# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=92

level: medium

position: ...8....2.....4.5..63...9....2.9...1..1...6..3...5.7....4...23..7.1.....5....7... initial

# Autosolve

position: ..58....2.27..4.5..63...9....2.9...1..1...6..3...517....4...23727.1.....53...7... autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # D3: 7 => CTR => D3: 2,5
* DIS # H3: 4,8 => CTR => H3: 1,7
* DIS # A3: 1 => CTR => A3: 4,8
* DIS # I8: 4,8 => CTR => I8: 5,6,9
* DIS # H6: 4,8 => CTR => H6: 2,9
* DIS # B4: 5 => CTR => B4: 4,8
* DIS # H3: 4,8 => CTR => H3: 1,7
* CNT   7 HDP CHAINS /  24 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # D3: 7 => CTR => D3: 2,5
* DIS D3: 2,5 # H3: 4,8 => CTR => H3: 1,7
* DIS D3: 2,5 + H3: 1,7 # I8: 4,8 => CTR => I8: 5,6,9
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 # H6: 4,8 => CTR => H6: 2,9
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # B4: 5 => CTR => B4: 4,8
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # I6: 9 => CTR => I6: 4,8
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # F7: 6,8 => CTR => F7: 5,9
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 # E8: 6,8 => CTR => E8: 3,4
* PRF D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 # F8: 6,8 => SOL
* STA D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 + F8: 6,8
* CNT   9 HDP CHAINS /  22 HYP OPENED
```

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

# Details

## Positions

 ...8....2.....4.5..63...9....2.9...1..1...6..3...5.7....4...23..7.1.....5....7... initial ..58....2.27..4.5..63...9....2.9...1..1...6..3...517....4...23727.1.....53...7... autosolve 145869372927314856863572914782693541451728693396451728614985237279136485538247169 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (6)
F3: 2,5
I3: 4,8
G4: 3,5
H4: 4,8
I5: 3,5
E7: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A7,B7: 1.. / A7 = 1  => 19 pairs (_) / B7 = 1  =>  9 pairs (_)
G9,H9: 1.. / G9 = 1  => 16 pairs (_) / H9 = 1  =>  7 pairs (_)
B1,B7: 1.. / B1 = 1  => 19 pairs (_) / B7 = 1  =>  9 pairs (_)
H5,H6: 2.. / H5 = 2  =>  0 pairs (X) / H6 = 2  =>  7 pairs (_)
D9,E9: 2.. / D9 = 2  =>  8 pairs (_) / E9 = 2  =>  8 pairs (_)
D6,H6: 2.. / D6 = 2  =>  0 pairs (X) / H6 = 2  =>  7 pairs (_)
F3,F5: 2.. / F3 = 2  =>  8 pairs (_) / F5 = 2  =>  7 pairs (_)
G4,I5: 3.. / G4 = 3  =>  0 pairs (X) / I5 = 3  => 10 pairs (_)
E8,F8: 3.. / E8 = 3  => 16 pairs (_) / F8 = 3  =>  9 pairs (_)
I2,I5: 3.. / I2 = 3  =>  0 pairs (X) / I5 = 3  => 10 pairs (_)
D3,F3: 5.. / D3 = 5  =>  8 pairs (_) / F3 = 5  =>  7 pairs (_)
B4,B5: 5.. / B4 = 5  =>  0 pairs (X) / B5 = 5  => 10 pairs (_)
G4,I5: 5.. / G4 = 5  => 10 pairs (_) / I5 = 5  =>  0 pairs (X)
D7,F7: 5.. / D7 = 5  =>  7 pairs (_) / F7 = 5  =>  8 pairs (_)
G8,I8: 5.. / G8 = 5  =>  0 pairs (X) / I8 = 5  => 10 pairs (_)
B4,G4: 5.. / B4 = 5  =>  0 pairs (X) / G4 = 5  => 10 pairs (_)
B5,I5: 5.. / B5 = 5  => 10 pairs (_) / I5 = 5  =>  0 pairs (X)
D3,D7: 5.. / D3 = 5  =>  8 pairs (_) / D7 = 5  =>  7 pairs (_)
