# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=117

level: medium

position: ..36..9...2..19.8..4.....7....3....2..1.7.4..5....8..........6..9.15......8..37.. initial

# Autosolve

position: ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37.. autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # F1: 2,5 => CTR => F1: 4,7
* DIS # A5: 3,6 => CTR => A5: 2,8,9
* CNT   2 HDP CHAINS /  22 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # F1: 2,5 => CTR => F1: 4,7
* DIS F1: 4,7 # A5: 3,6 => CTR => A5: 2,8,9
* DIS F1: 4,7 + A5: 2,8,9 # D2: 5 => CTR => D2: 4,7
* DIS F1: 4,7 + A5: 2,8,9 + D2: 4,7 # F8: 4,7 => CTR => F8: 2,6
* PRF F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # F5: 6 => SOL
* STA F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 + F5: 6
* CNT   5 HDP CHAINS /  34 HYP OPENED
```

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

# Details

## Positions

 ..36..9...2..19.8..4.....7....3....2..1.7.4..5....8..........6..9.15......8..37.. initial ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37.. autosolve 873624915625719384149835276987341652231576498564298137312487569796152843458963721 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (5)
A2: 6,7
F3: 2,5
B6: 3,6
H4: 5,9
H5: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G6,H6: 1.. / G6 = 1  =>  8 pairs (_) / H6 = 1  =>  6 pairs (_)
H1,G3: 2.. / H1 = 2  =>  8 pairs (_) / G3 = 2  => 10 pairs (_)
A5,C6: 2.. / A5 = 2  =>  7 pairs (_) / C6 = 2  => 13 pairs (_)
G2,I2: 3.. / G2 = 3  =>  7 pairs (_) / I2 = 3  => 16 pairs (_)
D2,I2: 4.. / D2 = 4  => 13 pairs (_) / I2 = 4  => 11 pairs (_)
D5,F5: 5.. / D5 = 5  =>  8 pairs (_) / F5 = 5  => 17 pairs (_)
G4,H4: 5.. / G4 = 5  =>  0 pairs (X) / H4 = 5  =>  5 pairs (_)
F8,E9: 6.. / F8 = 6  =>  8 pairs (_) / E9 = 6  => 14 pairs (_)
F5,F8: 6.. / F5 = 6  => 14 pairs (_) / F8 = 6  =>  8 pairs (_)
F1,D2: 7.. / F1 = 7  => 10 pairs (_) / D2 = 7  =>  9 pairs (_)
D2,D7: 7.. / D2 = 7  =>  9 pairs (_) / D7 = 7  => 10 pairs (_)
E1,D3: 8.. / E1 = 8  => 17 pairs (_) / D3 = 8  =>  6 pairs (_)
G4,I5: 8.. / G4 = 8  =>  6 pairs (_) / I5 = 8  => 12 pairs (_)
D7,E7: 8.. / D7 = 8  => 17 pairs (_) / E7 = 8  =>  6 pairs (_)
G8,I8: 8.. / G8 = 8  => 12 pairs (_) / I8 = 8  =>  6 pairs (_)
A3,D3: 8.. / A3 = 8  => 17 pairs (_) / D3 = 8  =>  6 pairs (_)
D3,D7: 8.. / D3 = 8  =>  6 pairs (_) / D7 = 8  => 17 pairs (_)
E1,E7: 8.. / E1 = 8  => 17 pairs (_) / E7 = 8  =>  6 pairs (_)
G4,G8: 8.. / G4 = 8  =>  6 pairs (_) / G8 = 8  => 12 pairs (_)
I5,I8: 8.. / I5 = 8  => 12 pairs (_) / I8 = 8  =>  6 pairs (_)
A3,C3: 9.. / A3 = 9  => 17 pairs (_) / C3 = 9  =>  5 pairs (_)
* DURATION: 0:00:23.041297  START: 05:37:18.223250  END: 05:37:41.264547 2017-05-01
* CP COUNT: (21)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B6,F3,H4,H5)
* ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37..
