# Original Sudoku

level: medium

position: ..2..5..13...7......5...29.5..71...27..5.8..68...24..7.46...1......3...41..9..6.. initial

# Autosolve

position: 492365..13..27946567548129356.713..272.5983.68..624..72468571399..136.241..9426.8 autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* PRF # C6: 1,3 => SOL
* DIS # C6: 9 => CTR => C6: 1,3
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* PRF # C6: 1,3 => SOL
* STA C6: 1,3
* CNT   1 HDP CHAINS /   1 HYP OPENED
```

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

# Details

## Positions

 ..2..5..13...7......5...29.5..71...27..5.8..68...24..7.46...1......3...41..9..6.. initial 492365..13..27946567548129356.713..272.5983.68..624..72468571399..136.241..9426.8 autosolve 492365781318279465675481293569713842724598316831624957246857139987136524153942678 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (18)
B2: 1,8
C2: 1,8
G1: 7,8
H1: 7,8
C4: 4,9
C5: 1,4
B6: 1,3
G4: 8,9
H4: 4,8
H5: 1,4
G6: 5,9
H6: 1,5
B8: 5,8
C8: 7,8
B9: 3,5
C9: 3,7
G8: 5,7
H9: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B2,C2: 1.. / B2 = 1  =>  0 pairs (*) / C2 = 1  =>  0 pairs (X)
H5,H6: 1.. / H5 = 1  =>  0 pairs (*) / H6 = 1  =>  0 pairs (X)
C5,H5: 1.. / C5 = 1  =>  0 pairs (X) / H5 = 1  =>  0 pairs (_)
B2,B6: 1.. / B2 = 1  =>  0 pairs (*) / B6 = 1  =>  0 pairs (X)
B6,C6: 3.. / B6 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
B9,C9: 3.. / B9 = 3  =>  0 pairs (X) / C9 = 3  =>  0 pairs (_)
B6,B9: 3.. / B6 = 3  =>  0 pairs (*) / B9 = 3  =>  0 pairs (X)
C6,C9: 3.. / C6 = 3  =>  0 pairs (X) / C9 = 3  =>  0 pairs (_)
C4,C5: 4.. / C4 = 4  =>  0 pairs (X) / C5 = 4  =>  0 pairs (_)
H4,H5: 4.. / H4 = 4  =>  0 pairs (*) / H5 = 4  =>  0 pairs (X)
C4,H4: 4.. / C4 = 4  =>  0 pairs (X) / H4 = 4  =>  0 pairs (_)
C5,H5: 4.. / C5 = 4  =>  0 pairs (*) / H5 = 4  =>  0 pairs (X)
G6,H6: 5.. / G6 = 5  =>  0 pairs (X) / H6 = 5  =>  0 pairs (_)
B8,B9: 5.. / B8 = 5  =>  0 pairs (X) / B9 = 5  =>  0 pairs (_)
G8,H9: 5.. / G8 = 5  =>  0 pairs (*) / H9 = 5  =>  0 pairs (X)
B8,G8: 5.. / B8 = 5  =>  0 pairs (X) / G8 = 5  =>  0 pairs (_)
B9,H9: 5.. / B9 = 5  =>  0 pairs (*) / H9 = 5  =>  0 pairs (X)
G6,G8: 5.. / G6 = 5  =>  0 pairs (X) / G8 = 5  =>  0 pairs (_)
H6,H9: 5.. / H6 = 5  =>  0 pairs (*) / H9 = 5  =>  0 pairs (X)
G1,H1: 7.. / G1 = 7  =>  0 pairs (*) / H1 = 7  =>  0 pairs (X)
C8,C9: 7.. / C8 = 7  =>  0 pairs (*) / C9 = 7  =>  0 pairs (X)
G8,H9: 7.. / G8 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
C8,G8: 7.. / C8 = 7  =>  0 pairs (*) / G8 = 7  =>  0 pairs (X)
C9,H9: 7.. / C9 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
G1,G8: 7.. / G1 = 7  =>  0 pairs (*) / G8 = 7  =>  0 pairs (X)
H1,H9: 7.. / H1 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
B2,C2: 8.. / B2 = 8  =>  0 pairs (X) / C2 = 8  =>  0 pairs (_)
G1,H1: 8.. / G1 = 8  =>  0 pairs (X) / H1 = 8  =>  0 pairs (_)
G4,H4: 8.. / G4 = 8  =>  0 pairs (*) / H4 = 8  =>  0 pairs (X)
B8,C8: 8.. / B8 = 8  =>  0 pairs (*) / C8 = 8  =>  0 pairs (X)
B2,B8: 8.. / B2 = 8  =>  0 pairs (X) / B8 = 8  =>  0 pairs (_)
C2,C8: 8.. / C2 = 8  =>  0 pairs (*) / C8 = 8  =>  0 pairs (X)
G1,G4: 8.. / G1 = 8  =>  0 pairs (X) / G4 = 8  =>  0 pairs (_)
H1,H4: 8.. / H1 = 8  =>  0 pairs (*) / H4 = 8  =>  0 pairs (X)
C4,C6: 9.. / C4 = 9  =>  0 pairs (*) / C6 = 9  =>  0 pairs (X)
G4,G6: 9.. / G4 = 9  =>  0 pairs (X) / G6 = 9  =>  0 pairs (_)
C4,G4: 9.. / C4 = 9  =>  0 pairs (*) / G4 = 9  =>  0 pairs (X)
C6,G6: 9.. / C6 = 9  =>  0 pairs (X) / G6 = 9  =>  0 pairs (_)
* DURATION: 0:01:02.291485  START: 08:02:21.292853  END: 08:03:23.584338 2017-05-01
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,B8,B9,C2,C4,C5,C8,C9,G1,G4,G6,G8,H1,H4,H5,H6,H9)
* 492365..13..27946567548129356.713..272.5983.68..624..72468571399..136.241..9426.8
* PAIR B6: 1,3 BLK 4
C6: 1,3,9                                # reduction candidate for 1,3
C6: 1,3 => SOLVED
* 492365781318279465675481293569713842724598316831624957246857139987136524153942678
C6: 9 => CTR
* 492365..13..27946567548129356.713..272.5983.683962451724685713995.136.241..9426.8
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-705274-base-pr-000.dot
