Analysis of zz-sudoku-de-697744-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .6.2.4.7.3..9.7..8.4..1..5...5...8..63.....91..7...3...7..9..8.8..4.2..6.1.5.6.3. initial

Autosolve

position: .682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # G3: 2,9 => SOL
* DIS # G3: 6 => CTR => G3: 2,9
* DIS # I3: 2,9 => CTR => I3: 3
* PRF # I3: 3 => SOL
* DIS # C9: 4 => CTR => C9: 2,9
* DIS # D3: 3,8 => CTR => D3: 6
* PRF # D3: 6 => SOL
* DIS # I3: 2 => CTR => I3: 3,9
* DIS # G2: 2,4 => CTR => G2: 6
* PRF # G2: 6 => SOL
* DIS # A4: 2,9 => CTR => A4: 1,4
* DIS # A4: 2,4 => CTR => A4: 1,9
* PRF # A6: 2,4 => SOL
* PRF # C9: 2,4 => SOL
* DIS # C9: 9 => CTR => C9: 2,4
* DIS # E4: 2,4 => CTR => E4: 3,6
* DIS # D4: 1,6 => CTR => D4: 3,7
* DIS # D4: 1,3 => CTR => D4: 6,7
* DIS # F4: 9 => CTR => F4: 1,3
* CNT  19 HDP CHAINS /  32 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 # G3: 2,9 => SOL
* STA G3: 2,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.6.2.4.7.3..9.7..8.4..1..5...5...8..63.....91..7...3...7..9..8.8..4.2..6.1.5.6.3. initial
.682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3. autosolve
568234179321957648749618253195763824634825791287149365476391582853472916912586437 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
A1: 5,9
B2: 2,5
C3: 2,9
E1: 3,5
E2: 5,6
F3: 3,8
I1: 3,9
H2: 2,4
B4: 2,9
C5: 2,4
D5: 7,8
E5: 2,4
F5: 5,8
D6: 1,6
G5: 5,7
B8: 5,9
D7: 1,3
F7: 1,3
G8: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,A6: 1.. / A4 = 1  => 20 pairs (_) / A6 = 1  =>  0 pairs (X)
D7,F7: 1.. / D7 = 1  =>  0 pairs (X) / F7 = 1  => 20 pairs (_)
B2,C3: 2.. / B2 = 2  =>  0 pairs (*) / C3 = 2  =>  0 pairs (X)
C5,E5: 2.. / C5 = 2  =>  0 pairs (X) / E5 = 2  => 19 pairs (_)
B2,B4: 2.. / B2 = 2  =>  0 pairs (*) / B4 = 2  =>  0 pairs (X)
I1,I3: 3.. / I1 = 3  =>  0 pairs (X) / I3 = 3  =>  0 pairs (_)
D7,F7: 3.. / D7 = 3  => 20 pairs (_) / F7 = 3  =>  0 pairs (X)
E1,I1: 3.. / E1 = 3  =>  0 pairs (*) / I1 = 3  =>  0 pairs (X)
E1,E4: 3.. / E1 = 3  =>  0 pairs (*) / E4 = 3  =>  0 pairs (X)
G2,H2: 4.. / G2 = 4  =>  0 pairs (X) / H2 = 4  => 24 pairs (_)
C5,E5: 4.. / C5 = 4  => 19 pairs (_) / E5 = 4  =>  0 pairs (X)
C5,C9: 4.. / C5 = 4  => 19 pairs (_) / C9 = 4  =>  0 pairs (X)
A1,B2: 5.. / A1 = 5  =>  0 pairs (*) / B2 = 5  =>  0 pairs (X)
E1,E2: 5.. / E1 = 5  =>  0 pairs (X) / E2 = 5  =>  0 pairs (_)
F5,F6: 5.. / F5 = 5  => 21 pairs (_) / F6 = 5  =>  0 pairs (X)
G5,I6: 5.. / G5 = 5  =>  0 pairs (X) / I6 = 5  => 21 pairs (_)
A7,B8: 5.. / A7 = 5  =>  0 pairs (X) / B8 = 5  =>  0 pairs (_)
A1,E1: 5.. / A1 = 5  =>  0 pairs (*) / E1 = 5  =>  0 pairs (X)
B2,E2: 5.. / B2 = 5  =>  0 pairs (X) / E2 = 5  =>  0 pairs (_)
F5,G5: 5.. / F5 = 5  => 21 pairs (_) / G5 = 5  =>  0 pairs (X)
F6,I6: 5.. / F6 = 5  =>  0 pairs (X) / I6 = 5  => 21 pairs (_)
B8,G8: 5.. / B8 = 5  =>  0 pairs (*) / G8 = 5  =>  0 pairs (X)
A1,A7: 5.. / A1 = 5  =>  0 pairs (*) / A7 = 5  =>  0 pairs (X)
B2,B8: 5.. / B2 = 5  =>  0 pairs (X) / B8 = 5  =>  0 pairs (_)
I6,I7: 5.. / I6 = 5  => 21 pairs (_) / I7 = 5  =>  0 pairs (X)
E2,D3: 6.. / E2 = 6  =>  0 pairs (X) / D3 = 6  =>  0 pairs (_)
G2,G3: 6.. / G2 = 6  =>  0 pairs (*) / G3 = 6  =>  0 pairs (X)
H4,H6: 6.. / H4 = 6  => 20 pairs (_) / H6 = 6  => 24 pairs (_)
E2,G2: 6.. / E2 = 6  =>  0 pairs (X) / G2 = 6  =>  0 pairs (_)
D3,G3: 6.. / D3 = 6  =>  0 pairs (*) / G3 = 6  =>  0 pairs (X)
D4,D5: 7.. / D4 = 7  => 21 pairs (_) / D5 = 7  =>  0 pairs (X)
I4,G5: 7.. / I4 = 7  =>  0 pairs (X) / G5 = 7  => 21 pairs (_)
