# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=208

level: very deep

position: .1..4.6..9......2...2..5...5..9....8.7..3.4....8.......4.1....7.....31......7..46 initial

# Autosolve

position: .1..4.6..9......2...2..5...5..9....8.7..3.4....8.......4.1....7...4.31......7..46 autosolve

# Pair Reduction Variants

## Deep Constraint Pair Analysis

Time used: 0:00:00.000006

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

## Very Deep Constraint Pair Analysis

Time used: 0:01:06.188206

List of important HDP chains detected for F1,E3: 9..:

```* DIS # F1: 9 # H1: 3,5 # B2: 3,6 => CTR => B2: 5
* DIS # F1: 9 # H1: 3,5 + B2: 5 # A3: 3,6 => CTR => A3: 4
* DIS # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 # D3: 7,8 => CTR => D3: 3,6
* DIS # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 # H7: 3,5 => CTR => H7: 8,9
* DIS # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # D5: 6 => CTR => D5: 5,8
* PRF # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 + D5: 5,8 # F7: 2,8 => SOL
* STA # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 + D5: 5,8 + F7: 2,8
* CNT   6 HDP CHAINS /  43 HYP OPENED
```

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

# Details

This sudoku is very deep. Here is some information that may be helpful on how to proceed.

## Positions

 .1..4.6..9......2...2..5...5..9....8.7..3.4....8.......4.1....7.....31......7..46 initial .1..4.6..9......2...2..5...5..9....8.7..3.4....8.......4.1....7...4.31......7..46 autosolve

