# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=61

level: medium

position: .7.....8.4..8....25..4..9......23.5...39.41...2.78......7..9..11....8..9.6.....3. initial

# Autosolve

position: .7.....8.4..8....25..4..9......23.5...39.412.62.78..9...7..9..11....8..9.6.....3. autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* PRF # A4: 9 => SOL
* PRF # I5: 6 => SOL
* CNT   2 HDP CHAINS /  19 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* PRF # A4: 9 => SOL
* STA A4: 9
* CNT   1 HDP CHAINS /   2 HYP OPENED
```

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

# Details

## Positions

 .7.....8.4..8....25..4..9......23.5...39.41...2.78......7..9..11....8..9.6.....3. initial .7.....8.4..8....25..4..9......23.5...39.412.62.78..9...7..9..11....8..9.6.....3. autosolve 271396584496875312538412967914623758783954126625781493357269841142538679869147235 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (9)
A5: 7,8
B5: 5,8
C6: 1,5
D4: 1,6
E5: 5,6
F6: 1,5
G6: 3,4
I6: 3,4
H7: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H2,H3: 1.. / H2 = 1  => 12 pairs (_) / H3 = 1  =>  0 pairs (X)
D4,F6: 1.. / D4 = 1  => 10 pairs (_) / F6 = 1  =>  0 pairs (*)
C6,F6: 1.. / C6 = 1  => 10 pairs (_) / F6 = 1  =>  0 pairs (*)
C3,F3: 2.. / C3 = 2  =>  0 pairs (X) / F3 = 2  =>  9 pairs (_)
G6,I6: 3.. / G6 = 3  =>  7 pairs (_) / I6 = 3  => 12 pairs (_)
A1,A7: 3.. / A1 = 3  => 13 pairs (_) / A7 = 3  => 20 pairs (_)
G1,I1: 4.. / G1 = 4  =>  7 pairs (_) / I1 = 4  => 12 pairs (_)
B4,C4: 4.. / B4 = 4  =>  0 pairs (X) / C4 = 4  => 10 pairs (_)
G6,I6: 4.. / G6 = 4  => 12 pairs (_) / I6 = 4  =>  7 pairs (_)
H7,H8: 4.. / H7 = 4  =>  9 pairs (_) / H8 = 4  => 13 pairs (_)
C9,E9: 4.. / C9 = 4  =>  0 pairs (X) / E9 = 4  =>  9 pairs (_)
G1,G6: 4.. / G1 = 4  =>  7 pairs (_) / G6 = 4  => 12 pairs (_)
I1,I6: 4.. / I1 = 4  => 12 pairs (_) / I6 = 4  =>  7 pairs (_)
B5,C6: 5.. / B5 = 5  => 10 pairs (_) / C6 = 5  =>  0 pairs (*)
E5,F6: 5.. / E5 = 5  =>  0 pairs (*) / F6 = 5  =>  0 pairs (X)
B5,E5: 5.. / B5 = 5  => 10 pairs (_) / E5 = 5  =>  0 pairs (*)
C6,F6: 5.. / C6 = 5  =>  0 pairs (*) / F6 = 5  =>  0 pairs (X)
I1,I9: 5.. / I1 = 5  => 12 pairs (_) / I9 = 5  => 12 pairs (_)
D4,E5: 6.. / D4 = 6  =>  0 pairs (*) / E5 = 6  =>  0 pairs (X)
E5,I5: 6.. / E5 = 6  => 10 pairs (_) / I5 = 6  =>  0 pairs (*)
A4,A5: 7.. / A4 = 7  => 16 pairs (_) / A5 = 7  => 10 pairs (_)
A5,I5: 7.. / A5 = 7  => 10 pairs (_) / I5 = 7  => 16 pairs (_)
B3,C3: 8.. / B3 = 8  =>  0 pairs (X) / C3 = 8  => 11 pairs (_)
E1,E2: 9.. / E1 = 9  => 10 pairs (_) / E2 = 9  =>  0 pairs (X)
A9,C9: 9.. / A9 = 9  => 15 pairs (_) / C9 = 9  => 11 pairs (_)
B2,B4: 9.. / B2 = 9  => 11 pairs (_) / B4 = 9  =>  0 pairs (X)
* DURATION: 0:00:37.354550  START: 04:31:13.978951  END: 04:31:51.333501 2017-05-01
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B5,C6,D4,E5,F6,G6,H7,I6)
* .7.....8.4..8....25..4..9......23.5...39.412.62.78..9...7..9..11....8..9.6.....3.
* PAIR A5: 7,8 BLK 4
A4: 7,8,9                                # reduction candidate for 7,8
A4: 9 => SOLVED
* 271396584496875312538412967914623758783954126625781493357269841142538679869147235
A4: 7,8                                  # 15 pairs
* PAIR A5: 7,8 ROW 5
I5: 7,8,6                                # reduction candidate for 7,8
