# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=14

level: medium

position: .........6..9...2..28..53....5.248..9.2.5.1.4..487.5....34..95..5...8..1......... initial

# Autosolve

position: 5........6..98..25.28..53....51248..982.5.174..48795.2..34..95..5...8..1...5..... autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # F2: 3 => CTR => F2: 1,7
* DIS # D1: 6,7 => CTR => D1: 2,3
* DIS # D1: 3,6 => CTR => D1: 2,7
* DIS # A7: 1,7 => CTR => A7: 2,8
* DIS # F7: 1,7 => CTR => F7: 2,6
* DIS # B1: 3 => CTR => B1: 4,9
* DIS # F7: 1,6 => CTR => F7: 2,7
* DIS # E1: 1,6 => CTR => E1: 3,4
* CNT   8 HDP CHAINS /  43 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # F2: 3 => CTR => F2: 1,7
* DIS F2: 1,7 # D1: 6,7 => CTR => D1: 2,3
* DIS F2: 1,7 + D1: 2,3 # F1: 6,7 => CTR => F1: 1,2,3
* DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 # I3: 6,7 => CTR => I3: 9
* DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 # D8: 2,3 => CTR => D8: 6,7
* DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 # H8: 3,6 => CTR => H8: 4
* PRF F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4 => SOL
* STA F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4
* CNT   7 HDP CHAINS /  18 HYP OPENED
```

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

# Details

## Positions

 .........6..9...2..28..53....5.248..9.2.5.1.4..487.5....34..95..5...8..1......... initial 5........6..98..25.28..53....51248..982.5.174..48795.2..34..95..5...8..1...5..... autosolve 591243687637981425428765319765124893982356174314879562873412956259638741146597238 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (14)
B2: 3,4
C2: 1,7
D3: 6,7
G2: 4,7
A4: 3,7
B4: 6,7
A6: 1,3
B6: 1,6
D5: 3,6
F5: 3,6
H6: 3,6
B7: 1,7
B9: 4,9
E7: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 16 pairs (_) / H3 = 1  => 17 pairs (_)
A6,B6: 1.. / A6 = 1  => 16 pairs (_) / B6 = 1  => 15 pairs (_)
C2,F2: 1.. / C2 = 1  => 16 pairs (_) / F2 = 1  => 17 pairs (_)
B6,B7: 1.. / B6 = 1  => 15 pairs (_) / B7 = 1  => 16 pairs (_)
D1,F1: 2.. / D1 = 2  => 14 pairs (_) / F1 = 2  =>  0 pairs (X)
G8,G9: 2.. / G8 = 2  => 17 pairs (_) / G9 = 2  => 14 pairs (_)
A7,F7: 2.. / A7 = 2  =>  0 pairs (X) / F7 = 2  => 14 pairs (_)
D1,D8: 2.. / D1 = 2  => 14 pairs (_) / D8 = 2  =>  0 pairs (X)
B1,B2: 3.. / B1 = 3  =>  0 pairs (X) / B2 = 3  => 15 pairs (_)
A4,A6: 3.. / A4 = 3  => 16 pairs (_) / A6 = 3  => 15 pairs (_)
