# Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=119

level: medium

position: .7.1.42......9......9...48.4....3.....8.4.19....6....5.26...9......3......17.2.5. initial

# Autosolve

position: .7.1.42.9....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......17.2.5. autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # A1: 3,6 => CTR => A1: 5,8
* DIS # D4: 2,5 => CTR => D4: 8,9
* DIS # E4: 2,5 => CTR => E4: 1,7,8
* DIS # E4: 5,7 => CTR => E4: 1,2,8
* PRF # A5: 5,7 => SOL
* DIS # F8: 6,8 => CTR => F8: 1,5,9
* DIS # I9: 6,8 => CTR => I9: 3,4
* CNT   7 HDP CHAINS /  29 HYP OPENED
```

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

## Pair Reduction

The following important HDP chains were detected:

```* DIS # A1: 3,6 => CTR => A1: 5,8
* DIS A1: 5,8 # D4: 2,5 => CTR => D4: 8,9
* DIS A1: 5,8 + D4: 8,9 # E4: 2,5 => CTR => E4: 1,7,8
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F8: 6,8 => CTR => F8: 1,5,9
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 # A7: 5,8 => CTR => A7: 3,7
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 7 => CTR => A8: 5,8
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 # E7: 1 => CTR => E7: 5,8
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 # A5: 3,6 => CTR => A5: 2,7
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 # E6: 1 => CTR => E6: 2,7
* PRF A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 # D8: 4 => SOL
* STA A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 + D8: 4
* CNT  10 HDP CHAINS /  28 HYP OPENED
```

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

# Details

## Positions

 .7.1.42......9......9...48.4....3.....8.4.19....6....5.26...9......3......17.2.5. initial .7.1.42.9....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......17.2.5. autosolve 873154269214896537659327481465913728738245196192678345326581974587439612941762853 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (5)
C1: 3,5
H1: 3,6
D5: 2,5
F5: 5,7
E9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B4,E4: 1.. / B4 = 1  => 13 pairs (_) / E4 = 1  => 11 pairs (_)
H8,I8: 2.. / H8 = 2  =>  6 pairs (_) / I8 = 2  =>  6 pairs (_)
H4,H8: 2.. / H4 = 2  =>  6 pairs (_) / H8 = 2  =>  6 pairs (_)
D2,D3: 3.. / D2 = 3  =>  9 pairs (_) / D3 = 3  =>  6 pairs (_)
I5,G6: 3.. / I5 = 3  => 12 pairs (_) / G6 = 3  => 10 pairs (_)
G6,G9: 3.. / G6 = 3  => 10 pairs (_) / G9 = 3  => 12 pairs (_)
B2,C2: 4.. / B2 = 4  =>  9 pairs (_) / C2 = 4  =>  6 pairs (_)
D7,D8: 4.. / D7 = 4  =>  5 pairs (_) / D8 = 4  => 15 pairs (_)
D7,I7: 4.. / D7 = 4  =>  5 pairs (_) / I7 = 4  => 15 pairs (_)
B9,I9: 4.. / B9 = 4  => 16 pairs (_) / I9 = 4  =>  5 pairs (_)
C2,C8: 4.. / C2 = 4  =>  6 pairs (_) / C8 = 4  =>  9 pairs (_)
F8,E9: 6.. / F8 = 6  =>  0 pairs (X) / E9 = 6  =>  6 pairs (_)
A1,E1: 8.. / A1 = 8  =>  8 pairs (_) / E1 = 8  => 13 pairs (_)
D4,F6: 9.. / D4 = 9  => 11 pairs (_) / F6 = 9  =>  0 pairs (X)
A9,B9: 9.. / A9 = 9  =>  5 pairs (_) / B9 = 9  => 16 pairs (_)
D8,F8: 9.. / D8 = 9  =>  0 pairs (X) / F8 = 9  => 11 pairs (_)
B4,D4: 9.. / B4 = 9  =>  0 pairs (X) / D4 = 9  => 11 pairs (_)
A6,A9: 9.. / A6 = 9  => 16 pairs (_) / A9 = 9  =>  5 pairs (_)
D4,D8: 9.. / D4 = 9  => 11 pairs (_) / D8 = 9  =>  0 pairs (X)
F6,F8: 9.. / F6 = 9  =>  0 pairs (X) / F8 = 9  => 11 pairs (_)
* DURATION: 0:00:22.752853  START: 05:40:06.852798  END: 05:40:29.605651 2017-05-01
* CP COUNT: (20)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D5,E9,F5,H1)
* .7.1.42.9....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......17.2.5.
* PAIR C1: 3,5 BLK 1
A1: 3,5,6,8                              # reduction candidate for 3,5
A1: 3,5                                  # 16 pairs
A3: 3,5,1,2,6                            # reduction candidate for 3,5
A3: 3,5                                  # 10 pairs
B3: 3,5,1,6                              # reduction candidate for 3,5
B3: 3,5                                  #  8 pairs
* PAIR H1: 3,6 BLK 3
H2: 3,6,1,7                              # reduction candidate for 3,6
H2: 3,6                                  # 10 pairs