* PAIR A2: 6,7 BLK 1
C2: 6,7,5                                # reduction candidate for 6,7
C2: 6,7                                  # 14 pairs
C2: 5                                    #  8 pairs
* PAIR A2: 6,7 COL A
A4: 6,7,4,8,9                            # reduction candidate for 6,7
A4: 6,7                                  # 11 pairs
A8: 6,7,2,3,4                            # reduction candidate for 6,7
A8: 6,7                                  #  7 pairs
* PAIR F3: 2,5 BLK 2
F1: 2,5,4,7                              # reduction candidate for 2,5
F1: 2,5 => CTR
* ..364.9..62571938414983..7....3.1..22.15764..5.6428197....8..6..9.15....468..37..
F1: 4,7                                  #  6 pairs
D3: 2,5,8                                # reduction candidate for 2,5
D3: 2,5                                  # 17 pairs
* PAIR F3: 2,5 ROW 3
G3: 2,5,1,6                              # reduction candidate for 2,5
G3: 2,5                                  #  9 pairs
G3: 1,6                                  #  9 pairs
* PAIR F3: 2,5 COL F
F5: 2,5,6                                # reduction candidate for 2,5
F5: 6                                    # 14 pairs
F5: 2,5                                  #  8 pairs
* PAIR B6: 3,6 BLK 4
A5: 3,6,2,8,9                            # reduction candidate for 3,6
A5: 3,6 => CTR
* 8536.79..726.19.8.14983..76974361852681.7.4.3532..8617.15784.69.97156..8..8..37.5
A5: 2,8,9                                #  5 pairs
B5: 3,6,8                                # reduction candidate for 3,6
B5: 3,6                                  #  8 pairs
* PAIR B6: 3,6 ROW 6
G6: 3,6,1                                # reduction candidate for 3,6
G6: 1                                    #  8 pairs
G6: 3,6                                  #  6 pairs
* PAIR H4: 5,9 COL H
H9: 5,9,1,2,4                            # reduction candidate for 5,9
H9: 5,9                                  # 10 pairs
H9: 1,2,4                                #  5 pairs
* PAIR H5: 3,9 BLK 6
I5: 3,9,6,8                              # reduction candidate for 3,9
I5: 3,9                                  # 10 pairs
H6: 3,9,1                                # reduction candidate for 3,9
H6: 3,9                                  #  8 pairs
* PAIR H5: 3,9 ROW 5
A5: 3,9,2,6,8                            # reduction candidate for 3,9
A5: 3,9                                  # 16 pairs
A5: 2,6,8                                #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0117-base-pr-000.dot
* REASONING
* DIS # F1: 2,5 => CTR => F1: 4,7
* DIS # A5: 3,6 => CTR => A5: 2,8,9
* CNT   2 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B6,F3,H4,H5)
* ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37..
* PAIR A2: 6,7 BLK 1
C2: 6,7,5                                # reduction candidate for 6,7
C2: 6,7                                  # 14 pairs
C2: 5                                    #  8 pairs
* PAIR A2: 6,7 COL A
A4: 6,7,4,8,9                            # reduction candidate for 6,7
A4: 6,7                                  # 11 pairs
A8: 6,7,2,3,4                            # reduction candidate for 6,7
A8: 6,7                                  #  7 pairs
* PAIR F3: 2,5 BLK 2
F1: 2,5,4,7                              # reduction candidate for 2,5
F1: 2,5 => CTR
* ..364.9..62571938414983..7....3.1..22.15764..5.6428197....8..6..9.15....468..37..
