Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=319

level: hard

position: .8..9...32.9.8....5..3.78...5......6..1...9..8......2...85.6..7....7.1.97...3..5. initial

Autosolve

position: .87.9...3239.8....5..3.789..5......6..1...9..8......2...85.6..7..5.7.1.97...3..5. autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # A8: 4,6 => CTR => A8: 3
* DIS # A7: 3,4 => CTR => A7: 1,9
* CNT   2 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 # A8: 4,6 => CTR => A8: 3
* STA A8: 3
* CNT   1 HDP CHAINS /  55 HYP OPENED
```

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

Pair Reduction Position

position: .87.9...3239.8....5..3.789..5......6..1...9..8......2...85.6..73.5.7.1.97...3..5. pair_reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Time used: 0:00:32.221829

The following important HDP chains were detected:

```* DIS # A1: 4,6 # C6: 4,6 => CTR => C6: 3
* DIS # A1: 4,6 + C6: 3 # C9: 2 => CTR => C9: 4,6
* DIS # A1: 4,6 + C6: 3 + C9: 4,6 # E6: 4,6 => CTR => E6: 1,5
* PRF # A1: 4,6 + C6: 3 + C9: 4,6 + E6: 1,5 # E5: 2,5 => SOL
* STA # A1: 4,6 + C6: 3 + C9: 4,6 + E6: 1,5 + E5: 2,5
* CNT   4 HDP CHAINS /  37 HYP OPENED
```

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

Details

Positions

 .8..9...32.9.8....5..3.78...5......6..1...9..8......2...85.6..7....7.1.97...3..5. initial .87.9...3239.8....5..3.789..5......6..1...9..8......2...85.6..7..5.7.1.97...3..5. autosolve .87.9...3239.8....5..3.789..5......6..1...9..8......2...85.6..73.5.7.1.97...3..5. pair_reduction 687294513239185674514367892952718346471623985863459721198546237345872169726931458 solved

level: hard

Pairing Analysis