I2: 3,6,1,7                              # reduction candidate for 3,6
I2: 3,6                                  #  8 pairs
I3: 3,6,1,7                              # reduction candidate for 3,6
I3: 3,6                                  #  9 pairs
* PAIR H1: 3,6 ROW 1
A1: 3,6,5,8                              # reduction candidate for 3,6
A1: 3,6 => CTR
* .751842.9..4.9.5....9...48.45.913.....8.4.19...3628745.26.519..5.7.39.....1762.5.
A1: 5,8                                  #  6 pairs
* PAIR D5: 2,5 BLK 5
D4: 2,5,8,9                              # reduction candidate for 2,5
D4: 2,5 => CTR
* .7.1.42.9....9.5....9...48.49..13.....8.4.19....689.45.2645.9.....93....9.17.2.5.
D4: 8,9                                  #  6 pairs
E4: 2,5,1,7,8                            # reduction candidate for 2,5
E4: 2,5 => CTR
* .7.1.42.9....9.5171.927.48.415923768..8547192.9.6..345.26...97.....396219.176285.
E4: 1,7,8                                #  5 pairs
* PAIR D5: 2,5 ROW 5
A5: 2,5,3,6,7                            # reduction candidate for 2,5
A5: 2,5                                  # 15 pairs
A5: 3,6,7                                #  5 pairs
* PAIR D5: 2,5 COL D
D3: 2,5,3                                # reduction candidate for 2,5
D3: 2,5                                  #  9 pairs
D3: 3                                    #  6 pairs
* PAIR F5: 5,7 BLK 5
E4: 5,7,1,2,8                            # reduction candidate for 5,7
E4: 5,7 => CTR
* .731.4269284.9.5....9.2.48.4159738..768245193..26..745326...97...7.396....176235.
E4: 1,2,8                                #  5 pairs
* PAIR F5: 5,7 ROW 5
A5: 5,7,2,3,6                            # reduction candidate for 5,7
A5: 5,7 => SOLVED
* 873154269214896537659327481465913728738245196192678345326581974587439612941762853
A5: 2,3,6                                #  5 pairs
* PAIR F5: 5,7 COL F
F3: 5,7,6                                # reduction candidate for 5,7
F3: 5,7                                  #  8 pairs
F3: 6                                    #  7 pairs
* PAIR E9: 6,8 BLK 8
F8: 6,8,1,5,9                            # reduction candidate for 6,8
F8: 6,8 => CTR
* 573184269842396517..9...48.495813.....8.4.193...6.9845326451978.5493.6..981762354
F8: 1,5,9                                #  6 pairs
* PAIR E9: 6,8 ROW 9
G9: 6,8,3                                # reduction candidate for 6,8
G9: 6,8                                  # 10 pairs
I9: 6,8,3,4                              # reduction candidate for 6,8
I9: 6,8 => CTR
* .731.42692.4.9.53...932.48.4....3.26..824.193.326.9.45326...97....9316..941762358
I9: 3,4                                  #  6 pairs
* PAIR E9: 6,8 COL E
E1: 6,8,5                                # reduction candidate for 6,8
E1: 6,8                                  # 13 pairs
E1: 5                                    # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0119-base-pr-000.dot
* REASONING
* DIS # A1: 3,6 => CTR => A1: 5,8
* DIS # D4: 2,5 => CTR => D4: 8,9
* DIS # E4: 2,5 => CTR => E4: 1,7,8
* DIS # E4: 5,7 => CTR => E4: 1,2,8
* PRF # A5: 5,7 => SOL
* DIS # F8: 6,8 => CTR => F8: 1,5,9
* DIS # I9: 6,8 => CTR => I9: 3,4
* CNT   7 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D5,E9,F5,H1)
* .7.1.42.9....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......17.2.5.
* PAIR C1: 3,5 BLK 1
A1: 3,5,6,8                              # reduction candidate for 3,5
A1: 3,5                                  # 16 pairs
A3: 3,5,1,2,6                            # reduction candidate for 3,5
A3: 3,5                                  # 10 pairs
B3: 3,5,1,6                              # reduction candidate for 3,5
B3: 3,5                                  #  8 pairs
* PAIR H1: 3,6 BLK 3
H2: 3,6,1,7                              # reduction candidate for 3,6
H2: 3,6                                  # 10 pairs
I2: 3,6,1,7                              # reduction candidate for 3,6
I2: 3,6                                  #  8 pairs
I3: 3,6,1,7                              # reduction candidate for 3,6
I3: 3,6                                  #  9 pairs
