Analysis of zz-sudoku-de-710629-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .6..9.1.7...5.7.69..........36..9.7....8.5....8.1..42..........74.9.2...6.9.1..38 initial

Autosolve

position: 56..9.1.7...5.7369.97..15.2136..9875.7.8.591.98517.42.....5.79474.9.2651659714238 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E3: 3,8 => CTR => E3: 4,6
* PRF # F7: 3,8 => SOL
* DIS # F7: 6 => CTR => F7: 3,8
* DIS # C1: 4,8 => CTR => C1: 2,3
* DIS # A3: 4,8 => CTR => A3: 3
* DIS # E3: 4,8 => CTR => E3: 3,6
* PRF # E3: 3,6 => SOL
* PRF # D1: 3 => SOL
* DIS # E2: 8 => CTR => E2: 2,4
* PRF # E3: 3,6 => SOL
* DIS # E3: 4,8 => CTR => E3: 3,6
* PRF # F7: 3,6 => SOL
* DIS # F7: 8 => CTR => F7: 3,6
* DIS # C7: 3,8 => CTR => C7: 1,2
* DIS # C7: 3,8 => CTR => C7: 1,2
* PRF # F7: 3,6 => SOL
* DIS # F7: 8 => CTR => F7: 3,6
* PRF # D3: 4 => SOL
* PRF # F7: 3,8 => SOL
* DIS # F7: 6 => CTR => F7: 3,8
* DIS # E3: 3,8 => CTR => E3: 4,6
* CNT  21 HDP CHAINS /  41 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 # E3: 3,8 => CTR => E3: 4,6
* PRF E3: 4,6 # C1: 2,4 => SOL
* STA E3: 4,6 + C1: 2,4
* CNT   2 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.6..9.1.7...5.7.69..........36..9.7....8.5....8.1..42..........74.9.2...6.9.1..38 initial
56..9.1.7...5.7369.97..15.2136..9875.7.8.591.98517.42.....5.79474.9.2651659714238 autosolve
562398147418527369397461582136249875274835916985176423821653794743982651659714238 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
B2: 1,2
F1: 3,8
H1: 4,8
H3: 4,8
A5: 2,4
C5: 2,4
D4: 2,4
E4: 2,4
E5: 3,6
F6: 3,6
I5: 3,6
I6: 3,6
B7: 1,2
C8: 3,8
D7: 3,6
E8: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,C2: 1.. / B2 = 1  => 15 pairs (_) / C2 = 1  => 15 pairs (_)
B7,C7: 1.. / B7 = 1  => 15 pairs (_) / C7 = 1  => 15 pairs (_)
B2,B7: 1.. / B2 = 1  => 15 pairs (_) / B7 = 1  => 15 pairs (_)
C2,C7: 1.. / C2 = 1  => 15 pairs (_) / C7 = 1  => 15 pairs (_)
D1,E2: 2.. / D1 = 2  => 16 pairs (_) / E2 = 2  =>  0 pairs (*)
A5,C5: 2.. / A5 = 2  => 17 pairs (_) / C5 = 2  => 16 pairs (_)
D4,E4: 2.. / D4 = 2  =>  0 pairs (*) / E4 = 2  =>  0 pairs (X)
C1,D1: 2.. / C1 = 2  =>  0 pairs (*) / D1 = 2  =>  0 pairs (X)
B2,B7: 2.. / B2 = 2  => 15 pairs (_) / B7 = 2  => 15 pairs (_)
D1,D4: 2.. / D1 = 2  => 16 pairs (_) / D4 = 2  =>  0 pairs (*)
E2,E4: 2.. / E2 = 2  =>  0 pairs (*) / E4 = 2  =>  0 pairs (X)
C1,A3: 3.. / C1 = 3  =>  0 pairs (X) / A3 = 3  => 18 pairs (_)
E5,F6: 3.. / E5 = 3  =>  0 pairs (*) / F6 = 3  =>  0 pairs (X)
I5,I6: 3.. / I5 = 3  =>  0 pairs (X) / I6 = 3  =>  0 pairs (_)
E5,I5: 3.. / E5 = 3  =>  0 pairs (*) / I5 = 3  =>  0 pairs (X)
F6,I6: 3.. / F6 = 3  =>  0 pairs (X) / I6 = 3  =>  0 pairs (_)
C8,E8: 3.. / C8 = 3  =>  0 pairs (*) / E8 = 3  =>  0 pairs (X)
A3,A7: 3.. / A3 = 3  => 18 pairs (_) / A7 = 3  =>  0 pairs (X)
H1,H3: 4.. / H1 = 4  => 16 pairs (_) / H3 = 4  =>  0 pairs (X)
A5,C5: 4.. / A5 = 4  => 16 pairs (_) / C5 = 4  => 17 pairs (_)
D4,E4: 4.. / D4 = 4  => 16 pairs (_) / E4 = 4  =>  0 pairs (*)
D3,E3: 6.. / D3 = 6  =>  0 pairs (X) / E3 = 6  =>  0 pairs (_)
E5,F6: 6.. / E5 = 6  =>  0 pairs (X) / F6 = 6  =>  0 pairs (_)
I5,I6: 6.. / I5 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
D7,F7: 6.. / D7 = 6  =>  0 pairs (*) / F7 = 6  =>  0 pairs (X)
E5,I5: 6.. / E5 = 6  =>  0 pairs (X) / I5 = 6  =>  0 pairs (_)
F6,I6: 6.. / F6 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
D3,D7: 6.. / D3 = 6  =>  0 pairs (X) / D7 = 6  =>  0 pairs (_)
E3,E5: 6.. / E3 = 6  =>  0 pairs (*) / E5 = 6  =>  0 pairs (X)
F6,F7: 6.. / F6 = 6  =>  0 pairs (*) / F7 = 6  =>  0 pairs (X)
H1,H3: 8.. / H1 = 8  =>  0 pairs (X) / H3 = 8  => 16 pairs (_)
F7,E8: 8.. / F7 = 8  =>  0 pairs (X) / E8 = 8  =>  0 pairs (_)
C8,E8: 8.. / C8 = 8  =>  0 pairs (X) / E8 = 8  =>  0 pairs (_)
