# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=317

level: deep

position: 98.76....6.....9...54......7..3..2...4.....5...8..1......69...3....3.7.......8.1. initial

# Autosolve

position: 98.76....6.....9...54......7..3..2...4.....5...8..1......69...3...13.7.......8.1. autosolve

# Pair Reduction Variants

## Deep Constraint Pair Analysis

Time used: 0:00:00.000008

List of important HDP chains detected for D3,F3: 9..:

```* DIS # D3: 9 # H3: 2,3 => CTR => H3: 6,7,8
* DIS # D3: 9 + H3: 6,7,8 # C4: 6,9 => CTR => C4: 1,5
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 # H4: 6,9 => CTR => H4: 4,8
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 # I4: 6,9 => CTR => I4: 1,4,8
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 # A7: 1,2 => CTR => A7: 4,5,8
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 # C7: 1,2 => CTR => C7: 5
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 + C7: 5 # I2: 8 => CTR => I2: 4,5
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 + C7: 5 + I2: 4,5 # D9: 2 => CTR => D9: 4,5
* DIS # F3: 9 # H3: 2,8 => CTR => H3: 3,6,7
* CNT   9 HDP CHAINS /  51 HYP OPENED
```

List of important HDP chains detected for F5,F7: 7..:

```* DIS # F5: 7 # H3: 2,8 => CTR => H3: 3,6,7
* DIS # F5: 7 + H3: 3,6,7 # C5: 1,9 => CTR => C5: 2,3,6
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 # D5: 2,8 => CTR => D5: 9
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 # A3: 1,2 => CTR => A3: 3
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 # E2: 1,2 => CTR => E2: 4,5
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 # C4: 5 => CTR => C4: 1,9
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 # C2: 1,2 => CTR => C2: 7
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 + C2: 7 # D2: 2,8 => CTR => D2: 5
* PRF # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 + C2: 7 + D2: 5 => SOL
* STA F5: 7
* CNT   9 HDP CHAINS /  42 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

 98.76....6.....9...54......7..3..2...4.....5...8..1......69...3....3.7.......8.1. initial 98.76....6.....9...54......7..3..2...4.....5...8..1......69...3...13.7.......8.1. autosolve

level: deep

## Pairing Analysis

```--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E2,E3: 1.. / E2 = 1  =>  1 pairs (_) / E3 = 1  =>  1 pairs (_)
C4,A6: 5.. / C4 = 5  =>  3 pairs (_) / A6 = 5  =>  0 pairs (_)
F4,F5: 6.. / F4 = 6  =>  1 pairs (_) / F5 = 6  =>  1 pairs (_)
B2,C2: 7.. / B2 = 7  =>  1 pairs (_) / C2 = 7  =>  0 pairs (_)
H3,I3: 7.. / H3 = 7  =>  0 pairs (_) / I3 = 7  =>  0 pairs (_)
F7,E9: 7.. / F7 = 7  =>  1 pairs (_) / E9 = 7  =>  3 pairs (_)
F5,F7: 7.. / F5 = 7  =>  3 pairs (_) / F7 = 7  =>  1 pairs (_)
H3,H6: 7.. / H3 = 7  =>  0 pairs (_) / H6 = 7  =>  0 pairs (_)
A7,A8: 8.. / A7 = 8  =>  2 pairs (_) / A8 = 8  =>  0 pairs (_)
D3,F3: 9.. / D3 = 9  =>  5 pairs (_) / F3 = 9  =>  1 pairs (_)
* DURATION: 0:00:06.175966  START: 17:52:50.676139  END: 17:52:56.852105 2019-04-28
* CP COUNT: (10)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
D3,F3: 9.. / D3 = 9 ==> 18 pairs (_) / F3 = 9 ==>  1 pairs (_)
F5,F7: 7.. / F5 = 7 ==>  0 pairs (*) / F7 = 7  =>  0 pairs (X)
* DURATION: 0:01:01.695627  START: 17:52:56.852743  END: 17:53:58.548370 2019-04-28
* REASONING D3,F3: 9..
* DIS # D3: 9 # H3: 2,3 => CTR => H3: 6,7,8
* DIS # D3: 9 + H3: 6,7,8 # C4: 6,9 => CTR => C4: 1,5
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 # H4: 6,9 => CTR => H4: 4,8
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 # I4: 6,9 => CTR => I4: 1,4,8
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 # A7: 1,2 => CTR => A7: 4,5,8
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 # C7: 1,2 => CTR => C7: 5
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 + C7: 5 # I2: 8 => CTR => I2: 4,5
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 + C7: 5 + I2: 4,5 # D9: 2 => CTR => D9: 4,5
* DIS # F3: 9 # H3: 2,8 => CTR => H3: 3,6,7
* CNT   9 HDP CHAINS /  51 HYP OPENED
* REASONING F5,F7: 7..
* DIS # F5: 7 # H3: 2,8 => CTR => H3: 3,6,7
* DIS # F5: 7 + H3: 3,6,7 # C5: 1,9 => CTR => C5: 2,3,6
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 # D5: 2,8 => CTR => D5: 9
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 # A3: 1,2 => CTR => A3: 3
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 # E2: 1,2 => CTR => E2: 4,5
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 # C4: 5 => CTR => C4: 1,9
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 # C2: 1,2 => CTR => C2: 7
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 + C2: 7 # D2: 2,8 => CTR => D2: 5
* PRF # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 + C2: 7 + D2: 5 => SOL
* STA F5: 7
* CNT   9 HDP CHAINS /  42 HYP OPENED
* DCP COUNT: (2)
* SOLUTION FOUND
```

## Header Info

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=317
```

