# Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6913279

level: medium

position: 89.4.....4....6.....3....5..34.....8...3..7.66....89....1..5.8....2....3....6..9. initial

# Autosolve

position: 89.4.....4....6.....3....5..346....8...3..7.66....893...1..5.8....2....3....6..9. autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # G4: 1,2 => CTR => G4: 5
* DIS # H5: 1,2 => CTR => H5: 4
* DIS # H1: 1,2 => CTR => H1: 6,7
* DIS # E8: 7,9 => CTR => E8: 1,4,8
* DIS # A7: 7,9 => CTR => A7: 2,3
* CNT   5 HDP CHAINS /  19 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # G4: 1,2 => CTR => G4: 5
* DIS G4: 5 # H5: 1,2 => CTR => H5: 4
* DIS G4: 5 + H5: 4 # H1: 1,2 => CTR => H1: 6,7
* DIS G4: 5 + H5: 4 + H1: 6,7 # H2: 7 => CTR => H2: 1,2
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E8: 7,9 => CTR => E8: 1,8
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 # F8: 7,9 => CTR => F8: 1,4
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 # E7: 3 => CTR => E7: 7,9
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 # D3: 7,9 => CTR => D3: 8
* PRF G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 # B2: 2,7 => SOL
* STA G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 + B2: 2,7
* CNT   9 HDP CHAINS /  20 HYP OPENED
```

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

# Details

## Positions

 89.4.....4....6.....3....5..34.....8...3..7.66....89....1..5.8....2....3....6..9. initial 89.4.....4....6.....3....5..346....8...3..7.66....893...1..5.8....2....3....6..9. autosolve 892451367475936821163827459234679518589312746617548932321795684956284173748163295 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (2)
H4: 1,2
D7: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G1,G2: 3.. / G1 = 3  =>  2 pairs (_) / G2 = 3  => 16 pairs (_)
A7,A9: 3.. / A7 = 3  =>  2 pairs (_) / A9 = 3  => 16 pairs (_)
E7,F9: 3.. / E7 = 3  => 16 pairs (_) / F9 = 3  =>  2 pairs (_)
E2,G2: 3.. / E2 = 3  =>  2 pairs (_) / G2 = 3  => 16 pairs (_)
A7,E7: 3.. / A7 = 3  =>  2 pairs (_) / E7 = 3  => 16 pairs (_)
A9,F9: 3.. / A9 = 3  => 16 pairs (_) / F9 = 3  =>  2 pairs (_)
F1,F9: 3.. / F1 = 3  => 16 pairs (_) / F9 = 3  =>  2 pairs (_)
G3,I3: 4.. / G3 = 4  =>  4 pairs (_) / I3 = 4  =>  5 pairs (_)
H5,I6: 4.. / H5 = 4  =>  2 pairs (_) / I6 = 4  =>  0 pairs (X)
E6,I6: 4.. / E6 = 4  =>  2 pairs (_) / I6 = 4  =>  0 pairs (X)
H5,H8: 4.. / H5 = 4  =>  2 pairs (_) / H8 = 4  =>  0 pairs (X)
G4,I6: 5.. / G4 = 5  =>  2 pairs (_) / I6 = 5  =>  0 pairs (X)
C1,E1: 5.. / C1 = 5  =>  8 pairs (_) / E1 = 5  =>  3 pairs (_)
D2,D6: 5.. / D2 = 5  =>  6 pairs (_) / D6 = 5  =>  3 pairs (_)
I6,I9: 5.. / I6 = 5  =>  0 pairs (X) / I9 = 5  =>  2 pairs (_)
C1,B3: 6.. / C1 = 6  =>  0 pairs (X) / B3 = 6  =>  3 pairs (_)
B3,G3: 6.. / B3 = 6  =>  3 pairs (_) / G3 = 6  =>  0 pairs (X)
B7,G7: 6.. / B7 = 6  =>  0 pairs (X) / G7 = 6  =>  3 pairs (_)
C1,C8: 6.. / C1 = 6  =>  0 pairs (X) / C8 = 6  =>  3 pairs (_)
H1,H8: 6.. / H1 = 6  =>  3 pairs (_) / H8 = 6  =>  0 pairs (X)
G2,G3: 8.. / G2 = 8  =>  2 pairs (_) / G3 = 8  => 15 pairs (_)
B5,C5: 8.. / B5 = 8  =>  2 pairs (_) / C5 = 8  =>  0 pairs (X)
E8,D9: 8.. / E8 = 8  =>  3 pairs (_) / D9 = 8  =>  0 pairs (X)
I2,I3: 9.. / I2 = 9  =>  2 pairs (_) / I3 = 9  => 14 pairs (_)
C5,C8: 9.. / C5 = 9  =>  2 pairs (_) / C8 = 9  =>  0 pairs (X)
* DURATION: 0:00:30.482086  START: 07:08:19.874099  END: 07:08:50.356185 2017-05-01
* CP COUNT: (25)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D7,H4)
* 89.4.....4....6.....3....5..346....8...3..7.66....893...1..5.8....2....3....6..9.
* PAIR H4: 1,2 BLK 6
G4: 1,2,5                                # reduction candidate for 1,2
G4: 1,2 => CTR
* 8954..36.4.75368191638...5.7346591285893..7466127489353.197568.9.6284573..8163.9.
G4: 5                                    #  2 pairs
H5: 1,2,4                                # reduction candidate for 1,2
H5: 1,2 => CTR
* 89745.36.4...3687..63...45..346..5.8..93..7.66....8934321945687956287143748163295
H5: 4                                    #  2 pairs
I6: 1,2,4,5                              # reduction candidate for 1,2
I6: 1,2                                  #  3 pairs
* PAIR H4: 1,2 ROW 4
A4: 1,2,5,7,9                            # reduction candidate for 1,2
A4: 1,2                                  #  6 pairs
E4: 1,2,5,7,9                            # reduction candidate for 1,2
E4: 1,2                                  #  5 pairs
F4: 1,2,7,9                              # reduction candidate for 1,2
F4: 1,2                                  #  5 pairs
* PAIR H4: 1,2 COL H
H1: 1,2,6,7                              # reduction candidate for 1,2
H1: 1,2 => CTR
* 8964573..4...36879..3...654.3467.5.8...3..7466..54893.361.9548....2...63....6..95
H1: 6,7                                  #  3 pairs
H2: 1,2,7                                # reduction candidate for 1,2
H2: 1,2                                  #  5 pairs
* PAIR D7: 7,9 BLK 8
E7: 7,9,3,4                              # reduction candidate for 7,9
E7: 7,9                                  #  6 pairs
E8: 7,9,1,4,8                            # reduction candidate for 7,9
E8: 7,9 => CTR
