# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=53

level: medium

position: 32.8.9...14.........7.6....6....3.2.2...8...1.8.5....3....3.4.........17...9.4.68 initial

# Autosolve

position: 32.8.9...14.........7.6....6....382.2...8...1.8.5....3....3.4.........17...9.4.68 autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # A3: 5,9 => CTR => A3: 8
* DIS # I3: 5,9 => CTR => I3: 2,4
* DIS # B4: 5,9 => CTR => B4: 1,7
* DIS # F6: 6,7 => CTR => F6: 1,2
* DIS # F7: 2,5 => CTR => F7: 1,6,7,8
* PRF # E9: 2,5 => SOL
* CNT   6 HDP CHAINS /  46 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # A3: 5,9 => CTR => A3: 8
* DIS A3: 8 # I3: 5,9 => CTR => I3: 2,4
* DIS A3: 8 + I3: 2,4 # B4: 5,9 => CTR => B4: 1,7
* DIS A3: 8 + I3: 2,4 + B4: 1,7 # B5: 3,7 => CTR => B5: 5,9
* DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # D5: 6,7 => CTR => D5: 4
* DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 # F6: 6,7 => CTR => F6: 1,2
* DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 # D7: 2,6 => CTR => D7: 1,7
* PRF A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 # C7: 2,8 => SOL
* STA A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 + C7: 2,8
* CNT   8 HDP CHAINS /  25 HYP OPENED
```

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

# Details

## Positions

 32.8.9...14.........7.6....6....3.2.2...8...1.8.5....3....3.4.........17...9.4.68 initial 32.8.9...14.........7.6....6....382.2...8...1.8.5....3....3.4.........17...9.4.68 autosolve 325849176146375289897261534614793825253486791789512643968137452432658917571924368 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (9)
C1: 5,6
B3: 5,9
H2: 3,8
H3: 3,8
F5: 6,7
A9: 5,7
D8: 2,6
E8: 2,5
H7: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G1,G3: 1.. / G1 = 1  =>  9 pairs (_) / G3 = 1  =>  0 pairs (X)
E1,G1: 1.. / E1 = 1  =>  0 pairs (X) / G1 = 1  =>  9 pairs (_)
E6,F6: 2.. / E6 = 2  =>  0 pairs (X) / F6 = 2  => 11 pairs (_)
D2,D3: 3.. / D2 = 3  =>  7 pairs (_) / D3 = 3  =>  0 pairs (X)
H2,H3: 3.. / H2 = 3  =>  0 pairs (X) / H3 = 3  =>  7 pairs (_)
B5,C5: 3.. / B5 = 3  =>  9 pairs (_) / C5 = 3  =>  9 pairs (_)
G8,G9: 3.. / G8 = 3  => 10 pairs (_) / G9 = 3  =>  9 pairs (_)
D2,H2: 3.. / D2 = 3  =>  7 pairs (_) / H2 = 3  =>  0 pairs (X)
D3,H3: 3.. / D3 = 3  =>  0 pairs (X) / H3 = 3  =>  7 pairs (_)
E1,D3: 4.. / E1 = 4  => 17 pairs (_) / D3 = 4  => 22 pairs (_)
A8,C8: 4.. / A8 = 4  => 10 pairs (_) / C8 = 4  => 11 pairs (_)
D3,I3: 4.. / D3 = 4  => 22 pairs (_) / I3 = 4  => 17 pairs (_)
A6,A8: 4.. / A6 = 4  => 11 pairs (_) / A8 = 4  => 10 pairs (_)
C1,C2: 6.. / C1 = 6  =>  9 pairs (_) / C2 = 6  =>  8 pairs (_)
I1,I2: 6.. / I1 = 6  =>  8 pairs (_) / I2 = 6  =>  9 pairs (_)
G5,G6: 6.. / G5 = 6  =>  0 pairs (X) / G6 = 6  =>  9 pairs (_)
B7,B8: 6.. / B7 = 6  =>  9 pairs (_) / B8 = 6  => 12 pairs (_)
C1,I1: 6.. / C1 = 6  =>  9 pairs (_) / I1 = 6  =>  8 pairs (_)
C2,I2: 6.. / C2 = 6  =>  8 pairs (_) / I2 = 6  =>  9 pairs (_)
F6,G6: 6.. / F6 = 6  =>  0 pairs (X) / G6 = 6  =>  9 pairs (_)
C2,A3: 8.. / C2 = 8  =>  0 pairs (X) / A3 = 8  =>  7 pairs (_)
H2,H3: 8.. / H2 = 8  =>  7 pairs (_) / H3 = 8  =>  0 pairs (X)
F7,F8: 8.. / F7 = 8  => 15 pairs (_) / F8 = 8  =>  9 pairs (_)
C2,H2: 8.. / C2 = 8  =>  0 pairs (X) / H2 = 8  =>  7 pairs (_)