# Appendix: Full HDP Chains

## A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for D3,F3: 9..:

```* INC # D3: 9 # F1: 2,3 => UNS
* INC # D3: 9 # F2: 2,3 => UNS
* INC # D3: 9 # A3: 2,3 => UNS
* DIS # D3: 9 # H3: 2,3 => CTR => H3: 6,7,8
* INC # D3: 9 + H3: 6,7,8 # A3: 2,3 => UNS
* INC # D3: 9 + H3: 6,7,8 # A3: 1 => UNS
* INC # D3: 9 + H3: 6,7,8 # F1: 2,3 => UNS
* INC # D3: 9 + H3: 6,7,8 # F2: 2,3 => UNS
* INC # D3: 9 + H3: 6,7,8 # A3: 2,3 => UNS
* INC # D3: 9 + H3: 6,7,8 # A3: 1 => UNS
* INC # D3: 9 + H3: 6,7,8 # B4: 6,9 => UNS
* DIS # D3: 9 + H3: 6,7,8 # C4: 6,9 => CTR => C4: 1,5
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 # H4: 6,9 => CTR => H4: 4,8
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 # I4: 6,9 => CTR => I4: 1,4,8
* INC # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 # E5: 2,8 => UNS
* INC # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 # E5: 7 => UNS
* INC # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 # D2: 2,8 => UNS
* INC # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 # D2: 4,5 => UNS
* INC # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 # C5: 6,9 => UNS
* INC # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 # I5: 6,9 => UNS
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 # A7: 1,2 => CTR => A7: 4,5,8
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 # C7: 1,2 => CTR => C7: 5
* INC # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 + C7: 5 # I2: 4,5 => UNS
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 + C7: 5 # I2: 8 => CTR => I2: 4,5
* INC # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 + C7: 5 + I2: 4,5 # D9: 4,5 => UNS
* DIS # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 + C7: 5 + I2: 4,5 # D9: 2 => CTR => D9: 4,5
* INC # D3: 9 + H3: 6,7,8 + C4: 1,5 + H4: 4,8 + I4: 1,4,8 + A7: 4,5,8 + C7: 5 + I2: 4,5 + D9: 4,5 => UNS
* INC # F3: 9 # D2: 2,8 => UNS
* INC # F3: 9 # E2: 2,8 => UNS
* INC # F3: 9 # E3: 2,8 => UNS
* DIS # F3: 9 # H3: 2,8 => CTR => H3: 3,6,7
* INC # F3: 9 + H3: 3,6,7 # I3: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # I3: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # I3: 1,6,7 => UNS
* INC # F3: 9 + H3: 3,6,7 # D5: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # D5: 9 => UNS
* INC # F3: 9 + H3: 3,6,7 # D2: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # E2: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # E3: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # I3: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # I3: 1,6,7 => UNS
* INC # F3: 9 + H3: 3,6,7 # D5: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # D5: 9 => UNS
* INC # F3: 9 + H3: 3,6,7 # D2: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # E2: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # E3: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # I3: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # I3: 1,6,7 => UNS
* INC # F3: 9 + H3: 3,6,7 # D5: 2,8 => UNS
* INC # F3: 9 + H3: 3,6,7 # D5: 9 => UNS
* INC # F3: 9 + H3: 3,6,7 => UNS
* CNT  51 HDP CHAINS /  51 HYP OPENED
```

Full list of HDP chains traversed for F5,F7: 7..:

```* INC # F5: 7 # D2: 2,8 => UNS
* INC # F5: 7 # E2: 2,8 => UNS
* INC # F5: 7 # E3: 2,8 => UNS
* DIS # F5: 7 # H3: 2,8 => CTR => H3: 3,6,7
* INC # F5: 7 + H3: 3,6,7 # I3: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 # I3: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 # I3: 1,6,7 => UNS
* INC # F5: 7 + H3: 3,6,7 # D5: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 # D5: 9 => UNS
* INC # F5: 7 + H3: 3,6,7 # D2: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 # E2: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 # E3: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 # I3: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 # I3: 1,6,7 => UNS
* INC # F5: 7 + H3: 3,6,7 # D5: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 # D5: 9 => UNS
* INC # F5: 7 + H3: 3,6,7 # C4: 1,9 => UNS
* DIS # F5: 7 + H3: 3,6,7 # C5: 1,9 => CTR => C5: 2,3,6
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 # C4: 1,9 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 # C4: 5 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 # I4: 1,9 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 # I4: 4,8 => UNS
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 # D5: 2,8 => CTR => D5: 9
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 # D2: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 # D2: 4,5 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 # I3: 2,8 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 # I3: 1,6,7 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 # E2: 1,2 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 # E2: 4,5 => UNS
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 # A3: 1,2 => CTR => A3: 3
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 # I3: 1,2 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 # I3: 1,2 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 # I3: 6,7,8 => UNS
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 # E2: 1,2 => CTR => E2: 4,5
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 # C4: 1,9 => UNS
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 # C4: 5 => CTR => C4: 1,9
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 # B2: 1,2 => UNS
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 # C2: 1,2 => CTR => C2: 7
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 + C2: 7 # I1: 1,2 => UNS
* INC # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 + C2: 7 # I1: 4,5 => UNS
* DIS # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 + C2: 7 # D2: 2,8 => CTR => D2: 5
* PRF # F5: 7 + H3: 3,6,7 + C5: 2,3,6 + D5: 9 + A3: 3 + E2: 4,5 + C4: 1,9 + C2: 7 + D2: 5 => SOL
* STA F5: 7
* CNT  42 HDP CHAINS /  42 HYP OPENED
```