# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=32

level: medium

position: 2.......3..87.4....3....4..5..1...9..1..9..3..8...6..5.93....1....6.1...8.......2 initial

# Autosolve

position: 2...1...3..8734....3..6.4..5..1.3.9..1..9..3.389..61.5.93....1....6.13.98.13.9..2 autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # F3: 5,8 => CTR => F3: 2
* DIS # G1: 5,8 => CTR => G1: 6,7,9
* DIS # H1: 5,8 => CTR => H1: 6,7
* DIS # F5: 2,7 => CTR => F5: 5,8
* PRF # A7: 4,7 => SOL
* PRF # A5: 6 => SOL
* CNT   6 HDP CHAINS /  38 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # F3: 5,8 => CTR => F3: 2
* DIS F3: 2 # G1: 5,8 => CTR => G1: 6,7,9
* DIS F3: 2 + G1: 6,7,9 # H1: 5,8 => CTR => H1: 6,7
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 # F5: 7 => CTR => F5: 5,8
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 # D1: 9 => CTR => D1: 5,8
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # E6: 2,4 => CTR => E6: 7
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # B8: 4,7 => CTR => B8: 2,5
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 # C8: 4,7 => CTR => C8: 2,5
* PRF F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 6 => SOL
* STA F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 + B9: 6
* CNT   9 HDP CHAINS /  35 HYP OPENED
```

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

# Details

## Positions

 2.......3..87.4....3....4..5..1...9..1..9..3..8...6..5.93....1....6.1...8.......2 initial 2...1...3..8734....3..6.4..5..1.3.9..1..9..3.389..61.5.93....1....6.13.98.13.9..2 autosolve 246518973958734261137962458572183694614295837389476125493827516725641389861359742 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (8)
A2: 1,9
B2: 5,6
A3: 1,9
C3: 5,7
F1: 5,8
I2: 1,6
D6: 2,4
A8: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,A3: 1.. / A2 = 1  => 15 pairs (_) / A3 = 1  =>  9 pairs (_)
I2,I3: 1.. / I2 = 1  =>  9 pairs (_) / I3 = 1  => 15 pairs (_)
A2,I2: 1.. / A2 = 1  => 15 pairs (_) / I2 = 1  =>  9 pairs (_)
A3,I3: 1.. / A3 = 1  =>  9 pairs (_) / I3 = 1  => 15 pairs (_)
D3,F3: 2.. / D3 = 2  =>  0 pairs (X) / F3 = 2  =>  9 pairs (_)
G2,H2: 2.. / G2 = 2  => 15 pairs (_) / H2 = 2  =>  9 pairs (_)
B8,C8: 2.. / B8 = 2  =>  8 pairs (_) / C8 = 2  => 13 pairs (_)
B4,B8: 2.. / B4 = 2  => 13 pairs (_) / B8 = 2  =>  8 pairs (_)
H2,H6: 2.. / H2 = 2  =>  9 pairs (_) / H6 = 2  => 15 pairs (_)
B1,C1: 4.. / B1 = 4  =>  8 pairs (_) / C1 = 4  =>  9 pairs (_)
D5,F5: 5.. / D5 = 5  =>  9 pairs (_) / F5 = 5  => 11 pairs (_)
E7,G7: 5.. / E7 = 5  =>  0 pairs (X) / G7 = 5  =>  9 pairs (_)
A7,B9: 6.. / A7 = 6  =>  9 pairs (_) / B9 = 6  =>  0 pairs (*)
A5,A7: 6.. / A5 = 6  =>  0 pairs (*) / A7 = 6  =>  0 pairs (X)
E6,H6: 7.. / E6 = 7  => 11 pairs (_) / H6 = 7  => 12 pairs (_)
F5,F7: 7.. / F5 = 7  =>  0 pairs (X) / F7 = 7  => 10 pairs (_)
E8,H8: 8.. / E8 = 8  => 14 pairs (_) / H8 = 8  => 22 pairs (_)
A2,A3: 9.. / A2 = 9  =>  9 pairs (_) / A3 = 9  => 15 pairs (_)
D1,D3: 9.. / D1 = 9  => 15 pairs (_) / D3 = 9  =>  9 pairs (_)
G1,G2: 9.. / G1 = 9  =>  9 pairs (_) / G2 = 9  => 15 pairs (_)
D1,G1: 9.. / D1 = 9  => 15 pairs (_) / G1 = 9  =>  9 pairs (_)
A2,G2: 9.. / A2 = 9  =>  9 pairs (_) / G2 = 9  => 15 pairs (_)
A3,D3: 9.. / A3 = 9  => 15 pairs (_) / D3 = 9  =>  9 pairs (_)
* DURATION: 0:00:34.473140  START: 04:01:14.937755  END: 04:01:49.410895 2017-05-01