G9,I9: 7.. / G9 = 7  =>  0 pairs (X) / I9 = 7  => 21 pairs (_)
D4,I4: 7.. / D4 = 7  => 21 pairs (_) / I4 = 7  =>  0 pairs (X)
D5,G5: 7.. / D5 = 7  =>  0 pairs (X) / G5 = 7  => 21 pairs (_)
G5,G9: 7.. / G5 = 7  => 21 pairs (_) / G9 = 7  =>  0 pairs (X)
I4,I9: 7.. / I4 = 7  =>  0 pairs (X) / I9 = 7  => 21 pairs (_)
D3,F3: 8.. / D3 = 8  =>  0 pairs (X) / F3 = 8  => 21 pairs (_)
D5,F5: 8.. / D5 = 8  => 21 pairs (_) / F5 = 8  =>  0 pairs (X)
D3,D5: 8.. / D3 = 8  =>  0 pairs (X) / D5 = 8  => 21 pairs (_)
F3,F5: 8.. / F3 = 8  => 21 pairs (_) / F5 = 8  =>  0 pairs (X)
A1,C3: 9.. / A1 = 9  =>  0 pairs (X) / C3 = 9  =>  0 pairs (_)
F4,F6: 9.. / F4 = 9  =>  0 pairs (X) / F6 = 9  => 21 pairs (_)
A1,I1: 9.. / A1 = 9  =>  0 pairs (X) / I1 = 9  =>  0 pairs (_)
A6,F6: 9.. / A6 = 9  =>  0 pairs (X) / F6 = 9  => 21 pairs (_)
B8,G8: 9.. / B8 = 9  =>  0 pairs (X) / G8 = 9  =>  0 pairs (_)
B4,B8: 9.. / B4 = 9  =>  0 pairs (*) / B8 = 9  =>  0 pairs (X)
C3,C9: 9.. / C3 = 9  =>  0 pairs (*) / C9 = 9  =>  0 pairs (X)
* DURATION: 0:01:16.012117  START: 07:55:12.155782  END: 07:56:28.167899 2017-05-01
* CP COUNT: (48)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B4,B8,C3,C5,D5,D6,D7,E1,E2,E5,F3,F5,F7,G5,G8,H2,I1)
* .682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3.
* PAIR C3: 2,9 ROW 3
G3: 2,9,6                                # reduction candidate for 2,9
G3: 2,9 => SOLVED
* 568234179321957648749618253195763824634825791287149365476391582853472916912586437
G3: 6 => CTR
* .68254173351967..8742.1.659.25.3.8..634.2..91.87.4.3..576.9..8.893472.16.1.586.3.
I3: 2,9,3                                # reduction candidate for 2,9
I3: 2,9 => CTR
* 968254173351967..8742.1.659..5.3.8..63.....91.87...3...76.9..8.8.3472.16.1.586.3.
I3: 3 => SOLVED
* 568234179321957648749618253195763824634825791287149365476391582853472916912586437
* PAIR C3: 2,9 COL C
C9: 2,9,4                                # reduction candidate for 2,9
C9: 4 => CTR
* 568234179321957648749618253.95...8..632845791.871.93.5276.9..8.8.3472.16.14586.3.
C9: 2,9                                  # 19 pairs
* PAIR F3: 3,8 BLK 2
D3: 3,8,6                                # reduction candidate for 3,8
D3: 3,8 => CTR
* .68254173351967..8742.1.659.25.3.8..634.2..91.87.4.3..576.9..8.893472.16.1.586.3.
D3: 6 => SOLVED
* 568234179321957648749618253195763824634825791287149365476391582853472916912586437
* PAIR I1: 3,9 BLK 3
I3: 3,9,2                                # reduction candidate for 3,9
I3: 2 => CTR
* .682.41733.19.7..874..1.952..5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3.
I3: 3,9                                  # 21 pairs
* PAIR H2: 2,4 BLK 3
G2: 2,4,6                                # reduction candidate for 2,4
G2: 2,4 => CTR
* .68254173351967..8742.1.659.25.3.8..634.2..91.87.4.3..576.9..8.893472.16.1.586.3.
G2: 6 => SOLVED
* 568234179321957648749618253195763824634825791287149365476391582853472916912586437
* PAIR H2: 2,4 COL H
H4: 2,4,6                                # reduction candidate for 2,4
H4: 2,4                                  # 24 pairs
H6: 2,4,6                                # reduction candidate for 2,4
H6: 2,4                                  # 20 pairs
* PAIR B4: 2,9 BLK 4
A4: 2,9,1,4                              # reduction candidate for 2,9
A4: 2,9 => CTR
* .68254173351967248742.18659.25731864634825791187649325576193482893472.16.1.586.37
A4: 1,4                                  # 20 pairs
A6: 2,9,1,4                              # reduction candidate for 2,9
A6: 2,9                                  # 21 pairs
