# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=105

level: medium

position: ..4..58..6.....9...8.2...1.....63.7...37.82...7.41.....4...7.2...9.....3..85..7.. initial

# Autosolve

position: ..4..58..6.....9...8.2...1....963.7...37582...7.412....4...7.2.7.9.....3..85..7.. autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* PRF # G6: 5,6 => SOL
* CNT   1 HDP CHAINS /  18 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* PRF # G6: 5,6 => SOL
* STA G6: 5,6
* CNT   1 HDP CHAINS /  13 HYP OPENED
```

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

# Details

## Positions

 ..4..58..6.....9...8.2...1.....63.7...37.82...7.41.....4...7.2...9.....3..85..7.. initial ..4..58..6.....9...8.2...1....963.7...37582...7.412....4...7.2.7.9.....3..85..7.. autosolve 194375862632841957587296314821963475463758291975412638346187529759624183218539746 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (4)
C3: 5,7
F2: 1,4
H1: 3,6
C6: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I1,I2: 2.. / I1 = 2  =>  5 pairs (_) / I2 = 2  =>  6 pairs (_)
E8,E9: 2.. / E8 = 2  =>  4 pairs (_) / E9 = 2  => 11 pairs (_)
B8,E8: 2.. / B8 = 2  => 11 pairs (_) / E8 = 2  =>  4 pairs (_)
C2,C4: 2.. / C2 = 2  =>  5 pairs (_) / C4 = 2  =>  5 pairs (_)
G6,H6: 3.. / G6 = 3  =>  4 pairs (_) / H6 = 3  =>  0 pairs (*)
G3,G6: 3.. / G3 = 3  =>  0 pairs (*) / G6 = 3  =>  0 pairs (X)
A4,A5: 4.. / A4 = 4  =>  9 pairs (_) / A5 = 4  =>  5 pairs (_)
D1,F3: 6.. / D1 = 6  =>  8 pairs (_) / F3 = 6  => 13 pairs (_)
B5,C6: 6.. / B5 = 6  => 16 pairs (_) / C6 = 6  =>  6 pairs (_)
C6,C7: 6.. / C6 = 6  =>  6 pairs (_) / C7 = 6  => 16 pairs (_)
C2,C3: 7.. / C2 = 7  =>  9 pairs (_) / C3 = 7  =>  5 pairs (_)
E1,I1: 7.. / E1 = 7  =>  6 pairs (_) / I1 = 7  =>  6 pairs (_)
D2,E2: 8.. / D2 = 8  =>  7 pairs (_) / E2 = 8  =>  7 pairs (_)
A4,A6: 8.. / A4 = 8  =>  6 pairs (_) / A6 = 8  =>  7 pairs (_)
I7,H8: 8.. / I7 = 8  => 13 pairs (_) / H8 = 8  =>  6 pairs (_)
A4,I4: 8.. / A4 = 8  =>  6 pairs (_) / I4 = 8  =>  7 pairs (_)
H6,H8: 8.. / H6 = 8  => 13 pairs (_) / H8 = 8  =>  6 pairs (_)
E7,I7: 9.. / E7 = 9  =>  9 pairs (_) / I7 = 9  => 10 pairs (_)
B1,B5: 9.. / B1 = 9  => 10 pairs (_) / B5 = 9  =>  8 pairs (_)
F3,F9: 9.. / F3 = 9  =>  9 pairs (_) / F9 = 9  => 11 pairs (_)
* DURATION: 0:00:21.632143  START: 05:21:06.653067  END: 05:21:28.285210 2017-05-01
* CP COUNT: (20)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C6,F2,H1)
* ..4..58..6.....9...8.2...1....963.7...37582...7.412....4...7.2.7.9.....3..85..7..
* PAIR C3: 5,7 BLK 1
C2: 5,7,1,2                              # reduction candidate for 5,7
C2: 5,7                                  # 11 pairs
C2: 1,2                                  #  6 pairs
* PAIR C3: 5,7 ROW 3
I3: 5,7,4,6                              # reduction candidate for 5,7
I3: 4,6                                  #  7 pairs
I3: 5,7                                  #  6 pairs
* PAIR F2: 1,4 COL F
F8: 1,4,6                                # reduction candidate for 1,4
F8: 1,4                                  #  7 pairs
F9: 1,4,6,9                              # reduction candidate for 1,4
F9: 1,4                                  # 10 pairs
* PAIR H1: 3,6 BLK 3
G3: 3,6,4,5                              # reduction candidate for 3,6
G3: 3,6                                  #  7 pairs
G3: 4,5                                  #  6 pairs
* PAIR H1: 3,6 ROW 1
D1: 3,6,1                                # reduction candidate for 3,6
D1: 1                                    # 16 pairs
D1: 3,6                                  #  7 pairs
* PAIR H1: 3,6 COL H
H6: 3,6,5,8,9                            # reduction candidate for 3,6
H6: 3,6                                  # 11 pairs
H6: 5,8,9                                #  4 pairs
* PAIR C6: 5,6 ROW 6
G6: 5,6,3                                # reduction candidate for 5,6
G6: 5,6 => SOLVED
* 194375862632841957587296314821963475463758291975412638346187529759624183218539746
G6: 3                                    #  4 pairs
H6: 5,6,3,8,9                            # reduction candidate for 5,6
H6: 5,6                                  #  9 pairs
I6: 5,6,8,9                              # reduction candidate for 5,6
I6: 5,6                                  #  7 pairs
* PAIR C6: 5,6 COL C
C7: 5,6,1                                # reduction candidate for 5,6
C7: 1                                    #  9 pairs
C7: 5,6                                  #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0105-base-pr-000.dot
* REASONING
* PRF # G6: 5,6 => SOL
* CNT   1 HDP CHAINS /  18 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C3,C6,F2,H1)
* ..4..58..6.....9...8.2...1....963.7...37582...7.412....4...7.2.7.9.....3..85..7..
* PAIR C3: 5,7 BLK 1
C2: 5,7,1,2                              # reduction candidate for 5,7
C2: 5,7                                  # 11 pairs
C2: 1,2                                  #  6 pairs
* PAIR C3: 5,7 ROW 3
I3: 5,7,4,6                              # reduction candidate for 5,7
I3: 4,6                                  #  7 pairs
I3: 5,7                                  #  6 pairs
* PAIR F2: 1,4 COL F
F8: 1,4,6                                # reduction candidate for 1,4
F8: 1,4                                  #  7 pairs
F9: 1,4,6,9                              # reduction candidate for 1,4
F9: 1,4                                  # 10 pairs
* PAIR H1: 3,6 BLK 3
G3: 3,6,4,5                              # reduction candidate for 3,6
G3: 3,6                                  #  7 pairs
G3: 4,5                                  #  6 pairs
* PAIR H1: 3,6 ROW 1
D1: 3,6,1                                # reduction candidate for 3,6
D1: 1                                    # 16 pairs
D1: 3,6                                  #  7 pairs
* PAIR H1: 3,6 COL H
H6: 3,6,5,8,9                            # reduction candidate for 3,6
H6: 3,6                                  # 11 pairs
H6: 5,8,9                                #  4 pairs
* PAIR C6: 5,6 ROW 6
G6: 5,6,3                                # reduction candidate for 5,6
G6: 5,6 => SOLVED
* 194375862632841957587296314821963475463758291975412638346187529759624183218539746
* DURATION: 0:00:09.195396  START: 05:21:39.726085  END: 05:21:48.921481 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0105-base-pr-001.dot
* REASONING
* PRF # G6: 5,6 => SOL
* STA G6: 5,6
* CNT   1 HDP CHAINS /  13 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=105
```

