Analysis of zz-menneske-no-06909146-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158.........6.8..4..5..... initial

Autosolve

position: ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A1: 5,7 => SOL
* DIS # B1: 5,7 => CTR => B1: 3,8
* DIS # F2: 5,7 => CTR => F2: 4,6,8
* PRF # D2: 4,7 => SOL
* DIS # F2: 4,7 => CTR => F2: 5,6,8
* DIS # D8: 4,7 => CTR => D8: 1,3
* PRF # D2: 4,9 => SOL
* DIS # F2: 4,8 => CTR => F2: 5,6,7
* DIS # F3: 4,8 => CTR => F3: 5
* DIS # F5: 1,3 => CTR => F5: 4,8
* DIS # D4: 1,3 => CTR => D4: 2,6
* DIS # A7: 2,9 => CTR => A7: 3,6,7
* DIS # G7: 2,9 => CTR => G7: 3,6,7
* DIS # F8: 3,7 => CTR => F8: 1,4
* PRF # A7: 3,7 => SOL
* DIS # G7: 3,7 => CTR => G7: 2,6,9
* DIS # C9: 2,9 => CTR => C9: 3,7,8
* PRF # G9: 2,9 => SOL
* DIS # G9: 1,3 => CTR => G9: 2,6,7,9
* CNT  19 HDP CHAINS /  56 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 # A1: 5,7 => SOL
* STA A1: 5,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