* PAIR H1: 3,6 ROW 1
A1: 3,6,5,8                              # reduction candidate for 3,6
A1: 3,6 => CTR
* .751842.9..4.9.5....9...48.45.913.....8.4.19...3628745.26.519..5.7.39.....1762.5.
* PAIR RESTART
* PAIR H1: 3,6 BLK 3
H2: 3,6,1,7                              # reduction candidate for 3,6
H2: 3,6                                  # 11 pairs
I2: 3,6,1,7                              # reduction candidate for 3,6
I2: 3,6                                  #  9 pairs
I3: 3,6,1,7                              # reduction candidate for 3,6
I3: 3,6                                  # 10 pairs
* PAIR D5: 2,5 BLK 5
D4: 2,5,8,9                              # reduction candidate for 2,5
D4: 2,5 => CTR
* .7.1.42.9....9.5....9...48.49..13.....8.4.19....689.45.2645.9.....93....9.17.2.5.
E4: 2,5,1,7,8                            # reduction candidate for 2,5
E4: 2,5 => CTR
* .731.4269....9.5....9.7.48.41.923.76..8547192...6..345.26...937....396....1762.5.
* RESTART
* PAIR D5: 2,5 COL D
D3: 2,5,3                                # reduction candidate for 2,5
D3: 2,5                                  # 11 pairs
D3: 3                                    #  9 pairs
* PAIR F5: 5,7 COL F
F3: 5,7,6                                # reduction candidate for 5,7
F3: 6                                    # 12 pairs
F3: 5,7                                  # 11 pairs
* PAIR E9: 6,8 BLK 8
F8: 6,8,1,5,9                            # reduction candidate for 6,8
F8: 6,8 => CTR
* 573184269842.9.53...93.548.495813.....8547193.3.629845326451978.5.938612981762354

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,B5,C2,C6,D4,D5,E1,F5,G9,H4)
* .731.4269....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......1762.5.
* PAIR A1: 5,8 COL A
A7: 5,8,3,7                              # reduction candidate for 5,8
A7: 5,8 => CTR
* 873154269.4289.5...5932.48.465913728.38.4519691.6..345.264.19.....539612391762854
A8: 5,8,7                                # reduction candidate for 5,8
A8: 5,8                                  # 14 pairs
* RESTART
* PAIR A1: 5,8 COL A
A8: 5,8,7                                # reduction candidate for 5,8
A8: 7 => CTR
* .731.4269..2896537.693754814....3.2...854719....62..45326...97.7...39612..1762.5.
* PAIR RESTART
* PAIR E1: 5,8 COL E
E7: 5,8,1                                # reduction candidate for 5,8
E7: 1 => CTR
* 873154269.64.9.53..593264874159.3.26638.4.19...26.1.45.26.1.97.5.7.396.2..1762.5.
* PAIR RESTART
* PAIR B5: 3,6 BLK 4
A5: 3,6,2,7                              # reduction candidate for 3,6
A5: 3,6 => CTR
* .731.4269....9.5....9...48.4....3..8..8.4.19....6.8345.26...9......39..6..176285.
* PAIR C6: 2,7 ROW 6
E6: 2,7,1                                # reduction candidate for 2,7
E6: 1 => CTR
* .731.4269....9.5....9.2.48.4.5.73.2.7.824519...261.745326...9....7.3..129.1762.5.
* PAIR RESTART
* PAIR D4: 8,9 COL D
D8: 8,9,4                                # reduction candidate for 8,9
D8: 4 => SOLVED
* 873154269214896537659327481465913728738245196192678345326581974587439612941762853
* DURATION: 0:00:25.403627  START: 05:40:48.394585  END: 05:41:13.798212 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0119-base-pr-001.dot
* REASONING
* DIS # A1: 3,6 => CTR => A1: 5,8
* DIS A1: 5,8 # D4: 2,5 => CTR => D4: 8,9
* DIS A1: 5,8 + D4: 8,9 # E4: 2,5 => CTR => E4: 1,7,8
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F8: 6,8 => CTR => F8: 1,5,9
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 # A7: 5,8 => CTR => A7: 3,7
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 7 => CTR => A8: 5,8
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 # E7: 1 => CTR => E7: 5,8
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 # A5: 3,6 => CTR => A5: 2,7
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 # E6: 1 => CTR => E6: 2,7
* PRF A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 # D8: 4 => SOL
* STA A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 + D8: 4
* CNT  10 HDP CHAINS /  28 HYP OPENED
```

```http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=119
```

