Analysis of zz-menneske-no-06912234-base.sdk

Contents

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6912234
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6912234

level: medium

position: .5..4...6.....83.1.7.3....2....3.5..5..8.2..4...4............1.4.2.....91...9..3. initial

Autosolve

position: .5..4...6.....83.1.7.3....2....3.5..5..8.2..4...4....3.......1.4.2.....91...9..3. autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # D1: 1,9 => SOL
* DIS # D1: 2 => CTR => D1: 1,9
* DIS # F3: 1,9 => CTR => F3: 5,6
* DIS # C1: 1,9 => CTR => C1: 3,8
* DIS # C3: 8,9 => CTR => C3: 1,4,6
* DIS # I7: 7,8 => CTR => I7: 5
* PRF # A7: 3,8 => SOL
* DIS # A7: 6,7,9 => CTR => A7: 3,8
* DIS # B7: 3,8 => CTR => B7: 6,9
* DIS # C7: 3,8 => CTR => C7: 5,6,7,9
* DIS # A7: 6,8 => CTR => A7: 3,7,9
* DIS # B7: 6,8 => CTR => B7: 3,9
* DIS # C7: 6,8 => CTR => C7: 3,5,7,9
* DIS # C9: 6,8 => CTR => C9: 5,7
* DIS # B4: 6,8 => CTR => B4: 1,2,4,9
* DIS # B6: 6,8 => CTR => B6: 1,2,9
* CNT  16 HDP CHAINS /  41 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* PRF # D1: 1,9 => SOL
* STA D1: 1,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