* CP COUNT: (23)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A8,B2,C3,D6,F1,I2)
* 2...1...3..8734....3..6.4..5..1.3.9..1..9..3.389..61.5.93....1....6.13.98.13.9..2
* PAIR B2: 5,6 BLK 1
B1: 5,6,4,7                              # reduction candidate for 5,6
B1: 5,6                                  # 15 pairs
C1: 5,6,4,7                              # reduction candidate for 5,6
C1: 5,6                                  # 10 pairs
* PAIR B2: 5,6 ROW 2
G2: 5,6,2,9                              # reduction candidate for 5,6
G2: 5,6                                  # 11 pairs
H2: 5,6,2                                # reduction candidate for 5,6
H2: 5,6                                  # 15 pairs
* PAIR B2: 5,6 COL B
B9: 5,6,4,7                              # reduction candidate for 5,6
B9: 4,7                                  # 12 pairs
B9: 5,6                                  # 10 pairs
* PAIR C3: 5,7 BLK 1
B1: 5,7,4,6                              # reduction candidate for 5,7
B1: 5,7                                  # 13 pairs
C1: 5,7,4,6                              # reduction candidate for 5,7
C1: 5,7                                  # 13 pairs
* PAIR C3: 5,7 ROW 3
H3: 5,7,8                                # reduction candidate for 5,7
H3: 8                                    # 15 pairs
H3: 5,7                                  # 11 pairs
* PAIR C3: 5,7 COL C
C8: 5,7,2,4                              # reduction candidate for 5,7
C8: 2,4                                  # 13 pairs
C8: 5,7                                  # 10 pairs
* PAIR F1: 5,8 BLK 2
D1: 5,8,9                                # reduction candidate for 5,8
D1: 5,8                                  #  9 pairs
D3: 5,8,2,9                              # reduction candidate for 5,8
D3: 5,8                                  # 17 pairs
F3: 5,8,2                                # reduction candidate for 5,8
F3: 5,8 => CTR
* 2..91...3..873492.93.26.4.15..183.9..1.59..38389426175.938.2.17...6.13898.13.9.42
F3: 2                                    #  9 pairs
* PAIR F1: 5,8 ROW 1
G1: 5,8,6,7,9                            # reduction candidate for 5,8
G1: 5,8 => CTR
* 2..91..73158734926937.6.4515..1.3.9..1.59..3.389.761456934.7.18..56.13.98.13.9.62
G1: 6,7,9                                #  8 pairs
H1: 5,8,6,7                              # reduction candidate for 5,8
H1: 5,8 => CTR
* 2..91.7.3158734926937.6.4.15..1.3.98.1..9..3.38942617569325.81..256813.98.13.9562
H1: 6,7                                  #  9 pairs
* PAIR F1: 5,8 COL F
F5: 5,8,2,7                              # reduction candidate for 5,8
F5: 2,7 => CTR
* 2...1...3..8734..113.9624.85..183.9..1.59783.389..6175.93..8.177..6.13898.1379.42
F5: 5,8                                  # 11 pairs
* PAIR D6: 2,4 BLK 5
E4: 2,4,7,8                              # reduction candidate for 2,4
E4: 2,4                                  # 15 pairs
D5: 2,4,5,8                              # reduction candidate for 2,4
D5: 2,4                                  # 15 pairs
E6: 2,4,7                                # reduction candidate for 2,4
E6: 2,4                                  # 12 pairs
* PAIR D6: 2,4 ROW 6
H6: 2,4,7                                # reduction candidate for 2,4
H6: 7                                    # 12 pairs
H6: 2,4                                  # 11 pairs
* PAIR D6: 2,4 COL D
