# Original Sudoku

level: deep

position: 98.7.....6..89......5..4...7...3.9....6...7....2....41.6..8.3.......1..5.......2. initial

# Autosolve

position: 98.7.....6..89......5..4...7...3.9....6...7....2....41.6..8.3.......1..5.......2. autosolve

# Pair Reduction Variants

## Deep Constraint Pair Analysis

Time used: 0:00:00.000005

List of important HDP chains detected for B5,B6: 9..:

```* DIS # B6: 9 # B3: 1,2 => CTR => B3: 3,7
* PRF # B6: 9 + B3: 3,7 # G3: 1,2 => SOL
* STA # B6: 9 + B3: 3,7 + G3: 1,2
* CNT   2 HDP CHAINS /   8 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

 98.7.....6..89......5..4...7...3.9....6...7....2....41.6..8.3.......1..5.......2. initial 98.7.....6..89......5..4...7...3.9....6...7....2....41.6..8.3.......1..5.......2. autosolve

level: deep

## Pairing Analysis

```--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H7,G9: 1.. / H7 = 1  =>  0 pairs (_) / G9 = 1  =>  1 pairs (_)
I4,I5: 2.. / I4 = 2  =>  1 pairs (_) / I5 = 2  =>  1 pairs (_)
A6,B6: 3.. / A6 = 3  =>  2 pairs (_) / B6 = 3  =>  1 pairs (_)
H5,I5: 3.. / H5 = 3  =>  1 pairs (_) / I5 = 3  =>  3 pairs (_)
E6,F6: 7.. / E6 = 7  =>  0 pairs (_) / F6 = 7  =>  1 pairs (_)
H3,I3: 9.. / H3 = 9  =>  1 pairs (_) / I3 = 9  =>  1 pairs (_)
B5,B6: 9.. / B5 = 9  =>  1 pairs (_) / B6 = 9  =>  2 pairs (_)
* DURATION: 0:00:06.459972  START: 19:20:12.956197  END: 19:20:19.416169 2017-04-29
* CP COUNT: (7)

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
H5,I5: 3.. / H5 = 3 ==>  1 pairs (_) / I5 = 3 ==>  3 pairs (_)
B5,B6: 9.. / B5 = 9  =>  0 pairs (X) / B6 = 9 ==>  0 pairs (*)
* DURATION: 0:00:24.388513  START: 19:20:19.416541  END: 19:20:43.805054 2017-04-29
* REASONING B5,B6: 9..
* DIS # B6: 9 # B3: 1,2 => CTR => B3: 3,7
* PRF # B6: 9 + B3: 3,7 # G3: 1,2 => SOL
* STA # B6: 9 + B3: 3,7 + G3: 1,2
* CNT   2 HDP CHAINS /   8 HYP OPENED
* DCP COUNT: (2)
* SOLUTION FOUND
```

```25;H2;GP;22;11.80;11.80;2.60
```

# Appendix: Full HDP Chains

## A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for H5,I5: 3..:

```* INC # I5: 3 # G1: 4,6 => UNS
* INC # I5: 3 # G1: 1,2,5 => UNS
* INC # I5: 3 # I9: 4,6 => UNS
* INC # I5: 3 # I9: 7,8,9 => UNS
* INC # I5: 3 # B2: 4,7 => UNS
* INC # I5: 3 # C2: 4,7 => UNS
* INC # I5: 3 # I7: 4,7 => UNS
* INC # I5: 3 # I9: 4,7 => UNS
* INC # I5: 3 # H4: 5,8 => UNS
* INC # I5: 3 # G6: 5,8 => UNS
* INC # I5: 3 # A5: 5,8 => UNS
* INC # I5: 3 # F5: 5,8 => UNS
* INC # I5: 3 => UNS
* INC # H5: 3 # I4: 2,8 => UNS
* INC # H5: 3 # I4: 6 => UNS
* INC # H5: 3 # F5: 2,8 => UNS
* INC # H5: 3 # F5: 5,9 => UNS
* INC # H5: 3 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED
```

Full list of HDP chains traversed for B5,B6: 9..:

```* INC # B6: 9 # B2: 1,2 => UNS
* DIS # B6: 9 # B3: 1,2 => CTR => B3: 3,7
* INC # B6: 9 + B3: 3,7 # B2: 1,2 => UNS
* INC # B6: 9 + B3: 3,7 # B2: 3,4,7 => UNS
* INC # B6: 9 + B3: 3,7 # D3: 1,2 => UNS
* INC # B6: 9 + B3: 3,7 # E3: 1,2 => UNS
* PRF # B6: 9 + B3: 3,7 # G3: 1,2 => SOL
* STA # B6: 9 + B3: 3,7 + G3: 1,2
* CNT   7 HDP CHAINS /   8 HYP OPENED
```