# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=38

level: medium

position: ....2..7..5..97...6.73..2..4.......5.16...32.7.......6..2..94.3...47..1..8..5.... initial

# Autosolve

position: ....2..7.25..97.346.73..2..4.......5.16...32.7......46.72..94.3.6.47..1..84.5.... autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # D2: 6 => CTR => D2: 1,8
* DIS # D2: 1 => CTR => D2: 6,8
* DIS # D4: 8,9 => CTR => D4: 1,2,6,7
* DIS # H3: 8,9 => CTR => H3: 5
* DIS # I9: 2 => CTR => I9: 7,9
* CNT   5 HDP CHAINS /  26 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # D2: 6 => CTR => D2: 1,8
* DIS D2: 1,8 # C1: 1,8 => CTR => C1: 3,9
* DIS D2: 1,8 + C1: 3,9 # B1: 3 => CTR => B1: 4,9
* DIS D2: 1,8 + C1: 3,9 + B1: 4,9 # F5: 5 => CTR => F5: 4,8
* DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 # G6: 1 => CTR => G6: 8,9
* DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 # H3: 8,9 => CTR => H3: 5
* PRF D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5 => SOL
* STA D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5
* CNT   7 HDP CHAINS /  12 HYP OPENED
```

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

# Details

## Positions

 ....2..7..5..97...6.73..2..4.......5.16...32.7.......6..2..94.3...47..1..8..5.... initial ....2..7.25..97.346.73..2..4.......5.16...32.7......46.72..94.3.6.47..1..84.5.... autosolve 843625971251897634697341258428736195916584327735912846572169483369478512184253769 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (8)
C2: 1,8
B3: 4,9
G2: 6,8
E5: 4,8
H4: 8,9
A7: 1,5
G9: 7,9
H9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,C2: 1.. / C1 = 1  =>  0 pairs (X) / C2 = 1  =>  9 pairs (_)
I1,I3: 1.. / I1 = 1  => 10 pairs (_) / I3 = 1  => 12 pairs (_)
G4,G6: 1.. / G4 = 1  =>  9 pairs (_) / G6 = 1  =>  9 pairs (_)
A7,A9: 1.. / A7 = 1  =>  0 pairs (X) / A9 = 1  => 14 pairs (_)
C2,D2: 1.. / C2 = 1  =>  9 pairs (_) / D2 = 1  =>  0 pairs (X)
B4,B6: 2.. / B4 = 2  =>  9 pairs (_) / B6 = 2  => 11 pairs (_)
I8,I9: 2.. / I8 = 2  => 13 pairs (_) / I9 = 2  =>  0 pairs (X)
F8,I8: 2.. / F8 = 2  =>  0 pairs (X) / I8 = 2  => 13 pairs (_)
E4,E6: 3.. / E4 = 3  => 15 pairs (_) / E6 = 3  =>  9 pairs (_)
F8,F9: 3.. / F8 = 3  =>  0 pairs (X) / F9 = 3  => 10 pairs (_)
A9,F9: 3.. / A9 = 3  =>  0 pairs (X) / F9 = 3  => 10 pairs (_)
B1,B3: 4.. / B1 = 4  => 14 pairs (_) / B3 = 4  => 14 pairs (_)
E5,F5: 4.. / E5 = 4  =>  9 pairs (_) / F5 = 4  => 18 pairs (_)
B1,F1: 4.. / B1 = 4  => 14 pairs (_) / F1 = 4  => 14 pairs (_)
E3,E5: 4.. / E3 = 4  => 18 pairs (_) / E5 = 4  =>  9 pairs (_)
G1,H3: 5.. / G1 = 5  =>  0 pairs (X) / H3 = 5  => 14 pairs (_)
A5,C6: 5.. / A5 = 5  =>  0 pairs (X) / C6 = 5  => 10 pairs (_)
H7,G8: 5.. / H7 = 5  =>  0 pairs (X) / G8 = 5  => 14 pairs (_)
F3,H3: 5.. / F3 = 5  =>  0 pairs (X) / H3 = 5  => 14 pairs (_)
A7,H7: 5.. / A7 = 5  => 14 pairs (_) / H7 = 5  =>  0 pairs (X)
C6,C8: 5.. / C6 = 5  => 10 pairs (_) / C8 = 5  =>  0 pairs (X)
G1,G8: 5.. / G1 = 5  =>  0 pairs (X) / G8 = 5  => 14 pairs (_)
H3,H7: 5.. / H3 = 5  => 14 pairs (_) / H7 = 5  =>  0 pairs (X)
G1,G2: 6.. / G1 = 6  =>  0 pairs (X) / G2 = 6  =>  8 pairs (_)
H7,H9: 6.. / H7 = 6  =>  0 pairs (X) / H9 = 6  =>  9 pairs (_)
D2,G2: 6.. / D2 = 6  =>  0 pairs (X) / G2 = 6  =>  8 pairs (_)
E4,E7: 6.. / E4 = 6  => 10 pairs (_) / E7 = 6  => 10 pairs (_)
D4,D5: 7.. / D4 = 7  =>  8 pairs (_) / D5 = 7  => 13 pairs (_)
G4,I5: 7.. / G4 = 7  => 13 pairs (_) / I5 = 7  =>  8 pairs (_)
G9,I9: 7.. / G9 = 7  =>  8 pairs (_) / I9 = 7  => 13 pairs (_)
D4,G4: 7.. / D4 = 7  =>  8 pairs (_) / G4 = 7  => 13 pairs (_)
D5,I5: 7.. / D5 = 7  => 13 pairs (_) / I5 = 7  =>  8 pairs (_)
G4,G9: 7.. / G4 = 7  => 13 pairs (_) / G9 = 7  =>  8 pairs (_)
I5,I9: 7.. / I5 = 7  =>  8 pairs (_) / I9 = 7  => 13 pairs (_)
A1,A5: 8.. / A1 = 8  => 12 pairs (_) / A5 = 8  => 18 pairs (_)
* DURATION: 0:00:46.161570  START: 04:09:07.810506  END: 04:09:53.972076 2017-05-01
* CP COUNT: (35)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,C2,E5,G2,G9,H4,H9)
* ....2..7.25..97.346.73..2..4.......5.16...32.7......46.72..94.3.6.47..1..84.5....
* PAIR C2: 1,8 BLK 1
C1: 1,8,3,9                              # reduction candidate for 1,8
C1: 1,8                                  # 18 pairs
C1: 3,9                                  # 12 pairs
* PAIR C2: 1,8 ROW 2
D2: 1,8,6                                # reduction candidate for 1,8
D2: 6 => CTR
* 8...2.67.2516978346.738.25.428..6.95.16...3287.5..2146572.69483.6.478512184253967
D2: 1,8                                  #  8 pairs
* PAIR B3: 4,9 BLK 1
B1: 4,9,3                                # reduction candidate for 4,9
B1: 3                                    # 21 pairs
B1: 4,9                                  # 14 pairs
* PAIR G2: 6,8 BLK 3
G1: 6,8,5,9                              # reduction candidate for 6,8