D3: 2,5,8                                # reduction candidate for 2,5
D3: 2,5                                  # 17 pairs
* RESTART
* PAIR F3: 2,5 BLK 2
D3: 2,5,8                                # reduction candidate for 2,5
D3: 2,5                                  # 17 pairs
D3: 8                                    #  7 pairs
* PAIR F3: 2,5 ROW 3
G3: 2,5,1,6                              # reduction candidate for 2,5
G3: 2,5                                  # 10 pairs
G3: 1,6                                  # 10 pairs
* PAIR F3: 2,5 COL F
F5: 2,5,6                                # reduction candidate for 2,5
F5: 6                                    # 25 pairs
F5: 2,5                                  #  8 pairs
* PAIR B6: 3,6 BLK 4
A5: 3,6,2,8,9                            # reduction candidate for 3,6
A5: 3,6 => CTR
* 8536.79..726.19.8.14983..76974361852681.7.4.3532..8617.15784.69.97156..8..8..37.5
B5: 3,6,8                                # reduction candidate for 3,6
B5: 3,6                                  #  9 pairs
* RESTART
* PAIR B6: 3,6 BLK 4
B5: 3,6,8                                # reduction candidate for 3,6
B5: 8                                    #  9 pairs
B5: 3,6                                  #  9 pairs
* PAIR B6: 3,6 ROW 6
G6: 3,6,1                                # reduction candidate for 3,6
G6: 1                                    #  9 pairs
G6: 3,6                                  #  7 pairs
* PAIR H4: 5,9 COL H
H9: 5,9,1,2,4                            # reduction candidate for 5,9
H9: 5,9                                  # 11 pairs
H9: 1,2,4                                #  6 pairs
* PAIR H5: 3,9 BLK 6
I5: 3,9,6,8                              # reduction candidate for 3,9
I5: 3,9                                  # 12 pairs
H6: 3,9,1                                # reduction candidate for 3,9
H6: 3,9                                  #  9 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,B6,F1,F3,H4,H5)
* ..36..9...2..19.8..4..3..7....3.1..2..1.7.4..5....8..7.......6..9.15......8..37..
* PAIR A2: 6,7 BLK 1
C2: 6,7,5                                # reduction candidate for 6,7
C2: 6,7                                  # 15 pairs
C2: 5                                    # 11 pairs
* PAIR A2: 6,7 COL A
A4: 6,7,4,8,9                            # reduction candidate for 6,7
A4: 6,7                                  # 12 pairs
A8: 6,7,2,3,4                            # reduction candidate for 6,7
A8: 6,7                                  #  8 pairs
* PAIR F1: 4,7 BLK 2
D2: 4,7,5                                # reduction candidate for 4,7
D2: 5 => CTR
* .83647925726519384.45832176.7.3.1.52.61.754..53.4.8617312784569497156238658..3741
* PAIR F1: 4,7 COL F
F7: 4,7,2                                # reduction candidate for 4,7
F7: 4,7                                  # 13 pairs
F8: 4,7,2,6                              # reduction candidate for 4,7
F8: 4,7 => CTR
* ..36249..72..19.8..4.83527....3.1..22.15764..5..2.8..7....82.6.692157.....8.6372.
