Analysis of zz-www.sudokuwiki.org-0042-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=42

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=42

position: ...7..3...4.....9...3..9..1.9.1.7.82..8.6.4..35.8.2.6.1..5..9...6.....7...5..8... initial

Autosolve

position: ...7..3...4.....9...3..9..1.9.137582..89654..35.842.691..5..9...6.....75..5..8... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B5: 2,7 => CTR => B5: 1
* DIS # B5: 2 => CTR => B5: 1,7
* DIS # H9: 2,4 => CTR => H9: 1,3
* DIS # B7: 2,7 => CTR => B7: 3,8
* DIS # I7: 4,6 => CTR => I7: 3,8
* PRF # F1: 1 => SOL
* CNT   6 HDP CHAINS /  22 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 # B5: 2,7 => CTR => B5: 1
* DIS B5: 1 # B3: 2,8 => CTR => B3: 7
* DIS B5: 1 + B3: 7 # F8: 3 => CTR => F8: 1,4
* PRF B5: 1 + B3: 7 + F8: 1,4 # I1: 6,8 => SOL
* STA B5: 1 + B3: 7 + F8: 1,4 + I1: 6,8
* CNT   4 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

...7..3...4.....9...3..9..1.9.1.7.82..8.6.4..35.8.2.6.1..5..9...6.....7...5..8... initial
...7..3...4.....9...3..9..1.9.137582..89654..35.842.691..5..9...6.....75..5..8... autosolve
829751346541623798673489251496137582218965437357842169184576923962314875735298614 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A4: 4,6
C4: 4,6
A5: 2,7
C6: 1,7
H5: 1,3
I5: 3,7
G6: 1,7
E7: 2,7
F7: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,C6: 1.. / B5 = 1  => 14 pairs (_) / C6 = 1  =>  0 pairs (X)
H5,G6: 1.. / H5 = 1  =>  0 pairs (X) / G6 = 1  => 14 pairs (_)
B5,H5: 1.. / B5 = 1  => 14 pairs (_) / H5 = 1  =>  0 pairs (X)
C6,G6: 1.. / C6 = 1  =>  0 pairs (X) / G6 = 1  => 14 pairs (_)
B1,B5: 1.. / B1 = 1  =>  0 pairs (X) / B5 = 1  => 14 pairs (_)
H5,H9: 1.. / H5 = 1  =>  0 pairs (X) / H9 = 1  => 14 pairs (_)
A5,B5: 2.. / A5 = 2  =>  9 pairs (_) / B5 = 2  =>  0 pairs (X)
D2,F2: 3.. / D2 = 3  => 14 pairs (_) / F2 = 3  => 11 pairs (_)
H5,I5: 3.. / H5 = 3  => 14 pairs (_) / I5 = 3  =>  0 pairs (X)
B7,B9: 3.. / B7 = 3  => 17 pairs (_) / B9 = 3  => 13 pairs (_)
D8,F8: 3.. / D8 = 3  => 11 pairs (_) / F8 = 3  => 14 pairs (_)
D2,D8: 3.. / D2 = 3  => 14 pairs (_) / D8 = 3  => 11 pairs (_)
F2,F8: 3.. / F2 = 3  => 11 pairs (_) / F8 = 3  => 14 pairs (_)
F1,D3: 4.. / F1 = 4  => 16 pairs (_) / D3 = 4  => 13 pairs (_)
A4,C4: 4.. / A4 = 4  =>  7 pairs (_) / C4 = 4  => 11 pairs (_)
D3,H3: 4.. / D3 = 4  => 13 pairs (_) / H3 = 4  => 16 pairs (_)
H1,H3: 5.. / H1 = 5  => 10 pairs (_) / H3 = 5  => 14 pairs (_)
A2,E2: 5.. / A2 = 5  =>  9 pairs (_) / E2 = 5  => 10 pairs (_)
A4,C4: 6.. / A4 = 6  => 11 pairs (_) / C4 = 6  =>  7 pairs (_)
F7,D9: 6.. / F7 = 6  => 11 pairs (_) / D9 = 6  =>  0 pairs (X)
F7,I7: 6.. / F7 = 6  => 11 pairs (_) / I7 = 6  =>  0 pairs (X)
I5,G6: 7.. / I5 = 7  => 14 pairs (_) / G6 = 7  =>  0 pairs (X)
E7,E9: 7.. / E7 = 7  =>  9 pairs (_) / E9 = 7  =>  0 pairs (X)
C6,G6: 7.. / C6 = 7  => 14 pairs (_) / G6 = 7  =>  0 pairs (X)
I2,I5: 7.. / I2 = 7  =>  0 pairs (X) / I5 = 7  => 14 pairs (_)
B7,A8: 8.. / B7 = 8  => 14 pairs (_) / A8 = 8  => 14 pairs (_)
I7,G8: 8.. / I7 = 8  => 14 pairs (_) / G8 = 8  => 14 pairs (_)
B7,I7: 8.. / B7 = 8  => 14 pairs (_) / I7 = 8  => 14 pairs (_)
A8,G8: 8.. / A8 = 8  => 14 pairs (_) / G8 = 8  => 14 pairs (_)
A1,C1: 9.. / A1 = 9  => 11 pairs (_) / C1 = 9  => 10 pairs (_)
E8,E9: 9.. / E8 = 9  => 10 pairs (_) / E9 = 9  => 11 pairs (_)
A9,E9: 9.. / A9 = 9  => 10 pairs (_) / E9 = 9  => 11 pairs (_)
C1,C8: 9.. / C1 = 9  => 10 pairs (_) / C8 = 9  => 11 pairs (_)
