# Original Sudoku

level: hard

position: ........7..9.5.2..1....6.8....5..6...9.....3...64.2....8.6.......4.2.9..7......61 initial

# Autosolve

position: ........7..9.5.2.61....6.8....5..6...9..6..3...64.2...98.6.......4.2.9..7......61 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: 0:01:20.848708

The following important HDP chains were detected:

```* DIS # H1: 1,4 # H7: 5,7 => CTR => H7: 2
* PRF # H1: 1,4 + H7: 2 # H6: 5 => SOL
* STA # H1: 1,4 + H7: 2 + H6: 5
* CNT   2 HDP CHAINS /  75 HYP OPENED
```

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

# Details

## Positions

 ........7..9.5.2..1....6.8....5..6...9.....3...64.2....8.6.......4.2.9..7......61 initial ........7..9.5.2.61....6.8....5..6...9..6..3...64.2...98.6.......4.2.9..7......61 autosolve 263189547849357216157246389478513692592768134316492758981675423634821975725934861 solved

level: hard

## Pairing Analysis

```--------------------------------------------------
* PAIRS (2)
H2: 1,4
H8: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C7,B8: 1.. / C7 = 1  =>  2 pairs (_) / B8 = 1  =>  3 pairs (_)
D1,D3: 2.. / D1 = 2  =>  2 pairs (_) / D3 = 2  =>  2 pairs (_)
B9,C9: 2.. / B9 = 2  =>  3 pairs (_) / C9 = 2  =>  3 pairs (_)
H7,I7: 2.. / H7 = 2  =>  2 pairs (_) / I7 = 2  =>  2 pairs (_)
H4,H7: 2.. / H4 = 2  =>  2 pairs (_) / H7 = 2  =>  2 pairs (_)
A1,B1: 6.. / A1 = 6  =>  3 pairs (_) / B1 = 6  =>  2 pairs (_)
A8,B8: 6.. / A8 = 6  =>  2 pairs (_) / B8 = 6  =>  3 pairs (_)
A1,A8: 6.. / A1 = 6  =>  3 pairs (_) / A8 = 6  =>  2 pairs (_)
B1,B8: 6.. / B1 = 6  =>  2 pairs (_) / B8 = 6  =>  3 pairs (_)
I8,G9: 8.. / I8 = 8  =>  3 pairs (_) / G9 = 8  =>  4 pairs (_)
H1,I3: 9.. / H1 = 9  =>  2 pairs (_) / I3 = 9  =>  3 pairs (_)
* DURATION: 0:00:10.126247  START: 21:31:04.620592  END: 21:31:14.746839 2017-04-30
* CP COUNT: (11)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:01:20.493883  START: 21:31:27.631235  END: 21:32:48.125118 2017-04-30
* SOLUTION FOUND
* SAVE PR GRAPH xx-tarx0004-base-pr-002.dot
* REASONING
* DIS # H1: 1,4 # H7: 5,7 => CTR => H7: 2
* PRF # H1: 1,4 + H7: 2 # H6: 5 => SOL
* STA # H1: 1,4 + H7: 2 + H6: 5
* CNT   2 HDP CHAINS /  75 HYP OPENED
```

```tarx0004,tarek, 5.3 *3BB r5c46 r4c3 r6c7
```

# Solution

position: 263189547849357216157246389478513692592768134316492758981675423634821975725934861 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 # G1: 1,4 => UNS
* INC # H1: 1,4 => UNS
* INC # F2: 1,4 => UNS
* INC # F2: 3,7,8 => UNS
* INC # H4: 1,4 => UNS
* INC # H4: 2,7,9 => UNS
* INC # G7: 5,7 => UNS
* INC # H7: 5,7 => UNS
* INC # F8: 5,7 => UNS
* INC # F8: 1,3,8 => UNS
* INC # H6: 5,7 => UNS
* INC # H6: 1,9 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # G1: 1,4 => UNS
* INC # H1: 1,4 => UNS
* INC # F2: 1,4 => UNS
* INC # F2: 3,7,8 => UNS
* INC # H4: 1,4 => UNS
* INC # H4: 2,7,9 => UNS
* INC # G7: 5,7 => UNS
* INC # H7: 5,7 => UNS
* INC # F8: 5,7 => UNS
* INC # F8: 1,3,8 => UNS
* INC # H6: 5,7 => UNS
* INC # H6: 1,9 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED
```

## A3. Deep Pair Reduction

Full list of HDP chains traversed:

