# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=283

level: medium

position: ....47..9..4.3...8.1.2....6..3....97.2....6..6.....5..5..1.......8.96.7......4... initial

# Autosolve

position: ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1.......8.96.7......4... autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # H1: 2,5 => CTR => H1: 1,3
* DIS # I8: 3,4 => CTR => I8: 1,2,5
* 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:

```* DIS # H1: 2,5 => CTR => H1: 1,3
* DIS H1: 1,3 # A8: 3,4 => CTR => A8: 1,2
* DIS H1: 1,3 + A8: 1,2 # G8: 3,4 => CTR => G8: 1,2
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 # I8: 3,4 => CTR => I8: 5
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 # F3: 5,8 => CTR => F3: 9
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # E9: 2,7 => CTR => E9: 5,8
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # G1: 2 => CTR => G1: 1,3
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H9: 1,3 => CTR => H9: 2,6,8
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # F4: 5,8 => CTR => F4: 2
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 # A9: 1,2 => CTR => A9: 9
* PRF H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9 => SOL
* STA H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9
* CNT  11 HDP CHAINS /  30 HYP OPENED
```

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

# Details

## Positions

 ....47..9..4.3...8.1.2....6..3....97.2....6..6.....5..5..1.......8.96.7......4... initial ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1.......8.96.7......4... autosolve 862547319794631258315289746153862497427915683689473521576128934248396175931754862 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (5)
E3: 5,8
G2: 2,7
H2: 2,5
B8: 3,4
D8: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G1,H1: 1.. / G1 = 1  =>  0 pairs (X) / H1 = 1  =>  6 pairs (_)
E5,E6: 1.. / E5 = 1  =>  6 pairs (_) / E6 = 1  =>  7 pairs (_)
A4,G4: 1.. / A4 = 1  =>  8 pairs (_) / G4 = 1  => 13 pairs (_)
F4,G4: 2.. / F4 = 2  =>  6 pairs (_) / G4 = 2  => 14 pairs (_)
G3,H3: 4.. / G3 = 4  =>  6 pairs (_) / H3 = 4  =>  6 pairs (_)
B4,C5: 5.. / B4 = 5  =>  7 pairs (_) / C5 = 5  =>  8 pairs (_)
I8,I9: 5.. / I8 = 5  =>  7 pairs (_) / I9 = 5  =>  9 pairs (_)
D8,I8: 5.. / D8 = 5  =>  9 pairs (_) / I8 = 5  =>  7 pairs (_)
D1,D2: 6.. / D1 = 6  =>  7 pairs (_) / D2 = 6  =>  8 pairs (_)
H7,H9: 6.. / H7 = 6  =>  5 pairs (_) / H9 = 6  =>  5 pairs (_)
B2,D2: 6.. / B2 = 6  =>  7 pairs (_) / D2 = 6  =>  8 pairs (_)
G2,G3: 7.. / G2 = 7  =>  6 pairs (_) / G3 = 7  => 11 pairs (_)
D2,F3: 9.. / D2 = 9  =>  9 pairs (_) / F3 = 9  =>  8 pairs (_)
G7,G9: 9.. / G7 = 9  =>  5 pairs (_) / G9 = 9  =>  5 pairs (_)
* DURATION: 0:00:09.543885  START: 14:48:37.088320  END: 14:48:46.632205 2019-04-28
* CP COUNT: (14)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D8,E3,G2,H2)
* ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1.......8.96.7......4...
* PAIR E3: 5,8 BLK 2
D1: 5,8,6                                # reduction candidate for 5,8
D1: 5,8                                  #  8 pairs
F3: 5,8,9                                # reduction candidate for 5,8
F3: 5,8                                  #  9 pairs
* PAIR E3: 5,8 COL E
E5: 5,8,1,7                              # reduction candidate for 5,8
E5: 5,8                                  # 17 pairs
E9: 5,8,2,7                              # reduction candidate for 5,8
E9: 5,8                                  #  9 pairs
* PAIR G2: 2,7 ROW 2
A2: 2,7,9                                # reduction candidate for 2,7
A2: 9                                    #  9 pairs
A2: 2,7                                  #  8 pairs
* PAIR H2: 2,5 BLK 3
H1: 2,5,1,3                              # reduction candidate for 2,5
H1: 2,5 => CTR
* ..2.47159954631728.17259..61.3.6529742597.613679.125845.6183.422485963717.1.24..5
H1: 1,3                                  #  6 pairs
* PAIR B8: 3,4 BLK 7
B7: 3,4,6,7,9                            # reduction candidate for 3,4
B7: 3,4                                  #  8 pairs
A8: 3,4,1,2                              # reduction candidate for 3,4
A8: 3,4                                  # 13 pairs
* PAIR B8: 3,4 ROW 8
G8: 3,4,1,2                              # reduction candidate for 3,4
G8: 3,4                                  # 13 pairs
I8: 3,4,1,2,5                            # reduction candidate for 3,4
I8: 3,4 => CTR
* ..2.47319..4.3125831.2..7461.3.62.97425...6..6.....5..5.61.....2.859617...1..4.65
