# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=46

level: medium

position: .32.5..9.8.....6....74.6..2.8....5.....1.9.....3....6.7..6.31....4.....6.6..2.83. initial

# Autosolve

position: 632.5..9.84....6....74.63.2.8....5.....1.9.....3....6.7.86.31..3.4.....6.6..2.83. autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # D6: 7,8 => CTR => D6: 2,5
* PRF # I1: 4,7 => SOL
* CNT   2 HDP CHAINS /  13 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # D6: 7,8 => CTR => D6: 2,5
* PRF D6: 2,5 # I1: 4,7 => SOL
* STA D6: 2,5 + I1: 4,7
* CNT   2 HDP CHAINS /  15 HYP OPENED
```

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

# Details

## Positions

 .32.5..9.8.....6....74.6..2.8....5.....1.9.....3....6.7..6.31....4.....6.6..2.83. initial 632.5..9.84....6....74.63.2.8....5.....1.9.....3....6.7.86.31..3.4.....6.6..2.83. autosolve 632851497849372615517496382981764523256139748473285961728643159394518276165927834 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (5)
D1: 7,8
G1: 4,7
B5: 5,7
C5: 5,6
E7: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,I1: 1.. / F1 = 1  =>  7 pairs (_) / I1 = 1  => 20 pairs (_)
D2,F2: 2.. / D2 = 2  =>  0 pairs (X) / F2 = 2  =>  6 pairs (_)
B7,B8: 2.. / B7 = 2  =>  7 pairs (_) / B8 = 2  =>  8 pairs (_)
B7,H7: 2.. / B7 = 2  =>  7 pairs (_) / H7 = 2  =>  8 pairs (_)
D2,E2: 3.. / D2 = 3  => 12 pairs (_) / E2 = 3  =>  5 pairs (_)
I4,I5: 3.. / I4 = 3  => 12 pairs (_) / I5 = 3  =>  5 pairs (_)
E5,I5: 3.. / E5 = 3  => 12 pairs (_) / I5 = 3  =>  5 pairs (_)
D2,D4: 3.. / D2 = 3  => 12 pairs (_) / D4 = 3  =>  5 pairs (_)
G1,I1: 4.. / G1 = 4  =>  5 pairs (_) / I1 = 4  =>  0 pairs (X)
E7,F9: 4.. / E7 = 4  =>  7 pairs (_) / F9 = 4  =>  0 pairs (X)
F9,I9: 4.. / F9 = 4  =>  0 pairs (X) / I9 = 4  =>  7 pairs (_)
D6,F6: 5.. / D6 = 5  => 12 pairs (_) / F6 = 5  =>  5 pairs (_)
C4,C5: 6.. / C4 = 6  =>  0 pairs (X) / C5 = 6  =>  5 pairs (_)
E4,E5: 6.. / E4 = 6  =>  5 pairs (_) / E5 = 6  =>  0 pairs (X)
C4,E4: 6.. / C4 = 6  =>  0 pairs (X) / E4 = 6  =>  5 pairs (_)
C5,E5: 6.. / C5 = 6  =>  5 pairs (_) / E5 = 6  =>  0 pairs (X)
B5,B6: 7.. / B5 = 7  =>  6 pairs (_) / B6 = 7  => 10 pairs (_)
I1,H3: 8.. / I1 = 8  =>  0 pairs (X) / H3 = 8  => 13 pairs (_)
E3,H3: 8.. / E3 = 8  =>  0 pairs (X) / H3 = 8  => 13 pairs (_)
H3,H5: 8.. / H3 = 8  => 13 pairs (_) / H5 = 8  =>  0 pairs (X)
G6,G8: 9.. / G6 = 9  =>  7 pairs (_) / G8 = 9  =>  6 pairs (_)
* DURATION: 0:00:27.107096  START: 04:20:14.370803  END: 04:20:41.477899 2017-05-01
* CP COUNT: (21)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C5,D1,E7,G1)
* 632.5..9.84....6....74.63.2.8....5.....1.9.....3....6.7.86.31..3.4.....6.6..2.83.
* PAIR D1: 7,8 BLK 2
F1: 7,8,1                                # reduction candidate for 7,8
F1: 7,8                                  # 20 pairs
F1: 1                                    #  7 pairs
* PAIR D1: 7,8 ROW 1
I1: 7,8,1,4                              # reduction candidate for 7,8
I1: 1,4                                  # 14 pairs
I1: 7,8                                  #  8 pairs
* PAIR D1: 7,8 COL D
D6: 7,8,2,5                              # reduction candidate for 7,8
D6: 7,8 => CTR
* 632.5.49.84...26....74.6382.8.2.451.2..1.974.4.3..526.7.86431..3.4...976.6.927834
D6: 2,5                                  #  6 pairs
D8: 7,8,5,9                              # reduction candidate for 7,8
D8: 7,8                                  # 11 pairs
* PAIR G1: 4,7 BLK 3
I1: 4,7,1,8                              # reduction candidate for 4,7
I1: 4,7 => SOLVED
* 632851497849372615517496382981764523256139748473285961728643159394518276165927834
I1: 1,8                                  #  7 pairs
* PAIR G1: 4,7 COL G
G5: 4,7,2                                # reduction candidate for 4,7
G5: 4,7                                  #  8 pairs
G6: 4,7,2,9                              # reduction candidate for 4,7
G6: 4,7                                  #  8 pairs
* PAIR E7: 4,9 ROW 7
I7: 4,9,5                                # reduction candidate for 4,9
I7: 5                                    #  9 pairs
I7: 4,9                                  #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0046-base-pr-000.dot
* REASONING
* DIS # D6: 7,8 => CTR => D6: 2,5
* PRF # I1: 4,7 => SOL
* CNT   2 HDP CHAINS /  13 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,C5,D1,E7,G1)
* 632.5..9.84....6....74.63.2.8....5.....1.9.....3....6.7.86.31..3.4.....6.6..2.83.
* PAIR D1: 7,8 BLK 2
F1: 7,8,1                                # reduction candidate for 7,8
F1: 7,8                                  # 20 pairs
F1: 1                                    #  7 pairs
* PAIR D1: 7,8 ROW 1
I1: 7,8,1,4                              # reduction candidate for 7,8
I1: 1,4                                  # 14 pairs
I1: 7,8                                  #  8 pairs
* PAIR D1: 7,8 COL D
D6: 7,8,2,5                              # reduction candidate for 7,8
D6: 7,8 => CTR
* 632.5.49.84...26....74.6382.8.2.451.2..1.974.4.3..526.7.86431..3.4...976.6.927834
D8: 7,8,5,9                              # reduction candidate for 7,8
D8: 7,8                                  # 11 pairs
* RESTART
* PAIR D1: 7,8 COL D
D8: 7,8,5,9                              # reduction candidate for 7,8
D8: 5,9                                  # 17 pairs
D8: 7,8                                  # 11 pairs
* PAIR RESTART
* PAIR D1: 7,8 BLK 2
F1: 7,8,1                                # reduction candidate for 7,8
F1: 7,8                                  # 21 pairs
F1: 1                                    #  8 pairs
* PAIR D1: 7,8 ROW 1
I1: 7,8,1,4                              # reduction candidate for 7,8
I1: 1,4                                  # 15 pairs
I1: 7,8                                  #  9 pairs
* PAIR D1: 7,8 COL D
D8: 7,8,5,9                              # reduction candidate for 7,8
D8: 5,9                                  # 17 pairs
D8: 7,8                                  # 11 pairs
* PAIR G1: 4,7 BLK 3
I1: 4,7,1,8                              # reduction candidate for 4,7
I1: 4,7 => SOLVED
* 632851497849372615517496382981764523256139748473285961728643159394518276165927834
* DURATION: 0:00:13.079119  START: 04:20:51.252690  END: 04:21:04.331809 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0046-base-pr-001.dot
* REASONING
* DIS # D6: 7,8 => CTR => D6: 2,5
* PRF D6: 2,5 # I1: 4,7 => SOL
* STA D6: 2,5 + I1: 4,7
* CNT   2 HDP CHAINS /  15 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=46
```

