# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=289

level: deep

position: 12.34....3.....1...56......4..7..8...6.....5...2..9......41...7....7.3.......2.9. initial

# Autosolve

position: 12.34....3.....1...56......4..7..8...6...4.5...2..9......41...7...97.3.......2.9. autosolve

# Pair Reduction Variants

## Deep Constraint Pair Analysis

Time used: 0:00:00.000007

List of important HDP chains detected for F3,F4: 1..:

```* DIS # F4: 1 # H3: 7,8 => CTR => H3: 2,3,4
* DIS # F4: 1 + H3: 2,3,4 # C5: 3,9 => CTR => C5: 1,7,8
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 # C4: 5 => CTR => C4: 3,9
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 # E5: 2,8 => CTR => E5: 3
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 # A7: 8,9 => CTR => A7: 2,6
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 + A7: 2,6 => CTR => F4: 3,5,6
* STA F4: 3,5,6
* CNT   6 HDP CHAINS /  18 HYP OPENED
```

List of important HDP chains detected for D3,F3: 1..:

```* DIS # D3: 1 # H3: 7,8 => CTR => H3: 2,3,4
* DIS # D3: 1 + H3: 2,3,4 # C5: 3,9 => CTR => C5: 1,7,8
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 # C4: 5 => CTR => C4: 3,9
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 # E5: 2,8 => CTR => E5: 3
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 # A7: 8,9 => CTR => A7: 2,6
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 + A7: 2,6 => CTR => D3: 2,8
* STA D3: 2,8
* CNT   6 HDP CHAINS /  18 HYP OPENED
```

List of important HDP chains detected for F4,F7: 3..:

```* DIS # F4: 3 # H3: 2,8 => CTR => H3: 3,4,7
* DIS # F4: 3 + H3: 3,4,7 # I3: 2,8 => CTR => I3: 3,4,9
* PRF # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # C4: 1,9 => SOL
* STA # F4: 3 + H3: 3,4,7 + I3: 3,4,9 + C4: 1,9
* CNT   3 HDP CHAINS /  14 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

 12.34....3.....1...56......4..7..8...6.....5...2..9......41...7....7.3.......2.9. initial 12.34....3.....1...56......4..7..8...6...4.5...2..9......41...7...97.3.......2.9. autosolve

level: deep

## Pairing Analysis

```--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,F3: 1.. / D3 = 1  =>  4 pairs (_) / F3 = 1  =>  1 pairs (_)
F3,F4: 1.. / F3 = 1  =>  1 pairs (_) / F4 = 1  =>  4 pairs (_)
A7,A8: 2.. / A7 = 2  =>  2 pairs (_) / A8 = 2  =>  0 pairs (_)
H3,I3: 3.. / H3 = 3  =>  0 pairs (_) / I3 = 3  =>  0 pairs (_)
F7,E9: 3.. / F7 = 3  =>  1 pairs (_) / E9 = 3  =>  3 pairs (_)
F4,F7: 3.. / F4 = 3  =>  3 pairs (_) / F7 = 3  =>  1 pairs (_)
B2,C2: 4.. / B2 = 4  =>  1 pairs (_) / C2 = 4  =>  0 pairs (_)
C4,A6: 5.. / C4 = 5  =>  2 pairs (_) / A6 = 5  =>  0 pairs (_)
E2,E3: 9.. / E2 = 9  =>  1 pairs (_) / E3 = 9  =>  1 pairs (_)
* DURATION: 0:00:05.483235  START: 14:55:46.261323  END: 14:55:51.744558 2019-04-28
* CP COUNT: (9)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
F3,F4: 1.. / F3 = 1  =>  1 pairs (_) / F4 = 1 ==>  0 pairs (X)
D3,F3: 1.. / D3 = 1 ==>  0 pairs (X) / F3 = 1  =>  1 pairs (_)
F4,F7: 3.. / F4 = 3 ==>  0 pairs (*) / F7 = 3  =>  0 pairs (X)
* DURATION: 0:00:32.175956  START: 14:55:51.745096  END: 14:56:23.921052 2019-04-28
* REASONING F3,F4: 1..
* DIS # F4: 1 # H3: 7,8 => CTR => H3: 2,3,4
* DIS # F4: 1 + H3: 2,3,4 # C5: 3,9 => CTR => C5: 1,7,8
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 # C4: 5 => CTR => C4: 3,9
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 # E5: 2,8 => CTR => E5: 3
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 # A7: 8,9 => CTR => A7: 2,6
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 + A7: 2,6 => CTR => F4: 3,5,6
* STA F4: 3,5,6
* CNT   6 HDP CHAINS /  18 HYP OPENED
* REASONING D3,F3: 1..
* DIS # D3: 1 # H3: 7,8 => CTR => H3: 2,3,4
* DIS # D3: 1 + H3: 2,3,4 # C5: 3,9 => CTR => C5: 1,7,8
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 # C4: 5 => CTR => C4: 3,9
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 # E5: 2,8 => CTR => E5: 3
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 # A7: 8,9 => CTR => A7: 2,6
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 + A7: 2,6 => CTR => D3: 2,8
* STA D3: 2,8
* CNT   6 HDP CHAINS /  18 HYP OPENED
* REASONING F4,F7: 3..
* DIS # F4: 3 # H3: 2,8 => CTR => H3: 3,4,7
* DIS # F4: 3 + H3: 3,4,7 # I3: 2,8 => CTR => I3: 3,4,9
* PRF # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # C4: 1,9 => SOL
* STA # F4: 3 + H3: 3,4,7 + I3: 3,4,9 + C4: 1,9
* CNT   3 HDP CHAINS /  14 HYP OPENED
* DCP COUNT: (3)
* SOLUTION FOUND
```

## Header Info

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=289
```