I8: 1,2,5                                #  5 pairs
* PAIR D8: 3,5 BLK 8
D9: 3,5,7,8                              # reduction candidate for 3,5
D9: 3,5                                  # 12 pairs
D9: 7,8                                  #  6 pairs
* PAIR D8: 3,5 ROW 8
I8: 3,5,1,2,4                            # reduction candidate for 3,5
I8: 1,2,4                                #  9 pairs
I8: 3,5                                  #  8 pairs
* PAIR D8: 3,5 COL D
D5: 3,5,4,7,8,9                          # reduction candidate for 3,5
D5: 3,5                                  # 12 pairs
D5: 4,7,8,9                              #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0283-base-pr-000.dot
* REASONING
* DIS # H1: 2,5 => CTR => H1: 1,3
* DIS # I8: 3,4 => CTR => I8: 1,2,5
* CNT   2 HDP CHAINS /  19 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,D8,E3,G2,H2)
* ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1.......8.96.7......4...
* PAIR E3: 5,8 BLK 2
D1: 5,8,6                                # reduction candidate for 5,8
D1: 5,8                                  #  8 pairs
F3: 5,8,9                                # reduction candidate for 5,8
F3: 5,8                                  #  9 pairs
* PAIR E3: 5,8 COL E
E5: 5,8,1,7                              # reduction candidate for 5,8
E5: 5,8                                  # 17 pairs
E9: 5,8,2,7                              # reduction candidate for 5,8
E9: 5,8                                  #  9 pairs
* PAIR G2: 2,7 ROW 2
A2: 2,7,9                                # reduction candidate for 2,7
A2: 9                                    #  9 pairs
A2: 2,7                                  #  8 pairs
* PAIR H2: 2,5 BLK 3
H1: 2,5,1,3                              # reduction candidate for 2,5
H1: 2,5 => CTR
* ..2.47159954631728.17259..61.3.6529742597.613679.125845.6183.422485963717.1.24..5
* PAIR B8: 3,4 BLK 7
B7: 3,4,6,7,9                            # reduction candidate for 3,4
B7: 3,4                                  #  9 pairs
A8: 3,4,1,2                              # reduction candidate for 3,4
A8: 3,4 => CTR
* ..5.47.19..4.31.58.1.2....6153.62.97.2....6..6.....52.5..1.......8596172..1..4..5
* RESTART
* PAIR B8: 3,4 BLK 7
B7: 3,4,6,7,9                            # reduction candidate for 3,4
B7: 3,4                                  #  9 pairs
B7: 6,7,9                                #  7 pairs
* PAIR B8: 3,4 ROW 8
G8: 3,4,1,2                              # reduction candidate for 3,4
G8: 3,4 => CTR
* ..5.47..9..4.31.58.1.2....6.53.62197.2....6..6.....52.5..1.....1.8596.72.....4.15
I8: 3,4,5                                # reduction candidate for 3,4
I8: 3,4 => CTR
* ..2.47319..4.3125831.2..7461.3.62.97425...6..6.....5..5.61.....2.859617...1..4.65
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A8,B4,E3,F7,G2,G8,H1,H2)
* ....47..9..4.31..8.1.2....6..3.6..97.2....6..6.....5..5..1......48396.75.....4...
* PAIR E3: 5,8 BLK 2
D1: 5,8,6                                # reduction candidate for 5,8
D1: 5,8                                  # 11 pairs
F3: 5,8,9                                # reduction candidate for 5,8
F3: 5,8 => CTR
* ..26473197649312583192857461.3.62.97425..96..697.135..5.61.89.42483961759.1.54862
* RESTART
* PAIR E3: 5,8 BLK 2
D1: 5,8,6                                # reduction candidate for 5,8
D1: 6                                    # 17 pairs
D1: 5,8                                  # 11 pairs
* PAIR E3: 5,8 COL E
E9: 5,8,2,7                              # reduction candidate for 5,8
E9: 2,7 => CTR
* ...847..9..4631.58817259..6..346..9742....6..67.9..5..5..178....48396.757..524...
* PAIR RESTART
* PAIR E3: 5,8 BLK 2
D1: 5,8,6                                # reduction candidate for 5,8
D1: 6                                    # 17 pairs
D1: 5,8                                  # 15 pairs
* PAIR H1: 1,3 BLK 3
G1: 1,3,2                                # reduction candidate for 1,3
G1: 2 => CTR
* ....47219294631758.1.2.9..6..3.62.97.2...56..6....35..5..128...148396.75.....4...
* PAIR H1: 1,3 COL H
H5: 1,3,4,8                              # reduction candidate for 1,3
H5: 1,3                                  # 21 pairs
H6: 1,3,2,4,8                            # reduction candidate for 1,3
H6: 1,3                                  # 22 pairs
H9: 1,3,2,6,8                            # reduction candidate for 1,3
H9: 1,3 => CTR
* ....47319..4.31728317289..6..3.6.197.2....6.36....35.253.128964148396275...754831