....12.96....3..2...6....7..4..59....9.....6...1.7..8..158.........6.8..4..5..... initial
....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5..... autosolve
584712396179436528236985174842659713793148265651273489315897642927364851468521937 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
B2: 5,7
D1: 4,7
D3: 4,9
E3: 4,8
E5: 4,8
H4: 1,3
E7: 2,9
F7: 3,7
E9: 2,9
H9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,A3: 1.. / A2 = 1  => 11 pairs (_) / A3 = 1  => 11 pairs (_)
H4,H9: 1.. / H4 = 1  =>  9 pairs (_) / H9 = 1  => 12 pairs (_)
A3,B3: 2.. / A3 = 2  => 12 pairs (_) / B3 = 2  => 11 pairs (_)
E7,E9: 2.. / E7 = 2  =>  8 pairs (_) / E9 = 2  =>  8 pairs (_)
H4,H9: 3.. / H4 = 3  => 12 pairs (_) / H9 = 3  =>  9 pairs (_)
C1,C2: 4.. / C1 = 4  => 11 pairs (_) / C2 = 4  => 15 pairs (_)
D8,F8: 4.. / D8 = 4  =>  0 pairs (X) / F8 = 4  => 12 pairs (_)
E3,E5: 4.. / E3 = 4  =>  0 pairs (X) / E5 = 4  => 12 pairs (_)
F2,F3: 5.. / F2 = 5  =>  0 pairs (X) / F3 = 5  => 11 pairs (_)
D2,F2: 6.. / D2 = 6  =>  0 pairs (X) / F2 = 6  =>  0 pairs (_)
A7,B9: 6.. / A7 = 6  =>  0 pairs (X) / B9 = 6  =>  0 pairs (_)
G7,G9: 6.. / G7 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
A4,D4: 6.. / A4 = 6  =>  0 pairs (X) / D4 = 6  =>  0 pairs (_)
A7,G7: 6.. / A7 = 6  =>  0 pairs (X) / G7 = 6  =>  0 pairs (_)
B9,G9: 6.. / B9 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
B6,B9: 6.. / B6 = 6  =>  0 pairs (X) / B9 = 6  =>  0 pairs (_)
F2,F6: 6.. / F2 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
I2,I3: 8.. / I2 = 8  => 10 pairs (_) / I3 = 8  =>  0 pairs (X)
A4,C4: 8.. / A4 = 8  =>  0 pairs (*) / C4 = 8  =>  0 pairs (X)
E5,F5: 8.. / E5 = 8  =>  0 pairs (X) / F5 = 8  => 12 pairs (_)
B9,C9: 8.. / B9 = 8  =>  0 pairs (X) / C9 = 8  =>  0 pairs (_)
F2,I2: 8.. / F2 = 8  =>  0 pairs (X) / I2 = 8  => 10 pairs (_)
A1,A4: 8.. / A1 = 8  =>  0 pairs (X) / A4 = 8  =>  0 pairs (_)
B1,B9: 8.. / B1 = 8  =>  0 pairs (*) / B9 = 8  =>  0 pairs (X)
E3,E5: 8.. / E3 = 8  => 12 pairs (_) / E5 = 8  =>  0 pairs (X)
D2,D3: 9.. / D2 = 9  =>  0 pairs (X) / D3 = 9  =>  9 pairs (_)
G6,I6: 9.. / G6 = 9  => 10 pairs (_) / I6 = 9  => 17 pairs (_)
E7,E9: 9.. / E7 = 9  =>  8 pairs (_) / E9 = 9  =>  8 pairs (_)
A3,D3: 9.. / A3 = 9  =>  0 pairs (X) / D3 = 9  =>  9 pairs (_)
* DURATION: 0:00:41.190268  START: 06:47:05.862949  END: 06:47:47.053217 2017-05-01
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,D1,D3,E3,E5,E7,E9,F7,H4,H9)
* ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5.....
* PAIR B2: 5,7 BLK 1
A1: 5,7,3,8                              # reduction candidate for 5,7
A1: 5,7 => SOLVED
* 584712396179436528236985174842659713793148265651273489315897642927364851468521937
A1: 3,8                                  # 11 pairs
B1: 5,7,3,8                              # reduction candidate for 5,7
B1: 5,7 => CTR
* ....12.96....36.28..6.85.7..4.659....9.148.6..61273.8.6158.7.4....3648514835..6..
B1: 3,8                                  # 11 pairs
A2: 5,7,1,9                              # reduction candidate for 5,7
A2: 5,7                                  # 15 pairs
* PAIR B2: 5,7 ROW 2
F2: 5,7,4,6,8                            # reduction candidate for 5,7
F2: 5,7 => CTR
* ....12.96...63..28..69...7.648.59....9.....6...1.76.8..158..64.....6.85.4..5.....
F2: 4,6,8                                # 11 pairs
* PAIR D1: 4,7 BLK 2
D2: 4,7,6,9                              # reduction candidate for 4,7
D2: 4,7 => SOLVED
* 584712396179436528236985174842659713793148265651273489315897642927364851468521937
D2: 6,9                                  # 11 pairs
F2: 4,7,5,6,8                            # reduction candidate for 4,7
F2: 4,7 => CTR
* ....12.96...63..28..69.5.7.648.59....9...8.6...1.76.8..158..64.....6.85.4..5.....
F2: 5,6,8                                # 10 pairs
* PAIR D1: 4,7 ROW 1
C1: 4,7,3,8                              # reduction candidate for 4,7
C1: 3,8                                  # 16 pairs
C1: 4,7                                  # 12 pairs
* PAIR D1: 4,7 COL D
D8: 4,7,1,3                              # reduction candidate for 4,7
D8: 4,7 => CTR
* ....12.96...63..2...69...7.648.59....9.....6...1.76.8..158..64.....6.85.4..5.....
D8: 1,3                                  # 13 pairs
* PAIR D3: 4,9 BLK 2
D2: 4,9,6,7                              # reduction candidate for 4,9
D2: 4,9 => SOLVED
* 584712396179436528236985174842659713793148265651273489315897642927364851468521937
D2: 6,7                                  # 10 pairs
* PAIR E3: 4,8 BLK 2
F2: 4,8,5,6,7                            # reduction candidate for 4,8
F2: 4,8 => CTR
* ....12.96...63..2...69.5.7.648.59....9.....6...1.76.8..158..64.....6.85.4..5.....
F2: 5,6,7                                # 10 pairs
F3: 4,8,5                                # reduction candidate for 4,8
F3: 4,8 => CTR
* ....12.96....35.28..6....7..4..59....9.....6...1.76.8..158...4.....6.85.4685.....
F3: 5                                    # 11 pairs
* PAIR E3: 4,8 ROW 3
I3: 4,8,1,3,5                            # reduction candidate for 4,8
I3: 4,8                                  # 12 pairs
I3: 1,3,5                                # 10 pairs
* PAIR E5: 4,8 BLK 5
