# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=35

level: medium

position: .7.9.....4...3...8..5..1...6.....5.....792.....8.....7...4..1..8...7...4.1...9.2. initial

# Autosolve

position: .7.9.....4...37..8.85..1...6.7...5.....792.....8.....7...42.1..8..17...4.14..9.2. autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* PRF # D2: 2,6 => SOL
* DIS # H5: 1,3 => CTR => H5: 4,6,8
* CNT   2 HDP CHAINS /  21 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* PRF # D2: 2,6 => SOL
* STA D2: 2,6
* CNT   1 HDP CHAINS /   1 HYP OPENED
```

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

# Details

## Positions

 .7.9.....4...3...8..5..1...6.....5.....792.....8.....7...4..1..8...7...4.1...9.2. initial .7.9.....4...37..8.85..1...6.7...5.....792.....8.....7...42.1..8..17...4.14..9.2. autosolve 376958412491237658285641379627384591153792846948516237769423185832175964514869723 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (6)
D3: 2,6
E3: 4,6
C5: 1,3
D4: 3,8
H7: 7,8
G9: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,E6: 1.. / E4 = 1  =>  6 pairs (_) / E6 = 1  => 13 pairs (_)
C2,H2: 1.. / C2 = 1  => 18 pairs (_) / H2 = 1  =>  7 pairs (_)
D2,D3: 2.. / D2 = 2  =>  0 pairs (*) / D3 = 2  =>  0 pairs (X)
I4,G6: 2.. / I4 = 2  =>  6 pairs (_) / G6 = 2  =>  0 pairs (*)
B8,C8: 2.. / B8 = 2  =>  0 pairs (X) / C8 = 2  =>  6 pairs (_)
B4,I4: 2.. / B4 = 2  =>  0 pairs (*) / I4 = 2  =>  0 pairs (X)
A5,B5: 5.. / A5 = 5  =>  8 pairs (_) / B5 = 5  => 16 pairs (_)
D2,H2: 5.. / D2 = 5  =>  7 pairs (_) / H2 = 5  =>  0 pairs (*)
G3,H3: 7.. / G3 = 7  =>  6 pairs (_) / H3 = 7  =>  5 pairs (_)
A7,A9: 7.. / A7 = 7  =>  5 pairs (_) / A9 = 7  =>  6 pairs (_)
H7,G9: 7.. / H7 = 7  =>  6 pairs (_) / G9 = 7  =>  5 pairs (_)
A7,H7: 7.. / A7 = 7  =>  5 pairs (_) / H7 = 7  =>  6 pairs (_)
A9,G9: 7.. / A9 = 7  =>  6 pairs (_) / G9 = 7  =>  5 pairs (_)
G3,G9: 7.. / G3 = 7  =>  6 pairs (_) / G9 = 7  =>  5 pairs (_)
H3,H7: 7.. / H3 = 7  =>  5 pairs (_) / H7 = 7  =>  6 pairs (_)
E1,F1: 8.. / E1 = 8  =>  8 pairs (_) / F1 = 8  =>  7 pairs (_)
G5,H5: 8.. / G5 = 8  =>  5 pairs (_) / H5 = 8  =>  6 pairs (_)
H7,G9: 8.. / H7 = 8  =>  5 pairs (_) / G9 = 8  =>  6 pairs (_)
F7,H7: 8.. / F7 = 8  =>  6 pairs (_) / H7 = 8  =>  5 pairs (_)
D4,D9: 8.. / D4 = 8  =>  7 pairs (_) / D9 = 8  =>  7 pairs (_)
G5,G9: 8.. / G5 = 8  =>  5 pairs (_) / G9 = 8  =>  6 pairs (_)
H5,H7: 8.. / H5 = 8  =>  6 pairs (_) / H7 = 8  =>  5 pairs (_)
* DURATION: 0:00:30.832522  START: 04:06:47.502518  END: 04:07:18.335040 2017-05-01
* CP COUNT: (22)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,D3,D4,E3,G9,H7)
* .7.9.....4...37..8.85..1...6.7...5.....792.....8.....7...42.1..8..17...4.14..9.2.
* PAIR D3: 2,6 BLK 2
D2: 2,6,5                                # reduction candidate for 2,6
D2: 2,6 => SOLVED
* 376958412491237658285641379627384591153792846948516237769423185832175964514869723
D2: 5                                    #  7 pairs
* PAIR D3: 2,6 ROW 3
G3: 2,6,3,4,7,9                          # reduction candidate for 2,6
G3: 2,6                                  #  8 pairs
I3: 2,6,3,9                              # reduction candidate for 2,6
I3: 2,6                                  #  8 pairs
* PAIR E3: 4,6 BLK 2
E1: 4,6,5,8                              # reduction candidate for 4,6
E1: 4,6                                  # 11 pairs