D5,F5: 3.. / D5 = 3  => 12 pairs (_) / F5 = 3  => 18 pairs (_)
B2,F2: 3.. / B2 = 3  => 15 pairs (_) / F2 = 3  =>  0 pairs (X)
A6,H6: 3.. / A6 = 3  => 15 pairs (_) / H6 = 3  => 16 pairs (_)
I4,I9: 3.. / I4 = 3  =>  0 pairs (*) / I9 = 3  =>  0 pairs (X)
E1,E3: 4.. / E1 = 4  => 19 pairs (_) / E3 = 4  => 18 pairs (_)
B2,G2: 4.. / B2 = 4  =>  0 pairs (X) / G2 = 4  => 15 pairs (_)
B4,B6: 6.. / B4 = 6  => 15 pairs (_) / B6 = 6  => 16 pairs (_)
D5,F5: 6.. / D5 = 6  => 18 pairs (_) / F5 = 6  => 12 pairs (_)
C8,C9: 6.. / C8 = 6  => 15 pairs (_) / C9 = 6  => 16 pairs (_)
B6,H6: 6.. / B6 = 6  => 16 pairs (_) / H6 = 6  => 15 pairs (_)
A4,B4: 7.. / A4 = 7  => 15 pairs (_) / B4 = 7  => 16 pairs (_)
B4,B7: 7.. / B4 = 7  => 16 pairs (_) / B7 = 7  => 15 pairs (_)
H1,I1: 8.. / H1 = 8  => 18 pairs (_) / I1 = 8  => 15 pairs (_)
A7,A9: 8.. / A7 = 8  => 15 pairs (_) / A9 = 8  =>  0 pairs (X)
A7,I7: 8.. / A7 = 8  => 15 pairs (_) / I7 = 8  =>  0 pairs (X)
H1,H9: 8.. / H1 = 8  => 18 pairs (_) / H9 = 8  => 15 pairs (_)
B1,C1: 9.. / B1 = 9  => 22 pairs (_) / C1 = 9  => 18 pairs (_)
H3,I3: 9.. / H3 = 9  => 22 pairs (_) / I3 = 9  => 15 pairs (_)
H4,I4: 9.. / H4 = 9  => 15 pairs (_) / I4 = 9  => 22 pairs (_)
E8,E9: 9.. / E8 = 9  => 15 pairs (_) / E9 = 9  => 22 pairs (_)
C8,E8: 9.. / C8 = 9  => 22 pairs (_) / E8 = 9  => 15 pairs (_)
B1,B9: 9.. / B1 = 9  => 22 pairs (_) / B9 = 9  => 18 pairs (_)
H3,H4: 9.. / H3 = 9  => 22 pairs (_) / H4 = 9  => 15 pairs (_)
I3,I4: 9.. / I3 = 9  => 15 pairs (_) / I4 = 9  => 22 pairs (_)
* DURATION: 0:00:53.010560  START: 03:38:23.136989  END: 03:39:16.147549 2017-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B2,B4,B6,B7,B9,C2,D3,D5,E7,F5,G2,H6)
* 5........6..98..25.28..53....51248..982.5.174..48795.2..34..95..5...8..1...5.....
* PAIR B2: 3,4 BLK 1
B1: 3,4,9                                # reduction candidate for 3,4
B1: 9                                    # 22 pairs
B1: 3,4                                  # 18 pairs
* PAIR C2: 1,7 BLK 1
C1: 1,7,9                                # reduction candidate for 1,7
C1: 1,7                                  # 22 pairs
A3: 1,7,4                                # reduction candidate for 1,7
A3: 1,7                                  # 18 pairs
* PAIR C2: 1,7 ROW 2
F2: 1,7,3                                # reduction candidate for 1,7
F2: 3 => CTR
* 539......6419837257286.53.9375124896982356174164879532.1346.95..5...8..1...5.....