A3,H3: 8.. / A3 = 8  =>  7 pairs (_) / H3 = 8  =>  0 pairs (X)
E4,E6: 9.. / E4 = 9  => 10 pairs (_) / E6 = 9  => 13 pairs (_)
* DURATION: 0:00:34.411319  START: 04:25:04.809951  END: 04:25:39.221270 2017-05-01
* CP COUNT: (26)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,C1,D8,E8,F5,H2,H3,H7)
* 32.8.9...14.........7.6....6....382.2...8...1.8.5....3....3.4.........17...9.4.68
* PAIR C1: 5,6 BLK 1
C2: 5,6,8,9                              # reduction candidate for 5,6
C2: 8,9                                  # 11 pairs
C2: 5,6                                  #  8 pairs
* PAIR C1: 5,6 ROW 1
I1: 5,6,4                                # reduction candidate for 5,6
I1: 4                                    # 27 pairs
I1: 5,6                                  # 12 pairs
* PAIR B3: 5,9 BLK 1
C2: 5,9,6,8                              # reduction candidate for 5,9
C2: 5,9                                  #  8 pairs
A3: 5,9,8                                # reduction candidate for 5,9
A3: 5,9 => CTR
* 326849175148...9369573612846.54138292.4.8.7.1.8.592643....3.4924....8.17...9.4.68
A3: 8                                    #  7 pairs
* PAIR B3: 5,9 ROW 3
G3: 5,9,1,2                              # reduction candidate for 5,9
G3: 5,9                                  # 10 pairs
I3: 5,9,2,4                              # reduction candidate for 5,9
I3: 5,9 => CTR
* 32.87915414.3257868.746123.67.1.382.2.3.8.941.815.2673518.3.492.6.258317732914568
I3: 2,4                                  # 10 pairs
* PAIR B3: 5,9 COL B
B4: 5,9,1,7                              # reduction candidate for 5,9
B4: 5,9 => CTR
* 32.84917.14..2.5.9..7.652.46.4..382.23.4867.1781592643...63.4.246.258.175.29.4368
B4: 1,7                                  # 10 pairs
B5: 5,9,3,7                              # reduction candidate for 5,9
B5: 5,9                                  # 12 pairs
B7: 5,9,1,6,7                            # reduction candidate for 5,9
B7: 5,9                                  # 21 pairs
B8: 5,9,3,6                              # reduction candidate for 5,9
B8: 5,9                                  # 14 pairs
* PAIR F5: 6,7 BLK 5
D5: 6,7,4                                # reduction candidate for 6,7
D5: 6,7                                  # 22 pairs
F6: 6,7,1,2                              # reduction candidate for 6,7
F6: 6,7 => CTR
* 32.84917.14..7......7.61..46..1938252..48..9198152..43.1.73645.46.258.17...914.68
F6: 1,2                                  # 10 pairs
* PAIR F5: 6,7 ROW 5
G5: 6,7,5,9                              # reduction candidate for 6,7
G5: 5,9                                  # 22 pairs
G5: 6,7                                  # 17 pairs
* PAIR F5: 6,7 COL F
F7: 6,7,1,2,5,8                          # reduction candidate for 6,7
F7: 6,7                                  # 13 pairs
F7: 1,2,5,8                              #  9 pairs
* PAIR A9: 5,7 BLK 7
A7: 5,7,8,9                              # reduction candidate for 5,7
A7: 5,7                                  # 13 pairs
B7: 5,7,1,6,9                            # reduction candidate for 5,7
B7: 5,7                                  # 15 pairs
B9: 5,7,1,3                              # reduction candidate for 5,7
B9: 5,7                                  # 13 pairs
