Analysis of zz-menneske-no-06911767-base.sdk

Contents

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6911767

level: medium

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6911767

position: ....4......4..1.9....7..68..8.5......9.....4..6...9.3..1...3..7......9..6...82... initial

Autosolve

position: ..6.48...8.4..1.9....7.5684.8.5....9.9.....4..6...9.3..1...3..7......9..6...82... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 2,3 => CTR => A1: 5,7,9
* DIS # B1: 2,3 => CTR => B1: 5,7
* DIS # B2: 2,3 => CTR => B2: 5,7
* PRF # A3: 2,3 => SOL
* DIS # C3: 2,3 => CTR => C3: 1,9
* DIS # E3: 2,3 => CTR => E3: 9
* PRF # E3: 9 => SOL
* DIS # B8: 2,3 => CTR => B8: 4,5
* DIS # F4: 6,7 => CTR => F4: 4
* DIS # E5: 6,7 => CTR => E5: 1,2,3
* DIS # F8: 4 => CTR => F8: 6,7
* DIS # H8: 1,5 => CTR => H8: 2,6
* DIS # I8: 1,5 => CTR => I8: 2,3,6,8
* DIS # G9: 1,5 => CTR => G9: 3,4
* PRF # I9: 1,5 => SOL
* DIS # H1: 1,5 => CTR => H1: 2,7
* CNT  16 HDP CHAINS /  31 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 # A1: 2,3 => CTR => A1: 5,7,9
* DIS A1: 5,7,9 # B1: 2,3 => CTR => B1: 5,7
* DIS A1: 5,7,9 + B1: 5,7 # B2: 2,3 => CTR => B2: 5,7
* PRF A1: 5,7,9 + B1: 5,7 + B2: 5,7 => SOL
* STA A1: 5,7,9 + B1: 5,7 + B2: 5,7
* CNT   4 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