* DURATION: 0:00:44.521841  START: 04:15:08.732785  END: 04:15:53.254626 2017-05-01
* CP COUNT: (33)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,C4,C6,E7,F7,G6,H5,I5)
* ...7..3...4.....9...3..9..1.9.137582..89654..35.842.691..5..9...6.....75..5..8...
* PAIR A5: 2,7 BLK 4
B5: 2,7,1                                # reduction candidate for 2,7
B5: 2,7 => CTR
* .1978.354542613897..3..96.1.9.137582..89654133518427691.752.9.8864391275925.78136
B5: 1                                    # 14 pairs
* PAIR A5: 2,7 COL A
A2: 2,7,5,6,8                            # reduction candidate for 2,7
A2: 2,7                                  # 13 pairs
A3: 2,7,5,6,8                            # reduction candidate for 2,7
A3: 2,7                                  # 11 pairs
A9: 2,7,4,9                              # reduction candidate for 2,7
A9: 2,7                                  # 12 pairs
* PAIR C6: 1,7 BLK 4
B5: 1,7,2                                # reduction candidate for 1,7
B5: 2 => CTR
* .197..3.8.4..13.97.73..9..1.9.13758272896541335184276918752.93..6..91875935.7812.
B5: 1,7                                  #  9 pairs
* PAIR C6: 1,7 COL C
C2: 1,7,2,6                              # reduction candidate for 1,7
C2: 2,6                                  # 13 pairs
C2: 1,7                                  # 11 pairs
* PAIR H5: 1,3 COL H
H9: 1,3,2,4                              # reduction candidate for 1,3
H9: 2,4 => CTR
* .197..3.8.4..13.97..3..9..1.9.137582..896541335184276918752.93..6..91875935.7812.
H9: 1,3                                  # 15 pairs
* PAIR E7: 2,7 BLK 8
E9: 2,7,1,9                              # reduction candidate for 2,7
E9: 2,7                                  # 19 pairs
E9: 1,9                                  # 10 pairs
* PAIR E7: 2,7 ROW 7
B7: 2,7,3,8                              # reduction candidate for 2,7
B7: 2,7 => CTR
* ...7..3...4.....97..3..9..1.9.137582..89654133518427691..5.693886.....75.35..8...
B7: 3,8                                  # 10 pairs
C7: 2,7,4                                # reduction candidate for 2,7
C7: 2,7                                  # 12 pairs
* PAIR F7: 4,6 BLK 8
D9: 4,6,2                                # reduction candidate for 4,6
D9: 2                                    # 19 pairs
D9: 4,6                                  # 15 pairs
* PAIR F7: 4,6 ROW 7
I7: 4,6,3,8                              # reduction candidate for 4,6
I7: 4,6 => CTR
* .1975.34854.....97..3..9..1.9.137582..896541335184276918752.93..6..91875935.7812.
I7: 3,8                                  # 12 pairs
* PAIR F7: 4,6 COL F
F1: 4,6,1                                # reduction candidate for 4,6
F1: 1 => SOLVED
* 829751346541623798673489251496137582218965437357842169184576923962314875735298614
F1: 4,6                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0042-base-pr-000.dot
* REASONING
* DIS # B5: 2,7 => CTR => B5: 1
* DIS # B5: 2 => CTR => B5: 1,7
* DIS # H9: 2,4 => CTR => H9: 1,3
* DIS # B7: 2,7 => CTR => B7: 3,8
* DIS # I7: 4,6 => CTR => I7: 3,8
* PRF # F1: 1 => SOL
* CNT   6 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,C4,C6,E7,F7,G6,H5,I5)
* ...7..3...4.....9...3..9..1.9.137582..89654..35.842.691..5..9...6.....75..5..8...
* PAIR A5: 2,7 BLK 4
B5: 2,7,1                                # reduction candidate for 2,7
B5: 2,7 => CTR
* .1978.354542613897..3..96.1.9.137582..89654133518427691.752.9.8864391275925.78136