* PAIR A9: 5,7 ROW 9
E9: 5,7,1,2                              # reduction candidate for 5,7
E9: 5,7                                  # 15 pairs
E9: 1,2                                  # 10 pairs
* PAIR D8: 2,6 BLK 8
D7: 2,6,1,7                              # reduction candidate for 2,6
D7: 2,6                                  # 15 pairs
F7: 2,6,1,5,7,8                          # reduction candidate for 2,6
F7: 2,6                                  # 13 pairs
F8: 2,6,5,8                              # reduction candidate for 2,6
F8: 2,6                                  # 16 pairs
* PAIR E8: 2,5 BLK 8
F7: 2,5,1,6,7,8                          # reduction candidate for 2,5
F7: 2,5 => CTR
* 325849176146.759828972615346.4.9382525348..9198152..4376..3.4594..658.17...9.4.68
F7: 1,6,7,8                              #  9 pairs
F8: 2,5,6,8                              # reduction candidate for 2,5
F8: 2,5                                  # 16 pairs
E9: 2,5,1,7                              # reduction candidate for 2,5
E9: 2,5 => SOLVED
* 325849176146375289897261534614793825253486791789512643968137452432658917571924368
E9: 1,7                                  # 10 pairs
* PAIR E8: 2,5 ROW 8
C8: 2,5,3,4,8,9                          # reduction candidate for 2,5
C8: 2,5                                  # 13 pairs
G8: 2,5,3,9                              # reduction candidate for 2,5
G8: 2,5                                  # 12 pairs
* PAIR E8: 2,5 COL E
E2: 2,5,7                                # reduction candidate for 2,5
E2: 2,5                                  # 13 pairs
E2: 7                                    # 11 pairs
* PAIR H7: 5,9 BLK 9
I7: 5,9,2                                # reduction candidate for 5,9
I7: 5,9                                  # 13 pairs
G8: 5,9,2,3                              # reduction candidate for 5,9
G8: 5,9                                  # 10 pairs
* PAIR H7: 5,9 ROW 7
A7: 5,9,7,8                              # reduction candidate for 5,9
A7: 5,9                                  # 12 pairs
B7: 5,9,1,6,7                            # reduction candidate for 5,9
B7: 5,9                                  # 21 pairs
C7: 5,9,1,2,8                            # reduction candidate for 5,9
C7: 5,9                                  # 12 pairs
* PAIR H7: 5,9 COL H
H5: 5,9,4,7                              # reduction candidate for 5,9
H5: 4,7                                  # 27 pairs
H5: 5,9                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0053-base-pr-000.dot
* REASONING
* DIS # A3: 5,9 => CTR => A3: 8
* DIS # I3: 5,9 => CTR => I3: 2,4
* DIS # B4: 5,9 => CTR => B4: 1,7
* DIS # F6: 6,7 => CTR => F6: 1,2
* DIS # F7: 2,5 => CTR => F7: 1,6,7,8
* PRF # E9: 2,5 => SOL
* CNT   6 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,C1,D8,E8,F5,H2,H3,H7)
* 32.8.9...14.........7.6....6....382.2...8...1.8.5....3....3.4.........17...9.4.68
* PAIR C1: 5,6 BLK 1
C2: 5,6,8,9                              # reduction candidate for 5,6
C2: 8,9                                  # 11 pairs
C2: 5,6                                  #  8 pairs
* PAIR C1: 5,6 ROW 1
I1: 5,6,4                                # reduction candidate for 5,6
I1: 4                                    # 27 pairs