# Solution

position: 194375862632841957587296314821963475463758291975412638346187529759624183218539746 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 # C2: 5,7 => UNS
* INC # C2: 1,2 => UNS
* INC # I3: 5,7 => UNS
* INC # I3: 4,6 => UNS
* INC # F8: 1,4 => UNS
* INC # F9: 1,4 => UNS
* INC # G3: 3,6 => UNS
* INC # G3: 4,5 => UNS
* INC # D1: 3,6 => UNS
* INC # D1: 1 => UNS
* INC # H6: 3,6 => UNS
* INC # H6: 5,8,9 => UNS
* PRF # G6: 5,6 => SOL
* INC # G6: 3 => UNS
* INC # H6: 5,6 => UNS
* INC # I6: 5,6 => UNS
* INC # C7: 5,6 => UNS
* INC # C7: 1 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # C2: 5,7 => UNS
* INC # C2: 1,2 => UNS
* INC # I3: 5,7 => UNS
* INC # I3: 4,6 => UNS
* INC # F8: 1,4 => UNS
* INC # F9: 1,4 => UNS
* INC # G3: 3,6 => UNS
* INC # G3: 4,5 => UNS
* INC # D1: 3,6 => UNS
* INC # D1: 1 => UNS
* INC # H6: 3,6 => UNS
* INC # H6: 5,8,9 => UNS
* PRF # G6: 5,6 => SOL
* STA G6: 5,6
* CNT  13 HDP CHAINS /  13 HYP OPENED
```