```--------------------------------------------------
* PAIRS (4)
C3: 4,6
A4: 4,9
A5: 4,6
H7: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B3: 1.. / A1 = 1  => 10 pairs (_) / B3 = 1  => 10 pairs (_)
H4,I6: 1.. / H4 = 1  =>  7 pairs (_) / I6 = 1  =>  6 pairs (_)
A1,A7: 1.. / A1 = 1  => 10 pairs (_) / A7 = 1  => 10 pairs (_)
G1,I3: 2.. / G1 = 2  =>  0 pairs (X) / I3 = 2  =>  5 pairs (_)
C4,B5: 2.. / C4 = 2  =>  6 pairs (_) / B5 = 2  =>  8 pairs (_)
E3,I3: 2.. / E3 = 2  =>  0 pairs (X) / I3 = 2  =>  5 pairs (_)
C4,C9: 2.. / C4 = 2  =>  6 pairs (_) / C9 = 2  =>  8 pairs (_)
I3,I9: 2.. / I3 = 2  =>  5 pairs (_) / I9 = 2  =>  0 pairs (X)
C4,C6: 3.. / C4 = 3  => 10 pairs (_) / C6 = 3  =>  5 pairs (_)
A7,A8: 3.. / A7 = 3  =>  0 pairs (X) / A8 = 3  =>  4 pairs (_)
F5,H5: 3.. / F5 = 3  =>  4 pairs (_) / H5 = 3  => 12 pairs (_)
A8,H8: 3.. / A8 = 3  =>  4 pairs (_) / H8 = 3  =>  0 pairs (X)
F1,F2: 5.. / F1 = 5  =>  5 pairs (_) / F2 = 5  =>  6 pairs (_)
E5,E6: 5.. / E5 = 5  =>  5 pairs (_) / E6 = 5  =>  6 pairs (_)
F1,G1: 5.. / F1 = 5  =>  5 pairs (_) / G1 = 5  =>  6 pairs (_)
E5,I5: 5.. / E5 = 5  =>  5 pairs (_) / I5 = 5  =>  6 pairs (_)
H8,G9: 6.. / H8 = 6  =>  8 pairs (_) / G9 = 6  =>  5 pairs (_)
G2,H2: 7.. / G2 = 7  =>  5 pairs (_) / H2 = 7  =>  4 pairs (_)
B5,B6: 7.. / B5 = 7  =>  6 pairs (_) / B6 = 7  =>  3 pairs (_)
H8,I9: 8.. / H8 = 8  =>  0 pairs (X) / I9 = 8  =>  5 pairs (_)
I5,I9: 8.. / I5 = 8  =>  0 pairs (X) / I9 = 8  =>  5 pairs (_)
A4,B6: 9.. / A4 = 9  =>  3 pairs (_) / B6 = 9  =>  0 pairs (X)
A7,B7: 9.. / A7 = 9  =>  0 pairs (X) / B7 = 9  =>  3 pairs (_)
D9,F9: 9.. / D9 = 9  =>  4 pairs (_) / F9 = 9  =>  4 pairs (_)
A4,A7: 9.. / A4 = 9  =>  3 pairs (_) / A7 = 9  =>  0 pairs (X)
B6,B7: 9.. / B6 = 9  =>  0 pairs (X) / B7 = 9  =>  3 pairs (_)
* DURATION: 0:00:21.161554  START: 17:54:49.179381  END: 17:55:10.340935 2019-04-28
* CP COUNT: (26)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:32.003715  START: 17:55:51.874288  END: 17:56:23.878003 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0319-base-pr-002.dot
* REASONING
* DIS # A1: 4,6 # C6: 4,6 => CTR => C6: 3
* DIS # A1: 4,6 + C6: 3 # C9: 2 => CTR => C9: 4,6
* DIS # A1: 4,6 + C6: 3 + C9: 4,6 # E6: 4,6 => CTR => E6: 1,5
* PRF # A1: 4,6 + C6: 3 + C9: 4,6 + E6: 1,5 # E5: 2,5 => SOL
* STA # A1: 4,6 + C6: 3 + C9: 4,6 + E6: 1,5 + E5: 2,5
* CNT   4 HDP CHAINS /  37 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=319
```

Solution

position: 687294513239185674514367892952718346471623985863459721198546237345872169726931458 solved

See section Deep 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 # A1: 4,6 => UNS
* INC # B3: 4,6 => UNS
* INC # E3: 4,6 => UNS
* INC # E3: 1,2 => UNS
* INC # C6: 4,6 => UNS
* INC # C9: 4,6 => UNS
* INC # B6: 4,9 => UNS
* INC # B6: 6,7 => UNS
* INC # D4: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # A7: 4,9 => UNS
* INC # A7: 1,3 => UNS
* INC # B5: 4,6 => UNS
* INC # B6: 4,6 => UNS
* INC # C6: 4,6 => UNS
* INC # D5: 4,6 => UNS
* INC # E5: 4,6 => UNS
* INC # A1: 4,6 => UNS
* DIS # A8: 4,6 => CTR => A8: 3
* INC # A8: 3 => UNS
* INC # G7: 3,4 => UNS
* INC # H8: 3,4 => UNS
* DIS # A7: 3,4 => CTR => A7: 1,9
* INC # A7: 1,9 => UNS
* INC # H4: 3,4 => UNS
* INC # H5: 3,4 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED
```