* PAIR C5: 2,4 BLK 4
A4: 2,4,1,9                              # reduction candidate for 2,4
A4: 2,4 => CTR
* .682.417.3.1967..874..1.65..95...86.63...57911876.93.5.76.9..8.853472.16.1.586.3.
A4: 1,9                                  # 20 pairs
A6: 2,4,1,9                              # reduction candidate for 2,4
A6: 2,4 => SOLVED
* 568234179321957648749618253195763824634825791287149365476391582853472916912586437
A6: 1,9                                  # 20 pairs
* PAIR C5: 2,4 COL C
C9: 2,4,9                                # reduction candidate for 2,4
C9: 2,4 => SOLVED
* 568234179321957648749618253195763824634825791287149365476391582853472916912586437
C9: 9 => CTR
* 9682541733519.7..874..1..5...5...8..634.2..91.87...3...76.9..8.8.3472.16.19586.3.
* PAIR E5: 2,4 BLK 5
E4: 2,4,3,6                              # reduction candidate for 2,4
E4: 2,4 => CTR
* 568234179321957648749618253195...86.63.8.5791.87169325.76391.8.85347291691.586437
E4: 3,6                                  # 21 pairs
E6: 2,4,6                                # reduction candidate for 2,4
E6: 2,4                                  # 21 pairs
* PAIR D6: 1,6 BLK 5
D4: 1,6,3,7                              # reduction candidate for 1,6
D4: 1,6 => CTR
* 56823417.3.19.7..874..1..5...5...8.763.7.8591.87..53...76.9..85853472916.1.58673.
D4: 3,7                                  # 20 pairs
* PAIR D7: 1,3 COL D
D4: 1,3,6,7                              # reduction candidate for 1,3
D4: 1,3 => CTR
* 56823417.3.19.7..874..1..5...5...8.763.7.8591.87..53...76.9..85853472916.1.58673.
D4: 6,7                                  # 20 pairs
* PAIR F7: 1,3 COL F
F4: 1,3,9                                # reduction candidate for 1,3
F4: 9 => CTR
* 5682341793219.7..874..1..5...5..98..63.....91987...3...76.9..8.893472516.1.586.3.
F4: 1,3                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-697744-base-pr-000.dot
* REASONING
* PRF # G3: 2,9 => SOL
* DIS # G3: 6 => CTR => G3: 2,9
* DIS # I3: 2,9 => CTR => I3: 3
* PRF # I3: 3 => SOL
* DIS # C9: 4 => CTR => C9: 2,9
* DIS # D3: 3,8 => CTR => D3: 6
* PRF # D3: 6 => SOL
* DIS # I3: 2 => CTR => I3: 3,9
* DIS # G2: 2,4 => CTR => G2: 6
* PRF # G2: 6 => SOL
* DIS # A4: 2,9 => CTR => A4: 1,4
* DIS # A4: 2,4 => CTR => A4: 1,9
* PRF # A6: 2,4 => SOL
* PRF # C9: 2,4 => SOL
* DIS # C9: 9 => CTR => C9: 2,4
* DIS # E4: 2,4 => CTR => E4: 3,6
* DIS # D4: 1,6 => CTR => D4: 3,7
* DIS # D4: 1,3 => CTR => D4: 6,7
* DIS # F4: 9 => CTR => F4: 1,3
* CNT  19 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B4,B8,C3,C5,D5,D6,D7,E1,E2,E5,F3,F5,F7,G5,G8,H2,I1)
* .682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3.
* PAIR C3: 2,9 ROW 3
G3: 2,9,6                                # reduction candidate for 2,9
G3: 2,9 => SOLVED
* 568234179321957648749618253195763824634825791287149365476391582853472916912586437
* DURATION: 0:00:02.307301  START: 07:56:59.589552  END: 07:57:01.896853 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-697744-base-pr-001.dot
* REASONING
* PRF # G3: 2,9 => SOL
* STA G3: 2,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokus.de/697744.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: .682.417.3.19.7..874..1..5...5...8..63.....91.87...3...76.9..8.8.3472.16.1.586.3.
A1: 5,9
B2: 2,5
C3: 2,9
G3: 2,6,9                                # reduction candidate for 2,9
G3: 2,9 => SOLVED
* 568234179321957648749618253195763824634825791287149365476391582853472916912586437
* SOLVED!
--------------------------------------------------

