# Original Sudoku

level: medium

position: 32.....75..93.21..6.......8..81.47..2.......1..57.96..1.......6..74.83..84.....17 initial

# Autosolve

position: 32....97578935216465.9..238938164752276...49141572968319....84656741832984..9.517 autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* PRF # F7: 3,5 => SOL
* DIS # F7: 7 => CTR => F7: 3,5
* PRF # F7: 3,7 => SOL
* DIS # F7: 5 => CTR => F7: 3,7
* CNT   4 HDP CHAINS /   4 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* PRF # F7: 3,5 => SOL
* STA F7: 3,5
* CNT   1 HDP CHAINS /   1 HYP OPENED
```

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

# Details

## Positions

 32.....75..93.21..6.......8..81.47..2.......1..57.96..1.......6..74.83..84.....17 initial 32....97578935216465.9..238938164752276...49141572968319....84656741832984..9.517 autosolve 324681975789352164651947238938164752276835491415729683192573846567418329843296517 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (16)
C1: 1,4
C3: 1,4
D1: 6,8
E1: 4,8
F1: 1,6
E3: 4,7
F3: 1,7
D5: 5,8
E5: 3,8
F5: 3,5
C7: 2,3
C9: 2,3
D7: 2,5
E7: 3,7
D9: 2,6
F9: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,C3: 1.. / C1 = 1  =>  0 pairs (X) / C3 = 1  =>  0 pairs (_)
F1,F3: 1.. / F1 = 1  =>  0 pairs (*) / F3 = 1  =>  0 pairs (X)
C1,F1: 1.. / C1 = 1  =>  0 pairs (X) / F1 = 1  =>  0 pairs (_)
C3,F3: 1.. / C3 = 1  =>  0 pairs (*) / F3 = 1  =>  0 pairs (X)
C7,C9: 2.. / C7 = 2  =>  0 pairs (*) / C9 = 2  =>  0 pairs (X)
D7,D9: 2.. / D7 = 2  =>  0 pairs (X) / D9 = 2  =>  0 pairs (_)
C7,D7: 2.. / C7 = 2  =>  0 pairs (*) / D7 = 2  =>  0 pairs (X)
C9,D9: 2.. / C9 = 2  =>  0 pairs (X) / D9 = 2  =>  0 pairs (_)
E5,F5: 3.. / E5 = 3  =>  0 pairs (*) / F5 = 3  =>  0 pairs (X)
C7,C9: 3.. / C7 = 3  =>  0 pairs (X) / C9 = 3  =>  0 pairs (_)
C9,F9: 3.. / C9 = 3  =>  0 pairs (*) / F9 = 3  =>  0 pairs (X)
E5,E7: 3.. / E5 = 3  =>  0 pairs (*) / E7 = 3  =>  0 pairs (X)
C1,C3: 4.. / C1 = 4  =>  0 pairs (*) / C3 = 4  =>  0 pairs (X)
E1,E3: 4.. / E1 = 4  =>  0 pairs (X) / E3 = 4  =>  0 pairs (_)
C1,E1: 4.. / C1 = 4  =>  0 pairs (*) / E1 = 4  =>  0 pairs (X)
C3,E3: 4.. / C3 = 4  =>  0 pairs (X) / E3 = 4  =>  0 pairs (_)
D5,F5: 5.. / D5 = 5  =>  0 pairs (X) / F5 = 5  =>  0 pairs (_)
D7,F7: 5.. / D7 = 5  =>  0 pairs (*) / F7 = 5  =>  0 pairs (X)
D5,D7: 5.. / D5 = 5  =>  0 pairs (X) / D7 = 5  =>  0 pairs (_)
F5,F7: 5.. / F5 = 5  =>  0 pairs (*) / F7 = 5  =>  0 pairs (X)
D1,F1: 6.. / D1 = 6  =>  0 pairs (*) / F1 = 6  =>  0 pairs (X)
D9,F9: 6.. / D9 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
D1,D9: 6.. / D1 = 6  =>  0 pairs (*) / D9 = 6  =>  0 pairs (X)
F1,F9: 6.. / F1 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
E3,F3: 7.. / E3 = 7  =>  0 pairs (X) / F3 = 7  =>  0 pairs (_)
E7,F7: 7.. / E7 = 7  =>  0 pairs (*) / F7 = 7  =>  0 pairs (X)
E3,E7: 7.. / E3 = 7  =>  0 pairs (X) / E7 = 7  =>  0 pairs (_)
F3,F7: 7.. / F3 = 7  =>  0 pairs (*) / F7 = 7  =>  0 pairs (X)
D1,E1: 8.. / D1 = 8  =>  0 pairs (X) / E1 = 8  =>  0 pairs (_)
