Analysis of zz-knacker-132282-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1.........5....89..36..4...6..7.3..87.......92.561.37..4..7..1..682....73.......5 initial

Autosolve

position: 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D5: 5,8 => CTR => D5: 4
* PRF # D5: 4 => SOL
* PRF # D7: 5,8 => SOL
* DIS # D7: 3 => CTR => D7: 5,8
* DIS # E5: 5,8 => CTR => E5: 2,4
* PRF # E2: 2,6 => SOL
* DIS # E2: 3 => CTR => E2: 2,6
* PRF # D7: 5,8 => SOL
* DIS # D7: 3 => CTR => D7: 5,8
* PRF # F5: 5,8 => SOL
* DIS # F5: 2 => CTR => F5: 5,8
* DIS # D7: 3,5 => CTR => D7: 8
* PRF # D7: 8 => SOL
* PRF # E9: 4,9 => SOL
* DIS # E9: 6 => CTR => E9: 4,9
* DIS # E9: 6,9 => CTR => E9: 4
* PRF # E9: 4 => SOL
* CNT  17 HDP CHAINS /  18 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 # D5: 5,8 => CTR => D5: 4
* PRF D5: 4 => SOL
* STA D5: 4
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

1.........5....89..36..4...6..7.3..87.......92.561.37..4..7..1..682....73.......5 initial
129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285 autosolve
129587436457362891836194752694753128713428569285619374942875613568231947371946285 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (28)
D1: 5,8
E1: 5,8
D2: 1,3
F2: 2,6
D3: 1,9
E3: 2,9
G1: 4,6
H1: 3,4
I1: 3,6
I2: 1,2
I3: 1,2
B4: 1,9
B5: 1,8
B6: 8,9
E4: 5,9
F6: 8,9
G4: 1,5
G5: 1,5
A7: 5,9
A8: 5,9
F7: 5,8
E8: 3,5
D9: 4,9
F9: 6,9
G7: 6,9
I7: 3,6
G8: 4,9
H8: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  =>  0 pairs (X) / D3 = 1  =>  0 pairs (_)
I2,I3: 1.. / I2 = 1  =>  0 pairs (*) / I3 = 1  =>  0 pairs (X)
B4,B5: 1.. / B4 = 1  =>  0 pairs (X) / B5 = 1  =>  0 pairs (_)
G4,G5: 1.. / G4 = 1  =>  0 pairs (*) / G5 = 1  =>  0 pairs (X)
D2,I2: 1.. / D2 = 1  =>  0 pairs (X) / I2 = 1  =>  0 pairs (_)
D3,I3: 1.. / D3 = 1  =>  0 pairs (*) / I3 = 1  =>  0 pairs (X)
B4,G4: 1.. / B4 = 1  =>  0 pairs (X) / G4 = 1  =>  0 pairs (_)
B5,G5: 1.. / B5 = 1  =>  0 pairs (*) / G5 = 1  =>  0 pairs (X)
I2,I3: 2.. / I2 = 2  =>  0 pairs (X) / I3 = 2  =>  0 pairs (_)
E5,F5: 2.. / E5 = 2  =>  0 pairs (*) / F5 = 2  =>  0 pairs (X)
E3,I3: 2.. / E3 = 2  =>  0 pairs (X) / I3 = 2  =>  0 pairs (_)
F2,F5: 2.. / F2 = 2  =>  0 pairs (*) / F5 = 2  =>  0 pairs (X)
D2,E2: 3.. / D2 = 3  =>  0 pairs (*) / E2 = 3  =>  0 pairs (X)
H1,I1: 3.. / H1 = 3  =>  0 pairs (*) / I1 = 3  =>  0 pairs (X)
D7,E8: 3.. / D7 = 3  =>  0 pairs (X) / E8 = 3  =>  0 pairs (_)
I7,H8: 3.. / I7 = 3  =>  0 pairs (*) / H8 = 3  =>  0 pairs (X)
D7,I7: 3.. / D7 = 3  =>  0 pairs (X) / I7 = 3  =>  0 pairs (_)
E8,H8: 3.. / E8 = 3  =>  0 pairs (*) / H8 = 3  =>  0 pairs (X)
D2,D7: 3.. / D2 = 3  =>  0 pairs (*) / D7 = 3  =>  0 pairs (X)
E2,E8: 3.. / E2 = 3  =>  0 pairs (X) / E8 = 3  =>  0 pairs (_)
H1,H8: 3.. / H1 = 3  =>  0 pairs (*) / H8 = 3  =>  0 pairs (X)
I1,I7: 3.. / I1 = 3  =>  0 pairs (X) / I7 = 3  =>  0 pairs (_)
G1,H1: 4.. / G1 = 4  =>  0 pairs (*) / H1 = 4  =>  0 pairs (X)
D5,E5: 4.. / D5 = 4  =>  0 pairs (*) / E5 = 4  =>  0 pairs (X)
D9,E9: 4.. / D9 = 4  =>  0 pairs (X) / E9 = 4  =>  0 pairs (_)
