0 pairs (X)
B5,B8: 4.. / B5 = 4  =>  0 pairs (*) / B8 = 4  =>  0 pairs (X)
C5,C9: 4.. / C5 = 4  =>  0 pairs (X) / C9 = 4  =>  0 pairs (_)
G1,G4: 4.. / G1 = 4  =>  0 pairs (X) / G4 = 4  =>  0 pairs (_)
H2,H8: 4.. / H2 = 4  =>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
A1,A2: 5.. / A1 = 5  => 18 pairs (_) / A2 = 5  =>  0 pairs (X)
I8,I9: 5.. / I8 = 5  => 23 pairs (_) / I9 = 5  =>  0 pairs (*)
C1,B2: 6.. / C1 = 6  =>  0 pairs (X) / B2 = 6  =>  0 pairs (_)
G1,H2: 6.. / G1 = 6  =>  0 pairs (*) / H2 = 6  =>  0 pairs (X)
B5,C5: 6.. / B5 = 6  =>  0 pairs (X) / C5 = 6  =>  0 pairs (_)
G4,I4: 6.. / G4 = 6  =>  0 pairs (X) / I4 = 6  =>  0 pairs (_)
E8,E9: 6.. / E8 = 6  =>  0 pairs (X) / E9 = 6  => 21 pairs (_)
C1,G1: 6.. / C1 = 6  =>  0 pairs (X) / G1 = 6  =>  0 pairs (_)
B2,H2: 6.. / B2 = 6  =>  0 pairs (*) / H2 = 6  =>  0 pairs (X)
E9,I9: 6.. / E9 = 6  => 21 pairs (_) / I9 = 6  =>  0 pairs (X)
B2,B5: 6.. / B2 = 6  =>  0 pairs (*) / B5 = 6  =>  0 pairs (X)
C1,C5: 6.. / C1 = 6  =>  0 pairs (X) / C5 = 6  =>  0 pairs (_)
G1,G4: 6.. / G1 = 6  =>  0 pairs (*) / G4 = 6  =>  0 pairs (X)
H2,H8: 6.. / H2 = 6  =>  0 pairs (X) / H8 = 6  =>  0 pairs (_)
A1,A2: 7.. / A1 = 7  =>  0 pairs (X) / A2 = 7  => 18 pairs (_)
I1,I2: 7.. / I1 = 7  => 18 pairs (_) / I2 = 7  =>  0 pairs (X)
A1,I1: 7.. / A1 = 7  =>  0 pairs (X) / I1 = 7  => 18 pairs (_)
A2,I2: 7.. / A2 = 7  => 18 pairs (_) / I2 = 7  =>  0 pairs (X)
F1,F2: 8.. / F1 = 8  => 18 pairs (_) / F2 = 8  =>  0 pairs (X)
I1,I2: 8.. / I1 = 8  =>  0 pairs (X) / I2 = 8  => 18 pairs (_)
F1,I1: 8.. / F1 = 8  => 18 pairs (_) / I1 = 8  =>  0 pairs (X)
F2,I2: 8.. / F2 = 8  =>  0 pairs (X) / I2 = 8  => 18 pairs (_)
D1,E1: 9.. / D1 = 9  => 22 pairs (_) / E1 = 9  =>  0 pairs (X)
D5,E5: 9.. / D5 = 9  =>  0 pairs (X) / E5 = 9  => 22 pairs (_)
D1,D5: 9.. / D1 = 9  => 22 pairs (_) / D5 = 9  =>  0 pairs (X)
E1,E5: 9.. / E1 = 9  =>  0 pairs (X) / E5 = 9  => 22 pairs (_)
* DURATION: 0:01:24.893511  START: 07:25:02.274817  END: 07:26:27.168328 2017-05-01
* CP COUNT: (51)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B2,B5,B8,C1,C5,C9,D5,E2,E9,F5,F9,G1,G4,H2,H8,I1,I2,I4)
* .2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98.
* PAIR E2: 4,5 BLK 2
E1: 4,5,9                                # reduction candidate for 4,5
E1: 9 => CTR
* .2..9.43...9.4.26.4832765913958176241649..873872634159657489312948...7..23.7..98.
E1: 4,5                                  # 22 pairs
* PAIR D5: 5,9 BLK 5
E5: 5,9,2                                # reduction candidate for 5,9
E5: 2 => CTR
* .2..9.43...9.4.26.483276591395817624164925873872634159657489312948...7..23.7..98.
E5: 5,9                                  # 20 pairs
* PAIR D5: 5,9 COL D
D1: 5,9,1                                # reduction candidate for 5,9
D1: 1 => CTR
* .2.19.43..19.4.26.483276591395817624164...8738726341596574893129.8...7..23.7..98.
D1: 5,9                                  # 24 pairs
* PAIR F5: 2,5 BLK 5
E5: 2,5,9                                # reduction candidate for 2,5
E5: 2,5 => CTR
* .2..9.43...9.4.26.4832765913958176241649..873872634159657489312948...7..23.7..98.
E5: 9                                    # 22 pairs
* PAIR F5: 2,5 COL F
F8: 2,5,1,3                              # reduction candidate for 2,5
F8: 2,5 => SOLVED
* 521948637769153248483276591395817426146592873872634159657489312918325764234761985
F8: 1,3                                  # 21 pairs
* PAIR I4: 4,6 COL I
I8: 4,6,5                                # reduction candidate for 4,6
I8: 4,6 => SOLVED
* 521948637769153248483276591395817426146592873872634159657489312918325764234761985