# Appendix: Full HDP Chains

## A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for F3,F4: 1..:

```* INC # F4: 1 # F1: 7,8 => UNS
* INC # F4: 1 # F2: 7,8 => UNS
* INC # F4: 1 # A3: 7,8 => UNS
* DIS # F4: 1 # H3: 7,8 => CTR => H3: 2,3,4
* INC # F4: 1 + H3: 2,3,4 # A3: 7,8 => UNS
* INC # F4: 1 + H3: 2,3,4 # A3: 9 => UNS
* INC # F4: 1 + H3: 2,3,4 # F1: 7,8 => UNS
* INC # F4: 1 + H3: 2,3,4 # F2: 7,8 => UNS
* INC # F4: 1 + H3: 2,3,4 # A3: 7,8 => UNS
* INC # F4: 1 + H3: 2,3,4 # A3: 9 => UNS
* INC # F4: 1 + H3: 2,3,4 # C4: 3,9 => UNS
* DIS # F4: 1 + H3: 2,3,4 # C5: 3,9 => CTR => C5: 1,7,8
* INC # F4: 1 + H3: 2,3,4 + C5: 1,7,8 # C4: 3,9 => UNS
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 # C4: 5 => CTR => C4: 3,9
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 # E5: 2,8 => CTR => E5: 3
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 # A7: 8,9 => CTR => A7: 2,6
* DIS # F4: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 + A7: 2,6 => CTR => F4: 3,5,6
* INC F4: 3,5,6 # F3: 1 => UNS
* STA F4: 3,5,6
* CNT  18 HDP CHAINS /  18 HYP OPENED
```

Full list of HDP chains traversed for D3,F3: 1..:

```* INC # D3: 1 # F1: 7,8 => UNS
* INC # D3: 1 # F2: 7,8 => UNS
* INC # D3: 1 # A3: 7,8 => UNS
* DIS # D3: 1 # H3: 7,8 => CTR => H3: 2,3,4
* INC # D3: 1 + H3: 2,3,4 # A3: 7,8 => UNS
* INC # D3: 1 + H3: 2,3,4 # A3: 9 => UNS
* INC # D3: 1 + H3: 2,3,4 # F1: 7,8 => UNS
* INC # D3: 1 + H3: 2,3,4 # F2: 7,8 => UNS
* INC # D3: 1 + H3: 2,3,4 # A3: 7,8 => UNS
* INC # D3: 1 + H3: 2,3,4 # A3: 9 => UNS
* INC # D3: 1 + H3: 2,3,4 # C4: 3,9 => UNS
* DIS # D3: 1 + H3: 2,3,4 # C5: 3,9 => CTR => C5: 1,7,8
* INC # D3: 1 + H3: 2,3,4 + C5: 1,7,8 # C4: 3,9 => UNS
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 # C4: 5 => CTR => C4: 3,9
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 # E5: 2,8 => CTR => E5: 3
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 # A7: 8,9 => CTR => A7: 2,6
* DIS # D3: 1 + H3: 2,3,4 + C5: 1,7,8 + C4: 3,9 + E5: 3 + A7: 2,6 => CTR => D3: 2,8
* INC D3: 2,8 # F3: 1 => UNS
* STA D3: 2,8
* CNT  18 HDP CHAINS /  18 HYP OPENED
```

Full list of HDP chains traversed for F4,F7: 3..:

```* INC # F4: 3 # D2: 2,8 => UNS
* INC # F4: 3 # E2: 2,8 => UNS
* INC # F4: 3 # E3: 2,8 => UNS
* DIS # F4: 3 # H3: 2,8 => CTR => H3: 3,4,7
* DIS # F4: 3 + H3: 3,4,7 # I3: 2,8 => CTR => I3: 3,4,9
* INC # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # D5: 2,8 => UNS
* INC # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # D5: 1 => UNS
* INC # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # D2: 2,8 => UNS
* INC # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # E2: 2,8 => UNS
* INC # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # E3: 2,8 => UNS
* INC # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # D5: 2,8 => UNS
* INC # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # D5: 1 => UNS
* PRF # F4: 3 + H3: 3,4,7 + I3: 3,4,9 # C4: 1,9 => SOL
* STA # F4: 3 + H3: 3,4,7 + I3: 3,4,9 + C4: 1,9
* CNT  13 HDP CHAINS /  14 HYP OPENED
```