G8,H8: 4.. / G8 = 4  =>  0 pairs (X) / H8 = 4  =>  0 pairs (_)
D5,D9: 4.. / D5 = 4  =>  0 pairs (*) / D9 = 4  =>  0 pairs (X)
E5,E9: 4.. / E5 = 4  =>  0 pairs (X) / E9 = 4  =>  0 pairs (_)
G1,G8: 4.. / G1 = 4  =>  0 pairs (*) / G8 = 4  =>  0 pairs (X)
H1,H8: 4.. / H1 = 4  =>  0 pairs (X) / H8 = 4  =>  0 pairs (_)
D1,E1: 5.. / D1 = 5  => 28 pairs (_) / E1 = 5  =>  0 pairs (X)
G4,G5: 5.. / G4 = 5  =>  0 pairs (X) / G5 = 5  =>  0 pairs (_)
A7,A8: 5.. / A7 = 5  =>  0 pairs (X) / A8 = 5  =>  0 pairs (_)
E4,G4: 5.. / E4 = 5  =>  0 pairs (*) / G4 = 5  =>  0 pairs (X)
A8,E8: 5.. / A8 = 5  =>  0 pairs (*) / E8 = 5  =>  0 pairs (X)
F5,F7: 5.. / F5 = 5  =>  0 pairs (X) / F7 = 5  =>  0 pairs (_)
E2,F2: 6.. / E2 = 6  =>  0 pairs (*) / F2 = 6  =>  0 pairs (X)
G1,I1: 6.. / G1 = 6  =>  0 pairs (X) / I1 = 6  =>  0 pairs (_)
E9,F9: 6.. / E9 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
G7,I7: 6.. / G7 = 6  =>  0 pairs (*) / I7 = 6  =>  0 pairs (X)
E2,E9: 6.. / E2 = 6  =>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
F2,F9: 6.. / F2 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
G1,G7: 6.. / G1 = 6  =>  0 pairs (X) / G7 = 6  =>  0 pairs (_)
I1,I7: 6.. / I1 = 6  =>  0 pairs (*) / I7 = 6  =>  0 pairs (X)
D1,E1: 8.. / D1 = 8  =>  0 pairs (X) / E1 = 8  => 28 pairs (_)
B5,B6: 8.. / B5 = 8  =>  0 pairs (X) / B6 = 8  =>  0 pairs (_)
D7,F7: 8.. / D7 = 8  =>  0 pairs (*) / F7 = 8  =>  0 pairs (X)
B6,F6: 8.. / B6 = 8  =>  0 pairs (*) / F6 = 8  =>  0 pairs (X)
E1,E5: 8.. / E1 = 8  => 28 pairs (_) / E5 = 8  =>  0 pairs (X)
D3,E3: 9.. / D3 = 9  =>  0 pairs (X) / E3 = 9  =>  0 pairs (_)
B4,B6: 9.. / B4 = 9  =>  0 pairs (*) / B6 = 9  =>  0 pairs (X)
E4,F6: 9.. / E4 = 9  =>  0 pairs (X) / F6 = 9  =>  0 pairs (_)
A7,A8: 9.. / A7 = 9  =>  0 pairs (*) / A8 = 9  =>  0 pairs (X)
G7,G8: 9.. / G7 = 9  =>  0 pairs (X) / G8 = 9  =>  0 pairs (_)
B4,E4: 9.. / B4 = 9  =>  0 pairs (*) / E4 = 9  =>  0 pairs (X)
B6,F6: 9.. / B6 = 9  =>  0 pairs (X) / F6 = 9  =>  0 pairs (_)
A7,G7: 9.. / A7 = 9  =>  0 pairs (*) / G7 = 9  =>  0 pairs (X)
A8,G8: 9.. / A8 = 9  =>  0 pairs (X) / G8 = 9  =>  0 pairs (_)
D3,D9: 9.. / D3 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
F6,F9: 9.. / F6 = 9  =>  0 pairs (*) / F9 = 9  =>  0 pairs (X)
* DURATION: 0:01:45.416986  START: 06:26:38.050651  END: 06:28:23.467637 2017-05-01
* CP COUNT: (60)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B4,B5,B6,D1,D2,D3,D9,E1,E3,E4,E8,F2,F6,F7,F9,G1,G4,G5,G7,G8,H1,H8,I1,I2,I3,I7)
* 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285
* PAIR D1: 5,8 COL D
D5: 5,8,4                                # reduction candidate for 5,8
D5: 5,8 => CTR
* 129.874364573.689.836..475.6.47.3.287.3.42.692.561.374.42.75.1.5682319473714..285
D5: 4 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
D7: 5,8,3                                # reduction candidate for 5,8
D7: 5,8 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
D7: 3 => CTR
* 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42378.16.68251.37371...285
* PAIR E1: 5,8 COL E