F1,F7: 8.. / F1 = 8  =>  0 pairs (*) / F7 = 8  =>  0 pairs (X)
* DURATION: 0:00:56.627163  START: 08:10:49.340219  END: 08:11:45.967382 2017-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B2,B7,C5,C8,D4,D7,E4,E5,E8,F1,F6,H1,H3,I5,I6)
* 56..9.1.7...5.7369.97..15.2136..9875.7.8.591.98517.42.....5.79474.9.2651659714238
* PAIR B2: 1,2 BLK 1
C2: 1,2,4,8                              # reduction candidate for 1,2
C2: 1,2                                  # 18 pairs
C2: 4,8                                  # 16 pairs
* PAIR F1: 3,8 BLK 2
E3: 3,8,4,6                              # reduction candidate for 3,8
E3: 3,8 => CTR
* 56..9.1.7...5.7369.976.15.2136..9875.7.865913985173426...356794743982651659714238
E3: 4,6                                  # 17 pairs
* PAIR F1: 3,8 ROW 1
C1: 3,8,2,4                              # reduction candidate for 3,8
C1: 2,4                                  # 22 pairs
C1: 3,8                                  # 18 pairs
* PAIR F1: 3,8 COL F
F7: 3,8,6                                # reduction candidate for 3,8
F7: 3,8 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
F7: 6 => CTR
* 56..98147...5.7369.97631582136429875.7.8659139851734263...5679474.982651659714238
* PAIR H1: 4,8 ROW 1
C1: 4,8,2,3                              # reduction candidate for 4,8
C1: 4,8 => CTR
* 56.2931.7...5.7369397..15.2136429875.7.835916985176423....5.79474.9.2651659714238
C1: 2,3                                  # 17 pairs
* PAIR H3: 4,8 ROW 3
A3: 4,8,3                                # reduction candidate for 4,8
A3: 4,8 => CTR
* 563298147...547369.97..15.2136..9875.7.8.591.98517.42.....5.79474.9.2651659714238
A3: 3                                    # 18 pairs
E3: 4,8,3,6                              # reduction candidate for 4,8
E3: 4,8 => CTR
* 56..9.1.7...5.7369.976.15.2136..9875.7.865913985173426...356794743982651659714238
E3: 3,6 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
* PAIR A5: 2,4 COL A
A2: 2,4,8                                # reduction candidate for 2,4
A2: 2,4                                  # 20 pairs
A2: 8                                    # 19 pairs
* PAIR C5: 2,4 COL C
C1: 2,4,3,8                              # reduction candidate for 2,4
C1: 2,4                                  # 22 pairs
C2: 2,4,1,8                              # reduction candidate for 2,4
C2: 2,4                                  # 16 pairs
* PAIR D4: 2,4 COL D
D1: 2,4,3                                # reduction candidate for 2,4
D1: 3 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
D1: 2,4                                  # 18 pairs
* PAIR E4: 2,4 COL E
E2: 2,4,8                                # reduction candidate for 2,4
E2: 8 => CTR
* 56.29.1.7...587369.97..15.2136429875.7.8.591.98517.42.....58794748932651659714238
E2: 2,4                                  # 18 pairs
* PAIR E5: 3,6 COL E
E3: 3,6,4,8                              # reduction candidate for 3,6
E3: 3,6 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
E3: 4,8 => CTR
* 56..9.1.7...5.7369.976.15.2136..9875.7.865913985173426...356794743982651659714238
* PAIR F6: 3,6 COL F
F7: 3,6,8                                # reduction candidate for 3,6
F7: 3,6 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
F7: 8 => CTR
* 56..9.1.7...5.7369.97..15.2136..9875.7.8.591.985176423...658794748932651659714238
* PAIR B7: 1,2 BLK 7
C7: 1,2,3,8                              # reduction candidate for 1,2
C7: 3,8 => CTR
* 5642931878215473693976815.2136.29875.728.591.98517.42.21..5.79474.9.2651659714238
C7: 1,2                                  # 18 pairs
* PAIR C8: 3,8 BLK 7
A7: 3,8,2                                # reduction candidate for 3,8
A7: 3,8                                  # 18 pairs
