# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=94

level: hard

position: .8.1..9...6...7.5.3...4...77....2....2..5..4....7....66...8...1.4.3...8...9..6.7. initial

# Autosolve

position: .871..9...6...7.5.3...4...77....2....2..5.74....7....667..8...1.4.37.68.8.9..6.7. autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # A6: 1,9 => CTR => A6: 4,5
* CNT   1 HDP CHAINS /   8 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # A6: 1,9 => CTR => A6: 4,5
* STA A6: 4,5
* CNT   1 HDP CHAINS /  23 HYP OPENED
```

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

## Pair Reduction Position

position: .871..9...6...7.5.3...4...77....2....2..5.74....7....667..8...1.4.37.68.8.9..6.7. pair_reduction

See section Pair Reduction for the HDP chains leading to this result.

## Deep Pair Reduction

Time used: 0:00:23.565630

The following important HDP chains were detected:

```* DIS # B4: 1,9 # E4: 1,9 => CTR => E4: 3,6
* DIS # B4: 1,9 + E4: 3,6 # H4: 3 => CTR => H4: 1,9
* DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 # B3: 5 => CTR => B3: 1,9
* DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 # F5: 1,9 => CTR => F5: 3,8
* PRF # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 + F5: 3,8 => SOL
* STA B4: 1,9
* CNT   5 HDP CHAINS /  18 HYP OPENED
```

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

# Details

## Positions

 .8.1..9...6...7.5.3...4...77....2....2..5..4....7....66...8...1.4.3...8...9..6.7. initial .871..9...6...7.5.3...4...77....2....2..5.74....7....667..8...1.4.37.68.8.9..6.7. autosolve .871..9...6...7.5.3...4...77....2....2..5.74....7....667..8...1.4.37.68.8.9..6.7. pair_reduction 587163924964827153312945867796432518123658749458791236675284391241379685839516472 solved

level: hard

## Pairing Analysis

