# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=263

level: medium

position: ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... initial

# Autosolve

position: ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* PRF # I4: 1 => SOL
* DIS # H2: 9 => CTR => H2: 4,7
* 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:

```* PRF # I4: 1 => SOL
* STA I4: 1
* CNT   1 HDP CHAINS /  10 HYP OPENED
```

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

# Details

## Positions

 ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... initial ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6... autosolve 527394816498261573613875924965723481284619357731458269146982735859137642372546198 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (9)
I1: 6,8
G3: 3,9
H4: 5,8
G5: 1,3
H5: 5,8
G6: 2,3
C9: 2,3
H8: 4,7
H9: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,E5: 1.. / E4 = 1  => 11 pairs (_) / E5 = 1  =>  0 pairs (*)
I4,G5: 1.. / I4 = 1  =>  0 pairs (*) / G5 = 1  =>  0 pairs (X)
A7,A9: 1.. / A7 = 1  => 10 pairs (_) / A9 = 1  => 10 pairs (_)
E4,I4: 1.. / E4 = 1  => 11 pairs (_) / I4 = 1  =>  0 pairs (*)
E5,G5: 1.. / E5 = 1  =>  0 pairs (*) / G5 = 1  =>  0 pairs (X)
I4,G6: 2.. / I4 = 2  => 16 pairs (_) / G6 = 2  => 10 pairs (_)
C5,A6: 4.. / C5 = 4  =>  9 pairs (_) / A6 = 4  => 18 pairs (_)
D5,D6: 4.. / D5 = 4  => 18 pairs (_) / D6 = 4  =>  9 pairs (_)
E8,E9: 4.. / E8 = 4  => 14 pairs (_) / E9 = 4  => 11 pairs (_)
C5,D5: 4.. / C5 = 4  =>  9 pairs (_) / D5 = 4  => 18 pairs (_)
A6,D6: 4.. / A6 = 4  => 18 pairs (_) / D6 = 4  =>  9 pairs (_)
C3,C5: 4.. / C3 = 4  => 18 pairs (_) / C5 = 4  =>  9 pairs (_)
E1,F3: 5.. / E1 = 5  => 15 pairs (_) / F3 = 5  => 11 pairs (_)
H4,H5: 5.. / H4 = 5  =>  9 pairs (_) / H5 = 5  => 10 pairs (_)
I7,I8: 5.. / I7 = 5  => 11 pairs (_) / I8 = 5  => 13 pairs (_)
D5,E5: 6.. / D5 = 6  => 11 pairs (_) / E5 = 6  => 12 pairs (_)
A7,C7: 6.. / A7 = 6  => 11 pairs (_) / C7 = 6  => 10 pairs (_)
G1,H2: 7.. / G1 = 7  => 13 pairs (_) / H2 = 7  => 17 pairs (_)
C4,A6: 7.. / C4 = 7  => 10 pairs (_) / A6 = 7  =>  0 pairs (*)
G7,H8: 7.. / G7 = 7  => 17 pairs (_) / H8 = 7  => 13 pairs (_)
A2,H2: 7.. / A2 = 7  => 13 pairs (_) / H2 = 7  => 17 pairs (_)
F8,H8: 7.. / F8 = 7  => 17 pairs (_) / H8 = 7  => 13 pairs (_)
C1,C4: 7.. / C1 = 7  =>  0 pairs (*) / C4 = 7  =>  0 pairs (X)
G1,G7: 7.. / G1 = 7  => 13 pairs (_) / G7 = 7  => 17 pairs (_)
H2,H8: 7.. / H2 = 7  => 17 pairs (_) / H8 = 7  => 13 pairs (_)
D3,F3: 8.. / D3 = 8  => 11 pairs (_) / F3 = 8  => 16 pairs (_)
G1,I1: 8.. / G1 = 8  => 21 pairs (_) / I1 = 8  => 10 pairs (_)
H4,H5: 8.. / H4 = 8  => 10 pairs (_) / H5 = 8  =>  9 pairs (_)
G1,G9: 8.. / G1 = 8  => 21 pairs (_) / G9 = 8  => 10 pairs (_)
B1,B2: 9.. / B1 = 9  => 11 pairs (_) / B2 = 9  => 15 pairs (_)
H2,H9: 9.. / H2 = 9  =>  0 pairs (X) / H9 = 9  =>  9 pairs (_)
* DURATION: 0:00:28.897832  START: 13:51:47.775413  END: 13:52:16.673245 2019-04-28
* CP COUNT: (31)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,G3,G5,G6,H4,H5,H8,H9,I1)
* ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6...
* PAIR H4: 5,8 ROW 4
F4: 5,8,2,3,7                            # reduction candidate for 5,8
F4: 5,8                                  # 12 pairs
F4: 2,3,7                                #  9 pairs
* PAIR G5: 1,3 BLK 6
I4: 1,3,2                                # reduction candidate for 1,3
I4: 2                                    # 16 pairs
I4: 1,3                                  # 10 pairs
* PAIR G5: 1,3 ROW 5
E5: 1,3,5,6,9                            # reduction candidate for 1,3
E5: 1,3                                  # 15 pairs
E5: 5,6,9                                # 11 pairs
* PAIR H5: 5,8 ROW 5
B5: 5,8,3                                # reduction candidate for 5,8
B5: 5,8                                  # 12 pairs
F5: 5,8,3,9                              # reduction candidate for 5,8
F5: 5,8                                  # 21 pairs
* PAIR G6: 2,3 BLK 6
I4: 2,3,1                                # reduction candidate for 2,3
I4: 1 => SOLVED