* 89645....4....6.....3...654.346....8...3..7466..54893..61.3548....2....3...86..9.
E8: 1,4,8                                #  2 pairs
F8: 7,9,1,4                              # reduction candidate for 7,9
F8: 7,9                                  #  5 pairs
* PAIR D7: 7,9 ROW 7
A7: 7,9,2,3                              # reduction candidate for 7,9
A7: 7,9 => CTR
* 89.4.3.6741.8.6329.63...854.346....8.893..7466..548931.41.35682..628...3328.6..95
A7: 2,3                                  #  3 pairs
* PAIR D7: 7,9 COL D
D2: 7,9,1,5,8                            # reduction candidate for 7,9
D2: 7,9                                  #  8 pairs
D3: 7,9,1,8                              # reduction candidate for 7,9
D3: 7,9                                  #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06913279-base-pr-000.dot
* REASONING
* DIS # G4: 1,2 => CTR => G4: 5
* DIS # H5: 1,2 => CTR => H5: 4
* DIS # H1: 1,2 => CTR => H1: 6,7
* DIS # E8: 7,9 => CTR => E8: 1,4,8
* DIS # A7: 7,9 => CTR => A7: 2,3
* CNT   5 HDP CHAINS /  19 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D7,H4)
* 89.4.....4....6.....3....5..346....8...3..7.66....893...1..5.8....2....3....6..9.
* PAIR H4: 1,2 BLK 6
G4: 1,2,5                                # reduction candidate for 1,2
G4: 1,2 => CTR
* 8954..36.4.75368191638...5.7346591285893..7466127489353.197568.9.6284573..8163.9.
H5: 1,2,4                                # reduction candidate for 1,2
H5: 1,2 => CTR
* 89745.36.4...3687..63...45..346..5.8..93..7.66....8934321945687956287143748163295
* RESTART
* PAIR H4: 1,2 ROW 4
A4: 1,2,7,9                              # reduction candidate for 1,2
A4: 1,2                                  #  8 pairs
E4: 1,2,7,9                              # reduction candidate for 1,2
E4: 1,2                                  #  6 pairs
F4: 1,2,7,9                              # reduction candidate for 1,2
F4: 1,2                                  #  6 pairs
* PAIR H4: 1,2 COL H
H1: 1,2,6,7                              # reduction candidate for 1,2
H1: 1,2 => CTR
* 8964573..4...36879..3...654.3467.5.8...3..7466..54893..61..5487...2..163....6.295
H2: 1,2,7                                # reduction candidate for 1,2
H2: 1,2                                  #  6 pairs
* RESTART
* PAIR H4: 1,2 COL H
H2: 1,2,7                                # reduction candidate for 1,2
H2: 7 => CTR
* 89.4.31624..8.6379.637..8547346..5285.93..7466...489312419356879562874133.8164295
* PAIR RESTART
* PAIR H4: 1,2 ROW 4
A4: 1,2,7,9                              # reduction candidate for 1,2
A4: 1,2                                  # 11 pairs
E4: 1,2,7,9                              # reduction candidate for 1,2
E4: 1,2                                  #  9 pairs
F4: 1,2,7,9                              # reduction candidate for 1,2
F4: 1,2                                  #  9 pairs
* PAIR D7: 7,9 BLK 8
E7: 7,9,3                                # reduction candidate for 7,9
E7: 7,9                                  # 19 pairs
E8: 7,9,1,8                              # reduction candidate for 7,9
E8: 7,9 => CTR
* 8964532714....6.....3....5..346..5.8...3..7466...4893...1..5.8....2....3...86..95
F8: 7,9,1,4                              # reduction candidate for 7,9
F8: 7,9 => CTR
* 89.4.32674....6319163...854.346..528..93..7466..14893...1.3568...62..4733...64195
* RESTART
* PAIR D7: 7,9 BLK 8
E7: 7,9,3                                # reduction candidate for 7,9
E7: 3 => CTR
* 89.4.32674....63191637..854.34671528.1.3..7466...4893...193568...62...733...6..95
* PAIR D7: 7,9 COL D
D2: 7,9,8                                # reduction candidate for 7,9
D2: 7,9                                  # 19 pairs
D3: 7,9,8                                # reduction candidate for 7,9
D3: 7,9 => CTR
* 89.4...674..8.6.19163.2.8542346..5.85893..7466..54893.341..5682956284173..8163495
* RESTART
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A4,A9,B7,C1,C6,D2,D7,E3,E4,E5,E7,F4,F5,G3,G9,H2,H4,I6,I7)
* 89.45.36.4.5.368...638...5..346..5.85893..7466..54893.3.1..568.956284173..8163.95
* PAIR C1: 2,7 BLK 1
B2: 2,7,1                                # reduction candidate for 2,7
B2: 2,7 => SOLVED
* 892451367475936821163827459234679518589312746617548932321795684956284173748163295
* DURATION: 0:00:19.035519  START: 07:09:01.943432  END: 07:09:20.978951 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06913279-base-pr-001.dot
* REASONING
* DIS # G4: 1,2 => CTR => G4: 5
* DIS G4: 5 # H5: 1,2 => CTR => H5: 4
* DIS G4: 5 + H5: 4 # H1: 1,2 => CTR => H1: 6,7
* DIS G4: 5 + H5: 4 + H1: 6,7 # H2: 7 => CTR => H2: 1,2
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E8: 7,9 => CTR => E8: 1,8
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 # F8: 7,9 => CTR => F8: 1,4
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 # E7: 3 => CTR => E7: 7,9
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 # D3: 7,9 => CTR => D3: 8
* PRF G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 # B2: 2,7 => SOL
* STA G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 + B2: 2,7
* CNT   9 HDP CHAINS /  20 HYP OPENED
```

```http://www.menneske.no/sudoku/utskrift.html?number=6913279
umulig
```