A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # A1: 4,6 => UNS
* INC # B3: 4,6 => UNS
* INC # E3: 4,6 => UNS
* INC # E3: 1,2 => UNS
* INC # C6: 4,6 => UNS
* INC # C9: 4,6 => UNS
* INC # B6: 4,9 => UNS
* INC # B6: 6,7 => UNS
* INC # D4: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # A7: 4,9 => UNS
* INC # A7: 1,3 => UNS
* INC # B5: 4,6 => UNS
* INC # B6: 4,6 => UNS
* INC # C6: 4,6 => UNS
* INC # D5: 4,6 => UNS
* INC # E5: 4,6 => UNS
* INC # A1: 4,6 => UNS
* DIS # A8: 4,6 => CTR => A8: 3
* INC A8: 3 # A1: 4,6 => UNS
* INC A8: 3 # A1: 1 => UNS
* INC A8: 3 # B5: 4,6 => UNS
* INC A8: 3 # B6: 4,6 => UNS
* INC A8: 3 # C6: 4,6 => UNS
* INC A8: 3 # D5: 4,6 => UNS
* INC A8: 3 # E5: 4,6 => UNS
* INC A8: 3 # A1: 4,6 => UNS
* INC A8: 3 # A1: 1 => UNS
* INC A8: 3 # G7: 3,4 => UNS
* INC A8: 3 # G7: 2 => UNS
* INC A8: 3 # H4: 3,4 => UNS
* INC A8: 3 # H5: 3,4 => UNS
* INC A8: 3 # A1: 4,6 => UNS
* INC A8: 3 # B3: 4,6 => UNS
* INC A8: 3 # E3: 4,6 => UNS
* INC A8: 3 # E3: 1,2 => UNS
* INC A8: 3 # C6: 4,6 => UNS
* INC A8: 3 # C9: 4,6 => UNS
* INC A8: 3 # B6: 4,9 => UNS
* INC A8: 3 # B6: 6,7 => UNS
* INC A8: 3 # D4: 4,9 => UNS
* INC A8: 3 # F4: 4,9 => UNS
* INC A8: 3 # A7: 4,9 => UNS
* INC A8: 3 # A7: 1 => UNS
* INC A8: 3 # B5: 4,6 => UNS
* INC A8: 3 # B6: 4,6 => UNS
* INC A8: 3 # C6: 4,6 => UNS
* INC A8: 3 # D5: 4,6 => UNS
* INC A8: 3 # E5: 4,6 => UNS
* INC A8: 3 # A1: 4,6 => UNS
* INC A8: 3 # A1: 1 => UNS
* INC A8: 3 # G7: 3,4 => UNS
* INC A8: 3 # G7: 2 => UNS
* INC A8: 3 # H4: 3,4 => UNS
* INC A8: 3 # H5: 3,4 => UNS
* STA A8: 3
* CNT  55 HDP CHAINS /  55 HYP OPENED
```

A3. Deep Pair Reduction

Full list of HDP chains traversed:

```* INC # A1: 4,6 => UNS
* INC # B3: 4,6 => UNS
* INC # E3: 4,6 => UNS
* INC # E3: 1,2 => UNS
* INC # C6: 4,6 => UNS
* INC # C9: 4,6 => UNS
* INC # B6: 4,9 => UNS
* INC # B6: 6,7 => UNS
* INC # D4: 4,9 => UNS
* INC # F4: 4,9 => UNS
* INC # A7: 4,9 => UNS
* INC # A7: 1 => UNS
* INC # B5: 4,6 => UNS
* INC # B6: 4,6 => UNS
* INC # C6: 4,6 => UNS
* INC # D5: 4,6 => UNS
* INC # E5: 4,6 => UNS
* INC # A1: 4,6 => UNS
* INC # A1: 1 => UNS
* INC # G7: 3,4 => UNS
* INC # G7: 2 => UNS
* INC # H4: 3,4 => UNS
* INC # H5: 3,4 => UNS
* INC # A1: 4,6 # D1: 4,6 => UNS
* INC # A1: 4,6 # G1: 4,6 => UNS
* INC # A1: 4,6 # H1: 4,6 => UNS
* DIS # A1: 4,6 # C6: 4,6 => CTR => C6: 3
* INC # A1: 4,6 + C6: 3 # C9: 4,6 => UNS
* INC # A1: 4,6 + C6: 3 # C9: 4,6 => UNS
* DIS # A1: 4,6 + C6: 3 # C9: 2 => CTR => C9: 4,6
* INC # A1: 4,6 + C6: 3 + C9: 4,6 # D1: 4,6 => UNS
* INC # A1: 4,6 + C6: 3 + C9: 4,6 # D2: 4,6 => UNS
* INC # A1: 4,6 + C6: 3 + C9: 4,6 # E5: 4,6 => UNS
* DIS # A1: 4,6 + C6: 3 + C9: 4,6 # E6: 4,6 => CTR => E6: 1,5
* INC # A1: 4,6 + C6: 3 + C9: 4,6 + E6: 1,5 # E5: 4,6 => UNS
* PRF # A1: 4,6 + C6: 3 + C9: 4,6 + E6: 1,5 # E5: 2,5 => SOL
* STA # A1: 4,6 + C6: 3 + C9: 4,6 + E6: 1,5 + E5: 2,5
* CNT  36 HDP CHAINS /  37 HYP OPENED
```