`.5..4...6.....83.1.7.3....2....3.5..5..8.2..4...4............1.4.2.....91...9..3.`	initial
`.5..4...6.....83.1.7.3....2....3.5..5..8.2..4...4....3.......1.4.2.....91...9..3.`	autosolve
`253941876649728351871365942924136587536872194718459623397684215482513769165297438`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
F1: 1,9
H2: 4,5
G3: 8,9
H3: 4,5
I4: 7,8
B8: 3,8
B9: 6,8
G7: 2,4
G9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,C3: 1.. / C1 = 1  =>  0 pairs (X) / C3 = 1  =>  8 pairs (_)
G5,G6: 1.. / G5 = 1  => 12 pairs (_) / G6 = 1  =>  9 pairs (_)
H4,H6: 2.. / H4 = 2  =>  9 pairs (_) / H6 = 2  => 12 pairs (_)
G7,G9: 2.. / G7 = 2  =>  0 pairs (*) / G9 = 2  =>  0 pairs (X)
A1,D1: 2.. / A1 = 2  =>  0 pairs (*) / D1 = 2  =>  0 pairs (X)
D9,G9: 2.. / D9 = 2  =>  0 pairs (*) / G9 = 2  =>  0 pairs (X)
E2,E7: 2.. / E2 = 2  =>  0 pairs (*) / E7 = 2  =>  0 pairs (X)
A1,C1: 3.. / A1 = 3  =>  0 pairs (X) / C1 = 3  =>  0 pairs (_)
B5,C5: 3.. / B5 = 3  =>  0 pairs (*) / C5 = 3  =>  0 pairs (X)
F7,F8: 3.. / F7 = 3  =>  0 pairs (X) / F8 = 3  =>  0 pairs (_)
B8,F8: 3.. / B8 = 3  =>  0 pairs (X) / F8 = 3  =>  0 pairs (_)
A1,A7: 3.. / A1 = 3  =>  0 pairs (X) / A7 = 3  =>  0 pairs (_)
H2,H3: 4.. / H2 = 4  =>  0 pairs (X) / H3 = 4  =>  7 pairs (_)
B4,C4: 4.. / B4 = 4  => 10 pairs (_) / C4 = 4  =>  8 pairs (_)
F7,F9: 4.. / F7 = 4  =>  0 pairs (*) / F9 = 4  =>  0 pairs (X)
G7,G9: 4.. / G7 = 4  =>  8 pairs (_) / G9 = 4  =>  0 pairs (*)
C3,H3: 4.. / C3 = 4  =>  0 pairs (X) / H3 = 4  =>  7 pairs (_)
F7,G7: 4.. / F7 = 4  =>  0 pairs (*) / G7 = 4  =>  0 pairs (X)
F9,G9: 4.. / F9 = 4  =>  8 pairs (_) / G9 = 4  =>  0 pairs (*)
B2,B4: 4.. / B2 = 4  =>  8 pairs (_) / B4 = 4  => 10 pairs (_)
H2,H3: 5.. / H2 = 5  =>  7 pairs (_) / H3 = 5  =>  0 pairs (X)
E6,F6: 5.. / E6 = 5  => 10 pairs (_) / F6 = 5  =>  9 pairs (_)
C7,C9: 5.. / C7 = 5  =>  0 pairs (X) / C9 = 5  => 11 pairs (_)
I7,I9: 5.. / I7 = 5  => 11 pairs (_) / I9 = 5  =>  0 pairs (X)
C7,I7: 5.. / C7 = 5  =>  0 pairs (X) / I7 = 5  => 11 pairs (_)
C9,I9: 5.. / C9 = 5  => 11 pairs (_) / I9 = 5  =>  0 pairs (X)
D2,D8: 5.. / D2 = 5  =>  0 pairs (X) / D8 = 5  =>  9 pairs (_)
G8,H8: 6.. / G8 = 6  => 10 pairs (_) / H8 = 6  => 14 pairs (_)
D2,E2: 7.. / D2 = 7  =>  0 pairs (*) / E2 = 7  =>  0 pairs (X)
G1,H1: 7.. / G1 = 7  => 11 pairs (_) / H1 = 7  => 13 pairs (_)
E7,E8: 8.. / E7 = 8  =>  0 pairs (*) / E8 = 8  =>  0 pairs (X)
* DURATION: 0:00:50.475160  START: 06:56:55.904165  END: 06:57:46.379325 2017-05-01
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,F1,G3,G7,G9,H2,H3,I4)
* .5..4...6.....83.1.7.3....2....3.5..5..8.2..4...4....3.......1.4.2.....91...9..3.
* PAIR F1: 1,9 BLK 2
D1: 1,9,2                                # reduction candidate for 1,9
D1: 1,9 => SOLVED
* 253941876649728351871365942924136587536872194718459623397684215482513769165297438
D1: 2 => CTR
* 35.24...6.....83.1.7.3....2....3.5.75.3872..4...4....3....2341.432.876.91...9423.
F3: 1,9,5,6                              # reduction candidate for 1,9
F3: 1,9 => CTR
* .5.24...6...578341.74361.52...93.5..5..8.2..4...4....3....2.41.4.2185..91...9423.
F3: 5,6                                  # 10 pairs
* PAIR F1: 1,9 ROW 1
C1: 1,9,3,8                              # reduction candidate for 1,9
C1: 1,9 => CTR
* 35.24...6.....83.1.7.3..9.2....3.5.75.3872..4...4....3....2341.432.876.91...9423.
C1: 3,8                                  #  9 pairs
* PAIR F1: 1,9 COL F
F4: 1,9,6,7                              # reduction candidate for 1,9
F4: 1,9                                  # 11 pairs
F6: 1,9,5,6,7                            # reduction candidate for 1,9
F6: 1,9                                  # 13 pairs
* PAIR G3: 8,9 BLK 3
G1: 8,9,7                                # reduction candidate for 8,9
G1: 8,9                                  # 13 pairs
H1: 8,9,7                                # reduction candidate for 8,9
H1: 8,9                                  # 11 pairs
* PAIR G3: 8,9 ROW 3
A3: 8,9,6                                # reduction candidate for 8,9
A3: 8,9                                  # 10 pairs
C3: 8,9,1,4,6                            # reduction candidate for 8,9
C3: 8,9 => CTR
* 351249..6...5.83.1.7.3..942...93.5..5..8.2..4...4....3.......1.4.21....91...9..3.
C3: 1,4,6                                #  9 pairs
* PAIR G3: 8,9 COL G
G6: 8,9,1,6,7                            # reduction candidate for 8,9
G6: 8,9                                  # 15 pairs