I8: 5                                    # 23 pairs
I9: 4,6,5                                # reduction candidate for 4,6
I9: 4,6                                  # 23 pairs
* PAIR E9: 5,6 BLK 8
E8: 5,6,2                                # reduction candidate for 5,6
E8: 5,6 => CTR
* .21.98.3...9...2..483276591395817.2.1...258738726341596574893129.8..27..23.7.198.
E8: 2                                    # 20 pairs
* PAIR E9: 5,6 ROW 9
I9: 5,6,4                                # reduction candidate for 5,6
I9: 5,6 => SOLVED
* 521948637769153248483276591395817426146592873872634159657489312918325764234761985
I9: 4 => CTR
* .2.....3...9...24.4832765913958174261.4..2873872634159657489312948.2.765231765984
* PAIR F9: 1,5 BLK 8
D8: 1,5,3                                # reduction candidate for 1,5
D8: 1,5                                  # 21 pairs
F8: 1,5,2,3                              # reduction candidate for 1,5
F8: 1,5                                  # 20 pairs
* PAIR F9: 1,5 COL F
F1: 1,5,8                                # reduction candidate for 1,5
F1: 1,5 => CTR
* 72.....385.9348267483276591395817624164..2873872634159657489312948..37..23.7..98.
F1: 8                                    # 18 pairs
F2: 1,5,3,8                              # reduction candidate for 1,5
F2: 1,5                                  # 20 pairs
* PAIR H8: 4,6 BLK 9
I8: 4,6,5                                # reduction candidate for 4,6
I8: 4,6 => SOLVED
* 521948637769153248483276591395817426146592873872634159657489312918325764234761985
I8: 5                                    # 23 pairs
I9: 4,6,5                                # reduction candidate for 4,6
I9: 4,6                                  # 23 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-626776-base-pr-000.dot
* REASONING
* DIS # E1: 9 => CTR => E1: 4,5
* DIS # E5: 2 => CTR => E5: 5,9
* DIS # D1: 1 => CTR => D1: 5,9
* DIS # E5: 2,5 => CTR => E5: 9
* PRF # F8: 2,5 => SOL
* PRF # I8: 4,6 => SOL
* DIS # E8: 5,6 => CTR => E8: 2
* PRF # I9: 5,6 => SOL
* DIS # I9: 4 => CTR => I9: 5,6
* DIS # F1: 1,5 => CTR => F1: 8
* PRF # I8: 4,6 => SOL
* CNT  11 HDP CHAINS /  25 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B2,B5,B8,C1,C5,C9,D5,E2,E9,F5,F9,G1,G4,H2,H8,I1,I2,I4)
* .2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98.
* PAIR E2: 4,5 BLK 2
E1: 4,5,9                                # reduction candidate for 4,5
E1: 9 => CTR
* .2..9.43...9.4.26.4832765913958176241649..873872634159657489312948...7..23.7..98.
* PAIR I4: 4,6 COL I
I8: 4,6,5                                # reduction candidate for 4,6
I8: 4,6 => SOLVED
* 521948637769153248483276591395817426146592873872634159657489312918325764234761985
* DURATION: 0:00:05.076194  START: 07:26:52.760719  END: 07:26:57.836913 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-626776-base-pr-001.dot
* REASONING
* DIS # E1: 9 => CTR => E1: 4,5
* PRF E1: 4,5 # I8: 4,6 => SOL
* STA E1: 4,5 + I8: 4,6
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokus.de/626776.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: .2.....3...9...2..483276591395817.2.1.....8738726341596574893129.8...7..23.7..98.
A1: 5,7
C1: 1,6
A2: 5,7
B2: 1,6
E2: 4,5
E1: 4,5,9                                # reduction candidate for 4,5
E1: 9 => CTR
* .2..9.43...9.4.26.4832765913958176241649..873872634159657489312948...7..23.7..98.
G1: 4,6
I1: 7,8
H2: 4,6
I2: 7,8
B5: 4,6
C5: 4,6
G4: 4,6
I4: 4,6
I8: 4,5,6                                # reduction candidate for 4,6
I8: 4,6 => SOLVED
* 521948637769153248483276591395817426146592873872634159657489312918325764234761985
* SOLVED!