F2: 1,7                                  # 15 pairs
* PAIR C2: 1,7 COL C
C9: 1,7,6,9                              # reduction candidate for 1,7
C9: 1,7                                  # 19 pairs
C9: 6,9                                  # 16 pairs
* PAIR D3: 6,7 BLK 2
D1: 6,7,2,3                              # reduction candidate for 6,7
D1: 6,7 => CTR
* 5....2.8.6..98..25.28..5319..512489.982356174164879532213467958.5.238..18..5912.3
D1: 2,3                                  # 15 pairs
F1: 6,7,1,2,3                            # reduction candidate for 6,7
F1: 6,7                                  # 18 pairs
* PAIR D3: 6,7 ROW 3
I3: 6,7,9                                # reduction candidate for 6,7
I3: 6,7                                  # 22 pairs
I3: 9                                    # 15 pairs
* PAIR D3: 6,7 COL D
D8: 6,7,2,3                              # reduction candidate for 6,7
D8: 2,3                                  # 16 pairs
D8: 6,7                                  # 13 pairs
* PAIR G2: 4,7 BLK 3
G1: 4,7,6                                # reduction candidate for 4,7
G1: 4,7                                  # 22 pairs
G1: 6                                    # 16 pairs
* PAIR G2: 4,7 COL G
G8: 4,7,2,6                              # reduction candidate for 4,7
G8: 4,7                                  # 17 pairs
G9: 4,7,2,6                              # reduction candidate for 4,7
G9: 4,7                                  # 20 pairs
* PAIR D5: 3,6 COL D
D1: 3,6,2,7                              # reduction candidate for 3,6
D1: 3,6 => CTR
* 5....2.8.6..98..25.287.5319..512489.982.5.174164879532213467958.5.238..18..5912.3
D1: 2,7                                  # 15 pairs
D8: 3,6,2,7                              # reduction candidate for 3,6
D8: 3,6                                  # 23 pairs
* PAIR F5: 3,6 COL F
F1: 3,6,1,2,7                            # reduction candidate for 3,6
F1: 3,6                                  # 16 pairs
F9: 3,6,1,2,7                            # reduction candidate for 3,6
F9: 3,6                                  # 19 pairs
* PAIR H6: 3,6 BLK 6
H4: 3,6,9                                # reduction candidate for 3,6
H4: 3,6                                  # 22 pairs
I4: 3,6,9                                # reduction candidate for 3,6
I4: 3,6                                  # 15 pairs
* PAIR H6: 3,6 COL H
H8: 3,6,4                                # reduction candidate for 3,6
H8: 3,6                                  # 18 pairs
H9: 3,6,4,8                              # reduction candidate for 3,6
H9: 3,6                                  # 20 pairs
* PAIR B7: 1,7 BLK 7
A7: 1,7,2,8                              # reduction candidate for 1,7
A7: 1,7 => CTR
* 59.2...8.63.98.425428..5319..512489.982.5.174..48795.2..346295825...8..184.5..2..
A7: 2,8                                  # 15 pairs
A9: 1,7,2,4,8                            # reduction candidate for 1,7
A9: 1,7                                  # 22 pairs
C9: 1,7,6,9                              # reduction candidate for 1,7
C9: 1,7                                  # 19 pairs
* PAIR B7: 1,7 ROW 7
F7: 1,7,2,6                              # reduction candidate for 1,7
F7: 1,7 => CTR
* 5......876.7981.25.28..5319..512489.982.5.174164879532213467958.5...8..18..5....3
F7: 2,6                                  # 15 pairs
* PAIR B9: 4,9 COL B
B1: 4,9,3                                # reduction candidate for 4,9
B1: 3 => CTR
* 539......64.9837257286.53.9375124896982356174164879532.1346.95..5...8..1...5.....
B1: 4,9                                  # 15 pairs
* PAIR E7: 1,6 BLK 8
F7: 1,6,2,7                              # reduction candidate for 1,6
F7: 1,6 => CTR
* 5......8.6..98..25.28..5319..512489.982.5.1741648795.22.34..958.5...8..18..5.....
F7: 2,7                                  # 15 pairs
E9: 1,6,3,9                              # reduction candidate for 1,6
E9: 1,6                                  # 19 pairs
F9: 1,6,2,3,7                            # reduction candidate for 1,6
F9: 1,6                                  # 19 pairs
* PAIR E7: 1,6 COL E
E1: 1,6,3,4                              # reduction candidate for 1,6
E1: 1,6 => CTR
* 5.9......6.7981425128.4539...51248.3982.5.174314879562.734..95..56.98.31.9153....