G6: 1,6,7                                #  9 pairs
* PAIR I4: 7,8 BLK 6
H4: 7,8,2,6,9                            # reduction candidate for 7,8
H4: 7,8                                  # 14 pairs
G6: 7,8,1,6,9                            # reduction candidate for 7,8
G6: 7,8                                  # 16 pairs
H6: 7,8,2,6,9                            # reduction candidate for 7,8
H6: 7,8                                  # 11 pairs
* PAIR I4: 7,8 ROW 4
A4: 7,8,2,6,9                            # reduction candidate for 7,8
A4: 7,8                                  # 10 pairs
C4: 7,8,4,6,9                            # reduction candidate for 7,8
C4: 7,8                                  # 11 pairs
* PAIR I4: 7,8 COL I
I7: 7,8,5                                # reduction candidate for 7,8
I7: 7,8 => CTR
* 35.24...6.....83.1.7.3....2....3.5.75.3872..4...4....3..5.23418432.876.91...94235
I7: 5                                    # 11 pairs
I9: 7,8,5                                # reduction candidate for 7,8
I9: 7,8                                  # 11 pairs
* PAIR B8: 3,8 BLK 7
A7: 3,8,6,7,9                            # reduction candidate for 3,8
A7: 3,8 => SOLVED
* 253941876649728351871365942924136587536872194718459623397684215482513769165297438
A7: 6,7,9 => CTR
* 35.24...6.....83.1.7.3....2....3.5.75.3872..4...4....3....2341.432.876.91...9423.
B7: 3,8,6,9                              # reduction candidate for 3,8
B7: 3,8 => CTR
* 35.24...6....783.1.7.3....2....3.5.75.38.2..4...4.7..3789623415432.8...9165794238
B7: 6,9                                  # 10 pairs
C7: 3,8,5,6,7,9                          # reduction candidate for 3,8
C7: 3,8 => CTR
* 35.24...6....783.1.7.3....2....3.5.75.78.2..4...4.7..379.62.4154.2.8...9165794238
C7: 5,6,7,9                              #  9 pairs
* PAIR B9: 6,8 BLK 7
A7: 6,8,3,7,9                            # reduction candidate for 6,8
A7: 6,8 => CTR
* 35.24...6.....83.1.7.3....2....3.5.75.3872..47..4....3....2341.432.876.91...9423.
A7: 3,7,9                                #  9 pairs
B7: 6,8,3,9                              # reduction candidate for 6,8
B7: 6,8 => CTR
* 35.24...6.....83.1.7.3....2....3.5.75.3872..4...4....3....2341.432.876.91...9423.
B7: 3,9                                  # 10 pairs
C7: 6,8,3,5,7,9                          # reduction candidate for 6,8
C7: 6,8 => CTR
* 35.24...6....783.1.7.3....2....3.5.75138629.4...4....379.623415432.8...9165794238
C7: 3,5,7,9                              #  9 pairs
C9: 6,8,5,7                              # reduction candidate for 6,8
C9: 6,8 => CTR
* 35.24...6.....83.1.7.3....2....3.5.75.3872..4..74....3795623418432.87..91...94235
C9: 5,7                                  # 10 pairs
* PAIR B9: 6,8 COL B
B4: 6,8,1,2,4,9                          # reduction candidate for 6,8
B4: 6,8 => CTR
* 351249..6249..8351.7.3159429.413.52.5138.2.94.2.45.1.3.9..2341.432581..91...9423.
B4: 1,2,4,9                              #  9 pairs
B6: 6,8,1,2,9                            # reduction candidate for 6,8
B6: 6,8 => CTR
* 351249876...578341.74316952.4.9315..513862794...4..1.3.9..2341.432185..91...9423.
B6: 1,2,9                                #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06912234-base-pr-000.dot
* REASONING
* PRF # D1: 1,9 => SOL
* DIS # D1: 2 => CTR => D1: 1,9
* DIS # F3: 1,9 => CTR => F3: 5,6
* DIS # C1: 1,9 => CTR => C1: 3,8
* DIS # C3: 8,9 => CTR => C3: 1,4,6
* DIS # I7: 7,8 => CTR => I7: 5
* PRF # A7: 3,8 => SOL
* DIS # A7: 6,7,9 => CTR => A7: 3,8
* DIS # B7: 3,8 => CTR => B7: 6,9
* DIS # C7: 3,8 => CTR => C7: 5,6,7,9
* DIS # A7: 6,8 => CTR => A7: 3,7,9
* DIS # B7: 6,8 => CTR => B7: 3,9
* DIS # C7: 6,8 => CTR => C7: 3,5,7,9
* DIS # C9: 6,8 => CTR => C9: 5,7
* DIS # B4: 6,8 => CTR => B4: 1,2,4,9
* DIS # B6: 6,8 => CTR => B6: 1,2,9
* CNT  16 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,B9,F1,G3,G7,G9,H2,H3,I4)
* .5..4...6.....83.1.7.3....2....3.5..5..8.2..4...4....3.......1.4.2.....91...9..3.
* PAIR F1: 1,9 BLK 2
D1: 1,9,2                                # reduction candidate for 1,9
D1: 1,9 => SOLVED
* 253941876649728351871365942924136587536872194718459623397684215482513769165297438
* DURATION: 0:00:02.583353  START: 06:58:20.075292  END: 06:58:22.658645 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06912234-base-pr-001.dot
* REASONING
* PRF # D1: 1,9 => SOL
* STA D1: 1,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6912234
umulig

