# Original Sudoku

level: deep

position: 98.7..6..7..6...8...6...5..4.........3..2......78.9.5...92.7.6.....5...2......1.. initial

# Autosolve

position: 98.7..6..7..6...8...6...5..49..7.....3..2......78.9.5...92.7.6.....5...2......1.. autosolve

# Pair Reduction Variants

## Deep Constraint Pair Analysis

Time used: 0:00:00.000006

List of important HDP chains detected for E6,E9: 6..:

```* DIS # E6: 6 # F3: 1,3 => CTR => F3: 2,4,8
* DIS # E6: 6 + F3: 2,4,8 # F2: 1,4 => CTR => F2: 2,3
* PRF # E6: 6 + F3: 2,4,8 + F2: 2,3 # B3: 4 => SOL
* STA # E6: 6 + F3: 2,4,8 + F2: 2,3 + B3: 4
* CNT   3 HDP CHAINS /  46 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..7..6...8...6...5..4.........3..2......78.9.5...92.7.6.....5...2......1.. initial 98.7..6..7..6...8...6...5..49..7.....3..2......78.9.5...92.7.6.....5...2......1.. autosolve

level: deep

## Pairing Analysis

```--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,F2: 5.. / F1 = 5  =>  0 pairs (_) / F2 = 5  =>  2 pairs (_)
D4,D5: 5.. / D4 = 5  =>  1 pairs (_) / D5 = 5  =>  4 pairs (_)
I7,I9: 5.. / I7 = 5  =>  1 pairs (_) / I9 = 5  =>  0 pairs (_)
C1,F1: 5.. / C1 = 5  =>  2 pairs (_) / F1 = 5  =>  0 pairs (_)
C4,D4: 5.. / C4 = 5  =>  4 pairs (_) / D4 = 5  =>  1 pairs (_)
F4,I4: 6.. / F4 = 6  =>  1 pairs (_) / I4 = 6  =>  1 pairs (_)
E6,E9: 6.. / E6 = 6  => 13 pairs (_) / E9 = 6  =>  0 pairs (_)
H3,I3: 7.. / H3 = 7  =>  0 pairs (_) / I3 = 7  =>  0 pairs (_)
B8,B9: 7.. / B8 = 7  =>  0 pairs (_) / B9 = 7  =>  0 pairs (_)
G5,G8: 7.. / G5 = 7  =>  0 pairs (_) / G8 = 7  =>  0 pairs (_)
E3,F3: 8.. / E3 = 8  =>  0 pairs (_) / F3 = 8  =>  2 pairs (_)
* DURATION: 0:00:07.235587  START: 09:12:20.489226  END: 09:12:27.724813 2020-10-09
* CP COUNT: (11)
* INCONCLUSIVE

--------------------------------------------------
* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
E6,E9: 6.. / E6 = 6 ==>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
* DURATION: 0:00:36.662395  START: 09:12:27.725373  END: 09:13:04.387768 2020-10-09
* REASONING E6,E9: 6..
* DIS # E6: 6 # F3: 1,3 => CTR => F3: 2,4,8
* DIS # E6: 6 + F3: 2,4,8 # F2: 1,4 => CTR => F2: 2,3
* PRF # E6: 6 + F3: 2,4,8 + F2: 2,3 # B3: 4 => SOL
* STA # E6: 6 + F3: 2,4,8 + F2: 2,3 + B3: 4
* CNT   3 HDP CHAINS /  46 HYP OPENED
* DCP COUNT: (1)
* SOLUTION FOUND
```

```2236569;2018_12_25;PAQ;23;11.50;1.20;1.20
```

# Appendix: Full HDP Chains

## A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for E6,E9: 6..:

```* INC # E6: 6 # A3: 1,2 => UNS
* INC # E6: 6 # A3: 3 => UNS
* INC # E6: 6 # B3: 1,2 => UNS
* INC # E6: 6 # B3: 4 => UNS
* INC # E6: 6 # D4: 1,3 => UNS
* INC # E6: 6 # D4: 5 => UNS
* INC # E6: 6 # F2: 1,3 => UNS
* DIS # E6: 6 # F3: 1,3 => CTR => F3: 2,4,8
* INC # E6: 6 + F3: 2,4,8 # F8: 1,3 => UNS
* INC # E6: 6 + F3: 2,4,8 # D4: 1,3 => UNS
* INC # E6: 6 + F3: 2,4,8 # D4: 5 => UNS
* INC # E6: 6 + F3: 2,4,8 # F2: 1,3 => UNS
* INC # E6: 6 + F3: 2,4,8 # F8: 1,3 => UNS
* INC # E6: 6 + F3: 2,4,8 # D5: 1,4 => UNS
* INC # E6: 6 + F3: 2,4,8 # D5: 5 => UNS
* DIS # E6: 6 + F3: 2,4,8 # F2: 1,4 => CTR => F2: 2,3
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # F8: 1,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # F8: 1,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # F8: 3,6,8 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # D5: 1,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # D5: 5 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # F8: 1,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # F8: 3,6,8 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # H1: 1,2 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # H3: 1,2 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # G2: 3,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # G7: 3,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # G8: 3,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # I1: 3,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # I2: 3,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # I3: 3,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # I7: 3,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # I9: 3,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # C8: 1,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # C8: 3 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # E7: 1,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # E7: 3,8 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # B3: 1,4 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # B3: 2 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # C2: 2,3 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # G2: 2,3 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # A3: 1,2 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # A3: 3 => UNS
* INC # E6: 6 + F3: 2,4,8 + F2: 2,3 # B3: 1,2 => UNS
* PRF # E6: 6 + F3: 2,4,8 + F2: 2,3 # B3: 4 => SOL
* STA # E6: 6 + F3: 2,4,8 + F2: 2,3 + B3: 4
* CNT  45 HDP CHAINS /  46 HYP OPENED
```