# Original Sudoku

level: hard

position: .....4..67..1....9..3.9.5....8.3...5...2..3.....4..8....9.8..5.2....1....7....... initial

# Autosolve

position: .....4..67..1....9..3.9.5....8.3...5...2.83.....4..8....9.8..5.2....1....7....... 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: 0:00:14.287239

The following important HDP chains were detected:

```* DIS # H2: 2,4 # C5: 5,6 => CTR => C5: 1,4,7
* PRF # H2: 2,4 + C5: 1,4,7 # C9: 5,6 => SOL
* STA # H2: 2,4 + C5: 1,4,7 + C9: 5,6
* CNT   2 HDP CHAINS /  12 HYP OPENED
```

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

# Details

## Positions

 .....4..67..1....9..3.9.5....8.3...5...2..3.....4..8....9.8..5.2....1....7....... initial .....4..67..1....9..3.9.5....8.3...5...2.83.....4..8....9.8..5.2....1....7....... autosolve 591824736786153249423796518148937625657218394932465871319682457264571983875349162 solved

level: hard

## Pairing Analysis

```--------------------------------------------------
* PAIRS (1)
G2: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E5,E6: 1.. / E5 = 1  =>  2 pairs (_) / E6 = 1  =>  2 pairs (_)
D1,F2: 3.. / D1 = 3  =>  6 pairs (_) / F2 = 3  =>  1 pairs (_)
H1,H2: 3.. / H1 = 3  =>  1 pairs (_) / H2 = 3  =>  6 pairs (_)
A6,B6: 3.. / A6 = 3  =>  1 pairs (_) / B6 = 3  =>  1 pairs (_)
D1,H1: 3.. / D1 = 3  =>  6 pairs (_) / H1 = 3  =>  1 pairs (_)
F2,H2: 3.. / F2 = 3  =>  1 pairs (_) / H2 = 3  =>  6 pairs (_)
E8,E9: 4.. / E8 = 4  =>  2 pairs (_) / E9 = 4  =>  2 pairs (_)
C5,C6: 7.. / C5 = 7  =>  2 pairs (_) / C6 = 7  =>  2 pairs (_)
D1,D3: 8.. / D1 = 8  =>  2 pairs (_) / D3 = 8  =>  3 pairs (_)
B8,A9: 8.. / B8 = 8  =>  1 pairs (_) / A9 = 8  =>  1 pairs (_)
B2,H2: 8.. / B2 = 8  =>  3 pairs (_) / H2 = 8  =>  1 pairs (_)
A1,B1: 9.. / A1 = 9  =>  1 pairs (_) / B1 = 9  =>  1 pairs (_)
* DURATION: 0:00:10.992747  START: 23:26:04.117918  END: 23:26:15.110665 2017-04-30
* CP COUNT: (12)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:14.156211  START: 23:26:23.999662  END: 23:26:38.155873 2017-04-30
* SOLUTION FOUND
* SAVE PR GRAPH xx-cola351_56_5_48_0_466K_1BB_r2c7_r4c8_r7c9_5_5_110K-base-pr-002.dot
* REASONING
* DIS # H2: 2,4 # C5: 5,6 => CTR => C5: 1,4,7
* PRF # H2: 2,4 + C5: 1,4,7 # C9: 5,6 => SOL
* STA # H2: 2,4 + C5: 1,4,7 + C9: 5,6
* CNT   2 HDP CHAINS /  12 HYP OPENED
```

```cola351 (56.5) 48.0 466K 1BB<< r2c7 r4c8 r7c9 5.5 110K
```

# Solution

position: 591824736786153249423796518148937625657218394932465871319682457264571983875349162 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 # H2: 2,4 => UNS
* INC # H3: 2,4 => UNS
* INC # I3: 2,4 => UNS
* INC # B2: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # G4: 2,4 => UNS
* INC # G7: 2,4 => UNS
* INC # G9: 2,4 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # H2: 2,4 => UNS
* INC # H3: 2,4 => UNS
* INC # I3: 2,4 => UNS
* INC # B2: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # G4: 2,4 => UNS
* INC # G7: 2,4 => UNS
* INC # G9: 2,4 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED
```

## A3. Deep Pair Reduction

Full list of HDP chains traversed:

```* INC # H2: 2,4 => UNS
* INC # H3: 2,4 => UNS
* INC # I3: 2,4 => UNS
* INC # B2: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # G4: 2,4 => UNS
* INC # G7: 2,4 => UNS
* INC # G9: 2,4 => UNS
* DIS # H2: 2,4 # C5: 5,6 => CTR => C5: 1,4,7
* INC # H2: 2,4 + C5: 1,4,7 # C8: 5,6 => UNS
* PRF # H2: 2,4 + C5: 1,4,7 # C9: 5,6 => SOL
* STA # H2: 2,4 + C5: 1,4,7 + C9: 5,6
* CNT  11 HDP CHAINS /  12 HYP OPENED
```