level: very deep

## Pairing Analysis

```--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A9,C9: 1.. / A9 = 1  =>  1 pairs (_) / C9 = 1  =>  1 pairs (_)
D1,F1: 2.. / D1 = 2  =>  1 pairs (_) / F1 = 2  =>  1 pairs (_)
C2,A3: 4.. / C2 = 4  =>  0 pairs (_) / A3 = 4  =>  0 pairs (_)
I2,I3: 4.. / I2 = 4  =>  0 pairs (_) / I3 = 4  =>  0 pairs (_)
C4,A6: 4.. / C4 = 4  =>  0 pairs (_) / A6 = 4  =>  0 pairs (_)
F4,F6: 4.. / F4 = 4  =>  0 pairs (_) / F6 = 4  =>  0 pairs (_)
C2,I2: 4.. / C2 = 4  =>  0 pairs (_) / I2 = 4  =>  0 pairs (_)
A3,I3: 4.. / A3 = 4  =>  0 pairs (_) / I3 = 4  =>  0 pairs (_)
C4,F4: 4.. / C4 = 4  =>  0 pairs (_) / F4 = 4  =>  0 pairs (_)
A6,F6: 4.. / A6 = 4  =>  0 pairs (_) / F6 = 4  =>  0 pairs (_)
A3,A6: 4.. / A3 = 4  =>  0 pairs (_) / A6 = 4  =>  0 pairs (_)
C2,C4: 4.. / C2 = 4  =>  0 pairs (_) / C4 = 4  =>  0 pairs (_)
A8,C8: 7.. / A8 = 7  =>  1 pairs (_) / C8 = 7  =>  1 pairs (_)
D5,F5: 8.. / D5 = 8  =>  1 pairs (_) / F5 = 8  =>  1 pairs (_)
F1,E3: 9.. / F1 = 9  =>  3 pairs (_) / E3 = 9  =>  0 pairs (_)
C5,B6: 9.. / C5 = 9  =>  0 pairs (_) / B6 = 9  =>  1 pairs (_)
* DURATION: 0:00:14.173081  START: 06:28:16.244369  END: 06:28:30.417450 2017-04-28
* CP COUNT: (16)

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
F1,E3: 9.. / F1 = 9 ==>  3 pairs (_) / E3 = 9 ==>  0 pairs (_)
D5,F5: 8.. / D5 = 8 ==>  1 pairs (_) / F5 = 8 ==>  1 pairs (_)
A8,C8: 7.. / A8 = 7 ==>  1 pairs (_) / C8 = 7 ==>  1 pairs (_)
D1,F1: 2.. / D1 = 2 ==>  1 pairs (_) / F1 = 2 ==>  1 pairs (_)
A9,C9: 1.. / A9 = 1 ==>  1 pairs (_) / C9 = 1 ==>  1 pairs (_)
C5,B6: 9.. / C5 = 9 ==>  0 pairs (_) / B6 = 9 ==>  1 pairs (_)
C2,C4: 4.. / C2 = 4 ==>  0 pairs (_) / C4 = 4 ==>  0 pairs (_)
A3,A6: 4.. / A3 = 4 ==>  0 pairs (_) / A6 = 4 ==>  0 pairs (_)
A6,F6: 4.. / A6 = 4 ==>  0 pairs (_) / F6 = 4 ==>  0 pairs (_)
C4,F4: 4.. / C4 = 4 ==>  0 pairs (_) / F4 = 4 ==>  0 pairs (_)
A3,I3: 4.. / A3 = 4 ==>  0 pairs (_) / I3 = 4 ==>  0 pairs (_)
C2,I2: 4.. / C2 = 4 ==>  0 pairs (_) / I2 = 4 ==>  0 pairs (_)
F4,F6: 4.. / F4 = 4 ==>  0 pairs (_) / F6 = 4 ==>  0 pairs (_)
C4,A6: 4.. / C4 = 4 ==>  0 pairs (_) / A6 = 4 ==>  0 pairs (_)
I2,I3: 4.. / I2 = 4 ==>  0 pairs (_) / I3 = 4 ==>  0 pairs (_)
C2,A3: 4.. / C2 = 4 ==>  0 pairs (_) / A3 = 4 ==>  0 pairs (_)
* DURATION: 0:01:13.092106  START: 06:28:30.417806  END: 06:29:43.509912 2017-04-28
* DCP COUNT: (16)
* INCONCLUSIVE

--------------------------------------------------
* VERY DEEP CONSTRAINT PAIRS (PAIR REDUCTION, RECURSIVE)
F1,E3: 9.. / F1 = 9 ==>  0 pairs (*) / E3 = 9  =>  0 pairs (X)
* DURATION: 0:01:06.186734  START: 06:29:43.633896  END: 06:30:49.820630 2017-04-28
* REASONING F1,E3: 9..
* DIS # F1: 9 # H1: 3,5 # B2: 3,6 => CTR => B2: 5
* DIS # F1: 9 # H1: 3,5 + B2: 5 # A3: 3,6 => CTR => A3: 4
* DIS # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 # D3: 7,8 => CTR => D3: 3,6
* DIS # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 # H7: 3,5 => CTR => H7: 8,9
* DIS # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # D5: 6 => CTR => D5: 5,8
* PRF # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 + D5: 5,8 # F7: 2,8 => SOL
* STA # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 + D5: 5,8 + F7: 2,8
* CNT   6 HDP CHAINS /  43 HYP OPENED
* VDCP COUNT: (1)
* SOLUTION FOUND
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=208
```

# Appendix: Full HDP Chains

## A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for F1,E3: 9..:

```* INC # F1: 9 # H1: 3,5 => UNS
* INC # F1: 9 # G2: 3,5 => UNS
* INC # F1: 9 # I2: 3,5 => UNS
* INC # F1: 9 # C1: 3,5 => UNS
* INC # F1: 9 # C1: 7 => UNS
* INC # F1: 9 # I6: 3,5 => UNS
* INC # F1: 9 # I6: 1,2,9 => UNS
* INC # F1: 9 # E7: 5,8 => UNS
* INC # F1: 9 # E8: 5,8 => UNS
* INC # F1: 9 # B9: 5,8 => UNS
* INC # F1: 9 # G9: 5,8 => UNS
* INC # F1: 9 # D5: 5,8 => UNS
* INC # F1: 9 # D5: 6 => UNS
* INC # F1: 9 # E7: 2,8 => UNS
* INC # F1: 9 # F7: 2,8 => UNS
* INC # F1: 9 # E8: 2,8 => UNS
* INC # F1: 9 # A9: 2,8 => UNS
* INC # F1: 9 # B9: 2,8 => UNS
* INC # F1: 9 # G9: 2,8 => UNS
* INC # F1: 9 # F5: 2,8 => UNS
* INC # F1: 9 # F5: 1,6 => UNS
* INC # F1: 9 => UNS
* INC # E3: 9 => UNS
* CNT  23 HDP CHAINS /  23 HYP OPENED
```