F3,F7: 5.. / F3 = 5  =>  7 pairs (_) / F7 = 5  =>  8 pairs (_)
G4,G8: 5.. / G4 = 5  => 10 pairs (_) / G8 = 5  =>  0 pairs (X)
I5,I8: 5.. / I5 = 5  =>  0 pairs (X) / I8 = 5  => 10 pairs (_)
H1,I2: 6.. / H1 = 6  => 12 pairs (_) / I2 = 6  => 11 pairs (_)
A4,C6: 6.. / A4 = 6  => 15 pairs (_) / C6 = 6  => 13 pairs (_)
C6,D6: 6.. / C6 = 6  => 13 pairs (_) / D6 = 6  => 15 pairs (_)
A4,A7: 6.. / A4 = 6  => 15 pairs (_) / A7 = 6  => 13 pairs (_)
H1,H3: 7.. / H1 = 7  => 12 pairs (_) / H3 = 7  =>  9 pairs (_)
A4,A5: 7.. / A4 = 7  => 13 pairs (_) / A5 = 7  =>  9 pairs (_)
E1,H1: 7.. / E1 = 7  =>  9 pairs (_) / H1 = 7  => 12 pairs (_)
A4,D4: 7.. / A4 = 7  => 13 pairs (_) / D4 = 7  =>  9 pairs (_)
A2,A3: 8.. / A2 = 8  => 13 pairs (_) / A3 = 8  =>  9 pairs (_)
F1,D2: 9.. / F1 = 9  =>  0 pairs (*) / D2 = 9  =>  0 pairs (X)
A2,D2: 9.. / A2 = 9  =>  0 pairs (*) / D2 = 9  =>  0 pairs (X)
* DURATION: 0:00:43.276404  START: 05:07:49.005216  END: 05:08:32.281620 2017-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E7,F3,G4,H4,I3,I5)
* ..58....2.27..4.5..63...9....2.9...1..1...6..3...517....4...23727.1.....53...7...
* PAIR F3: 2,5 BLK 2
D3: 2,5,7                                # reduction candidate for 2,5
D3: 7 => CTR
* ..58...72.279.4.56.637259..7.2698341..13726.53.645172.61458923727.1..5..53.2.7...
D3: 2,5                                  #  8 pairs
* PAIR I3: 4,8 BLK 3
H3: 4,8,1,7                              # reduction candidate for 4,8
H3: 4,8 => CTR
* ..58...728279.4.56.63...9..7.23965.1.51...6.33.6.517..6145892372791.3.6553...7.19
H3: 1,7                                  #  8 pairs
* PAIR I3: 4,8 ROW 3
A3: 4,8,1                                # reduction candidate for 4,8
A3: 1 => CTR
* ..58...728279.4.56163...9..7.23965.1.51...6.33.6.517..6145892372791.3.6553...7.19
A3: 4,8                                  #  8 pairs
* PAIR I3: 4,8 COL I
I6: 4,8,9                                # reduction candidate for 4,8
I6: 4,8                                  # 11 pairs
I8: 4,8,5,6,9                            # reduction candidate for 4,8
I8: 4,8 => CTR
* 9.5873462827964153463.1.97865279.3.17913..6.53...517.9..4.8.23727.13.594539..7816
I8: 5,6,9                                #  6 pairs
I9: 4,8,6,9                              # reduction candidate for 4,8
I9: 4,8                                  # 18 pairs
* PAIR H4: 4,8 BLK 6
H5: 4,8,2,9                              # reduction candidate for 4,8
H5: 4,8                                  # 18 pairs
H6: 4,8,2,9                              # reduction candidate for 4,8
H6: 4,8 => CTR
* 1458.93.2927..4.5.8635.29.4..2.9...1.91..86253.62517.961498523727.1..5..53..2741.
H6: 2,9                                  #  7 pairs
I6: 4,8,9                                # reduction candidate for 4,8
I6: 4,8                                  # 11 pairs
* PAIR H4: 4,8 ROW 4
B4: 4,8,5                                # reduction candidate for 4,8
B4: 5 => CTR
* ..5873462.27964153463.1.9786527983417.13.26.53.9.517....4.8.23727.13.5..53...7.1.