Solution

position: 253941876649728351871365942924136587536872194718459623397684215482513769165297438 solved

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 # D1: 1,9 => SOL
* DIS # D1: 2 => CTR => D1: 1,9
* DIS # F3: 1,9 => CTR => F3: 5,6
* INC # F3: 5,6 => UNS
* DIS # C1: 1,9 => CTR => C1: 3,8
* INC # C1: 3,8 => UNS
* INC # F4: 1,9 => UNS
* INC # F6: 1,9 => UNS
* INC # G1: 8,9 => UNS
* INC # H1: 8,9 => UNS
* INC # A3: 8,9 => UNS
* DIS # C3: 8,9 => CTR => C3: 1,4,6
* INC # C3: 1,4,6 => UNS
* INC # G6: 8,9 => UNS
* INC # G6: 1,6,7 => UNS
* INC # H4: 7,8 => UNS
* INC # G6: 7,8 => UNS
* INC # H6: 7,8 => UNS
* INC # A4: 7,8 => UNS
* INC # C4: 7,8 => UNS
* DIS # I7: 7,8 => CTR => I7: 5
* INC # I7: 5 => UNS
* INC # I9: 7,8 => UNS
* PRF # A7: 3,8 => SOL
* DIS # A7: 6,7,9 => CTR => A7: 3,8
* DIS # B7: 3,8 => CTR => B7: 6,9
* INC # B7: 6,9 => UNS
* DIS # C7: 3,8 => CTR => C7: 5,6,7,9
* INC # C7: 5,6,7,9 => UNS
* DIS # A7: 6,8 => CTR => A7: 3,7,9
* INC # A7: 3,7,9 => UNS
* DIS # B7: 6,8 => CTR => B7: 3,9
* INC # B7: 3,9 => UNS
* DIS # C7: 6,8 => CTR => C7: 3,5,7,9
* INC # C7: 3,5,7,9 => UNS
* DIS # C9: 6,8 => CTR => C9: 5,7
* INC # C9: 5,7 => UNS
* DIS # B4: 6,8 => CTR => B4: 1,2,4,9
* INC # B4: 1,2,4,9 => UNS
* DIS # B6: 6,8 => CTR => B6: 1,2,9
* INC # B6: 1,2,9 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # D1: 1,9 => SOL
* STA D1: 1,9
* CNT   1 HDP CHAINS /   1 HYP OPENED