Full list of HDP chains traversed for D5,F5: 8..:

```* INC # D5: 8 # E7: 2,5 => UNS
* INC # D5: 8 # E8: 2,5 => UNS
* INC # D5: 8 # B9: 2,5 => UNS
* INC # D5: 8 # G9: 2,5 => UNS
* INC # D5: 8 # D6: 2,5 => UNS
* INC # D5: 8 # D6: 6,7 => UNS
* INC # D5: 8 => UNS
* INC # F5: 8 # E7: 2,9 => UNS
* INC # F5: 8 # F7: 2,9 => UNS
* INC # F5: 8 # E8: 2,9 => UNS
* INC # F5: 8 # B9: 2,9 => UNS
* INC # F5: 8 # G9: 2,9 => UNS
* INC # F5: 8 # F1: 2,9 => UNS
* INC # F5: 8 # F1: 7 => UNS
* INC # F5: 8 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED
```

Full list of HDP chains traversed for A8,C8: 7..:

```* INC # A8: 7 # B2: 3,8 => UNS
* INC # A8: 7 # A3: 3,8 => UNS
* INC # A8: 7 # B3: 3,8 => UNS
* INC # A8: 7 # D1: 3,8 => UNS
* INC # A8: 7 # H1: 3,8 => UNS
* INC # A8: 7 # A7: 3,8 => UNS
* INC # A8: 7 # A9: 3,8 => UNS
* INC # A8: 7 => UNS
* INC # C8: 7 # B2: 3,5 => UNS
* INC # C8: 7 # C2: 3,5 => UNS
* INC # C8: 7 # H1: 3,5 => UNS
* INC # C8: 7 # I1: 3,5 => UNS
* INC # C8: 7 # C7: 3,5 => UNS
* INC # C8: 7 # C9: 3,5 => UNS
* INC # C8: 7 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED
```

Full list of HDP chains traversed for D1,F1: 2..:

```* INC # D1: 2 # E7: 5,8 => UNS
* INC # D1: 2 # E8: 5,8 => UNS
* INC # D1: 2 # B9: 5,8 => UNS
* INC # D1: 2 # G9: 5,8 => UNS
* INC # D1: 2 # D5: 5,8 => UNS
* INC # D1: 2 # D5: 6 => UNS
* INC # D1: 2 => UNS
* INC # F1: 2 # F7: 8,9 => UNS
* INC # F1: 2 # F7: 6 => UNS
* INC # F1: 2 # B9: 8,9 => UNS
* INC # F1: 2 # G9: 8,9 => UNS
* INC # F1: 2 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED
```

Full list of HDP chains traversed for A9,C9: 1..:

```* INC # A9: 1 # B4: 2,6 => UNS
* INC # A9: 1 # A6: 2,6 => UNS
* INC # A9: 1 # B6: 2,6 => UNS
* INC # A9: 1 # D5: 2,6 => UNS
* INC # A9: 1 # F5: 2,6 => UNS
* INC # A9: 1 # A7: 2,6 => UNS
* INC # A9: 1 # A8: 2,6 => UNS
* INC # A9: 1 => UNS
* INC # C9: 1 # B6: 6,9 => UNS
* INC # C9: 1 # B6: 2,3 => UNS
* INC # C9: 1 # H5: 6,9 => UNS
* INC # C9: 1 # H5: 1,5 => UNS
* INC # C9: 1 # C7: 6,9 => UNS
* INC # C9: 1 # C8: 6,9 => UNS
* INC # C9: 1 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED
```

Full list of HDP chains traversed for C5,B6: 9..:

```* INC # B6: 9 # C4: 1,6 => UNS
* INC # B6: 9 # A5: 1,6 => UNS
* INC # B6: 9 # A6: 1,6 => UNS
* INC # B6: 9 # F5: 1,6 => UNS
* INC # B6: 9 # H5: 1,6 => UNS
* INC # B6: 9 => UNS
* INC # C5: 9 => UNS
* CNT   7 HDP CHAINS /   7 HYP OPENED
```