F1: 4,6,5,8                              # reduction candidate for 4,6
F1: 4,6                                  # 10 pairs
* PAIR E3: 4,6 ROW 3
G3: 4,6,2,3,7,9                          # reduction candidate for 4,6
G3: 4,6                                  #  8 pairs
H3: 4,6,3,7,9                            # reduction candidate for 4,6
H3: 4,6                                  #  9 pairs
* PAIR E3: 4,6 COL E
E6: 4,6,1,5                              # reduction candidate for 4,6
E6: 4,6                                  #  9 pairs
E6: 1,5                                  #  7 pairs
* PAIR C5: 1,3 BLK 4
A5: 1,3,5                                # reduction candidate for 1,3
A5: 1,3                                  # 16 pairs
A6: 1,3,2,9                              # reduction candidate for 1,3
A6: 1,3                                  # 13 pairs
* PAIR C5: 1,3 ROW 5
H5: 1,3,4,6,8                            # reduction candidate for 1,3
H5: 1,3 => CTR
* 1739....24...37.18.85..1.7.627...5.1541792836938.1.2477..42.18.8.217...4314..9725
H5: 4,6,8                                #  6 pairs
I5: 1,3,6                                # reduction candidate for 1,3
I5: 1,3                                  # 10 pairs
* PAIR C5: 1,3 COL C
C1: 1,3,2,6                              # reduction candidate for 1,3
C1: 1,3                                  # 10 pairs
C1: 2,6                                  #  9 pairs
* PAIR D4: 3,8 BLK 5
F4: 3,8,4                                # reduction candidate for 3,8
F4: 3,8                                  # 10 pairs
F4: 4                                    #  7 pairs
* PAIR D4: 3,8 COL D
D9: 3,8,5,6                              # reduction candidate for 3,8
D9: 5,6                                  #  9 pairs
D9: 3,8                                  #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0035-base-pr-000.dot
* REASONING
* PRF # D2: 2,6 => SOL
* DIS # H5: 1,3 => CTR => H5: 4,6,8
* CNT   2 HDP CHAINS /  21 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,D3,D4,E3,G9,H7)
* .7.9.....4...37..8.85..1...6.7...5.....792.....8.....7...42.1..8..17...4.14..9.2.
* PAIR D3: 2,6 BLK 2
D2: 2,6,5                                # reduction candidate for 2,6
D2: 2,6 => SOLVED
* 376958412491237658285641379627384591153792846948516237769423185832175964514869723
* DURATION: 0:00:02.717915  START: 04:07:34.720344  END: 04:07:37.438259 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0035-base-pr-001.dot
* REASONING
* PRF # D2: 2,6 => SOL
* STA D2: 2,6
* CNT   1 HDP CHAINS /   1 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=35
```

# Solution

position: 376958412491237658285641379627384591153792846948516237769423185832175964514869723 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 # D2: 2,6 => SOL
* INC # D2: 5 => UNS
* INC # G3: 2,6 => UNS
* INC # I3: 2,6 => UNS
* INC # E1: 4,6 => UNS
* INC # F1: 4,6 => UNS
* INC # G3: 4,6 => UNS
* INC # H3: 4,6 => UNS
* INC # E6: 4,6 => UNS
* INC # E6: 1,5 => UNS
* INC # A5: 1,3 => UNS
* INC # A6: 1,3 => UNS
* DIS # H5: 1,3 => CTR => H5: 4,6,8
* INC # H5: 4,6,8 => UNS
* INC # I5: 1,3 => UNS
* INC # C1: 1,3 => UNS
* INC # C1: 2,6 => UNS
* INC # F4: 3,8 => UNS
* INC # F4: 4 => UNS
* INC # D9: 3,8 => UNS
* INC # D9: 5,6 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* PRF # D2: 2,6 => SOL
* STA D2: 2,6
* CNT   1 HDP CHAINS /   1 HYP OPENED
```