F5: 4,8,1,3                              # reduction candidate for 4,8
F5: 1,3 => CTR
* ...712.96...63..2...694..7.648.59....9..8..6...1.76.8..158..64.....6485.4..5.....
F5: 4,8                                  # 14 pairs
* PAIR H4: 1,3 BLK 6
G4: 1,3,2,7                              # reduction candidate for 1,3
G4: 1,3                                  # 17 pairs
I4: 1,3,2,7                              # reduction candidate for 1,3
I4: 1,3                                  # 13 pairs
G5: 1,3,2,4,5,7                          # reduction candidate for 1,3
G5: 1,3                                  # 17 pairs
I5: 1,3,2,4,5,7                          # reduction candidate for 1,3
I5: 1,3                                  # 17 pairs
* PAIR H4: 1,3 ROW 4
D4: 1,3,2,6                              # reduction candidate for 1,3
D4: 1,3 => CTR
* ....12.96....3..2...6....7.648.59....9.....6...1.7..8..158..64.....6.85.4..5.....
D4: 2,6                                  # 11 pairs
* PAIR E7: 2,9 ROW 7
A7: 2,9,3,6,7                            # reduction candidate for 2,9
A7: 2,9 => CTR
* .8..12.96....36.28..6.85.7.84.659....9.148.6.6.1273.8..158.7643...3648514685.....
A7: 3,6,7                                # 10 pairs
G7: 2,9,3,6,7                            # reduction candidate for 2,9
G7: 2,9 => CTR
* ....12.96....36.28..6.85.7..4.659....9.148.6..61273.8.6158.7.43...3648514..5..6..
G7: 3,6,7                                # 10 pairs
I7: 2,9,3,7                              # reduction candidate for 2,9
I7: 2,9                                  # 11 pairs
* PAIR F7: 3,7 BLK 8
D8: 3,7,1,4                              # reduction candidate for 3,7
D8: 3,7                                  # 13 pairs
F8: 3,7,1,4                              # reduction candidate for 3,7
F8: 3,7 => CTR
* ...712.96...63..2...69...7.648.59.1..9.1...6...1.76.8..158..64....46.8514..5.1.3.
F8: 1,4                                  # 11 pairs
F9: 3,7,1                                # reduction candidate for 3,7
F9: 3,7                                  # 14 pairs
* PAIR F7: 3,7 ROW 7
A7: 3,7,2,6,9                            # reduction candidate for 3,7
A7: 3,7 => SOLVED
* 584712396179436528236985174842659713793148265651273489315897642927364851468521937
A7: 2,6,9                                # 10 pairs
G7: 3,7,2,6,9                            # reduction candidate for 3,7
G7: 3,7 => CTR
* ....12.96....36.28..6.85.7..4.659....9.148.6..612739846158.734....3648514..5..6..
G7: 2,6,9                                # 10 pairs
I7: 3,7,2,9                              # reduction candidate for 3,7
I7: 3,7                                  # 11 pairs
* PAIR E9: 2,9 ROW 9
C9: 2,9,3,7,8                            # reduction candidate for 2,9
C9: 2,9 => CTR
* ....12.96....36.28..6.85.7..4.659....9.148.6..61273.8.6158.7.4....36485148.5.1637
C9: 3,7,8                                # 10 pairs
G9: 2,9,1,3,6,7                          # reduction candidate for 2,9
G9: 2,9 => SOLVED
* 584712396179436528236985174842659713793148265651273489315897642927364851468521937
G9: 1,3,6,7                              # 10 pairs
I9: 2,9,1,3,7                            # reduction candidate for 2,9
I9: 2,9                                  # 11 pairs
* PAIR H9: 1,3 BLK 9
I8: 1,3,2,7,9                            # reduction candidate for 1,3
I8: 1,3                                  # 11 pairs
G9: 1,3,2,6,7,9                          # reduction candidate for 1,3
G9: 1,3 => CTR
* .8..12.96....36.28..6.85.7.84.659....9.148.6.6.1273984.158.764....3648514685.13..
G9: 2,6,7,9                              # 10 pairs
I9: 1,3,2,7,9                            # reduction candidate for 1,3
I9: 1,3                                  # 13 pairs
* PAIR H9: 1,3 ROW 9
F9: 1,3,7                                # reduction candidate for 1,3
F9: 7                                    # 12 pairs
F9: 1,3                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06909146-base-pr-000.dot
* REASONING
* PRF # A1: 5,7 => SOL
* DIS # B1: 5,7 => CTR => B1: 3,8
* DIS # F2: 5,7 => CTR => F2: 4,6,8
* PRF # D2: 4,7 => SOL
* DIS # F2: 4,7 => CTR => F2: 5,6,8
* DIS # D8: 4,7 => CTR => D8: 1,3
* PRF # D2: 4,9 => SOL
* DIS # F2: 4,8 => CTR => F2: 5,6,7
* DIS # F3: 4,8 => CTR => F3: 5
* DIS # F5: 1,3 => CTR => F5: 4,8
* DIS # D4: 1,3 => CTR => D4: 2,6
* DIS # A7: 2,9 => CTR => A7: 3,6,7
* DIS # G7: 2,9 => CTR => G7: 3,6,7
* DIS # F8: 3,7 => CTR => F8: 1,4
* PRF # A7: 3,7 => SOL
* DIS # G7: 3,7 => CTR => G7: 2,6,9
* DIS # C9: 2,9 => CTR => C9: 3,7,8
* PRF # G9: 2,9 => SOL
* DIS # G9: 1,3 => CTR => G9: 2,6,7,9
* CNT  19 HDP CHAINS /  56 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,D1,D3,E3,E5,E7,E9,F7,H4,H9)
* ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5.....
* PAIR B2: 5,7 BLK 1
A1: 5,7,3,8                              # reduction candidate for 5,7
A1: 5,7 => SOLVED
* 584712396179436528236985174842659713793148265651273489315897642927364851468521937
* DURATION: 0:00:02.661182  START: 06:48:26.813437  END: 06:48:29.474619 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06909146-base-pr-001.dot
* REASONING
* PRF # A1: 5,7 => SOL
* STA A1: 5,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6909146
umulig