D7: 2,4,8                                # reduction candidate for 2,4
D7: 8                                    # 23 pairs
D7: 2,4                                  # 11 pairs
* PAIR A8: 4,7 BLK 7
A7: 4,7,6                                # reduction candidate for 4,7
A7: 4,7 => SOLVED
* 246518973958734261137962458572183694614295837389476125493827516725641389861359742
A7: 6                                    #  9 pairs
B8: 4,7,2,5                              # reduction candidate for 4,7
B8: 4,7                                  # 18 pairs
C8: 4,7,2,5                              # reduction candidate for 4,7
C8: 4,7                                  # 20 pairs
B9: 4,7,5,6                              # reduction candidate for 4,7
B9: 4,7                                  # 12 pairs
* PAIR A8: 4,7 ROW 8
E8: 4,7,5,8                              # reduction candidate for 4,7
E8: 4,7                                  # 23 pairs
H8: 4,7,5,8                              # reduction candidate for 4,7
H8: 4,7                                  # 17 pairs
* PAIR A8: 4,7 COL A
A5: 4,7,6                                # reduction candidate for 4,7
A5: 6 => SOLVED
* 246518973958734261137962458572183694614295837389476125493827516725641389861359742
A5: 4,7                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0032-base-pr-000.dot
* REASONING
* DIS # F3: 5,8 => CTR => F3: 2
* DIS # G1: 5,8 => CTR => G1: 6,7,9
* DIS # H1: 5,8 => CTR => H1: 6,7
* DIS # F5: 2,7 => CTR => F5: 5,8
* PRF # A7: 4,7 => SOL
* PRF # A5: 6 => SOL
* CNT   6 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A8,B2,C3,D6,F1,I2)
* 2...1...3..8734....3..6.4..5..1.3.9..1..9..3.389..61.5.93....1....6.13.98.13.9..2
* PAIR B2: 5,6 BLK 1
B1: 5,6,4,7                              # reduction candidate for 5,6
B1: 5,6                                  # 15 pairs
C1: 5,6,4,7                              # reduction candidate for 5,6
C1: 5,6                                  # 10 pairs
* PAIR B2: 5,6 ROW 2
G2: 5,6,2,9                              # reduction candidate for 5,6
G2: 5,6                                  # 11 pairs
H2: 5,6,2                                # reduction candidate for 5,6
H2: 5,6                                  # 15 pairs
* PAIR B2: 5,6 COL B
B9: 5,6,4,7                              # reduction candidate for 5,6
B9: 4,7                                  # 12 pairs
B9: 5,6                                  # 10 pairs
* PAIR C3: 5,7 BLK 1
B1: 5,7,4,6                              # reduction candidate for 5,7
B1: 5,7                                  # 13 pairs
C1: 5,7,4,6                              # reduction candidate for 5,7
C1: 5,7                                  # 13 pairs
* PAIR C3: 5,7 ROW 3
H3: 5,7,8                                # reduction candidate for 5,7
H3: 8                                    # 15 pairs
H3: 5,7                                  # 11 pairs
* PAIR C3: 5,7 COL C
C8: 5,7,2,4                              # reduction candidate for 5,7
C8: 2,4                                  # 13 pairs
C8: 5,7                                  # 10 pairs
* PAIR F1: 5,8 BLK 2
D1: 5,8,9                                # reduction candidate for 5,8
D1: 5,8                                  #  9 pairs
D3: 5,8,2,9                              # reduction candidate for 5,8
D3: 5,8                                  # 17 pairs