# Solution

position: 873154269214896537659327481465913728738245196192678345326581974587439612941762853 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 # A1: 3,5 => UNS
* INC # A3: 3,5 => UNS
* INC # B3: 3,5 => UNS
* INC # H2: 3,6 => UNS
* INC # I2: 3,6 => UNS
* INC # I3: 3,6 => UNS
* DIS # A1: 3,6 => CTR => A1: 5,8
* INC # A1: 5,8 => UNS
* DIS # D4: 2,5 => CTR => D4: 8,9
* INC # D4: 8,9 => UNS
* DIS # E4: 2,5 => CTR => E4: 1,7,8
* INC # E4: 1,7,8 => UNS
* INC # A5: 2,5 => UNS
* INC # A5: 3,6,7 => UNS
* INC # D3: 2,5 => UNS
* INC # D3: 3 => UNS
* DIS # E4: 5,7 => CTR => E4: 1,2,8
* INC # E4: 1,2,8 => UNS
* PRF # A5: 5,7 => SOL
* INC # A5: 2,3,6 => UNS
* INC # F3: 5,7 => UNS
* INC # F3: 6 => UNS
* DIS # F8: 6,8 => CTR => F8: 1,5,9
* INC # F8: 1,5,9 => UNS
* INC # G9: 6,8 => UNS
* DIS # I9: 6,8 => CTR => I9: 3,4
* INC # I9: 3,4 => UNS
* INC # E1: 6,8 => UNS
* INC # E1: 5 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* INC # A1: 3,5 => UNS
* INC # A3: 3,5 => UNS
* INC # B3: 3,5 => UNS
* INC # H2: 3,6 => UNS
* INC # I2: 3,6 => UNS
* INC # I3: 3,6 => UNS
* DIS # A1: 3,6 => CTR => A1: 5,8
* INC A1: 5,8 # H2: 3,6 => UNS
* INC A1: 5,8 # I2: 3,6 => UNS
* INC A1: 5,8 # I3: 3,6 => UNS
* DIS A1: 5,8 # D4: 2,5 => CTR => D4: 8,9
* DIS A1: 5,8 + D4: 8,9 # E4: 2,5 => CTR => E4: 1,7,8
* INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 # D3: 2,5 => UNS
* INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 # D3: 3 => UNS
* INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F3: 5,7 => UNS
* INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F3: 6 => UNS
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F8: 6,8 => CTR => F8: 1,5,9
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 # A7: 5,8 => CTR => A7: 3,7
* INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 5,8 => UNS
* INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 5,8 => UNS
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 7 => CTR => A8: 5,8
* INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 # E7: 5,8 => UNS
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 # E7: 1 => CTR => E7: 5,8
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 # A5: 3,6 => CTR => A5: 2,7
* INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 # E6: 2,7 => UNS
* DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 # E6: 1 => CTR => E6: 2,7
* INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 # D8: 8,9 => UNS
* PRF A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 # D8: 4 => SOL
* STA A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 + D8: 4
* CNT  28 HDP CHAINS /  28 HYP OPENED
```