C7: 3,8,1,2                              # reduction candidate for 3,8
C7: 3,8 => CTR
* 5642931878215473693976815.2136.29875.728.591.98517.42.21..5.79474.9.2651659714238
C7: 1,2                                  # 18 pairs
* PAIR C8: 3,8 COL C
C1: 3,8,2,4                              # reduction candidate for 3,8
C1: 2,4                                  # 22 pairs
C1: 3,8                                  # 18 pairs
* PAIR D7: 3,6 BLK 8
F7: 3,6,8                                # reduction candidate for 3,6
F7: 3,6 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
F7: 8 => CTR
* 56..9.1.7...5.7369.97..15.2136..9875.7.8.591.985176423...658794748932651659714238
* PAIR D7: 3,6 COL D
D3: 3,6,4                                # reduction candidate for 3,6
D3: 4 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
D3: 3,6                                  # 18 pairs
* PAIR E8: 3,8 BLK 8
F7: 3,8,6                                # reduction candidate for 3,8
F7: 3,8 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
F7: 6 => CTR
* 56..98147...5.7369.97631582136429875.7.8659139851734263...5679474.982651659714238
* PAIR E8: 3,8 COL E
E3: 3,8,4,6                              # reduction candidate for 3,8
E3: 3,8 => CTR
* 56..9.1.7...5.7369.976.15.2136..9875.7.865913985173426...356794743982651659714238
E3: 4,6                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-710629-base-pr-000.dot
* REASONING
* DIS # E3: 3,8 => CTR => E3: 4,6
* PRF # F7: 3,8 => SOL
* DIS # F7: 6 => CTR => F7: 3,8
* DIS # C1: 4,8 => CTR => C1: 2,3
* DIS # A3: 4,8 => CTR => A3: 3
* DIS # E3: 4,8 => CTR => E3: 3,6
* PRF # E3: 3,6 => SOL
* PRF # D1: 3 => SOL
* DIS # E2: 8 => CTR => E2: 2,4
* PRF # E3: 3,6 => SOL
* DIS # E3: 4,8 => CTR => E3: 3,6
* PRF # F7: 3,6 => SOL
* DIS # F7: 8 => CTR => F7: 3,6
* DIS # C7: 3,8 => CTR => C7: 1,2
* DIS # C7: 3,8 => CTR => C7: 1,2
* PRF # F7: 3,6 => SOL
* DIS # F7: 8 => CTR => F7: 3,6
* PRF # D3: 4 => SOL
* PRF # F7: 3,8 => SOL
* DIS # F7: 6 => CTR => F7: 3,8
* DIS # E3: 3,8 => CTR => E3: 4,6
* CNT  21 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B2,B7,C5,C8,D4,D7,E4,E5,E8,F1,F6,H1,H3,I5,I6)
* 56..9.1.7...5.7369.97..15.2136..9875.7.8.591.98517.42.....5.79474.9.2651659714238
* PAIR B2: 1,2 BLK 1
C2: 1,2,4,8                              # reduction candidate for 1,2
C2: 1,2                                  # 18 pairs
C2: 4,8                                  # 16 pairs
* PAIR F1: 3,8 BLK 2
E3: 3,8,4,6                              # reduction candidate for 3,8
E3: 3,8 => CTR
* 56..9.1.7...5.7369.976.15.2136..9875.7.865913985173426...356794743982651659714238
* PAIR F1: 3,8 ROW 1
C1: 3,8,2,4                              # reduction candidate for 3,8
C1: 2,4 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
* DURATION: 0:00:07.398758  START: 08:12:27.663720  END: 08:12:35.062478 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-710629-base-pr-001.dot
* REASONING
* DIS # E3: 3,8 => CTR => E3: 4,6
* PRF E3: 4,6 # C1: 2,4 => SOL
* STA E3: 4,6 + C1: 2,4
* CNT   2 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokus.de/710629.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: 56..9.1.7...5.7369.97..15.2136..9875.7.8.591.98517.42.....5.79474.9.2651659714238
B2: 1,2
C2: 1,2,4,8                              # reduction candidate for 1,2
F1: 3,8
E3: 3,4,6,8                              # reduction candidate for 3,8
E3: 3,8 => CTR
* 56..9.1.7...5.7369.976.15.2136..9875.7.865913985173426...356794743982651659714238
C1: 2,3,4,8                              # reduction candidate for 3,8
C1: 2,4 => SOLVED
* 562398147418527369397461582136249875274835916985176423821653794743982651659714238
* SOLVED!
--------------------------------------------------