....4......4..1.9....7..68..8.5......9.....4..6...9.3..1...3..7......9..6...82... initial
..6.48...8.4..1.9....7.5684.8.5....9.9.....4..6...9.3..1...3..7......9..6...82... autosolve
956348172874621395321795684783564219192837546465219738219453867548176923637982451 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
B3: 2,3
F5: 6,7
H9: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A3,C3: 1.. / A3 = 1  =>  3 pairs (_) / C3 = 1  =>  4 pairs (_)
A4,A6: 4.. / A4 = 4  =>  0 pairs (X) / A6 = 4  =>  4 pairs (_)
F4,D6: 4.. / F4 = 4  =>  4 pairs (_) / D6 = 4  =>  0 pairs (X)
B8,B9: 4.. / B8 = 4  =>  5 pairs (_) / B9 = 4  =>  0 pairs (X)
G7,G9: 4.. / G7 = 4  =>  0 pairs (X) / G9 = 4  =>  7 pairs (_)
A4,F4: 4.. / A4 = 4  =>  0 pairs (X) / F4 = 4  =>  4 pairs (_)
A6,D6: 4.. / A6 = 4  =>  4 pairs (_) / D6 = 4  =>  0 pairs (X)
D7,G7: 4.. / D7 = 4  =>  7 pairs (_) / G7 = 4  =>  0 pairs (X)
F4,F8: 4.. / F4 = 4  =>  4 pairs (_) / F8 = 4  =>  0 pairs (X)
E7,E8: 5.. / E7 = 5  =>  0 pairs (*) / E8 = 5  =>  0 pairs (X)
D2,E2: 6.. / D2 = 6  =>  0 pairs (*) / E2 = 6  =>  0 pairs (X)
H4,I5: 6.. / H4 = 6  =>  0 pairs (X) / I5 = 6  =>  0 pairs (_)
I5,I8: 6.. / I5 = 6  =>  0 pairs (*) / I8 = 6  =>  0 pairs (X)
B9,C9: 7.. / B9 = 7  =>  0 pairs (X) / C9 = 7  =>  0 pairs (_)
E8,F8: 7.. / E8 = 7  =>  0 pairs (*) / F8 = 7  =>  0 pairs (X)
B2,G2: 7.. / B2 = 7  =>  0 pairs (*) / G2 = 7  =>  0 pairs (X)
H1,H4: 7.. / H1 = 7  =>  0 pairs (*) / H4 = 7  =>  0 pairs (X)
D5,D6: 8.. / D5 = 8  =>  5 pairs (_) / D6 = 8  =>  6 pairs (_)
C7,C8: 8.. / C7 = 8  =>  0 pairs (X) / C8 = 8  =>  7 pairs (_)
G7,I8: 8.. / G7 = 8  =>  7 pairs (_) / I8 = 8  =>  0 pairs (X)
C7,G7: 8.. / C7 = 8  =>  0 pairs (X) / G7 = 8  =>  7 pairs (_)
C8,I8: 8.. / C8 = 8  =>  7 pairs (_) / I8 = 8  =>  0 pairs (X)
D1,E3: 9.. / D1 = 9  =>  0 pairs (X) / E3 = 9  =>  0 pairs (_)
A1,D1: 9.. / A1 = 9  =>  0 pairs (*) / D1 = 9  =>  0 pairs (X)
C9,D9: 9.. / C9 = 9  =>  0 pairs (X) / D9 = 9  =>  0 pairs (_)
E3,E7: 9.. / E3 = 9  =>  0 pairs (*) / E7 = 9  =>  0 pairs (X)
* DURATION: 0:00:36.023175  START: 06:51:08.501561  END: 06:51:44.524736 2017-05-01
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,F5,H9)
* ..6.48...8.4..1.9....7.5684.8.5....9.9.....4..6...9.3..1...3..7......9..6...82...
* PAIR B3: 2,3 BLK 1
A1: 2,3,5,7,9                            # reduction candidate for 2,3
A1: 2,3 => CTR
* ..6948...8.4..1.9.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7....579.6679.82...
A1: 5,7,9                                #  3 pairs
B1: 2,3,5,7                              # reduction candidate for 2,3
B1: 2,3 => CTR
* 7.6948...854.6179.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7.4..579.6679.82...
B1: 5,7                                  #  4 pairs
B2: 2,3,5,7                              # reduction candidate for 2,3
B2: 2,3 => CTR
* 9.6.48...8.4..1795...795684.8.5...79.9...7.46.6...9.3..1..53..7....7.9..6...82...
B2: 5,7                                  #  4 pairs
A3: 2,3,1,9                              # reduction candidate for 2,3
A3: 2,3 => SOLVED
* 956348172874621395321795684783564219192837546465219738219453867548176923637982451
A3: 1,9                                  #  4 pairs
C3: 2,3,1,9                              # reduction candidate for 2,3
C3: 2,3 => CTR
* 9.6.48...8.46.1.9.123795684.8.564..9.9.837.4646...9738.19453867548..69.36379824..
C3: 1,9                                  #  4 pairs
* PAIR B3: 2,3 ROW 3
E3: 2,3,9                                # reduction candidate for 2,3
E3: 2,3 => CTR
* 7.6948...8.4.6179.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7....579.6679.82...
E3: 9 => SOLVED
* 956348172874621395321795684783564219192837546465219738219453867548176923637982451
* PAIR B3: 2,3 COL B
B8: 2,3,4,5                              # reduction candidate for 2,3
B8: 2,3 => CTR
* 9.6.48...8.4..1.9....795684.8.5....9.9.....4..6...9.3..19..3..7......9..647982...
B8: 4,5                                  #  4 pairs
* PAIR F5: 6,7 BLK 5
E4: 6,7,1,2,3                            # reduction candidate for 6,7
E4: 6,7                                  #  6 pairs
F4: 6,7,4                                # reduction candidate for 6,7
F4: 6,7 => CTR
* 9.6.48...8.4..1.9....79568448.5....9.9.8...46.6.4.983..1...34.7.....49.8647982...
F4: 4                                    #  4 pairs
E5: 6,7,1,2,3                            # reduction candidate for 6,7
E5: 6,7 => CTR
* 956.48.7.874..1.9....7.568478.5.4.69.9...6.4.46...973..1...38.7..8..79.66.79824.3
E5: 1,2,3                                #  3 pairs
* PAIR F5: 6,7 COL F
F8: 6,7,4                                # reduction candidate for 6,7
F8: 4 => CTR
* 9.6.48...8.4..1.9....79568448.5....9.9.....4..6.4.9.3..196.3..7....749..647982...
F8: 6,7                                  #  4 pairs
* PAIR H9: 1,5 BLK 9
H8: 1,5,2,6                              # reduction candidate for 1,5
H8: 1,5 => CTR
* ..6948...8.4..1.9....7.5684.8.5.4..9.9.....4646...9.3..1.493.67.4..5.9..6...824.3
H8: 2,6                                  #  4 pairs
I8: 1,5,2,3,6,8                          # reduction candidate for 1,5
I8: 1,5 => CTR
* ..6.48...8.46.1.9....7.5684.8.564..9.9.837.4646..19.38.1.4538673481769256..982413
I8: 2,3,6,8                              #  3 pairs
G9: 1,5,3,4                              # reduction candidate for 1,5
G9: 1,5 => CTR
* 9.6.48...8.4..1.9....795684.8.5....9.9...7.46.6...9.3.218953467....7.928679482..3
G9: 3,4                                  #  4 pairs
I9: 1,5,3                                # reduction candidate for 1,5
I9: 1,5 => SOLVED
* 956348172874621395321795684783564219192837546465219738219453867548176923637982451
I9: 3                                    #  4 pairs
* PAIR H9: 1,5 COL H
H1: 1,5,2,7                              # reduction candidate for 1,5
H1: 1,5 => CTR
* 9.6.48...8.4..1.9....795684.8.5...79.9...7.4676.4.9.3.21..53467....74928647982...
H1: 2,7                                  #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06911767-base-pr-000.dot
* REASONING
* DIS # A1: 2,3 => CTR => A1: 5,7,9
* DIS # B1: 2,3 => CTR => B1: 5,7
* DIS # B2: 2,3 => CTR => B2: 5,7
* PRF # A3: 2,3 => SOL
* DIS # C3: 2,3 => CTR => C3: 1,9
* DIS # E3: 2,3 => CTR => E3: 9
* PRF # E3: 9 => SOL
* DIS # B8: 2,3 => CTR => B8: 4,5
* DIS # F4: 6,7 => CTR => F4: 4
* DIS # E5: 6,7 => CTR => E5: 1,2,3
* DIS # F8: 4 => CTR => F8: 6,7
* DIS # H8: 1,5 => CTR => H8: 2,6
* DIS # I8: 1,5 => CTR => I8: 2,3,6,8
* DIS # G9: 1,5 => CTR => G9: 3,4
* PRF # I9: 1,5 => SOL
* DIS # H1: 1,5 => CTR => H1: 2,7
* CNT  16 HDP CHAINS /  31 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,F5,H9)
* ..6.48...8.4..1.9....7.5684.8.5....9.9.....4..6...9.3..1...3..7......9..6...82...
* PAIR B3: 2,3 BLK 1
A1: 2,3,5,7,9                            # reduction candidate for 2,3
A1: 2,3 => CTR
* ..6948...8.4..1.9.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7....579.6679.82...
B1: 2,3,5,7                              # reduction candidate for 2,3
B1: 2,3 => CTR
* 7.6948...854.6179.9.17.5684.8.5.4..9.9...6.4.46...9.3..1..93..7.4..579.6679.82...
B2: 2,3,5,7                              # reduction candidate for 2,3
B2: 2,3 => CTR
* 9.6.48...8.4..1795...795684.8.5...79.9...7.46.6...9.3..1..53..7....7.9..6...82...
B2: 5,7 => SOLVED
* 956348172874621395321795684783564219192837546465219738219453867548176923637982451
* DURATION: 0:00:03.507946  START: 06:52:06.841116  END: 06:52:10.349062 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06911767-base-pr-001.dot
* REASONING
* DIS # A1: 2,3 => CTR => A1: 5,7,9
* DIS A1: 5,7,9 # B1: 2,3 => CTR => B1: 5,7
* DIS A1: 5,7,9 + B1: 5,7 # B2: 2,3 => CTR => B2: 5,7
* PRF A1: 5,7,9 + B1: 5,7 + B2: 5,7 => SOL
* STA A1: 5,7,9 + B1: 5,7 + B2: 5,7
* CNT   4 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6911767
umulig