* REASONING
* PRF # C6: 1,3 => SOL
* DIS # C6: 9 => CTR => C6: 1,3
* CNT   2 HDP CHAINS /   2 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B6,B8,B9,C2,C4,C5,C8,C9,G1,G4,G6,G8,H1,H4,H5,H6,H9)
* 492365..13..27946567548129356.713..272.5983.68..624..72468571399..136.241..9426.8
* PAIR B6: 1,3 BLK 4
C6: 1,3,9                                # reduction candidate for 1,3
C6: 1,3 => SOLVED
* 492365781318279465675481293569713842724598316831624957246857139987136524153942678
* DURATION: 0:00:02.112464  START: 08:03:27.328461  END: 08:03:29.440925 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-705274-base-pr-001.dot
* REASONING
* PRF # C6: 1,3 => SOL
* STA C6: 1,3
* CNT   1 HDP CHAINS /   1 HYP OPENED
```

```http://www.sudokus.de/705274.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: 492365..13..27946567548129356.713..272.5983.68..624..72468571399..136.241..9426.8
B2: 1,8
C2: 1,8
G1: 7,8
H1: 7,8
C4: 4,9
C5: 1,4
B6: 1,3
C6: 1,3,9                                # reduction candidate for 1,3
C6: 1,3 => SOLVED
* 492365781318279465675481293569713842724598316831624957246857139987136524153942678
* SOLVED!
--------------------------------------------------

--------------------------------------------------
* AUTO ..
B3 = 7                # set value
B5 = 2                # set value
E5 = 9                # set value
I7 = 9                # set value
A7: 2                 # naked single
E9 = 4                # set value
F2: 9..               # hidden single
E7: 5..               # hidden single
H7: 3..               # hidden single
F2 = 9                # set value
A7 = 2                # set value
A8: 9                 # naked single
D7: 8                 # naked single
F7: 7                 # naked single
D7 = 8                # set value
E7: 5                 # naked single
E7 = 5                # set value
F7 = 7                # set value
F9: 2                 # naked single
H7: 3                 # naked single
H7 = 3                # set value
A8 = 9                # set value
F9 = 2                # set value
B1: 9..               # hidden single
D2: 2..               # hidden single
H8: 2..               # hidden single
I3: 3..               # hidden single
B1 = 9                # set value
D2 = 2                # set value
I3 = 3                # set value
H8 = 2                # set value
D1: 3..               # hidden single
E3: 8..               # hidden single
F4: 3..               # hidden single
D1 = 3                # set value
D6: 6                 # naked single
E3 = 8                # set value
E1: 6                 # naked single
F4 = 3                # set value
B4: 6                 # naked single
D6 = 6                # set value
D8: 1                 # naked single
D8 = 1                # set value
F8: 6                 # naked single
D3: 4                 # naked single
F8 = 6                # set value
F3: 1                 # naked single
A3: 6..               # hidden single
E1 = 6                # set value
A1: 4                 # naked single
A3 = 6                # set value
D3 = 4                # set value
F3 = 1                # set value
B4 = 6                # set value
H2: 6..               # hidden single
A1 = 4                # set value
H2 = 6                # set value
G2: 4..               # hidden single
G2 = 4                # set value
G5: 3                 # naked single
G5 = 3                # set value
I2: 5..               # hidden single
I2 = 5                # set value
I9: 8                 # naked single
I9 = 8                # set value
* UNSOLVED!

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

* DISABLE VALUE:: C6 != 3
B6: 3..               # hidden single
C9: 3..               # hidden single

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

# Solution

position: 492365781318279465675481293569713842724598316831624957246857139987136524153942678 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 # C6: 1,3 => SOL
* DIS # C6: 9 => CTR => C6: 1,3
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* PRF # C6: 1,3 => SOL
* STA C6: 1,3
* CNT   1 HDP CHAINS /   1 HYP OPENED
```