F3: 5,8,2                                # reduction candidate for 5,8
F3: 5,8 => CTR
* 2..91...3..873492.93.26.4.15..183.9..1.59..38389426175.938.2.17...6.13898.13.9.42
* PAIR F1: 5,8 ROW 1
G1: 5,8,6,7,9                            # reduction candidate for 5,8
G1: 5,8 => CTR
* 2..91..73158734926937.624515..1.3.9..1.59..3.389.76145693427518..56.13.98.13.9.62
H1: 5,8,6,7                              # reduction candidate for 5,8
H1: 5,8 => CTR
* 2..91.7.3158734926937.624.15..1.3.98.1..9..3.389..61.5693257814425681379871349562
* RESTART
* PAIR F1: 5,8 COL F
F5: 5,8,7                                # reduction candidate for 5,8
F5: 7 => CTR
* 2..815963..8734....3.9624..5..1.3.9..1.597.3.389..6175.93..8.1....6.13898.13.9.42
* PAIR RESTART
* PAIR F1: 5,8 BLK 2
D1: 5,8,9                                # reduction candidate for 5,8
D1: 9 => CTR
* 2..918..3..873492.93.5624.15..1.3.9..1..95.3.389..61.5.93..7.1....6.13.98.13.9..2
* PAIR D6: 2,4 BLK 5
E4: 2,4,7,8                              # reduction candidate for 2,4
E4: 2,4                                  # 15 pairs
D5: 2,4,5,8                              # reduction candidate for 2,4
D5: 2,4                                  # 15 pairs
E6: 2,4,7                                # reduction candidate for 2,4
E6: 2,4 => CTR
* 2...1.963968734.211359624875..173.9..1..9..3.389..6175693..7.1....6813.98.13.97.2
* PAIR D6: 2,4 COL D
D7: 2,4,8                                # reduction candidate for 2,4
D7: 8                                    # 15 pairs
D7: 2,4                                  # 15 pairs
* PAIR RESTART
* PAIR D6: 2,4 BLK 5
E4: 2,4,8                                # reduction candidate for 2,4
E4: 2,4                                  # 15 pairs
D5: 2,4,5,8                              # reduction candidate for 2,4
D5: 2,4                                  # 15 pairs
* PAIR D6: 2,4 COL D
D7: 2,4,8                                # reduction candidate for 2,4
D7: 8                                    # 15 pairs
D7: 2,4                                  # 15 pairs
* PAIR A8: 4,7 BLK 7
B8: 4,7,2,5                              # reduction candidate for 4,7
B8: 4,7 => CTR
* 2...1.9.396873425113.9624..52.1.3.9..1..9..3.389.761.5.93.2751...2651389851349..2
C8: 4,7,2,5                              # reduction candidate for 4,7
C8: 4,7 => CTR
* 2...1.963968734.211359624875..1.3.9..1.495.3.389276145693827514.2.6.13.9851349672
B9: 4,7,6                                # reduction candidate for 4,7
B9: 4,7                                  # 18 pairs
* RESTART
* PAIR A8: 4,7 BLK 7
B9: 4,7,6                                # reduction candidate for 4,7
B9: 6 => SOLVED
* 246518973958734261137962458572183694614295837389476125493827516725641389861359742
* DURATION: 0:00:32.702588  START: 04:02:20.737642  END: 04:02:53.440230 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0032-base-pr-001.dot
* REASONING
* DIS # F3: 5,8 => CTR => F3: 2
* DIS F3: 2 # G1: 5,8 => CTR => G1: 6,7,9
* DIS F3: 2 + G1: 6,7,9 # H1: 5,8 => CTR => H1: 6,7
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 # F5: 7 => CTR => F5: 5,8
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 # D1: 9 => CTR => D1: 5,8
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # E6: 2,4 => CTR => E6: 7
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # B8: 4,7 => CTR => B8: 2,5