B4: 4,8                                  # 10 pairs
* PAIR H4: 4,8 COL H
H3: 4,8,1,7                              # reduction candidate for 4,8
H3: 4,8 => CTR
* ..58...728279.4.56.63...9..7.23965.1.51...6.33.6.517..6145892372791.3.6553...7.19
H3: 1,7                                  #  8 pairs
H8: 4,8,6,9                              # reduction candidate for 4,8
H8: 4,8                                  # 15 pairs
H9: 4,8,1,6,9                            # reduction candidate for 4,8
H9: 4,8                                  # 22 pairs
* PAIR E7: 6,8 BLK 8
F7: 6,8,5,9                              # reduction candidate for 6,8
F7: 6,8                                  # 23 pairs
E8: 6,8,3,4                              # reduction candidate for 6,8
E8: 6,8                                  # 20 pairs
F8: 6,8,3,9                              # reduction candidate for 6,8
F8: 6,8                                  # 26 pairs
E9: 6,8,2,4                              # reduction candidate for 6,8
E9: 6,8                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0092-base-pr-000.dot
* REASONING
* DIS # D3: 7 => CTR => D3: 2,5
* DIS # H3: 4,8 => CTR => H3: 1,7
* DIS # A3: 1 => CTR => A3: 4,8
* DIS # I8: 4,8 => CTR => I8: 5,6,9
* DIS # H6: 4,8 => CTR => H6: 2,9
* DIS # B4: 5 => CTR => B4: 4,8
* DIS # H3: 4,8 => CTR => H3: 1,7
* CNT   7 HDP CHAINS /  24 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E7,F3,G4,H4,I3,I5)
* ..58....2.27..4.5..63...9....2.9...1..1...6..3...517....4...23727.1.....53...7...
* PAIR F3: 2,5 BLK 2
D3: 2,5,7                                # reduction candidate for 2,5
D3: 7 => CTR
* ..58...72.279.4.56.637259..7.2698341..13726.53.645172.61458923727.1..5..53.2.7...
* PAIR I3: 4,8 BLK 3
H3: 4,8,1,7                              # reduction candidate for 4,8
H3: 4,8 => CTR
* ..58...728279.4.56163.7.9..7.23965.1.517..6.33.6.517..6145892372791.3.6553...7.19
* PAIR I3: 4,8 COL I
I6: 4,8,9                                # reduction candidate for 4,8
I6: 4,8                                  # 15 pairs
I8: 4,8,5,6,9                            # reduction candidate for 4,8
I8: 4,8 => CTR
* 9.5873462827964153463.1.97865279.3.17913..6.53...517.9..4.8.23727.13.594539..7816
I9: 4,8,6,9                              # reduction candidate for 4,8
I9: 4,8                                  # 20 pairs
* PAIR RESTART
* PAIR I3: 4,8 COL I
I6: 4,8,9                                # reduction candidate for 4,8
I6: 4,8                                  # 15 pairs
I9: 4,8,6,9                              # reduction candidate for 4,8
I9: 4,8                                  # 20 pairs
* PAIR H4: 4,8 BLK 6
H5: 4,8,2,9                              # reduction candidate for 4,8
H5: 4,8                                  # 21 pairs
H6: 4,8,2,9                              # reduction candidate for 4,8
H6: 4,8 => CTR
* ..58.9..2927..4.5.8635.29.4..2.9...1.91..86253.62517.961498523727.1..5.653.627418
I6: 4,8,9                                # reduction candidate for 4,8
I6: 4,8                                  # 15 pairs
* PAIR H4: 4,8 ROW 4
B4: 4,8,5                                # reduction candidate for 4,8
B4: 5 => CTR
* ..5873462827964153463.1.9786527983.17.13..6.53...517....4.8.23727.13.54.53...781.
* PAIR H4: 4,8 COL H
H8: 4,8,6,9                              # reduction candidate for 4,8
H8: 4,8                                  # 26 pairs
H9: 4,8,1,6,9                            # reduction candidate for 4,8
H9: 4,8                                  # 24 pairs
* PAIR RESTART
* PAIR H4: 4,8 BLK 6
I6: 4,8,9                                # reduction candidate for 4,8
I6: 9 => CTR
* .958....2.279.4.5..63...9..74239658195172864338645172961458.23727.1....553...7...
