# Original Sudoku

level: medium

position: .7......8.8..6..9....9.45....3...4.54..2....38.....9....9..6....6..5..1.7....1... initial

# Autosolve

position: 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1... autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # A2: 2,3 => CTR => A2: 1,5
* PRF # A3: 2,3 => SOL
* CNT   2 HDP CHAINS /  13 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # A2: 2,3 => CTR => A2: 1,5
* PRF A2: 1,5 # A3: 2,3 => SOL
* STA A2: 1,5 + A3: 2,3
* CNT   2 HDP CHAINS /   7 HYP OPENED
```

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

# Details

## Positions

 .7......8.8..6..9....9.45....3...4.54..2....38.....9....9..6....6..5..1.7....1... initial 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1... autosolve 976532148584167392231984567613879425497215683825643971159726834362458719748391256 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (2)
A8: 2,3
C8: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G5,I6: 1.. / G5 = 1  =>  6 pairs (_) / I6 = 1  =>  4 pairs (_)
A7,B7: 1.. / A7 = 1  =>  4 pairs (_) / B7 = 1  =>  9 pairs (_)
C1,C2: 4.. / C1 = 4  =>  8 pairs (_) / C2 = 4  =>  3 pairs (_)
H1,I2: 4.. / H1 = 4  =>  3 pairs (_) / I2 = 4  =>  8 pairs (_)
D6,E6: 4.. / D6 = 4  =>  0 pairs (X) / E6 = 4  =>  2 pairs (_)
B7,B9: 4.. / B7 = 4  =>  6 pairs (_) / B9 = 4  =>  3 pairs (_)
C1,H1: 4.. / C1 = 4  =>  8 pairs (_) / H1 = 4  =>  3 pairs (_)
C2,I2: 4.. / C2 = 4  =>  3 pairs (_) / I2 = 4  =>  8 pairs (_)
D8,I8: 4.. / D8 = 4  =>  3 pairs (_) / I8 = 4  =>  6 pairs (_)
H7,H9: 5.. / H7 = 5  =>  4 pairs (_) / H9 = 5  =>  9 pairs (_)
A2,A7: 5.. / A2 = 5  =>  3 pairs (_) / A7 = 5  =>  0 pairs (X)
D4,D6: 6.. / D4 = 6  =>  7 pairs (_) / D6 = 6  =>  7 pairs (_)
A3,A4: 6.. / A3 = 6  =>  7 pairs (_) / A4 = 6  =>  0 pairs (*)
D2,F2: 7.. / D2 = 7  => 16 pairs (_) / F2 = 7  =>  4 pairs (_)
H3,I3: 7.. / H3 = 7  =>  9 pairs (_) / I3 = 7  =>  3 pairs (_)
C5,C6: 7.. / C5 = 7  =>  6 pairs (_) / C6 = 7  =>  4 pairs (_)
C8,C9: 8.. / C8 = 8  =>  2 pairs (_) / C9 = 8  => 10 pairs (_)
B4,B5: 9.. / B4 = 9  =>  5 pairs (_) / B5 = 9  =>  4 pairs (_)
F8,E9: 9.. / F8 = 9  =>  4 pairs (_) / E9 = 9  => 10 pairs (_)
I8,I9: 9.. / I8 = 9  => 10 pairs (_) / I9 = 9  =>  4 pairs (_)
F8,I8: 9.. / F8 = 9  =>  4 pairs (_) / I8 = 9  => 10 pairs (_)
E9,I9: 9.. / E9 = 9  => 10 pairs (_) / I9 = 9  =>  4 pairs (_)
* DURATION: 0:00:26.095615  START: 06:48:44.239839  END: 06:49:10.335454 2017-05-01
* CP COUNT: (22)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C8)
* 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1...
* PAIR A8: 2,3 BLK 7
A7: 2,3,1,5                              # reduction candidate for 2,3
A7: 2,3                                  # 11 pairs
B7: 2,3,1,4,5                            # reduction candidate for 2,3
B7: 2,3                                  #  7 pairs
B9: 2,3,4,5                              # reduction candidate for 2,3
B9: 2,3                                  #  6 pairs
* PAIR A8: 2,3 ROW 8
F8: 2,3,7,8,9                            # reduction candidate for 2,3
F8: 2,3                                  # 17 pairs
G8: 2,3,7,8                              # reduction candidate for 2,3
G8: 2,3                                  #  6 pairs
* PAIR A8: 2,3 COL A
A2: 2,3,1,5                              # reduction candidate for 2,3
A2: 2,3 => CTR
* 9741..6.828..6.1946319845.21.3.7.4.54.621.7838.7.4.9.1519..6.4736.457.1974..91.56
A2: 1,5                                  #  4 pairs
A3: 2,3,1,6                              # reduction candidate for 2,3
A3: 2,3 => SOLVED
* 976532148584167392231984567613879425497215683825643971159726834362458719748391256
A3: 1,6                                  #  3 pairs
* PAIR C8: 2,8 BLK 7
C9: 2,8,5                                # reduction candidate for 2,8