Full list of HDP chains traversed for C2,C4: 4..:

```* INC # C2: 4 => UNS
* INC # C4: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

Full list of HDP chains traversed for A3,A6: 4..:

```* INC # A3: 4 => UNS
* INC # A6: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

Full list of HDP chains traversed for A6,F6: 4..:

```* INC # A6: 4 => UNS
* INC # F6: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

Full list of HDP chains traversed for C4,F4: 4..:

```* INC # C4: 4 => UNS
* INC # F4: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

Full list of HDP chains traversed for A3,I3: 4..:

```* INC # A3: 4 => UNS
* INC # I3: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

Full list of HDP chains traversed for C2,I2: 4..:

```* INC # C2: 4 => UNS
* INC # I2: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

Full list of HDP chains traversed for F4,F6: 4..:

```* INC # F4: 4 => UNS
* INC # F6: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

Full list of HDP chains traversed for C4,A6: 4..:

```* INC # C4: 4 => UNS
* INC # A6: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

Full list of HDP chains traversed for I2,I3: 4..:

```* INC # I2: 4 => UNS
* INC # I3: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

Full list of HDP chains traversed for C2,A3: 4..:

```* INC # C2: 4 => UNS
* INC # A3: 4 => UNS
* CNT   2 HDP CHAINS /   2 HYP OPENED
```

## A2. Very Deep Constraint Pair Analysis

Full list of HDP chains traversed for F1,E3: 9..:

```* INC # F1: 9 # H1: 3,5 => UNS
* INC # F1: 9 # G2: 3,5 => UNS
* INC # F1: 9 # I2: 3,5 => UNS
* INC # F1: 9 # C1: 3,5 => UNS
* INC # F1: 9 # C1: 7 => UNS
* INC # F1: 9 # I6: 3,5 => UNS
* INC # F1: 9 # I6: 1,2,9 => UNS
* INC # F1: 9 # E7: 5,8 => UNS
* INC # F1: 9 # E8: 5,8 => UNS
* INC # F1: 9 # B9: 5,8 => UNS
* INC # F1: 9 # G9: 5,8 => UNS
* INC # F1: 9 # D5: 5,8 => UNS
* INC # F1: 9 # D5: 6 => UNS
* INC # F1: 9 # E7: 2,8 => UNS
* INC # F1: 9 # F7: 2,8 => UNS
* INC # F1: 9 # E8: 2,8 => UNS
* INC # F1: 9 # A9: 2,8 => UNS
* INC # F1: 9 # B9: 2,8 => UNS
* INC # F1: 9 # G9: 2,8 => UNS
* INC # F1: 9 # F5: 2,8 => UNS
* INC # F1: 9 # F5: 1,6 => UNS
* DIS # F1: 9 # H1: 3,5 # B2: 3,6 => CTR => B2: 5
* INC # F1: 9 # H1: 3,5 + B2: 5 # C2: 3,6 => UNS
* DIS # F1: 9 # H1: 3,5 + B2: 5 # A3: 3,6 => CTR => A3: 4
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 # D3: 3,6 => UNS
* DIS # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 # D3: 7,8 => CTR => D3: 3,6
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 # B4: 3,6 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 # B6: 3,6 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 # B4: 3,6 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 # B6: 3,6 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 # H6: 3,5 => UNS
* DIS # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 # H7: 3,5 => CTR => H7: 8,9
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # H6: 3,5 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # H6: 1,6,7,9 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # H6: 3,5 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # H6: 1,6,7,9 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # I6: 3,5 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # I6: 1,2,9 => UNS
* INC # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # D5: 5,8 => UNS
* DIS # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 # D5: 6 => CTR => D5: 5,8
* PRF # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 + D5: 5,8 # F7: 2,8 => SOL
* STA # F1: 9 # H1: 3,5 + B2: 5 + A3: 4 + D3: 3,6 + H7: 8,9 + D5: 5,8 + F7: 2,8
* CNT  41 HDP CHAINS /  43 HYP OPENED
```