```* INC # G1: 1,4 => UNS
* INC # H1: 1,4 => UNS
* INC # F2: 1,4 => UNS
* INC # F2: 3,7,8 => UNS
* INC # H4: 1,4 => UNS
* INC # H4: 2,7,9 => UNS
* INC # G7: 5,7 => UNS
* INC # H7: 5,7 => UNS
* INC # F8: 5,7 => UNS
* INC # F8: 1,3,8 => UNS
* INC # H6: 5,7 => UNS
* INC # H6: 1,9 => UNS
* INC # G1: 1,4 # E1: 1,4 => UNS
* INC # G1: 1,4 # F1: 1,4 => UNS
* INC # G1: 1,4 # G5: 1,4 => UNS
* INC # G1: 1,4 # G5: 5,7,8 => UNS
* INC # G1: 1,4 # I3: 5,9 => UNS
* INC # G1: 1,4 # I3: 3 => UNS
* INC # G1: 1,4 # H6: 5,9 => UNS
* INC # G1: 1,4 # H6: 1,7 => UNS
* INC # G1: 1,4 # F2: 1,4 => UNS
* INC # G1: 1,4 # F2: 3,7,8 => UNS
* INC # G1: 1,4 # H4: 1,4 => UNS
* INC # G1: 1,4 # H4: 2,7,9 => UNS
* INC # G1: 1,4 # I3: 3,5 => UNS
* INC # G1: 1,4 # I3: 9 => UNS
* INC # G1: 1,4 # G7: 3,5 => UNS
* INC # G1: 1,4 # G9: 3,5 => UNS
* INC # G1: 1,4 # G7: 5,7 => UNS
* INC # G1: 1,4 # H7: 5,7 => UNS
* INC # G1: 1,4 # F8: 5,7 => UNS
* INC # G1: 1,4 # F8: 1,3,8 => UNS
* INC # G1: 1,4 # H6: 5,7 => UNS
* INC # G1: 1,4 # H6: 1,9 => UNS
* INC # G1: 1,4 => UNS
* INC # H1: 1,4 # A1: 3,5 => UNS
* INC # H1: 1,4 # B1: 3,5 => UNS
* INC # H1: 1,4 # C1: 3,5 => UNS
* INC # H1: 1,4 # E1: 1,4 => UNS
* INC # H1: 1,4 # F1: 1,4 => UNS
* INC # H1: 1,4 # F2: 1,4 => UNS
* INC # H1: 1,4 # F2: 3,7,8 => UNS
* INC # H1: 1,4 # B3: 3,5 => UNS
* INC # H1: 1,4 # C3: 3,5 => UNS
* INC # H1: 1,4 # I5: 5,8 => UNS
* INC # H1: 1,4 # I5: 2,4 => UNS
* INC # H1: 1,4 # A6: 5,8 => UNS
* INC # H1: 1,4 # A6: 3 => UNS
* INC # H1: 1,4 # I8: 5,8 => UNS
* INC # H1: 1,4 # I8: 3 => UNS
* INC # H1: 1,4 # E7: 4,7 => UNS
* INC # H1: 1,4 # F7: 4,7 => UNS
* INC # H1: 1,4 # G5: 4,7 => UNS
* INC # H1: 1,4 # G5: 1,8 => UNS
* DIS # H1: 1,4 # H7: 5,7 => CTR => H7: 2
* INC # H1: 1,4 + H7: 2 # F8: 5,7 => UNS
* INC # H1: 1,4 + H7: 2 # F8: 1,3,8 => UNS
* INC # H1: 1,4 + H7: 2 # H6: 5,7 => UNS
* INC # H1: 1,4 + H7: 2 # H6: 9 => UNS
* INC # H1: 1,4 + H7: 2 # E9: 4,8 => UNS
* INC # H1: 1,4 + H7: 2 # F9: 4,8 => UNS
* INC # H1: 1,4 + H7: 2 # G5: 4,8 => UNS
* INC # H1: 1,4 + H7: 2 # G5: 1,7 => UNS
* INC # H1: 1,4 + H7: 2 # A1: 3,5 => UNS
* INC # H1: 1,4 + H7: 2 # B1: 3,5 => UNS
* INC # H1: 1,4 + H7: 2 # C1: 3,5 => UNS
* INC # H1: 1,4 + H7: 2 # E1: 1,4 => UNS
* INC # H1: 1,4 + H7: 2 # F1: 1,4 => UNS
* INC # H1: 1,4 + H7: 2 # F2: 1,4 => UNS
* INC # H1: 1,4 + H7: 2 # F2: 3,7,8 => UNS
* INC # H1: 1,4 + H7: 2 # B3: 3,5 => UNS
* INC # H1: 1,4 + H7: 2 # C3: 3,5 => UNS
* INC # H1: 1,4 + H7: 2 # H6: 7,9 => UNS
* PRF # H1: 1,4 + H7: 2 # H6: 5 => SOL
* STA # H1: 1,4 + H7: 2 + H6: 5
* CNT  74 HDP CHAINS /  75 HYP OPENED
```