# Original Sudoku

level: hard

position: 98.7..6..5...9..7...7..4...3...2.1....89...5......3..6.1..8.5.2..54...6.......... initial

# Autosolve

position: 98.7..6..5...9..7...7..4...3...2.1....89...5......3..6.1..8.5.2..54...6.......... autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

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

## Pair Reduction

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

## Deep Pair Reduction

Time used: 0:00:11.016196

The following important HDP chains were detected:

```* DIS # D9: 3,6 # E1: 1,5 => CTR => E1: 3
* PRF # D9: 3,6 + E1: 3 # E3: 1,5 => SOL
* STA # D9: 3,6 + E1: 3 + E3: 1,5
* CNT   2 HDP CHAINS /  10 HYP OPENED
```

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

# Details

## Positions

 98.7..6..5...9..7...7..4...3...2.1....89...5......3..6.1..8.5.2..54...6.......... initial 98.7..6..5...9..7...7..4...3...2.1....89...5......3..6.1..8.5.2..54...6.......... autosolve 984731625531296478627854931376528194148967253259143786713689542895412367462375819 solved

level: hard

## Pairing Analysis

```--------------------------------------------------
* PAIRS (1)
D7: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G5,I5: 3.. / G5 = 3  =>  2 pairs (_) / I5 = 3  =>  1 pairs (_)
E5,E6: 4.. / E5 = 4  =>  2 pairs (_) / E6 = 4  =>  1 pairs (_)
I1,I3: 5.. / I1 = 5  =>  3 pairs (_) / I3 = 5  =>  1 pairs (_)
B4,B6: 5.. / B4 = 5  =>  2 pairs (_) / B6 = 5  =>  2 pairs (_)
A7,F7: 7.. / A7 = 7  =>  3 pairs (_) / F7 = 7  =>  6 pairs (_)
A8,A9: 8.. / A8 = 8  =>  1 pairs (_) / A9 = 8  =>  2 pairs (_)
F2,F4: 8.. / F2 = 8  =>  1 pairs (_) / F4 = 8  =>  4 pairs (_)
* DURATION: 0:00:05.325740  START: 09:39:37.543605  END: 09:39:42.869345 2020-12-15
* CP COUNT: (7)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:10.907965  START: 09:39:48.688656  END: 09:39:59.596621 2020-12-15
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00034973-12_05-base-pr-002.dot
* REASONING
* DIS # D9: 3,6 # E1: 1,5 => CTR => E1: 3
* PRF # D9: 3,6 + E1: 3 # E3: 1,5 => SOL
* STA # D9: 3,6 + E1: 3 + E3: 1,5
* CNT   2 HDP CHAINS /  10 HYP OPENED
```

```34973;12_05;GP;24;11.30;11.30;8.00
```

# Solution

position: 984731625531296478627854931376528194148967253259143786713689542895412367462375819 solved

See section Deep Pair Reduction for the HDP chains leading to this result.

# Appendix: Full HDP Chains

## A1. Pair Reduction Analysis

Full list of HDP chains traversed:

```* INC # D9: 3,6 => UNS
* INC # E9: 3,6 => UNS
* INC # C7: 3,6 => UNS
* INC # C7: 4,9 => UNS
* INC # D2: 3,6 => UNS
* INC # D3: 3,6 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # D9: 3,6 => UNS
* INC # E9: 3,6 => UNS
* INC # C7: 3,6 => UNS
* INC # C7: 4,9 => UNS
* INC # D2: 3,6 => UNS
* INC # D3: 3,6 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED
```

## A3. Deep Pair Reduction

Full list of HDP chains traversed:

```* INC # D9: 3,6 => UNS
* INC # E9: 3,6 => UNS
* INC # C7: 3,6 => UNS
* INC # C7: 4,9 => UNS
* INC # D2: 3,6 => UNS
* INC # D3: 3,6 => UNS
* DIS # D9: 3,6 # E1: 1,5 => CTR => E1: 3
* INC # D9: 3,6 + E1: 3 # D3: 1,5 => UNS
* PRF # D9: 3,6 + E1: 3 # E3: 1,5 => SOL
* STA # D9: 3,6 + E1: 3 + E3: 1,5
* CNT   9 HDP CHAINS /  10 HYP OPENED
```