--------------------------------------------------
* AUTO ..
C3 = 3                # set value
C6: 2                 # naked single
G3 = 5                # set value
G5 = 8                # set value
I6: 9                 # naked single
H5 = 7                # set value
A6 = 8                # set value
C6 = 2                # set value
I6 = 9                # set value
G6: 1                 # naked single
C7 = 7                # set value
G7 = 3                # set value
D9 = 7                # set value
A4: 3..               # hidden single
G9: 9..               # hidden single
E6: 3..               # hidden single
A8: 9..               # hidden single
A4 = 3                # set value
E6 = 3                # set value
G6 = 1                # set value
A8 = 9                # set value
A9: 2                 # naked single
A9 = 2                # set value
G9 = 9                # set value
E4: 1..               # hidden single
E4 = 1                # set value
C4: 5..               # hidden single
C4 = 5                # set value
I1,I2: 7,8.. => I1,I2 != 4,6 # hidden pair
* UNSOLVED!

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

highlight 6
C1: 1,6
H2: 4,6
G4: 4,6
B5: 4,6
I8: 4,5,6

G1: 4,6
B2: 1,6
I4: 4,6
C5: 4,6
H8: 4,6

C1,H2,G4,B5,I8 = 6 => G1,B2,I4,C5,H8 != 6

C1 = 6 => C5 = 4 => H8 = 4
C5 = 4 =>  C9 != 4 => I9 = 4
H8,I9: 4 => CTR
=> C1 != 6 # forcing chain

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

Solution

position: 521948637769153248483276591395817426146592873872634159657489312918325764234761985 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 # E1: 4,5 => UNS
* DIS # E1: 9 => CTR => E1: 4,5
* INC # E5: 5,9 => UNS
* DIS # E5: 2 => CTR => E5: 5,9
* INC # D1: 5,9 => UNS
* DIS # D1: 1 => CTR => D1: 5,9
* DIS # E5: 2,5 => CTR => E5: 9
* INC # E5: 9 => UNS
* PRF # F8: 2,5 => SOL
* INC # F8: 1,3 => UNS
* PRF # I8: 4,6 => SOL
* INC # I8: 5 => UNS
* INC # I9: 4,6 => UNS
* DIS # E8: 5,6 => CTR => E8: 2
* INC # E8: 2 => UNS
* PRF # I9: 5,6 => SOL
* DIS # I9: 4 => CTR => I9: 5,6
* INC # D8: 1,5 => UNS
* INC # F8: 1,5 => UNS
* DIS # F1: 1,5 => CTR => F1: 8
* INC # F1: 8 => UNS
* INC # F2: 1,5 => UNS
* PRF # I8: 4,6 => SOL
* INC # I8: 5 => UNS
* INC # I9: 4,6 => UNS
* CNT  25 HDP CHAINS /  25 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 4,5 => UNS
* DIS # E1: 9 => CTR => E1: 4,5
* PRF E1: 4,5 # I8: 4,6 => SOL
* STA E1: 4,5 + I8: 4,6
* CNT   3 HDP CHAINS /   3 HYP OPENED