I1: 5,6                                  # 12 pairs
* PAIR B3: 5,9 BLK 1
C2: 5,9,6,8                              # reduction candidate for 5,9
C2: 5,9                                  #  8 pairs
A3: 5,9,8                                # reduction candidate for 5,9
A3: 5,9 => CTR
* 326849175148...9369573612846.54138292.4.8.7.1.8.592643....3.4924....8.17...9.4.68
* RESTART
* PAIR B3: 5,9 BLK 1
C2: 5,9,6                                # reduction candidate for 5,9
C2: 6                                    #  8 pairs
C2: 5,9                                  #  8 pairs
* PAIR B3: 5,9 ROW 3
G3: 5,9,1,2                              # reduction candidate for 5,9
G3: 5,9                                  # 10 pairs
I3: 5,9,2,4                              # reduction candidate for 5,9
I3: 5,9 => CTR
* 32.87915414.3257868.746123.67.1.382.2.3.8.941.815.2673518.3.492.6.258317732914568
* RESTART
* PAIR B3: 5,9 ROW 3
G3: 5,9,1,2                              # reduction candidate for 5,9
G3: 1,2                                  # 17 pairs
G3: 5,9                                  # 10 pairs
* PAIR B3: 5,9 COL B
B4: 5,9,1,7                              # reduction candidate for 5,9
B4: 5,9 => CTR
* 32.84917.14.3...89897.6..34654..382.2..4867.17815926439...3.4524.....9175..9.4368
B5: 5,9,3,7                              # reduction candidate for 5,9
B5: 5,9                                  # 12 pairs
* RESTART
* PAIR B3: 5,9 COL B
B5: 5,9,3,7                              # reduction candidate for 5,9
B5: 3,7 => CTR
* 3268.91741493.75868574619326.4.9382.2...8..9198.5....376..3.45949.....175..974.68
* PAIR RESTART
* PAIR B3: 5,9 BLK 1
C2: 5,9,6                                # reduction candidate for 5,9
C2: 5,9                                  # 20 pairs
C2: 6                                    # 17 pairs
* PAIR B3: 5,9 ROW 3
G3: 5,9,1,2                              # reduction candidate for 5,9
G3: 1,2                                  # 25 pairs
G3: 5,9                                  # 14 pairs
* PAIR F5: 6,7 BLK 5
D5: 6,7,4                                # reduction candidate for 6,7
D5: 6,7 => CTR
* 32681975414.3...868.746..3267.1.3829293.8.541481592673....3.4959.4..8.175.2974368
F6: 6,7,1,2                              # reduction candidate for 6,7
F6: 6,7 => CTR
* 32584917614637..8.897.615346.419382525348..91.8152..43.1..3.45.4...5..175..914.68
* PAIR D8: 2,6 BLK 8
D7: 2,6,1,7                              # reduction candidate for 2,6
D7: 2,6 => CTR
* 3258491761463...8989716..346147938252534867917895..6439..63.4524.....9175..9.4368

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A6,A7,B4,B9,C6,C9,D4,D7,E2,E6,E8,F2,F7,F8,G2,G8,I2,I7)
* 3258491761463...8.8972615346.4.93825253486791.8.5.2643.6..3.45.43.6...175..9.4368
* PAIR C6: 1,9 COL C
C7: 1,9,2,8                              # reduction candidate for 1,9
C7: 2,8 => SOLVED
* 325849176146375289897261534614793825253486791789512643968137452432658917571924368
* DURATION: 0:00:27.337114  START: 04:26:15.174801  END: 04:26:42.511915 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0053-base-pr-001.dot
* REASONING
* DIS # A3: 5,9 => CTR => A3: 8
* DIS A3: 8 # I3: 5,9 => CTR => I3: 2,4
* DIS A3: 8 + I3: 2,4 # B4: 5,9 => CTR => B4: 1,7