* PAIR REDUCTION ..
* ROUND 1: ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5.....
B2: 5,7
A1: 3,5,7,8                              # reduction candidate for 5,7
A1: 5,7 => SOLVED
* 584712396179436528236985174842659713793148265651273489315897642927364851468521937
* SOLVED!

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

D2 != 6,9 / D2 = 4,7 => SOL

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

Solution

position: 584712396179436528236985174842659713793148265651273489315897642927364851468521937 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 # A1: 5,7 => SOL
* INC # A1: 3,8 => UNS
* DIS # B1: 5,7 => CTR => B1: 3,8
* INC # B1: 3,8 => UNS
* INC # A2: 5,7 => UNS
* DIS # F2: 5,7 => CTR => F2: 4,6,8
* INC # F2: 4,6,8 => UNS
* PRF # D2: 4,7 => SOL
* INC # D2: 6,9 => UNS
* DIS # F2: 4,7 => CTR => F2: 5,6,8
* INC # F2: 5,6,8 => UNS
* INC # C1: 4,7 => UNS
* INC # C1: 3,8 => UNS
* DIS # D8: 4,7 => CTR => D8: 1,3
* INC # D8: 1,3 => UNS
* PRF # D2: 4,9 => SOL
* INC # D2: 6,7 => UNS
* DIS # F2: 4,8 => CTR => F2: 5,6,7
* INC # F2: 5,6,7 => UNS
* DIS # F3: 4,8 => CTR => F3: 5
* INC # F3: 5 => UNS
* INC # I3: 4,8 => UNS
* INC # I3: 1,3,5 => UNS
* INC # F5: 4,8 => UNS
* DIS # F5: 1,3 => CTR => F5: 4,8
* INC # G4: 1,3 => UNS
* INC # I4: 1,3 => UNS
* INC # G5: 1,3 => UNS
* INC # I5: 1,3 => UNS
* DIS # D4: 1,3 => CTR => D4: 2,6
* INC # D4: 2,6 => UNS
* DIS # A7: 2,9 => CTR => A7: 3,6,7
* INC # A7: 3,6,7 => UNS
* DIS # G7: 2,9 => CTR => G7: 3,6,7
* INC # G7: 3,6,7 => UNS
* INC # I7: 2,9 => UNS
* INC # D8: 3,7 => UNS
* DIS # F8: 3,7 => CTR => F8: 1,4
* INC # F8: 1,4 => UNS
* INC # F9: 3,7 => UNS
* PRF # A7: 3,7 => SOL
* INC # A7: 2,6,9 => UNS
* DIS # G7: 3,7 => CTR => G7: 2,6,9
* INC # G7: 2,6,9 => UNS
* INC # I7: 3,7 => UNS
* DIS # C9: 2,9 => CTR => C9: 3,7,8
* INC # C9: 3,7,8 => UNS
* PRF # G9: 2,9 => SOL
* INC # G9: 1,3,6,7 => UNS
* INC # I9: 2,9 => UNS
* INC # I8: 1,3 => UNS
* DIS # G9: 1,3 => CTR => G9: 2,6,7,9
* INC # G9: 2,6,7,9 => UNS
* INC # I9: 1,3 => UNS
* INC # F9: 1,3 => UNS
* INC # F9: 7 => UNS
* CNT  56 HDP CHAINS /  56 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A1: 5,7 => SOL
* STA A1: 5,7
* CNT   1 HDP CHAINS /   1 HYP OPENED