# Solution

position: 892451367475936821163827459234679518589312746617548932321795684956284173748163295 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:

```* DIS # G4: 1,2 => CTR => G4: 5
* INC # G4: 5 => UNS
* DIS # H5: 1,2 => CTR => H5: 4
* INC # H5: 4 => UNS
* INC # I6: 1,2 => UNS
* INC # A4: 1,2 => UNS
* INC # E4: 1,2 => UNS
* INC # F4: 1,2 => UNS
* DIS # H1: 1,2 => CTR => H1: 6,7
* INC # H1: 6,7 => UNS
* INC # H2: 1,2 => UNS
* INC # E7: 7,9 => UNS
* DIS # E8: 7,9 => CTR => E8: 1,4,8
* INC # E8: 1,4,8 => UNS
* INC # F8: 7,9 => UNS
* DIS # A7: 7,9 => CTR => A7: 2,3
* INC # A7: 2,3 => UNS
* INC # D2: 7,9 => UNS
* INC # D3: 7,9 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* DIS # G4: 1,2 => CTR => G4: 5
* DIS G4: 5 # H5: 1,2 => CTR => H5: 4
* INC G4: 5 + H5: 4 # A4: 1,2 => UNS
* INC G4: 5 + H5: 4 # E4: 1,2 => UNS
* INC G4: 5 + H5: 4 # F4: 1,2 => UNS
* DIS G4: 5 + H5: 4 # H1: 1,2 => CTR => H1: 6,7
* INC G4: 5 + H5: 4 + H1: 6,7 # H2: 1,2 => UNS
* INC G4: 5 + H5: 4 + H1: 6,7 # H2: 1,2 => UNS
* DIS G4: 5 + H5: 4 + H1: 6,7 # H2: 7 => CTR => H2: 1,2
* INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # A4: 1,2 => UNS
* INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E4: 1,2 => UNS
* INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # F4: 1,2 => UNS
* INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E7: 7,9 => UNS
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 # E8: 7,9 => CTR => E8: 1,8
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 # F8: 7,9 => CTR => F8: 1,4
* INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 # E7: 7,9 => UNS
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 # E7: 3 => CTR => E7: 7,9
* INC G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 # D2: 7,9 => UNS
* DIS G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 # D3: 7,9 => CTR => D3: 8
* PRF G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 # B2: 2,7 => SOL
* STA G4: 5 + H5: 4 + H1: 6,7 + H2: 1,2 + E8: 1,8 + F8: 1,4 + E7: 7,9 + D3: 8 + B2: 2,7
* CNT  20 HDP CHAINS /  20 HYP OPENED
```