I5: 6 => SOLVED
* 271396584496875312538412967914623758783954126625781493357269841142538679869147235
I5: 7,8                                  # 10 pairs
* PAIR B5: 5,8 COL B
B7: 5,8,3,4                              # reduction candidate for 5,8
B7: 5,8                                  # 13 pairs
B7: 3,4                                  # 10 pairs
* PAIR E5: 5,6 COL E
E7: 5,6,3,4                              # reduction candidate for 5,6
E7: 5,6                                  # 10 pairs
E8: 5,6,3,4,7                            # reduction candidate for 5,6
E8: 5,6                                  # 12 pairs
* PAIR F6: 1,5 COL F
F1: 1,5,2,6                              # reduction candidate for 1,5
F1: 1,5                                  # 12 pairs
F2: 1,5,6,7                              # reduction candidate for 1,5
F2: 1,5                                  # 12 pairs
F9: 1,5,2,7                              # reduction candidate for 1,5
F9: 1,5                                  # 13 pairs
* PAIR G6: 3,4 COL G
G1: 3,4,5,6                              # reduction candidate for 3,4
G1: 5,6                                  # 11 pairs
G1: 3,4                                  # 10 pairs
* PAIR I6: 3,4 COL I
I1: 3,4,5,6                              # reduction candidate for 3,4
I1: 3,4                                  # 14 pairs
I1: 5,6                                  # 10 pairs
* PAIR H7: 4,6 BLK 9
H8: 4,6,7                                # reduction candidate for 4,6
H8: 7                                    # 13 pairs
H8: 4,6                                  # 13 pairs
* PAIR H7: 4,6 ROW 7
E7: 4,6,3,5                              # reduction candidate for 4,6
E7: 4,6                                  # 10 pairs
E7: 3,5                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0061-base-pr-000.dot
* REASONING
* PRF # A4: 9 => SOL
* PRF # I5: 6 => SOL
* CNT   2 HDP CHAINS /  19 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B5,C6,D4,E5,F6,G6,H7,I6)
* .7.....8.4..8....25..4..9......23.5...39.412.62.78..9...7..9..11....8..9.6.....3.
* PAIR A5: 7,8 BLK 4
A4: 7,8,9                                # reduction candidate for 7,8
A4: 9 => SOLVED
* 271396584496875312538412967914623758783954126625781493357269841142538679869147235
* DURATION: 0:00:03.228521  START: 04:32:06.099165  END: 04:32:09.327686 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0061-base-pr-001.dot
* REASONING
* PRF # A4: 9 => SOL
* STA A4: 9
* CNT   1 HDP CHAINS /   2 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=61
```

# Solution

position: 271396584496875312538412967914623758783954126625781493357269841142538679869147235 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 # A4: 7,8 => UNS
* PRF # A4: 9 => SOL
* INC # I5: 7,8 => UNS
* PRF # I5: 6 => SOL
* INC # B7: 5,8 => UNS
* INC # B7: 3,4 => UNS
* INC # E7: 5,6 => UNS
* INC # E8: 5,6 => UNS
* INC # F1: 1,5 => UNS
* INC # F2: 1,5 => UNS
* INC # F9: 1,5 => UNS
* INC # G1: 3,4 => UNS
* INC # G1: 5,6 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 5,6 => UNS
* INC # H8: 4,6 => UNS
* INC # H8: 7 => UNS
* INC # E7: 4,6 => UNS
* INC # E7: 3,5 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # A4: 7,8 => UNS
* PRF # A4: 9 => SOL
* STA A4: 9
* CNT   2 HDP CHAINS /   2 HYP OPENED
```