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 # C8: 4,7 => CTR => C8: 2,5
* PRF F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 6 => SOL
* STA F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 + B9: 6
* CNT   9 HDP CHAINS /  35 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=32
```

# Solution

position: 246518973958734261137962458572183694614295837389476125493827516725641389861359742 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 # B1: 5,6 => UNS
* INC # C1: 5,6 => UNS
* INC # G2: 5,6 => UNS
* INC # H2: 5,6 => UNS
* INC # B9: 5,6 => UNS
* INC # B9: 4,7 => UNS
* INC # B1: 5,7 => UNS
* INC # C1: 5,7 => UNS
* INC # H3: 5,7 => UNS
* INC # H3: 8 => UNS
* INC # C8: 5,7 => UNS
* INC # C8: 2,4 => UNS
* INC # D1: 5,8 => UNS
* INC # D3: 5,8 => UNS
* DIS # F3: 5,8 => CTR => F3: 2
* INC # F3: 2 => UNS
* DIS # G1: 5,8 => CTR => G1: 6,7,9
* INC # G1: 6,7,9 => UNS
* DIS # H1: 5,8 => CTR => H1: 6,7
* INC # H1: 6,7 => UNS
* INC # F5: 5,8 => UNS
* DIS # F5: 2,7 => CTR => F5: 5,8
* INC # E4: 2,4 => UNS
* INC # D5: 2,4 => UNS
* INC # E6: 2,4 => UNS
* INC # H6: 2,4 => UNS
* INC # H6: 7 => UNS
* INC # D7: 2,4 => UNS
* INC # D7: 8 => UNS
* PRF # A7: 4,7 => SOL
* INC # A7: 6 => UNS
* INC # B8: 4,7 => UNS
* INC # C8: 4,7 => UNS
* INC # B9: 4,7 => UNS
* INC # E8: 4,7 => UNS
* INC # H8: 4,7 => UNS
* INC # A5: 4,7 => UNS
* PRF # A5: 6 => SOL
* CNT  38 HDP CHAINS /  38 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # B1: 5,6 => UNS
* INC # C1: 5,6 => UNS
* INC # G2: 5,6 => UNS
* INC # H2: 5,6 => UNS
* INC # B9: 5,6 => UNS
* INC # B9: 4,7 => UNS
* INC # B1: 5,7 => UNS
* INC # C1: 5,7 => UNS
* INC # H3: 5,7 => UNS
* INC # H3: 8 => UNS
* INC # C8: 5,7 => UNS
* INC # C8: 2,4 => UNS
* INC # D1: 5,8 => UNS
* INC # D3: 5,8 => UNS
* DIS # F3: 5,8 => CTR => F3: 2
* DIS F3: 2 # G1: 5,8 => CTR => G1: 6,7,9
* DIS F3: 2 + G1: 6,7,9 # H1: 5,8 => CTR => H1: 6,7
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 # F5: 5,8 => UNS
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 # F5: 7 => CTR => F5: 5,8
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 # D1: 5,8 => UNS
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 # D1: 9 => CTR => D1: 5,8
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # E4: 2,4 => UNS
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # D5: 2,4 => UNS
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 # E6: 2,4 => CTR => E6: 7
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D7: 2,4 => UNS
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D7: 8 => UNS
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # E4: 2,4 => UNS
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D5: 2,4 => UNS
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D7: 2,4 => UNS
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # D7: 8 => UNS
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 # B8: 4,7 => CTR => B8: 2,5
* DIS F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 # C8: 4,7 => CTR => C8: 2,5
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 4,7 => UNS
* INC F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 4,7 => UNS
* PRF F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 # B9: 6 => SOL
* STA F3: 2 + G1: 6,7,9 + H1: 6,7 + F5: 5,8 + D1: 5,8 + E6: 7 + B8: 2,5 + C8: 2,5 + B9: 6
* CNT  35 HDP CHAINS /  35 HYP OPENED
```