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,B1,B7,C4,C7,D9,E9,F1,F2,G8,G9,H7,I2,I7)
* ...7..3...4.....9...3..9..1.9.1375822189654373578421691..5769...6.....75..5..8.1.
* PAIR B1: 2,8 BLK 1
B3: 2,8,7                                # reduction candidate for 2,8
B3: 2,8 => CTR
* ...7..3.4.4.....96..3..9..1.9.1375822189654373578421691..5769...6.....75.75..8.13
* PAIR B1: 2,8 ROW 1
E1: 2,8,1,5                              # reduction candidate for 2,8
E1: 2,8                                  # 20 pairs
E1: 1,5                                  # 16 pairs
* PAIR F1: 1,4 COL F
F8: 1,4,3                                # reduction candidate for 1,4
F8: 3 => CTR
* .217.435..46..179..73..9.41.9.1375822189654373578421691.457692..6.4138757.5298614
* PAIR RESTART
* PAIR I2: 6,8 BLK 3
I1: 6,8,4                                # reduction candidate for 6,8
I1: 6,8 => SOLVED
* 829751346541623798673489251496137582218965437357842169184576923962314875735298614
* DURATION: 0:00:10.035251  START: 04:16:09.614085  END: 04:16:19.649336 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0042-base-pr-001.dot
* REASONING
* DIS # B5: 2,7 => CTR => B5: 1
* DIS B5: 1 # B3: 2,8 => CTR => B3: 7
* DIS B5: 1 + B3: 7 # F8: 3 => CTR => F8: 1,4
* PRF B5: 1 + B3: 7 + F8: 1,4 # I1: 6,8 => SOL
* STA B5: 1 + B3: 7 + F8: 1,4 + I1: 6,8
* CNT   4 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=42

Solution

position: 829751346541623798673489251496137582218965437357842169184576923962314875735298614 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 # B5: 2,7 => CTR => B5: 1
* INC # B5: 1 => UNS
* INC # A2: 2,7 => UNS
* INC # A3: 2,7 => UNS
* INC # A9: 2,7 => UNS
* INC # B5: 1,7 => UNS
* DIS # B5: 2 => CTR => B5: 1,7
* INC # C2: 1,7 => UNS
* INC # C2: 2,6 => UNS
* INC # H9: 1,3 => UNS
* DIS # H9: 2,4 => CTR => H9: 1,3
* INC # E9: 2,7 => UNS
* INC # E9: 1,9 => UNS
* DIS # B7: 2,7 => CTR => B7: 3,8
* INC # B7: 3,8 => UNS
* INC # C7: 2,7 => UNS
* INC # D9: 4,6 => UNS
* INC # D9: 2 => UNS
* DIS # I7: 4,6 => CTR => I7: 3,8
* INC # I7: 3,8 => UNS
* INC # F1: 4,6 => UNS
* PRF # F1: 1 => SOL
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B5: 2,7 => CTR => B5: 1
* DIS B5: 1 # B3: 2,8 => CTR => B3: 7
* INC B5: 1 + B3: 7 # E1: 2,8 => UNS
* INC B5: 1 + B3: 7 # E1: 1,5 => UNS
* INC B5: 1 + B3: 7 # F8: 1,4 => UNS
* DIS B5: 1 + B3: 7 # F8: 3 => CTR => F8: 1,4
* PRF B5: 1 + B3: 7 + F8: 1,4 # I1: 6,8 => SOL
* STA B5: 1 + B3: 7 + F8: 1,4 + I1: 6,8
* CNT   7 HDP CHAINS /   7 HYP OPENED