Original Sudoku

level: hard

position: ........7..1..9.8..3.6..5.9.9..25.......6....3..9...4...7....91.2.5..3..8........ initial

Autosolve

position: ........7..1..9.8..3.6..5.9.9..25.......6.9..3..9...4...7....91.2.5..3..8.3.9.... 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: 0:01:28.921940

The following important HDP chains were detected:

```* DIS # H1: 1,2 # H9: 6,7 => CTR => H9: 5
* PRF # H1: 1,2 + H9: 5 # H4: 6 => SOL
* STA # H1: 1,2 + H9: 5 + H4: 6
* CNT   2 HDP CHAINS /  81 HYP OPENED
```

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

Details

Positions

 ........7..1..9.8..3.6..5.9.9..25.......6....3..9...4...7....91.2.5..3..8........ initial ........7..1..9.8..3.6..5.9.9..25.......6.9..3..9...4...7....91.2.5..3..8.3.9.... autosolve 945813627671259483238647519194325768782164935356978142567432891429581376813796254 solved

level: hard

Pairing Analysis

```--------------------------------------------------
* PAIRS (2)
H3: 1,2
H8: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A8,B9: 1.. / A8 = 1  =>  3 pairs (_) / B9 = 1  =>  2 pairs (_)
H1,I2: 3.. / H1 = 3  =>  2 pairs (_) / I2 = 3  =>  3 pairs (_)
E1,E2: 5.. / E1 = 5  =>  2 pairs (_) / E2 = 5  =>  2 pairs (_)
A7,B7: 5.. / A7 = 5  =>  3 pairs (_) / B7 = 5  =>  3 pairs (_)
H9,I9: 5.. / H9 = 5  =>  2 pairs (_) / I9 = 5  =>  2 pairs (_)
H5,H9: 5.. / H5 = 5  =>  2 pairs (_) / H9 = 5  =>  2 pairs (_)
G7,I8: 8.. / G7 = 8  =>  4 pairs (_) / I8 = 8  =>  3 pairs (_)
A1,C1: 9.. / A1 = 9  =>  2 pairs (_) / C1 = 9  =>  3 pairs (_)
A8,C8: 9.. / A8 = 9  =>  3 pairs (_) / C8 = 9  =>  2 pairs (_)
A1,A8: 9.. / A1 = 9  =>  2 pairs (_) / A8 = 9  =>  3 pairs (_)
C1,C8: 9.. / C1 = 9  =>  3 pairs (_) / C8 = 9  =>  2 pairs (_)
* DURATION: 0:00:10.094361  START: 21:28:57.389221  END: 21:29:07.483582 2017-04-30
* CP COUNT: (11)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:01:28.438588  START: 21:29:20.474233  END: 21:30:48.912821 2017-04-30
* SOLUTION FOUND
* SAVE PR GRAPH xx-tarx0003-base-pr-002.dot
* REASONING
* DIS # H1: 1,2 # H9: 6,7 => CTR => H9: 5
* PRF # H1: 1,2 + H9: 5 # H4: 6 => SOL
* STA # H1: 1,2 + H9: 5 + H4: 6
* CNT   2 HDP CHAINS /  81 HYP OPENED
```

```tarx0003,tarek 6.1 *3BB r6c56 r4c7 r5c2
```

Solution

position: 945813627671259483238647519194325768782164935356978142567432891429581376813796254 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: 1,2 => UNS
* INC # H1: 1,2 => UNS
* INC # F3: 1,2 => UNS
* INC # F3: 4,7,8 => UNS
* INC # H5: 1,2 => UNS
* INC # H5: 3,5,7 => UNS
* INC # G9: 6,7 => UNS
* INC # H9: 6,7 => UNS
* INC # F8: 6,7 => UNS
* INC # F8: 1,4,8 => UNS
* INC # H4: 6,7 => UNS
* INC # H4: 1,3 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED
```

A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # G1: 1,2 => UNS
* INC # H1: 1,2 => UNS
* INC # F3: 1,2 => UNS
* INC # F3: 4,7,8 => UNS
* INC # H5: 1,2 => UNS
* INC # H5: 3,5,7 => UNS
* INC # G9: 6,7 => UNS
* INC # H9: 6,7 => UNS
* INC # F8: 6,7 => UNS
* INC # F8: 1,4,8 => UNS
* INC # H4: 6,7 => UNS
* INC # H4: 1,3 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED
```