* AUTO ..
Q4: 2.. = A5,C5: 2.. => E5 != 2
Q4: 4.. = A5,C5: 4.. => E5 != 4
* UNSOLVED!

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

pair quad |:guess:| highlight 2,4

A5,C5,C2,A2: 2,4.. => A2 = 8 or C2 = 1,8 # pair quad

C2 != 1,8 & A2 = 8 => CTR
=> A2 != 8 & C2 = 1,8 &

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

pair |:guess:|

* DISABLE VALUE:: E2 != 8
* AUTO ..
Q2,Q3: 8.. => C1,A3 != 8
* SOLVED!

Solution

position: 562398147418527369397461582136249875274835916985176423821653794743982651659714238 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 # C2: 1,2 => UNS
* INC # C2: 4,8 => UNS
* DIS # E3: 3,8 => CTR => E3: 4,6
* INC # E3: 4,6 => UNS
* INC # C1: 3,8 => UNS
* INC # C1: 2,4 => UNS
* PRF # F7: 3,8 => SOL
* DIS # F7: 6 => CTR => F7: 3,8
* DIS # C1: 4,8 => CTR => C1: 2,3
* INC # C1: 2,3 => UNS
* DIS # A3: 4,8 => CTR => A3: 3
* INC # A3: 3 => UNS
* DIS # E3: 4,8 => CTR => E3: 3,6
* PRF # E3: 3,6 => SOL
* INC # A2: 2,4 => UNS
* INC # A2: 8 => UNS
* INC # C1: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # D1: 2,4 => UNS
* PRF # D1: 3 => SOL
* INC # E2: 2,4 => UNS
* DIS # E2: 8 => CTR => E2: 2,4
* PRF # E3: 3,6 => SOL
* DIS # E3: 4,8 => CTR => E3: 3,6
* PRF # F7: 3,6 => SOL
* DIS # F7: 8 => CTR => F7: 3,6
* INC # C7: 1,2 => UNS
* DIS # C7: 3,8 => CTR => C7: 1,2
* INC # A7: 3,8 => UNS
* DIS # C7: 3,8 => CTR => C7: 1,2
* INC # C7: 1,2 => UNS
* INC # C1: 3,8 => UNS
* INC # C1: 2,4 => UNS
* PRF # F7: 3,6 => SOL
* DIS # F7: 8 => CTR => F7: 3,6
* INC # D3: 3,6 => UNS
* PRF # D3: 4 => SOL
* PRF # F7: 3,8 => SOL
* DIS # F7: 6 => CTR => F7: 3,8
* DIS # E3: 3,8 => CTR => E3: 4,6
* INC # E3: 4,6 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 1,2 => UNS
* INC # C2: 4,8 => UNS
* DIS # E3: 3,8 => CTR => E3: 4,6
* INC E3: 4,6 # C1: 3,8 => UNS
* PRF E3: 4,6 # C1: 2,4 => SOL
* STA E3: 4,6 + C1: 2,4
* CNT   5 HDP CHAINS /   5 HYP OPENED