E1: 3,4                                  # 15 pairs
E3: 1,6,4                                # reduction candidate for 1,6
E3: 1,6                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0014-base-pr-000.dot
* REASONING
* DIS # F2: 3 => CTR => F2: 1,7
* DIS # D1: 6,7 => CTR => D1: 2,3
* DIS # D1: 3,6 => CTR => D1: 2,7
* DIS # A7: 1,7 => CTR => A7: 2,8
* DIS # F7: 1,7 => CTR => F7: 2,6
* DIS # B1: 3 => CTR => B1: 4,9
* DIS # F7: 1,6 => CTR => F7: 2,7
* DIS # E1: 1,6 => CTR => E1: 3,4
* CNT   8 HDP CHAINS /  43 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B2,B4,B6,B7,B9,C2,D3,D5,E7,F5,G2,H6)
* 5........6..98..25.28..53....51248..982.5.174..48795.2..34..95..5...8..1...5.....
* PAIR B2: 3,4 BLK 1
B1: 3,4,9                                # reduction candidate for 3,4
B1: 9                                    # 22 pairs
B1: 3,4                                  # 18 pairs
* PAIR C2: 1,7 BLK 1
C1: 1,7,9                                # reduction candidate for 1,7
C1: 1,7                                  # 22 pairs
A3: 1,7,4                                # reduction candidate for 1,7
A3: 1,7                                  # 18 pairs
* PAIR C2: 1,7 ROW 2
F2: 1,7,3                                # reduction candidate for 1,7
F2: 3 => CTR
* 539......6419837257286.53.9375124896982356174164879532.1346.95..5...8..1...5.....
* PAIR C2: 1,7 COL C
C9: 1,7,6,9                              # reduction candidate for 1,7
C9: 1,7                                  # 19 pairs
C9: 6,9                                  # 17 pairs
* PAIR RESTART
* PAIR C2: 1,7 BLK 1
C1: 1,7,9                                # reduction candidate for 1,7
C1: 1,7                                  # 22 pairs
A3: 1,7,4                                # reduction candidate for 1,7
A3: 1,7                                  # 17 pairs
* PAIR C2: 1,7 COL C
C9: 1,7,6,9                              # reduction candidate for 1,7
C9: 1,7                                  # 19 pairs
C9: 6,9                                  # 17 pairs
* PAIR D3: 6,7 BLK 2
D1: 6,7,2,3                              # reduction candidate for 6,7
D1: 6,7 => CTR
* 5...32.8.63.98.425.28.45319..512489.98235617416487953221346795845.298.618965..2..
F1: 6,7,1,2,3                            # reduction candidate for 6,7
F1: 6,7 => CTR
* 54923.61863798142512864539776512483998235.174314879562873412956.56.98..1.9156..8.
* RESTART
* PAIR D3: 6,7 ROW 3
I3: 6,7,9                                # reduction candidate for 6,7
I3: 6,7 => CTR
* 597243618631987425428615397..51248.9982356174..48795.28.34.295..5..38.41...59..83
* PAIR D3: 6,7 COL D
D8: 6,7,2,3                              # reduction candidate for 6,7
D8: 2,3 => CTR
* 5..3.2.8.637981425.287.5319..512489.982653174164879532213467958.5.2.8..18..5..2..
* PAIR RESTART
* PAIR H6: 3,6 COL H
H8: 3,6,4                                # reduction candidate for 3,6
H8: 3,6 => CTR
* 5492...8.631987425728645319375124896982356174..48795.2..34..95.45..98231.9.5...4.