* DIS A3: 8 + I3: 2,4 + B4: 1,7 # B5: 3,7 => CTR => B5: 5,9
* DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # D5: 6,7 => CTR => D5: 4
* DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 # F6: 6,7 => CTR => F6: 1,2
* DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 # D7: 2,6 => CTR => D7: 1,7
* PRF A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 # C7: 2,8 => SOL
* STA A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 + C7: 2,8
* CNT   8 HDP CHAINS /  25 HYP OPENED
```

## Header Info

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=53
```

# Solution

position: 325849176146375289897261534614793825253486791789512643968137452432658917571924368 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 # C2: 5,6 => UNS
* INC # C2: 8,9 => UNS
* INC # I1: 5,6 => UNS
* INC # I1: 4 => UNS
* INC # C2: 5,9 => UNS
* DIS # A3: 5,9 => CTR => A3: 8
* INC # A3: 8 => UNS
* INC # G3: 5,9 => UNS
* DIS # I3: 5,9 => CTR => I3: 2,4
* INC # I3: 2,4 => UNS
* DIS # B4: 5,9 => CTR => B4: 1,7
* INC # B4: 1,7 => UNS
* INC # B5: 5,9 => UNS
* INC # B7: 5,9 => UNS
* INC # B8: 5,9 => UNS
* INC # D5: 6,7 => UNS
* DIS # F6: 6,7 => CTR => F6: 1,2
* INC # F6: 1,2 => UNS
* INC # G5: 6,7 => UNS
* INC # G5: 5,9 => UNS
* INC # F7: 6,7 => UNS
* INC # F7: 1,2,5,8 => UNS
* INC # A7: 5,7 => UNS
* INC # B7: 5,7 => UNS
* INC # B9: 5,7 => UNS
* INC # E9: 5,7 => UNS
* INC # E9: 1,2 => UNS
* INC # D7: 2,6 => UNS
* INC # F7: 2,6 => UNS
* INC # F8: 2,6 => UNS
* DIS # F7: 2,5 => CTR => F7: 1,6,7,8
* INC # F7: 1,6,7,8 => UNS
* INC # F8: 2,5 => UNS
* PRF # E9: 2,5 => SOL
* INC # E9: 1,7 => UNS
* INC # C8: 2,5 => UNS
* INC # G8: 2,5 => UNS
* INC # E2: 2,5 => UNS
* INC # E2: 7 => UNS
* INC # I7: 5,9 => UNS
* INC # G8: 5,9 => UNS
* INC # A7: 5,9 => UNS
* INC # B7: 5,9 => UNS
* INC # C7: 5,9 => UNS
* INC # H5: 5,9 => UNS
* INC # H5: 4,7 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # C2: 5,6 => UNS
* INC # C2: 8,9 => UNS
* INC # I1: 5,6 => UNS
* INC # I1: 4 => UNS
* INC # C2: 5,9 => UNS
* DIS # A3: 5,9 => CTR => A3: 8
* INC A3: 8 # C2: 5,9 => UNS
* INC A3: 8 # C2: 6 => UNS
* INC A3: 8 # G3: 5,9 => UNS
* DIS A3: 8 # I3: 5,9 => CTR => I3: 2,4
* INC A3: 8 + I3: 2,4 # G3: 5,9 => UNS
* INC A3: 8 + I3: 2,4 # G3: 1,2 => UNS
* DIS A3: 8 + I3: 2,4 # B4: 5,9 => CTR => B4: 1,7
* INC A3: 8 + I3: 2,4 + B4: 1,7 # B5: 5,9 => UNS
* INC A3: 8 + I3: 2,4 + B4: 1,7 # B5: 5,9 => UNS
* DIS A3: 8 + I3: 2,4 + B4: 1,7 # B5: 3,7 => CTR => B5: 5,9
* INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # C2: 5,9 => UNS
* INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # C2: 6 => UNS
* INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # G3: 5,9 => UNS
* INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # G3: 1,2 => UNS
* DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 # D5: 6,7 => CTR => D5: 4
* DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 # F6: 6,7 => CTR => F6: 1,2
* DIS A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 # D7: 2,6 => CTR => D7: 1,7
* INC A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 # C7: 1,9 => UNS
* PRF A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 # C7: 2,8 => SOL
* STA A3: 8 + I3: 2,4 + B4: 1,7 + B5: 5,9 + D5: 4 + F6: 1,2 + D7: 1,7 + C7: 2,8
* CNT  25 HDP CHAINS /  25 HYP OPENED
```