* 527394816498261573613875924965723481284619357731458269146982735859137642372546198
I4: 2,3                                  # 11 pairs
* PAIR G6: 2,3 ROW 6
E6: 2,3,5                                # reduction candidate for 2,3
E6: 2,3                                  # 11 pairs
F6: 2,3,5,7,8                            # reduction candidate for 2,3
F6: 2,3                                  # 15 pairs
* PAIR C9: 2,3 BLK 7
B8: 2,3,5,8                              # reduction candidate for 2,3
B8: 5,8                                  # 16 pairs
B8: 2,3                                  # 14 pairs
* PAIR C9: 2,3 ROW 9
E9: 2,3,4,9                              # reduction candidate for 2,3
E9: 2,3                                  # 22 pairs
E9: 4,9                                  # 11 pairs
* PAIR H8: 4,7 COL H
H2: 4,7,9                                # reduction candidate for 4,7
H2: 9 => CTR
* .923.4718738.21594.1..7.326967.1.4.32...3.1.73.1457269.46782931829143675.73596842
H2: 4,7                                  #  9 pairs
* PAIR H9: 4,9 ROW 9
E9: 4,9,2,3                              # reduction candidate for 4,9
E9: 2,3                                  # 22 pairs
E9: 4,9                                  # 11 pairs
* PAIR H9: 4,9 COL H
H2: 4,9,7                                # reduction candidate for 4,9
H2: 7                                    # 17 pairs
H2: 4,9                                  # 13 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0263-base-pr-000.dot
* REASONING
* PRF # I4: 1 => SOL
* DIS # H2: 9 => CTR => H2: 4,7
* CNT   2 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,G3,G5,G6,H4,H5,H8,H9,I1)
* ...3.4.1...8..15...1..7..2.96....4..2.......7..1....69.4..8..3...91..6...7.5.6...
* PAIR H4: 5,8 ROW 4
F4: 5,8,2,3,7                            # reduction candidate for 5,8
F4: 5,8                                  # 12 pairs
F4: 2,3,7                                #  9 pairs
* PAIR G5: 1,3 BLK 6
I4: 1,3,2                                # reduction candidate for 1,3
I4: 2                                    # 16 pairs
I4: 1,3                                  # 10 pairs
* PAIR G5: 1,3 ROW 5
E5: 1,3,5,6,9                            # reduction candidate for 1,3
E5: 1,3                                  # 15 pairs
E5: 5,6,9                                # 11 pairs
* PAIR H5: 5,8 ROW 5
B5: 5,8,3                                # reduction candidate for 5,8
B5: 5,8                                  # 12 pairs
F5: 5,8,3,9                              # reduction candidate for 5,8
F5: 5,8                                  # 21 pairs
* PAIR G6: 2,3 BLK 6
I4: 2,3,1                                # reduction candidate for 2,3
I4: 1 => SOLVED
* 527394816498261573613875924965723481284619357731458269146982735859137642372546198
* DURATION: 0:00:05.827161  START: 13:52:28.197527  END: 13:52:34.024688 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0263-base-pr-001.dot
* REASONING
* PRF # I4: 1 => SOL
* STA I4: 1
* CNT   1 HDP CHAINS /  10 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=263
```

# Solution

position: 527394816498261573613875924965723481284619357731458269146982735859137642372546198 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 # F4: 5,8 => UNS
* INC # F4: 2,3,7 => UNS
* INC # I4: 1,3 => UNS
* INC # I4: 2 => UNS
* INC # E5: 1,3 => UNS
* INC # E5: 5,6,9 => UNS
* INC # B5: 5,8 => UNS
* INC # F5: 5,8 => UNS
* INC # I4: 2,3 => UNS
* PRF # I4: 1 => SOL
* INC # E6: 2,3 => UNS
* INC # F6: 2,3 => UNS
* INC # B8: 2,3 => UNS
* INC # B8: 5,8 => UNS
* INC # E9: 2,3 => UNS
* INC # E9: 4,9 => UNS
* INC # H2: 4,7 => UNS
* DIS # H2: 9 => CTR => H2: 4,7
* INC # E9: 4,9 => UNS
* INC # E9: 2,3 => UNS
* INC # H2: 4,9 => UNS
* INC # H2: 7 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # F4: 5,8 => UNS
* INC # F4: 2,3,7 => UNS
* INC # I4: 1,3 => UNS
* INC # I4: 2 => UNS
* INC # E5: 1,3 => UNS
* INC # E5: 5,6,9 => UNS
* INC # B5: 5,8 => UNS
* INC # F5: 5,8 => UNS
* INC # I4: 2,3 => UNS
* PRF # I4: 1 => SOL
* STA I4: 1
* CNT  10 HDP CHAINS /  10 HYP OPENED
```