# Solution

position: 632851497849372615517496382981764523256139748473285961728643159394518276165927834 solved

See section 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 # F1: 7,8 => UNS
* INC # F1: 1 => UNS
* INC # I1: 7,8 => UNS
* INC # I1: 1,4 => UNS
* DIS # D6: 7,8 => CTR => D6: 2,5
* INC # D6: 2,5 => UNS
* INC # D8: 7,8 => UNS
* PRF # I1: 4,7 => SOL
* INC # I1: 1,8 => UNS
* INC # G5: 4,7 => UNS
* INC # G6: 4,7 => UNS
* INC # I7: 4,9 => UNS
* INC # I7: 5 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # F1: 7,8 => UNS
* INC # F1: 1 => UNS
* INC # I1: 7,8 => UNS
* INC # I1: 1,4 => UNS
* DIS # D6: 7,8 => CTR => D6: 2,5
* INC D6: 2,5 # D8: 7,8 => UNS
* INC D6: 2,5 # D8: 7,8 => UNS
* INC D6: 2,5 # D8: 5,9 => UNS
* INC D6: 2,5 # F1: 7,8 => UNS
* INC D6: 2,5 # F1: 1 => UNS
* INC D6: 2,5 # I1: 7,8 => UNS
* INC D6: 2,5 # I1: 1,4 => UNS
* INC D6: 2,5 # D8: 7,8 => UNS
* INC D6: 2,5 # D8: 5,9 => UNS
* PRF D6: 2,5 # I1: 4,7 => SOL
* STA D6: 2,5 + I1: 4,7
* CNT  15 HDP CHAINS /  15 HYP OPENED
```