# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=301

level: deep

position: ........9.....4178..8.7.6....5.9...7.1.2..5..3....5.....9.5..6.2....3....4.1..... initial

# Autosolve

position: ........9.....4178..8.7.6....5.9...7.1.2..5..3....5.....9.5..6.2....3....4.1..... autosolve

# Pair Reduction Variants

## Deep Constraint Pair Analysis

Time used: 0:00:00.000007

List of important HDP chains detected for F3,F9: 9..:

```* DIS # F3: 9 # D1: 3,5 => CTR => D1: 6,8
* DIS # F3: 9 + D1: 6,8 # H3: 3,5 => CTR => H3: 2,4
* DIS # F3: 9 + D1: 6,8 + H3: 2,4 # H1: 2,3 => CTR => H1: 5
* PRF # F3: 9 + D1: 6,8 + H3: 2,4 + H1: 5 # B1: 2,3 => SOL
* STA # F3: 9 + D1: 6,8 + H3: 2,4 + H1: 5 + B1: 2,3
* CNT   4 HDP CHAINS /  17 HYP OPENED
```

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

# Details

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

## Positions

 ........9.....4178..8.7.6....5.9...7.1.2..5..3....5.....9.5..6.2....3....4.1..... initial ........9.....4178..8.7.6....5.9...7.1.2..5..3....5.....9.5..6.2....3....4.1..... autosolve

level: deep

## Pairing Analysis

```--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F4,E6: 1.. / F4 = 1  =>  4 pairs (_) / E6 = 1  =>  1 pairs (_)
A7,C8: 1.. / A7 = 1  =>  0 pairs (X) / C8 = 1  =>  2 pairs (_)
A3,F3: 1.. / A3 = 1  =>  4 pairs (_) / F3 = 1  =>  1 pairs (_)
F4,H4: 1.. / F4 = 1  =>  4 pairs (_) / H4 = 1  =>  1 pairs (_)
A7,I7: 1.. / A7 = 1  =>  0 pairs (X) / I7 = 1  =>  2 pairs (_)
C1,C8: 1.. / C1 = 1  =>  0 pairs (X) / C8 = 1  =>  2 pairs (_)
E1,E6: 1.. / E1 = 1  =>  4 pairs (_) / E6 = 1  =>  1 pairs (_)
D4,E5: 3.. / D4 = 3  =>  1 pairs (_) / E5 = 3  =>  2 pairs (_)
B7,C9: 3.. / B7 = 3  =>  1 pairs (_) / C9 = 3  =>  3 pairs (_)
B8,A9: 5.. / B8 = 5  =>  1 pairs (_) / A9 = 5  =>  2 pairs (_)
I5,I6: 6.. / I5 = 6  =>  2 pairs (_) / I6 = 6  =>  1 pairs (_)
F5,D6: 7.. / F5 = 7  =>  2 pairs (_) / D6 = 7  =>  2 pairs (_)
A5,B6: 9.. / A5 = 9  =>  1 pairs (_) / B6 = 9  =>  0 pairs (_)
D8,F9: 9.. / D8 = 9  =>  4 pairs (_) / F9 = 9  =>  1 pairs (_)
A5,H5: 9.. / A5 = 9  =>  1 pairs (_) / H5 = 9  =>  0 pairs (_)
F3,F9: 9.. / F3 = 9  =>  4 pairs (_) / F9 = 9  =>  1 pairs (_)
* DURATION: 0:00:10.862255  START: 15:26:15.862293  END: 15:26:26.724548 2019-04-28
* CP COUNT: (16)
* CLUE FOUND

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
F3,F9: 9.. / F3 = 9 ==>  0 pairs (*) / F9 = 9  =>  0 pairs (X)
* DURATION: 0:00:20.617539  START: 15:26:26.725111  END: 15:26:47.342650 2019-04-28
* REASONING F3,F9: 9..
* DIS # F3: 9 # D1: 3,5 => CTR => D1: 6,8
* DIS # F3: 9 + D1: 6,8 # H3: 3,5 => CTR => H3: 2,4
* DIS # F3: 9 + D1: 6,8 + H3: 2,4 # H1: 2,3 => CTR => H1: 5
* PRF # F3: 9 + D1: 6,8 + H3: 2,4 + H1: 5 # B1: 2,3 => SOL
* STA # F3: 9 + D1: 6,8 + H3: 2,4 + H1: 5 + B1: 2,3
* CNT   4 HDP CHAINS /  17 HYP OPENED
* DCP COUNT: (1)
* SOLUTION FOUND
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=301
```

# Appendix: Full HDP Chains

## A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for F3,F9: 9..:

```* DIS # F3: 9 # D1: 3,5 => CTR => D1: 6,8
* INC # F3: 9 + D1: 6,8 # D2: 3,5 => UNS
* INC # F3: 9 + D1: 6,8 # D2: 3,5 => UNS
* INC # F3: 9 + D1: 6,8 # D2: 6 => UNS
* INC # F3: 9 + D1: 6,8 # B3: 3,5 => UNS
* DIS # F3: 9 + D1: 6,8 # H3: 3,5 => CTR => H3: 2,4
* INC # F3: 9 + D1: 6,8 + H3: 2,4 # I3: 3,5 => UNS
* INC # F3: 9 + D1: 6,8 + H3: 2,4 # D2: 3,5 => UNS
* INC # F3: 9 + D1: 6,8 + H3: 2,4 # D2: 6 => UNS
* INC # F3: 9 + D1: 6,8 + H3: 2,4 # B3: 3,5 => UNS
* INC # F3: 9 + D1: 6,8 + H3: 2,4 # I3: 3,5 => UNS
* DIS # F3: 9 + D1: 6,8 + H3: 2,4 # H1: 2,3 => CTR => H1: 5
* INC # F3: 9 + D1: 6,8 + H3: 2,4 + H1: 5 # I3: 2,3 => UNS
* INC # F3: 9 + D1: 6,8 + H3: 2,4 + H1: 5 # I3: 2,3 => UNS
* INC # F3: 9 + D1: 6,8 + H3: 2,4 + H1: 5 # I3: 4 => UNS
* PRF # F3: 9 + D1: 6,8 + H3: 2,4 + H1: 5 # B1: 2,3 => SOL
* STA # F3: 9 + D1: 6,8 + H3: 2,4 + H1: 5 + B1: 2,3
* CNT  16 HDP CHAINS /  17 HYP OPENED
```