C9: 2,8                                  #  7 pairs
C9: 5                                    #  3 pairs
* PAIR C8: 2,8 ROW 8
F8: 2,8,3,7,9                            # reduction candidate for 2,8
F8: 2,8                                  # 13 pairs
G8: 2,8,3,7                              # reduction candidate for 2,8
G8: 2,8                                  #  6 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06910690-base-pr-000.dot
* REASONING
* DIS # A2: 2,3 => CTR => A2: 1,5
* PRF # A3: 2,3 => SOL
* CNT   2 HDP CHAINS /  13 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C8)
* 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1...
* PAIR A8: 2,3 BLK 7
A7: 2,3,1,5                              # reduction candidate for 2,3
A7: 2,3                                  # 11 pairs
B7: 2,3,1,4,5                            # reduction candidate for 2,3
B7: 2,3                                  #  7 pairs
B9: 2,3,4,5                              # reduction candidate for 2,3
B9: 2,3                                  #  6 pairs
* PAIR A8: 2,3 ROW 8
F8: 2,3,7,8,9                            # reduction candidate for 2,3
F8: 2,3                                  # 17 pairs
G8: 2,3,7,8                              # reduction candidate for 2,3
G8: 2,3                                  #  6 pairs
* PAIR A8: 2,3 COL A
A2: 2,3,1,5                              # reduction candidate for 2,3
A2: 2,3 => CTR
* 9741..6.828..6.1946319845.21.3.7.4.54.621.7838.7.4.9.1519..6.4736.457.1974..91.56
A3: 2,3,1,6                              # reduction candidate for 2,3
A3: 2,3 => SOLVED
* 976532148584167392231984567613879425497215683825643971159726834362458719748391256
* DURATION: 0:00:07.641991  START: 06:49:20.961498  END: 06:49:28.603489 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06910690-base-pr-001.dot
* REASONING
* DIS # A2: 2,3 => CTR => A2: 1,5
* PRF A2: 1,5 # A3: 2,3 => SOL
* STA A2: 1,5 + A3: 2,3
* CNT   2 HDP CHAINS /   7 HYP OPENED
```

```http://www.menneske.no/sudoku/utskrift.html?number=6910690
umulig

* PAIR REDUCTION ..
* ROUND 1: 97......8.8..6..9....9845....3...4.54..2....38.....9....9..6....6..5..1.7....1...
A8: 2,3
A7: 1,2,3,5                              # reduction candidate for 2,3
B7: 1,2,3,4,5                            # reduction candidate for 2,3
B9: 2,3,4,5                              # reduction candidate for 2,3
F8: 2,3,7,8,9                            # reduction candidate for 2,3
G8: 2,3,7,8                              # reduction candidate for 2,3
A2: 1,2,3,5                              # reduction candidate for 2,3
A2: 2,3 => CTR
* 9741..6.828..6.1946319845.21.3.7.4.54.621.7838.7.4.9.1519..6.4736.457.1974..91.56
A3: 1,2,3,6                              # reduction candidate for 2,3
A3: 2,3 => SOLVED
* 976532148584167392231984567613879425497215683825643971159726834362458719748391256
* SOLVED!

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

C1 = 6 => SOL

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

# Solution

position: 976532148584167392231984567613879425497215683825643971159726834362458719748391256 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:

```* INC # A7: 2,3 => UNS
* INC # B7: 2,3 => UNS
* INC # B9: 2,3 => UNS
* INC # F8: 2,3 => UNS
* INC # G8: 2,3 => UNS
* DIS # A2: 2,3 => CTR => A2: 1,5
* INC # A2: 1,5 => UNS
* PRF # A3: 2,3 => SOL
* INC # A3: 1,6 => UNS
* INC # C9: 2,8 => UNS
* INC # C9: 5 => UNS
* INC # F8: 2,8 => UNS
* INC # G8: 2,8 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # A7: 2,3 => UNS
* INC # B7: 2,3 => UNS
* INC # B9: 2,3 => UNS
* INC # F8: 2,3 => UNS
* INC # G8: 2,3 => UNS
* DIS # A2: 2,3 => CTR => A2: 1,5
* PRF A2: 1,5 # A3: 2,3 => SOL
* STA A2: 1,5 + A3: 2,3
* CNT   7 HDP CHAINS /   7 HYP OPENED
```