* PAIR H4: 4,8 COL H
H8: 4,8,6                                # reduction candidate for 4,8
H8: 4,8                                  # 26 pairs
H9: 4,8,1,6                              # reduction candidate for 4,8
H9: 4,8                                  # 24 pairs
* PAIR E7: 6,8 BLK 8
F7: 6,8,5,9                              # reduction candidate for 6,8
F7: 6,8 => CTR
* ..58....2.279.4.56.632.59....23965.1.517826933...5172...45..23727.1.9..553..27..9
E8: 6,8,3,4                              # reduction candidate for 6,8
E8: 6,8 => CTR
* ..58....2.27..4.56.63...9....23965.1.517.86.33.6.517..614.8.237279163..5538..7.69
F8: 6,8,3,9                              # reduction candidate for 6,8
F8: 6,8 => SOLVED
* 145869372927314856863572914782693541451728693396451728614985237279136485538247169
* DURATION: 0:00:22.635944  START: 05:08:51.798170  END: 05:09:14.434114 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0092-base-pr-001.dot
* REASONING
* DIS # D3: 7 => CTR => D3: 2,5
* DIS D3: 2,5 # H3: 4,8 => CTR => H3: 1,7
* DIS D3: 2,5 + H3: 1,7 # I8: 4,8 => CTR => I8: 5,6,9
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 # H6: 4,8 => CTR => H6: 2,9
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # B4: 5 => CTR => B4: 4,8
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # I6: 9 => CTR => I6: 4,8
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # F7: 6,8 => CTR => F7: 5,9
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 # E8: 6,8 => CTR => E8: 3,4
* PRF D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 # F8: 6,8 => SOL
* STA D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 + F8: 6,8
* CNT   9 HDP CHAINS /  22 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=92
```

# Solution

position: 145869372927314856863572914782693541451728693396451728614985237279136485538247169 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 # D3: 2,5 => UNS
* DIS # D3: 7 => CTR => D3: 2,5
* DIS # H3: 4,8 => CTR => H3: 1,7
* INC # H3: 1,7 => UNS
* INC # A3: 4,8 => UNS
* DIS # A3: 1 => CTR => A3: 4,8
* INC # I6: 4,8 => UNS
* DIS # I8: 4,8 => CTR => I8: 5,6,9
* INC # I8: 5,6,9 => UNS
* INC # I9: 4,8 => UNS
* INC # H5: 4,8 => UNS
* DIS # H6: 4,8 => CTR => H6: 2,9
* INC # H6: 2,9 => UNS
* INC # I6: 4,8 => UNS
* INC # B4: 4,8 => UNS
* DIS # B4: 5 => CTR => B4: 4,8
* DIS # H3: 4,8 => CTR => H3: 1,7
* INC # H3: 1,7 => UNS
* INC # H8: 4,8 => UNS
* INC # H9: 4,8 => UNS
* INC # F7: 6,8 => UNS
* INC # E8: 6,8 => UNS
* INC # F8: 6,8 => UNS
* INC # E9: 6,8 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # D3: 2,5 => UNS
* DIS # D3: 7 => CTR => D3: 2,5
* DIS D3: 2,5 # H3: 4,8 => CTR => H3: 1,7
* INC D3: 2,5 + H3: 1,7 # I6: 4,8 => UNS
* DIS D3: 2,5 + H3: 1,7 # I8: 4,8 => CTR => I8: 5,6,9
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 # I9: 4,8 => UNS
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 # I6: 4,8 => UNS
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 # I9: 4,8 => UNS
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 # H5: 4,8 => UNS
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 # H6: 4,8 => CTR => H6: 2,9
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # I6: 4,8 => UNS
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # B4: 4,8 => UNS
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # B4: 5 => CTR => B4: 4,8
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # H8: 4,8 => UNS
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # H9: 4,8 => UNS
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # I6: 4,8 => UNS
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # I6: 9 => CTR => I6: 4,8
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # H8: 4,8 => UNS
* INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # H9: 4,8 => UNS
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # F7: 6,8 => CTR => F7: 5,9
* DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 # E8: 6,8 => CTR => E8: 3,4
* PRF D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 # F8: 6,8 => SOL
* STA D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 + F8: 6,8
* CNT  22 HDP CHAINS /  22 HYP OPENED
```