* PAIR RESTART
* PAIR H1: 1,3 COL H
H5: 1,3,4,8                              # reduction candidate for 1,3
H5: 1,3                                  # 21 pairs
H6: 1,3,2,4,8                            # reduction candidate for 1,3
H6: 1,3                                  # 22 pairs
* PAIR B4: 5,8 ROW 4
F4: 5,8,2                                # reduction candidate for 5,8
F4: 5,8 => CTR
* 8.2.47319..4.317283172894561.346.29742597.6.16798125..5.61289..2483961757...54..2
* PAIR RESTART
* PAIR A8: 1,2 BLK 7
A9: 1,2,9                                # reduction candidate for 1,2
A9: 1,2 => CTR
* 862547..9..4631.58315289746453862197.2...568368...35245..128....48396.75...754...
A9: 9 => SOLVED
* 862547319794631258315289746153862497427915683689473521576128934248396175931754862
* DURATION: 0:00:18.839125  START: 14:48:54.609115  END: 14:49:13.448240 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0283-base-pr-001.dot
* REASONING
* DIS # H1: 2,5 => CTR => H1: 1,3
* DIS H1: 1,3 # A8: 3,4 => CTR => A8: 1,2
* DIS H1: 1,3 + A8: 1,2 # G8: 3,4 => CTR => G8: 1,2
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 # I8: 3,4 => CTR => I8: 5
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 # F3: 5,8 => CTR => F3: 9
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # E9: 2,7 => CTR => E9: 5,8
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # G1: 2 => CTR => G1: 1,3
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H9: 1,3 => CTR => H9: 2,6,8
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # F4: 5,8 => CTR => F4: 2
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 # A9: 1,2 => CTR => A9: 9
* PRF H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9 => SOL
* STA H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9
* CNT  11 HDP CHAINS /  30 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=283
```

# Solution

position: 862547319794631258315289746153862497427915683689473521576128934248396175931754862 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 # D1: 5,8 => UNS
* INC # F3: 5,8 => UNS
* INC # E5: 5,8 => UNS
* INC # E9: 5,8 => UNS
* INC # A2: 2,7 => UNS
* INC # A2: 9 => UNS
* DIS # H1: 2,5 => CTR => H1: 1,3
* INC # H1: 1,3 => UNS
* INC # B7: 3,4 => UNS
* INC # A8: 3,4 => UNS
* INC # G8: 3,4 => UNS
* DIS # I8: 3,4 => CTR => I8: 1,2,5
* INC # I8: 1,2,5 => UNS
* INC # D9: 3,5 => UNS
* INC # D9: 7,8 => UNS
* INC # I8: 3,5 => UNS
* INC # I8: 1,2,4 => UNS
* INC # D5: 3,5 => UNS
* INC # D5: 4,7,8,9 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # D1: 5,8 => UNS
* INC # F3: 5,8 => UNS
* INC # E5: 5,8 => UNS
* INC # E9: 5,8 => UNS
* INC # A2: 2,7 => UNS
* INC # A2: 9 => UNS
* DIS # H1: 2,5 => CTR => H1: 1,3
* INC H1: 1,3 # B7: 3,4 => UNS
* DIS H1: 1,3 # A8: 3,4 => CTR => A8: 1,2
* INC H1: 1,3 + A8: 1,2 # B7: 3,4 => UNS
* INC H1: 1,3 + A8: 1,2 # B7: 6,7,9 => UNS
* DIS H1: 1,3 + A8: 1,2 # G8: 3,4 => CTR => G8: 1,2
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 # I8: 3,4 => CTR => I8: 5
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 # D1: 5,8 => UNS
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 # F3: 5,8 => CTR => F3: 9
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # D1: 5,8 => UNS
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # D1: 6 => UNS
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # E9: 5,8 => UNS
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 # E9: 2,7 => CTR => E9: 5,8
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # D1: 5,8 => UNS
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # D1: 6 => UNS
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # G1: 1,3 => UNS
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 # G1: 2 => CTR => G1: 1,3
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H5: 1,3 => UNS
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H6: 1,3 => UNS
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 # H9: 1,3 => CTR => H9: 2,6,8
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # H5: 1,3 => UNS
* INC H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # H6: 1,3 => UNS
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 # F4: 5,8 => CTR => F4: 2
* DIS H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 # A9: 1,2 => CTR => A9: 9
* PRF H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9 => SOL
* STA H1: 1,3 + A8: 1,2 + G8: 1,2 + I8: 5 + F3: 9 + E9: 5,8 + G1: 1,3 + H9: 2,6,8 + F4: 2 + A9: 9
* CNT  31 HDP CHAINS /  30 HYP OPENED
```