E5: 5,8,2,4                              # reduction candidate for 5,8
E5: 5,8 => CTR
* 129..7...457...89.836..475.6.47.3.287.34.2.692.561.374.42.75.1.568231947371946285
E5: 2,4                                  # 29 pairs
* PAIR F2: 2,6 BLK 2
E2: 2,6,3                                # reduction candidate for 2,6
E2: 2,6 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
E2: 3 => CTR
* 129..7...457.36892836.247516.47.3.287.3..2.692.561.374.4237..1..682.1..7371...285
* PAIR F7: 5,8 BLK 8
D7: 5,8,3                                # reduction candidate for 5,8
D7: 5,8 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
D7: 3 => CTR
* 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42378.16.68251.37371...285
* PAIR F7: 5,8 COL F
F5: 5,8,2                                # reduction candidate for 5,8
F5: 5,8 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
F5: 2 => CTR
* 129..74364573.6891836194752694753.287.3..2.692.561.374.42.75.1.568231947371...285
* PAIR E8: 3,5 BLK 8
D7: 3,5,8                                # reduction candidate for 3,5
D7: 3,5 => CTR
* 129..7...457...89.836..475.6.47.3.287.3..516928561.374.42.78.1..682.1..7371...285
D7: 8 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
* PAIR D9: 4,9 BLK 8
E9: 4,9,6                                # reduction candidate for 4,9
E9: 4,9 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
E9: 6 => CTR
* 129.8743645732.89.836..475.6.47.3.287.3.42.692.561.374.42.75.1.568231947371469285
* PAIR F9: 6,9 BLK 8
E9: 6,9,4                                # reduction candidate for 6,9
E9: 6,9 => CTR
* 129.874364573.689.836..475.6.47.3.287.3.42.692.561.374.42.75.1.5682319473714..285
E9: 4 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
* INCONCLUSIVE
* SAVE PR GRAPH zz-knacker-132282-base-pr-000.dot
* REASONING
* DIS # D5: 5,8 => CTR => D5: 4
* PRF # D5: 4 => SOL
* PRF # D7: 5,8 => SOL
* DIS # D7: 3 => CTR => D7: 5,8
* DIS # E5: 5,8 => CTR => E5: 2,4
* PRF # E2: 2,6 => SOL
* DIS # E2: 3 => CTR => E2: 2,6
* PRF # D7: 5,8 => SOL
* DIS # D7: 3 => CTR => D7: 5,8
* PRF # F5: 5,8 => SOL
* DIS # F5: 2 => CTR => F5: 5,8
* DIS # D7: 3,5 => CTR => D7: 8
* PRF # D7: 8 => SOL
* PRF # E9: 4,9 => SOL
* DIS # E9: 6 => CTR => E9: 4,9
* DIS # E9: 6,9 => CTR => E9: 4
* PRF # E9: 4 => SOL
* CNT  17 HDP CHAINS /  18 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,B4,B5,B6,D1,D2,D3,D9,E1,E3,E4,E8,F2,F6,F7,F9,G1,G4,G5,G7,G8,H1,H8,I1,I2,I3,I7)
* 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285
* PAIR D1: 5,8 COL D
D5: 5,8,4                                # reduction candidate for 5,8
D5: 5,8 => CTR
* 129.874364573.689.836..475.6.47.3.287.3.42.692.561.374.42.75.1.5682319473714..285
D5: 4 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
* DURATION: 0:00:01.801013  START: 06:28:45.403803  END: 06:28:47.204816 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-knacker-132282-base-pr-001.dot
* REASONING
* DIS # D5: 5,8 => CTR => D5: 4
* PRF D5: 4 => SOL
* STA D5: 4
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudoku-knacker.de/132282.htm
sehr schwierig