G1: 6,8                                  # 22 pairs
G1: 5,9                                  #  9 pairs
* PAIR G2: 6,8 ROW 2
D2: 6,8,1                                # reduction candidate for 6,8
D2: 1 => CTR
* 341526879258197634697384251439261.85816.4532.7.5.3..46572819463963472518184653.92
D2: 6,8                                  #  9 pairs
* PAIR E5: 4,8 BLK 5
F5: 4,8,5                                # reduction candidate for 4,8
F5: 4,8                                  # 15 pairs
F5: 5                                    # 14 pairs
* PAIR E5: 4,8 COL E
E3: 4,8,1                                # reduction candidate for 4,8
E3: 1                                    # 12 pairs
E3: 4,8                                  # 11 pairs
* PAIR H4: 8,9 BLK 6
G4: 8,9,1,7                              # reduction candidate for 8,9
G4: 8,9                                  # 20 pairs
I5: 8,9,7                                # reduction candidate for 8,9
I5: 8,9                                  # 13 pairs
G6: 8,9,1                                # reduction candidate for 8,9
G6: 8,9                                  #  9 pairs
* PAIR H4: 8,9 ROW 4
C4: 8,9,3                                # reduction candidate for 8,9
C4: 8,9                                  # 11 pairs
D4: 8,9,1,2,6,7                          # reduction candidate for 8,9
D4: 8,9 => CTR
* .3..2457.25..97634647385291423916785516748329798532146172869453.65473812384251967
D4: 1,2,6,7                              #  8 pairs
* PAIR H4: 8,9 COL H
H3: 8,9,5                                # reduction candidate for 8,9
H3: 8,9 => CTR
* 8..62457.2518976346.73.52..4.......5.16...32.7......46172..9453.6.47..1..84.5..6.
H3: 5                                    # 14 pairs
* PAIR G9: 7,9 BLK 9
I9: 7,9,2                                # reduction candidate for 7,9
I9: 2 => CTR
* ...526.7.25..976346.73..25.42.76..858169453277.5238146572..9463.6.472518184653792
I9: 7,9                                  # 13 pairs
* PAIR G9: 7,9 COL G
G4: 7,9,1,8                              # reduction candidate for 7,9
G4: 7,9                                  # 11 pairs
G4: 1,8                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0038-base-pr-000.dot
* REASONING
* DIS # D2: 6 => CTR => D2: 1,8
* DIS # D2: 1 => CTR => D2: 6,8
* DIS # D4: 8,9 => CTR => D4: 1,2,6,7
* DIS # H3: 8,9 => CTR => H3: 5
* DIS # I9: 2 => CTR => I9: 7,9
* CNT   5 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,C2,E5,G2,G9,H4,H9)
* ....2..7.25..97.346.73..2..4.......5.16...32.7......46.72..94.3.6.47..1..84.5....
* PAIR C2: 1,8 BLK 1
C1: 1,8,3,9                              # reduction candidate for 1,8
C1: 1,8                                  # 18 pairs
C1: 3,9                                  # 12 pairs
* PAIR C2: 1,8 ROW 2
D2: 1,8,6                                # reduction candidate for 1,8
D2: 6 => CTR
* 8...2.67.2516978346.738.25.428..6.95.16...3287.5..2146572.69483.6.478512184253967
* PAIR RESTART
* PAIR C2: 1,8 BLK 1
C1: 1,8,3,9                              # reduction candidate for 1,8
C1: 1,8 => CTR
* 34.5268792581976346973842514.9.6..858169453277.5.38.46572..946396347.518184653.92
* PAIR B3: 4,9 BLK 1
B1: 4,9,3                                # reduction candidate for 4,9
B1: 3 => CTR
* 8396245712518976346473152..4.3.6...5516.4832.7.853..46172.89453.6547..1..84.5..6.
* PAIR E5: 4,8 BLK 5
F5: 4,8,5                                # reduction candidate for 4,8
F5: 5 => CTR
* 8.3.2..7.2518976346.73..2..4.......5.16.453287.5....46.72..94.3.6947.812.84.5...7
* PAIR H4: 8,9 BLK 6
G6: 8,9,1                                # reduction candidate for 8,9
G6: 1 => CTR
* 8.352697.2518976346.73..2..4......85.16...3297.89.5146.72.894.3.6547.812.84.5...7
* PAIR H4: 8,9 COL H
H3: 8,9,5                                # reduction candidate for 8,9
H3: 8,9 => CTR
* 8.31265792518976346973452..4..7..1.5.16...3277......46172689453.6.47..1..84.5.76.
H3: 5 => SOLVED
* 843625971251897634697341258428736195916584327735912846572169483369478512184253769
* DURATION: 0:00:14.007945  START: 04:10:13.941014  END: 04:10:27.948959 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0038-base-pr-001.dot
* REASONING
* DIS # D2: 6 => CTR => D2: 1,8
* DIS D2: 1,8 # C1: 1,8 => CTR => C1: 3,9
* DIS D2: 1,8 + C1: 3,9 # B1: 3 => CTR => B1: 4,9
* DIS D2: 1,8 + C1: 3,9 + B1: 4,9 # F5: 5 => CTR => F5: 4,8
* DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 # G6: 1 => CTR => G6: 8,9
* DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 # H3: 8,9 => CTR => H3: 5
* PRF D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5 => SOL
* STA D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5
* CNT   7 HDP CHAINS /  12 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=38
```