```--------------------------------------------------
* PAIRS (3)
F1: 3,5
A5: 1,9
E9: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F8,E9: 1.. / F8 = 1  => 18 pairs (_) / E9 = 1  =>  6 pairs (_)
B9,E9: 1.. / B9 = 1  => 18 pairs (_) / E9 = 1  =>  6 pairs (_)
G6,H6: 2.. / G6 = 2  =>  4 pairs (_) / H6 = 2  =>  6 pairs (_)
C7,B9: 3.. / C7 = 3  =>  6 pairs (_) / B9 = 3  => 11 pairs (_)
D4,F6: 4.. / D4 = 4  =>  4 pairs (_) / F6 = 4  =>  9 pairs (_)
A1,I1: 4.. / A1 = 4  => 13 pairs (_) / I1 = 4  =>  4 pairs (_)
C4,D4: 4.. / C4 = 4  =>  9 pairs (_) / D4 = 4  =>  4 pairs (_)
F6,F7: 4.. / F6 = 4  =>  9 pairs (_) / F7 = 4  =>  4 pairs (_)
A1,F1: 5.. / A1 = 5  =>  8 pairs (_) / F1 = 5  =>  7 pairs (_)
E1,D3: 6.. / E1 = 6  =>  7 pairs (_) / D3 = 6  =>  8 pairs (_)
H1,H3: 6.. / H1 = 6  =>  8 pairs (_) / H3 = 6  =>  7 pairs (_)
C4,C5: 6.. / C4 = 6  =>  7 pairs (_) / C5 = 6  =>  4 pairs (_)
E1,H1: 6.. / E1 = 6  =>  7 pairs (_) / H1 = 6  =>  8 pairs (_)
D3,H3: 6.. / D3 = 6  =>  8 pairs (_) / H3 = 6  =>  7 pairs (_)
C5,D5: 6.. / C5 = 6  =>  4 pairs (_) / D5 = 6  =>  7 pairs (_)
E1,E4: 6.. / E1 = 6  =>  7 pairs (_) / E4 = 6  =>  8 pairs (_)
A2,B3: 9.. / A2 = 9  =>  0 pairs (*) / B3 = 9  =>  0 pairs (X)
H7,I8: 9.. / H7 = 9  =>  9 pairs (_) / I8 = 9  =>  7 pairs (_)
F8,I8: 9.. / F8 = 9  =>  9 pairs (_) / I8 = 9  =>  7 pairs (_)
* DURATION: 0:00:21.980311  START: 18:50:24.152625  END: 18:50:46.132936 2017-04-30
* CP COUNT: (19)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:23.433779  START: 18:51:09.917419  END: 18:51:33.351198 2017-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0094-base-pr-002.dot
* REASONING
* DIS # B4: 1,9 # E4: 1,9 => CTR => E4: 3,6
* DIS # B4: 1,9 + E4: 3,6 # H4: 3 => CTR => H4: 1,9
* DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 # B3: 5 => CTR => B3: 1,9
* DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 # F5: 1,9 => CTR => F5: 3,8
* PRF # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 + F5: 3,8 => SOL
* STA B4: 1,9
* CNT   5 HDP CHAINS /  18 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=94
```

# Solution

position: 587163924964827153312945867796432518123658749458791236675284391241379685839516472 solved

See section Deep 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 # B4: 1,9 => UNS
* DIS # A6: 1,9 => CTR => A6: 4,5
* INC # A6: 4,5 => UNS
* INC # B6: 1,9 => UNS
* INC # F5: 1,9 => UNS
* INC # F5: 3,8 => UNS
* INC # A2: 1,9 => UNS
* INC # A2: 2,4 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # B4: 1,9 => UNS
* DIS # A6: 1,9 => CTR => A6: 4,5
* INC A6: 4,5 # B6: 1,9 => UNS
* INC A6: 4,5 # F5: 1,9 => UNS
* INC A6: 4,5 # F5: 3,8 => UNS
* INC A6: 4,5 # A2: 1,9 => UNS
* INC A6: 4,5 # A2: 2,4 => UNS
* INC A6: 4,5 # B4: 1,9 => UNS
* INC A6: 4,5 # B6: 1,9 => UNS
* INC A6: 4,5 # F5: 1,9 => UNS
* INC A6: 4,5 # F5: 3,8 => UNS
* INC A6: 4,5 # A2: 1,9 => UNS
* INC A6: 4,5 # A2: 2,4 => UNS
* INC A6: 4,5 # B4: 1,9 => UNS
* INC A6: 4,5 # B6: 1,9 => UNS
* INC A6: 4,5 # F5: 1,9 => UNS
* INC A6: 4,5 # F5: 3,8 => UNS
* INC A6: 4,5 # A2: 1,9 => UNS
* INC A6: 4,5 # A2: 2,4 => UNS
* INC A6: 4,5 # C4: 4,5 => UNS
* INC A6: 4,5 # C6: 4,5 => UNS
* INC A6: 4,5 # A1: 4,5 => UNS
* INC A6: 4,5 # A1: 2 => UNS
* STA A6: 4,5
* CNT  23 HDP CHAINS /  23 HYP OPENED
```

## A3. Deep Pair Reduction

Full list of HDP chains traversed:

```* INC # B4: 1,9 => UNS
* INC # B6: 1,9 => UNS
* INC # F5: 1,9 => UNS
* INC # F5: 3,8 => UNS
* INC # A2: 1,9 => UNS
* INC # A2: 2,4 => UNS
* INC # C4: 4,5 => UNS
* INC # C6: 4,5 => UNS
* INC # A1: 4,5 => UNS
* INC # A1: 2 => UNS
* DIS # B4: 1,9 # E4: 1,9 => CTR => E4: 3,6
* INC # B4: 1,9 + E4: 3,6 # H4: 1,9 => UNS
* INC # B4: 1,9 + E4: 3,6 # H4: 1,9 => UNS
* DIS # B4: 1,9 + E4: 3,6 # H4: 3 => CTR => H4: 1,9
* INC # B4: 1,9 + E4: 3,6 + H4: 1,9 # B3: 1,9 => UNS
* DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 # B3: 5 => CTR => B3: 1,9
* DIS # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 # F5: 1,9 => CTR => F5: 3,8
* PRF # B4: 1,9 + E4: 3,6 + H4: 1,9 + B3: 1,9 + F5: 3,8 => SOL
* STA B4: 1,9
* CNT  18 HDP CHAINS /  18 HYP OPENED
```