level: medium

* PAIR REDUCTION ..
* ROUND 1: 129..7...457...89.836..475.6.47.3.287.3....692.561.374.42.7..1..682.1..7371...285
D1: 5,8
D5: 4,5,8                                # reduction candidate for 5,8
D5: 5,8 => CTR
* 129.874364573.689.836..475.6.47.3.287.3.42.692.561.374.42.75.1.5682319473714..285
D5: 4 => SOLVED
* 129587436457362891836194752694753128713428569285619374942875613568231947371946285
* SOLVED!

--------------------------------------------------
* AUTO ..
Q9: 4.. = G8,H8: 4.. => E8 != 4
Q9: 6.. = G7,I7: 6.. => F7 != 6
Q7,Q9: 9.. => D7,F7,E8 != 9
Q6: 2.. = H4,H5: 2.. => H3 != 2
D1,E1: 5,8.. => D1,E1 != 3,6 # hidden pair
I2,I3: 1,2.. => I2 != 3,6 # hidden pair
* UNSOLVED!

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

E1,E4,F6: 5,8,9 => E5 != 8 # xy-wing
D5,F6,D9: 4,8,9 => F9 != 9 # xy-wing

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

guess by pair quad 5,8:
D1,E1,D5,E5: 5,8..
D5 != 4 => CTR => D5 = 4
* SOLVED!

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

guess via swordfish -> forced chain
highlight 5
* DISABLE VALUE:: F7 != 5
F7: 8                 # naked single

=> D7,A7,A8,E8,E1: 5.. => E4,D5,E5 != 5 # swordfish
=> F5 = 5
=> G5 != 5 => G5 = 1
=> G4 = 5

G5 = 1 => B5 = 8 => B6 = 9
F7 = 8 => F6 = 9
=> B6,F6 = 9 => CTR
=> F7 = 5

* FORCE VALUE:: F7 = 5
F7 = 5                # set value
E8: 3                 # naked single
A7: 9                 # naked single
A8: 5..               # hidden single
D7: 8..               # hidden single

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

* AUTO ..
A7 = 9                # set value
A8: 5                 # naked single
G7: 6                 # naked single
D7 = 8                # set value
D1: 5                 # naked single
G7 = 6                # set value
I7: 3                 # naked single
G1: 4                 # naked single
I7 = 3                # set value
H8: 4                 # naked single
I1: 6                 # naked single
A8 = 5                # set value
E8 = 3                # set value
H8 = 4                # set value
G8: 9                 # naked single
H1: 3                 # naked single
D2: 3..               # hidden single
E1: 8..               # hidden single
D1 = 5                # set value
E1: 8                 # naked single
D5: 4                 # naked single
E1 = 8                # set value
G1 = 4                # set value
H1 = 3                # set value
I1 = 6                # set value
D2 = 3                # set value
D5 = 4                # set value
D9: 9                 # naked single
G8 = 9                # set value
D9 = 9                # set value
F9: 6                 # naked single
D3: 1                 # naked single
F9 = 6                # set value
E9: 4                 # naked single
F2: 2                 # naked single
E2: 6..               # hidden single
E3: 9..               # hidden single
I2: 1..               # hidden single
F6: 9..               # hidden single
E2 = 6                # set value
F2 = 2                # set value
E3: 9                 # naked single
F5: 8                 # naked single
I2: 1                 # naked single
I2 = 1                # set value
I3: 2                 # naked single
D3 = 1                # set value
E3 = 9                # set value
E4: 5                 # naked single
I3 = 2                # set value
E4 = 5                # set value
E5: 2                 # naked single
G4: 1                 # naked single
G4 = 1                # set value
G5: 5                 # naked single
B4: 9                 # naked single
E5 = 2                # set value
F5 = 8                # set value
F6: 9                 # naked single
B5: 1                 # naked single
G5 = 5                # set value
F6 = 9                # set value
B6: 8                 # naked single
E9 = 4                # set value
B4 = 9                # set value
B5 = 1                # set value
B6 = 8                # set value
* SOLVED!

--------------------------------------------------
wild |:guess:|
--------------------------------------------------
D7 = 3 => CTR => D7 != 3 => A7..C7,D8..F9,G7..I7 != 5,8

Solution

position: 129587436457362891836194752694753128713428569285619374942875613568231947371946285 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:

* DIS # D5: 5,8 => CTR => D5: 4
* PRF # D5: 4 => SOL
* PRF # D7: 5,8 => SOL
* DIS # D7: 3 => CTR => D7: 5,8
* DIS # E5: 5,8 => CTR => E5: 2,4
* INC # E5: 2,4 => UNS
* PRF # E2: 2,6 => SOL
* DIS # E2: 3 => CTR => E2: 2,6
* PRF # D7: 5,8 => SOL
* DIS # D7: 3 => CTR => D7: 5,8
* PRF # F5: 5,8 => SOL
* DIS # F5: 2 => CTR => F5: 5,8
* DIS # D7: 3,5 => CTR => D7: 8
* PRF # D7: 8 => SOL
* PRF # E9: 4,9 => SOL
* DIS # E9: 6 => CTR => E9: 4,9
* DIS # E9: 6,9 => CTR => E9: 4
* PRF # E9: 4 => SOL
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D5: 5,8 => CTR => D5: 4
* PRF D5: 4 => SOL
* STA D5: 4
* CNT   2 HDP CHAINS /   1 HYP OPENED