* RESTART
* PAIR RESTART
* PAIR F3: 2,5 BLK 2
D3: 2,5,8                                # reduction candidate for 2,5
D3: 2,5                                  # 20 pairs
D3: 8                                    # 13 pairs
* PAIR F3: 2,5 COL F
F5: 2,5,6                                # reduction candidate for 2,5
F5: 6 => SOLVED
* 873624915625719384149835276987341652231576498564298137312487569796152843458963721
* DURATION: 0:00:25.655502  START: 05:37:55.043973  END: 05:38:20.699475 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0117-base-pr-001.dot
* REASONING
* DIS # F1: 2,5 => CTR => F1: 4,7
* DIS F1: 4,7 # A5: 3,6 => CTR => A5: 2,8,9
* DIS F1: 4,7 + A5: 2,8,9 # D2: 5 => CTR => D2: 4,7
* DIS F1: 4,7 + A5: 2,8,9 + D2: 4,7 # F8: 4,7 => CTR => F8: 2,6
* PRF F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # F5: 6 => SOL
* STA F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 + F5: 6
* CNT   5 HDP CHAINS /  34 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=117
```

# Solution

position: 873624915625719384149835276987341652231576498564298137312487569796152843458963721 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: 6,7 => UNS
* INC # C2: 5 => UNS
* INC # A4: 6,7 => UNS
* INC # A8: 6,7 => UNS
* DIS # F1: 2,5 => CTR => F1: 4,7
* INC # F1: 4,7 => UNS
* INC # D3: 2,5 => UNS
* INC # G3: 2,5 => UNS
* INC # G3: 1,6 => UNS
* INC # F5: 2,5 => UNS
* INC # F5: 6 => UNS
* DIS # A5: 3,6 => CTR => A5: 2,8,9
* INC # A5: 2,8,9 => UNS
* INC # B5: 3,6 => UNS
* INC # G6: 3,6 => UNS
* INC # G6: 1 => UNS
* INC # H9: 5,9 => UNS
* INC # H9: 1,2,4 => UNS
* INC # I5: 3,9 => UNS
* INC # H6: 3,9 => UNS
* INC # A5: 3,9 => UNS
* INC # A5: 2,6,8 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # C2: 6,7 => UNS
* INC # C2: 5 => UNS
* INC # A4: 6,7 => UNS
* INC # A8: 6,7 => UNS
* DIS # F1: 2,5 => CTR => F1: 4,7
* INC F1: 4,7 # D3: 2,5 => UNS
* INC F1: 4,7 # D3: 2,5 => UNS
* INC F1: 4,7 # D3: 8 => UNS
* INC F1: 4,7 # G3: 2,5 => UNS
* INC F1: 4,7 # G3: 1,6 => UNS
* INC F1: 4,7 # F5: 2,5 => UNS
* INC F1: 4,7 # F5: 6 => UNS
* DIS F1: 4,7 # A5: 3,6 => CTR => A5: 2,8,9
* INC F1: 4,7 + A5: 2,8,9 # B5: 3,6 => UNS
* INC F1: 4,7 + A5: 2,8,9 # B5: 3,6 => UNS
* INC F1: 4,7 + A5: 2,8,9 # B5: 8 => UNS
* INC F1: 4,7 + A5: 2,8,9 # G6: 3,6 => UNS
* INC F1: 4,7 + A5: 2,8,9 # G6: 1 => UNS
* INC F1: 4,7 + A5: 2,8,9 # H9: 5,9 => UNS
* INC F1: 4,7 + A5: 2,8,9 # H9: 1,2,4 => UNS
* INC F1: 4,7 + A5: 2,8,9 # I5: 3,9 => UNS
* INC F1: 4,7 + A5: 2,8,9 # H6: 3,9 => UNS
* INC F1: 4,7 + A5: 2,8,9 # C2: 6,7 => UNS
* INC F1: 4,7 + A5: 2,8,9 # C2: 5 => UNS
* INC F1: 4,7 + A5: 2,8,9 # A4: 6,7 => UNS
* INC F1: 4,7 + A5: 2,8,9 # A8: 6,7 => UNS
* INC F1: 4,7 + A5: 2,8,9 # D2: 4,7 => UNS
* DIS F1: 4,7 + A5: 2,8,9 # D2: 5 => CTR => D2: 4,7
* INC F1: 4,7 + A5: 2,8,9 + D2: 4,7 # F7: 4,7 => UNS
* DIS F1: 4,7 + A5: 2,8,9 + D2: 4,7 # F8: 4,7 => CTR => F8: 2,6
* INC F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # D3: 2,5 => UNS
* INC F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # D3: 8 => UNS
* INC F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # F5: 2,5 => UNS
* PRF F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 # F5: 6 => SOL
* STA F1: 4,7 + A5: 2,8,9 + D2: 4,7 + F8: 2,6 + F5: 6
* CNT  34 HDP CHAINS /  34 HYP OPENED
```