A3. Deep Pair Reduction

Full list of HDP chains traversed:

```* INC # G1: 1,2 => UNS
* INC # H1: 1,2 => UNS
* INC # F3: 1,2 => UNS
* INC # F3: 4,7,8 => UNS
* INC # H5: 1,2 => UNS
* INC # H5: 3,5,7 => UNS
* INC # G9: 6,7 => UNS
* INC # H9: 6,7 => UNS
* INC # F8: 6,7 => UNS
* INC # F8: 1,4,8 => UNS
* INC # H4: 6,7 => UNS
* INC # H4: 1,3 => UNS
* INC # G1: 1,2 # D1: 1,2 => UNS
* INC # G1: 1,2 # F1: 1,2 => UNS
* INC # G1: 1,2 # G6: 1,2 => UNS
* INC # G1: 1,2 # G6: 6,7,8 => UNS
* INC # G1: 1,2 # I2: 3,6 => UNS
* INC # G1: 1,2 # I2: 4 => UNS
* INC # G1: 1,2 # H4: 3,6 => UNS
* INC # G1: 1,2 # H4: 1,7 => UNS
* INC # G1: 1,2 # I2: 4,6 => UNS
* INC # G1: 1,2 # I2: 3 => UNS
* INC # G1: 1,2 # G7: 4,6 => UNS
* INC # G1: 1,2 # G9: 4,6 => UNS
* INC # G1: 1,2 # F3: 1,2 => UNS
* INC # G1: 1,2 # F3: 4,7,8 => UNS
* INC # G1: 1,2 # H5: 1,2 => UNS
* INC # G1: 1,2 # H5: 3,5,7 => UNS
* INC # G1: 1,2 # G9: 6,7 => UNS
* INC # G1: 1,2 # H9: 6,7 => UNS
* INC # G1: 1,2 # F8: 6,7 => UNS
* INC # G1: 1,2 # F8: 1,4,8 => UNS
* INC # G1: 1,2 # H4: 6,7 => UNS
* INC # G1: 1,2 # H4: 1,3 => UNS
* INC # G1: 1,2 => UNS
* INC # H1: 1,2 # A1: 4,6 => UNS
* INC # H1: 1,2 # B1: 4,6 => UNS
* INC # H1: 1,2 # C1: 4,6 => UNS
* INC # H1: 1,2 # D1: 1,2 => UNS
* INC # H1: 1,2 # F1: 1,2 => UNS
* INC # H1: 1,2 # A2: 4,6 => UNS
* INC # H1: 1,2 # B2: 4,6 => UNS
* INC # H1: 1,2 # F3: 1,2 => UNS
* INC # H1: 1,2 # F3: 4,7,8 => UNS
* INC # H1: 1,2 # I6: 6,8 => UNS
* INC # H1: 1,2 # I6: 2,5 => UNS
* INC # H1: 1,2 # C4: 6,8 => UNS
* INC # H1: 1,2 # C4: 4 => UNS
* INC # H1: 1,2 # I8: 6,8 => UNS
* INC # H1: 1,2 # I8: 4 => UNS
* INC # H1: 1,2 # D7: 2,8 => UNS
* INC # H1: 1,2 # F7: 2,8 => UNS
* INC # H1: 1,2 # G6: 2,8 => UNS
* INC # H1: 1,2 # G6: 1,7 => UNS
* DIS # H1: 1,2 # H9: 6,7 => CTR => H9: 5
* INC # H1: 1,2 + H9: 5 # F8: 6,7 => UNS
* INC # H1: 1,2 + H9: 5 # F8: 1,4,8 => UNS
* INC # H1: 1,2 + H9: 5 # H4: 6,7 => UNS
* INC # H1: 1,2 + H9: 5 # H4: 3 => UNS
* INC # H1: 1,2 + H9: 5 # D9: 2,7 => UNS
* INC # H1: 1,2 + H9: 5 # F9: 2,7 => UNS
* INC # H1: 1,2 + H9: 5 # G6: 2,7 => UNS
* INC # H1: 1,2 + H9: 5 # G6: 1,8 => UNS
* INC # H1: 1,2 + H9: 5 # A1: 4,6 => UNS
* INC # H1: 1,2 + H9: 5 # B1: 4,6 => UNS
* INC # H1: 1,2 + H9: 5 # C1: 4,6 => UNS
* INC # H1: 1,2 + H9: 5 # D1: 1,2 => UNS
* INC # H1: 1,2 + H9: 5 # F1: 1,2 => UNS
* INC # H1: 1,2 + H9: 5 # A2: 4,6 => UNS
* INC # H1: 1,2 + H9: 5 # B2: 4,6 => UNS
* INC # H1: 1,2 + H9: 5 # F3: 1,2 => UNS
* INC # H1: 1,2 + H9: 5 # F3: 4,7,8 => UNS
* INC # H1: 1,2 + H9: 5 # I6: 6,8 => UNS
* INC # H1: 1,2 + H9: 5 # I6: 2,5 => UNS
* INC # H1: 1,2 + H9: 5 # C4: 6,8 => UNS
* INC # H1: 1,2 + H9: 5 # C4: 4 => UNS
* INC # H1: 1,2 + H9: 5 # I8: 6,8 => UNS
* INC # H1: 1,2 + H9: 5 # I8: 4 => UNS
* INC # H1: 1,2 + H9: 5 # H4: 3,7 => UNS
* PRF # H1: 1,2 + H9: 5 # H4: 6 => SOL
* STA # H1: 1,2 + H9: 5 + H4: 6
* CNT  80 HDP CHAINS /  81 HYP OPENED
```