D5,E5: 8.. / D5 = 8  =>  0 pairs (*) / E5 = 8  =>  0 pairs (X)
D1,D5: 8.. / D1 = 8  =>  0 pairs (X) / D5 = 8  =>  0 pairs (_)
E1,E5: 8.. / E1 = 8  =>  0 pairs (*) / E5 = 8  =>  0 pairs (X)
* DURATION: 0:00:52.724705  START: 08:49:43.046008  END: 08:50:35.770713 2017-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,C3,C7,C9,D1,D5,D7,D9,E1,E3,E5,E7,F1,F3,F5,F9)
* 32....97578935216465.9..238938164752276...49141572968319....84656741832984..9.517
* PAIR F5: 3,5 COL F
F7: 3,5,7                                # reduction candidate for 3,5
F7: 3,5 => SOLVED
* 324681975789352164651947238938164752276835491415729683192573846567418329843296517
F7: 7 => CTR
* 32....97578935216465.9..238938164752276..549141572968319.5.784656741832984.29.517
* PAIR E7: 3,7 BLK 8
F7: 3,7,5                                # reduction candidate for 3,7
F7: 3,7 => SOLVED
* 324681975789352164651947238938164752276835491415729683192573846567418329843296517
F7: 5 => CTR
* 32....97578935216465.9.7238938164752276...49141572968319..7584656741832984..93517
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-787906-base-pr-000.dot
* REASONING
* PRF # F7: 3,5 => SOL
* DIS # F7: 7 => CTR => F7: 3,5
* PRF # F7: 3,7 => SOL
* DIS # F7: 5 => CTR => F7: 3,7
* CNT   4 HDP CHAINS /   4 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,C3,C7,C9,D1,D5,D7,D9,E1,E3,E5,E7,F1,F3,F5,F9)
* 32....97578935216465.9..238938164752276...49141572968319....84656741832984..9.517
* PAIR F5: 3,5 COL F
F7: 3,5,7                                # reduction candidate for 3,5
F7: 3,5 => SOLVED
* 324681975789352164651947238938164752276835491415729683192573846567418329843296517
* DURATION: 0:00:02.157297  START: 08:50:41.620761  END: 08:50:43.778058 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-787906-base-pr-001.dot
* REASONING
* PRF # F7: 3,5 => SOL
* STA F7: 3,5
* CNT   1 HDP CHAINS /   1 HYP OPENED
```

```http://www.sudokus.de/787906.html
sehr schwierig

--------------------------------------------------
level: medium

* PAIR REDUCTION ..
* ROUND 1: 32....97578935216465.9..238938164752276...49141572968319....84656741832984..9.517
C1: 1,4
C3: 1,4
D1: 6,8
E1: 4,8
F1: 1,6
E3: 4,7
F3: 1,7
D5: 5,8
E5: 3,8
F5: 3,5
F7: 3,5,7                                # reduction candidate for 3,5
F7: 3,5 => SOLVED
* 324681975789352164651947238938164752276835491415729683192573846567418329843296517
* SOLVED!
--------------------------------------------------

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

pair reduction
* DISABLE VALUE:: F7 != 5

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

# Solution

position: 324681975789352164651947238938164752276835491415729683192573846567418329843296517 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 # F7: 3,5 => SOL
* DIS # F7: 7 => CTR => F7: 3,5
* PRF # F7: 3,7 => SOL
* DIS # F7: 5 => CTR => F7: 3,7
* CNT   4 HDP CHAINS /   4 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* PRF # F7: 3,5 => SOL
* STA F7: 3,5
* CNT   1 HDP CHAINS /   1 HYP OPENED
```