Solution

position: 956348172874621395321795684783564219192837546465219738219453867548176923637982451 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 # A1: 2,3 => CTR => A1: 5,7,9
* INC # A1: 5,7,9 => UNS
* DIS # B1: 2,3 => CTR => B1: 5,7
* INC # B1: 5,7 => UNS
* DIS # B2: 2,3 => CTR => B2: 5,7
* INC # B2: 5,7 => UNS
* PRF # A3: 2,3 => SOL
* INC # A3: 1,9 => UNS
* DIS # C3: 2,3 => CTR => C3: 1,9
* INC # C3: 1,9 => UNS
* DIS # E3: 2,3 => CTR => E3: 9
* PRF # E3: 9 => SOL
* DIS # B8: 2,3 => CTR => B8: 4,5
* INC # B8: 4,5 => UNS
* INC # E4: 6,7 => UNS
* DIS # F4: 6,7 => CTR => F4: 4
* INC # F4: 4 => UNS
* DIS # E5: 6,7 => CTR => E5: 1,2,3
* INC # E5: 1,2,3 => UNS
* INC # F8: 6,7 => UNS
* DIS # F8: 4 => CTR => F8: 6,7
* DIS # H8: 1,5 => CTR => H8: 2,6
* INC # H8: 2,6 => UNS
* DIS # I8: 1,5 => CTR => I8: 2,3,6,8
* INC # I8: 2,3,6,8 => UNS
* DIS # G9: 1,5 => CTR => G9: 3,4
* INC # G9: 3,4 => UNS
* PRF # I9: 1,5 => SOL
* INC # I9: 3 => UNS
* DIS # H1: 1,5 => CTR => H1: 2,7
* INC # H1: 2,7 => UNS
* CNT  31 HDP CHAINS /  31 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 2,3 => CTR => A1: 5,7,9
* DIS A1: 5,7,9 # B1: 2,3 => CTR => B1: 5,7
* DIS A1: 5,7,9 + B1: 5,7 # B2: 2,3 => CTR => B2: 5,7
* PRF A1: 5,7,9 + B1: 5,7 + B2: 5,7 => SOL
* STA A1: 5,7,9 + B1: 5,7 + B2: 5,7
* CNT   4 HDP CHAINS /   3 HYP OPENED