--------------------------------------------------
* AUTO ..
A3 = 7                # set value
B6 = 8                # set value
C7 = 6                # set value
H8 = 1                # set value
E9 = 8                # set value
C8: 3..               # hidden single
E8: 7..               # hidden single
C1: 8..               # hidden single
C1 = 8                # set value
C8 = 3                # set value
E8: 7                 # naked single
E8 = 7                # set value
C2: 1..               # hidden single
C2 = 1                # set value
G1: 1..               # hidden single
G1 = 1                # set value
Q2: 5.. = E1,E2: 5.. => E5,E6 != 5
Q6: 6.. = H4,H6: 6.. => H2 != 6
C5,E5: 2,4.. => G5 != 2,4 # naked pair
* UNSOLVED!

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

good |:guess:|
--------------------------------------------------

highlight 1,3
D7,F7,D4,F4: 1,3.. => D4 = 6,7 or F4 = 9 # pair quad

D4 != 6,7 => CTR => F4 != 9
* DISABLE VALUE:: F4 != 9

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

* AUTO ..
A3 = 7                # set value
B6 = 8                # set value
C7 = 6                # set value
H8 = 1                # set value
E9 = 8                # set value
F6: 9..               # hidden single
C8: 3..               # hidden single
E8: 7..               # hidden single
C1: 8..               # hidden single
C1 = 8                # set value
F6 = 9                # set value
C8 = 3                # set value
E8: 7                 # naked single
E8 = 7                # set value
F5: 5..               # hidden single
I6: 5..               # hidden single
C2: 1..               # hidden single
C2 = 1                # set value
F5 = 5                # set value
G5: 7                 # naked single
G5 = 7                # set value
D5: 8                 # naked single
I6 = 5                # set value
G1: 1..               # hidden single
D4: 7..               # hidden single
I9: 7..               # hidden single
F3: 8..               # hidden single
G1 = 1                # set value
F3 = 8                # set value
D4 = 7                # set value
D5 = 8                # set value
I9 = 7                # set value
Q9: 9.. = G8,G9: 9.. => G3 != 9
I1,I3: 3,9.. => I3 != 2 # hidden pair

|:step:| 02
--------------------------------------------------

Solution

position: 568234179321957648749618253195763824634825791287149365476391582853472916912586437 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 # G3: 2,9 => SOL
* DIS # G3: 6 => CTR => G3: 2,9
* DIS # I3: 2,9 => CTR => I3: 3
* PRF # I3: 3 => SOL
* INC # C9: 2,9 => UNS
* DIS # C9: 4 => CTR => C9: 2,9
* DIS # D3: 3,8 => CTR => D3: 6
* PRF # D3: 6 => SOL
* INC # I3: 3,9 => UNS
* DIS # I3: 2 => CTR => I3: 3,9
* DIS # G2: 2,4 => CTR => G2: 6
* PRF # G2: 6 => SOL
* INC # H4: 2,4 => UNS
* INC # H6: 2,4 => UNS
* DIS # A4: 2,9 => CTR => A4: 1,4
* INC # A4: 1,4 => UNS
* INC # A6: 2,9 => UNS
* DIS # A4: 2,4 => CTR => A4: 1,9
* INC # A4: 1,9 => UNS
* PRF # A6: 2,4 => SOL
* INC # A6: 1,9 => UNS
* PRF # C9: 2,4 => SOL
* DIS # C9: 9 => CTR => C9: 2,4
* DIS # E4: 2,4 => CTR => E4: 3,6
* INC # E4: 3,6 => UNS
* INC # E6: 2,4 => UNS
* DIS # D4: 1,6 => CTR => D4: 3,7
* INC # D4: 3,7 => UNS
* DIS # D4: 1,3 => CTR => D4: 6,7
* INC # D4: 6,7 => UNS
* INC # F4: 1,3 => UNS
* DIS # F4: 9 => CTR => F4: 1,3
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # G3: 2,9 => SOL
* STA G3: 2,9
* CNT   1 HDP CHAINS /   1 HYP OPENED