# Solution

position: 843625971251897634697341258428736195916584327735912846572169483369478512184253769 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 # C1: 1,8 => UNS
* INC # C1: 3,9 => UNS
* INC # D2: 1,8 => UNS
* DIS # D2: 6 => CTR => D2: 1,8
* INC # B1: 4,9 => UNS
* INC # B1: 3 => UNS
* INC # G1: 6,8 => UNS
* INC # G1: 5,9 => UNS
* INC # D2: 6,8 => UNS
* DIS # D2: 1 => CTR => D2: 6,8
* INC # F5: 4,8 => UNS
* INC # F5: 5 => UNS
* INC # E3: 4,8 => UNS
* INC # E3: 1 => UNS
* INC # G4: 8,9 => UNS
* INC # I5: 8,9 => UNS
* INC # G6: 8,9 => UNS
* INC # C4: 8,9 => UNS
* DIS # D4: 8,9 => CTR => D4: 1,2,6,7
* INC # D4: 1,2,6,7 => UNS
* DIS # H3: 8,9 => CTR => H3: 5
* INC # H3: 5 => UNS
* INC # I9: 7,9 => UNS
* DIS # I9: 2 => CTR => I9: 7,9
* INC # G4: 7,9 => UNS
* INC # G4: 1,8 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # C1: 1,8 => UNS
* INC # C1: 3,9 => UNS
* INC # D2: 1,8 => UNS
* DIS # D2: 6 => CTR => D2: 1,8
* DIS D2: 1,8 # C1: 1,8 => CTR => C1: 3,9
* INC D2: 1,8 + C1: 3,9 # B1: 4,9 => UNS
* DIS D2: 1,8 + C1: 3,9 # B1: 3 => CTR => B1: 4,9
* INC D2: 1,8 + C1: 3,9 + B1: 4,9 # F5: 4,8 => UNS
* DIS D2: 1,8 + C1: 3,9 + B1: 4,9 # F5: 5 => CTR => F5: 4,8
* INC D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 # G6: 8,9 => UNS
* DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 # G6: 1 => CTR => G6: 8,9
* DIS D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 # H3: 8,9 => CTR => H3: 5
* PRF D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5 => SOL
* STA D2: 1,8 + C1: 3,9 + B1: 4,9 + F5: 4,8 + G6: 8,9 + H3: 5
* CNT  13 HDP CHAINS /  12 HYP OPENED
```