H8: 4 => SOLVED
* 591243687637981425428765319765124893982356174314879562873412956259638741146597238
* DURATION: 0:00:19.456567  START: 03:39:52.467987  END: 03:40:11.924554 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0014-base-pr-001.dot
* REASONING
* DIS # F2: 3 => CTR => F2: 1,7
* DIS F2: 1,7 # D1: 6,7 => CTR => D1: 2,3
* DIS F2: 1,7 + D1: 2,3 # F1: 6,7 => CTR => F1: 1,2,3
* DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 # I3: 6,7 => CTR => I3: 9
* DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 # D8: 2,3 => CTR => D8: 6,7
* DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 # H8: 3,6 => CTR => H8: 4
* PRF F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4 => SOL
* STA F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4
* CNT   7 HDP CHAINS /  18 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=14
```

# Solution

position: 591243687637981425428765319765124893982356174314879562873412956259638741146597238 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 # B1: 3,4 => UNS
* INC # B1: 9 => UNS
* INC # C1: 1,7 => UNS
* INC # A3: 1,7 => UNS
* INC # F2: 1,7 => UNS
* DIS # F2: 3 => CTR => F2: 1,7
* INC # C9: 1,7 => UNS
* INC # C9: 6,9 => UNS
* DIS # D1: 6,7 => CTR => D1: 2,3
* INC # D1: 2,3 => UNS
* INC # F1: 6,7 => UNS
* INC # I3: 6,7 => UNS
* INC # I3: 9 => UNS
* INC # D8: 6,7 => UNS
* INC # D8: 2,3 => UNS
* INC # G1: 4,7 => UNS
* INC # G1: 6 => UNS
* INC # G8: 4,7 => UNS
* INC # G9: 4,7 => UNS
* DIS # D1: 3,6 => CTR => D1: 2,7
* INC # D1: 2,7 => UNS
* INC # D8: 3,6 => UNS
* INC # F1: 3,6 => UNS
* INC # F9: 3,6 => UNS
* INC # H4: 3,6 => UNS
* INC # I4: 3,6 => UNS
* INC # H8: 3,6 => UNS
* INC # H9: 3,6 => UNS
* DIS # A7: 1,7 => CTR => A7: 2,8
* INC # A7: 2,8 => UNS
* INC # A9: 1,7 => UNS
* INC # C9: 1,7 => UNS
* DIS # F7: 1,7 => CTR => F7: 2,6
* INC # F7: 2,6 => UNS
* INC # B1: 4,9 => UNS
* DIS # B1: 3 => CTR => B1: 4,9
* DIS # F7: 1,6 => CTR => F7: 2,7
* INC # F7: 2,7 => UNS
* INC # E9: 1,6 => UNS
* INC # F9: 1,6 => UNS
* DIS # E1: 1,6 => CTR => E1: 3,4
* INC # E1: 3,4 => UNS
* INC # E3: 1,6 => UNS
* CNT  43 HDP CHAINS /  43 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # B1: 3,4 => UNS
* INC # B1: 9 => UNS
* INC # C1: 1,7 => UNS
* INC # A3: 1,7 => UNS
* INC # F2: 1,7 => UNS
* DIS # F2: 3 => CTR => F2: 1,7
* INC F2: 1,7 # C9: 1,7 => UNS
* INC F2: 1,7 # C9: 6,9 => UNS
* INC F2: 1,7 # C1: 1,7 => UNS
* INC F2: 1,7 # A3: 1,7 => UNS
* INC F2: 1,7 # C9: 1,7 => UNS
* INC F2: 1,7 # C9: 6,9 => UNS
* DIS F2: 1,7 # D1: 6,7 => CTR => D1: 2,3
* DIS F2: 1,7 + D1: 2,3 # F1: 6,7 => CTR => F1: 1,2,3
* DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 # I3: 6,7 => CTR => I3: 9
* INC F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 # D8: 6,7 => UNS
* DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 # D8: 2,3 => CTR => D8: 6,7
* DIS F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 # H8: 3,6 => CTR => H8: 4
* PRF F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4 => SOL
* STA F2: 1,7 + D1: 2,3 + F1: 1,2,3 + I3: 9 + D8: 6,7 + H8: 4
* CNT  19 HDP CHAINS /  18 HYP OPENED
```