# Original Sudoku

level: medium

position: 25.6....9.......5.....3..6.6...43.....7.....5...21..4..7.1..4.........1.19...6..7 initial

# Autosolve

position: 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7 autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # F1: 7,8 => CTR => F1: 1,4
* DIS # F3: 7,8 => CTR => F3: 1,2,4,5,9
* DIS # D8: 8,9 => CTR => D8: 3,4,7
* DIS # F3: 8,9 => CTR => F3: 1,2,4,5,7
* DIS # F8: 8,9 => CTR => F8: 2,4,7
* PRF # F3: 1,2,4,8,9 => SOL
* DIS # H7: 2,3 => CTR => H7: 8,9
* CNT   7 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 # F1: 7,8 => CTR => F1: 1,4
* DIS F1: 1,4 # F3: 7,8 => CTR => F3: 1,2,4,5,9
* DIS F1: 1,4 + F3: 1,2,4,5,9 # D8: 8,9 => CTR => D8: 3,4,7
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F8: 8,9 => CTR => F8: 2,4,7
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # H7: 2,3 => CTR => H7: 8,9
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G1: 7,8 => CTR => G1: 1,3
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 3 => CTR => H1: 7,8
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 # E8: 7,8 => CTR => E8: 2,5,9
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 # E2: 2,9 => CTR => E2: 7,8
* PRF F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 # F2: 1,4 => SOL
* STA F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 + F2: 1,4
* CNT  10 HDP CHAINS /  66 HYP OPENED
```

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

# Details

## Positions

 25.6....9.......5.....3..6.6...43.....7.....5...21..4..7.1..4.........1.19...6..7 initial 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7 autosolve 251684379863971254749532861615743928427869135938215746376158492582497613194326587 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (8)
E1: 7,8
A5: 3,4
B6: 3,8
D4: 5,7
D5: 8,9
F5: 8,9
F6: 5,7
H5: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,G5: 1.. / B5 = 1  => 12 pairs (_) / G5 = 1  => 13 pairs (_)
D8,D9: 3.. / D8 = 3  =>  9 pairs (_) / D9 = 3  =>  9 pairs (_)
I2,I3: 4.. / I2 = 4  =>  8 pairs (_) / I3 = 4  =>  9 pairs (_)
A5,B5: 4.. / A5 = 4  =>  7 pairs (_) / B5 = 4  =>  0 pairs (X)
C1,F1: 4.. / C1 = 4  =>  9 pairs (_) / F1 = 4  => 10 pairs (_)
C9,D9: 4.. / C9 = 4  =>  9 pairs (_) / D9 = 4  =>  8 pairs (_)
D3,F3: 5.. / D3 = 5  => 24 pairs (_) / F3 = 5  =>  6 pairs (_)
D4,F6: 5.. / D4 = 5  =>  6 pairs (_) / F6 = 5  => 24 pairs (_)
G8,G9: 5.. / G8 = 5  => 16 pairs (_) / G9 = 5  =>  9 pairs (_)
C4,D4: 5.. / C4 = 5  => 24 pairs (_) / D4 = 5  =>  6 pairs (_)
D3,D4: 5.. / D3 = 5  => 24 pairs (_) / D4 = 5  =>  6 pairs (_)
F3,F6: 5.. / F3 = 5  =>  6 pairs (_) / F6 = 5  => 24 pairs (_)
B2,C2: 6.. / B2 = 6  =>  8 pairs (_) / C2 = 6  => 13 pairs (_)
G6,I6: 6.. / G6 = 6  => 11 pairs (_) / I6 = 6  => 13 pairs (_)
C7,I7: 6.. / C7 = 6  =>  8 pairs (_) / I7 = 6  => 12 pairs (_)
B2,B8: 6.. / B2 = 6  =>  8 pairs (_) / B8 = 6  => 13 pairs (_)
G6,G8: 6.. / G6 = 6  => 11 pairs (_) / G8 = 6  => 13 pairs (_)
A2,A3: 7.. / A2 = 7  =>  8 pairs (_) / A3 = 7  =>  8 pairs (_)
D4,F6: 7.. / D4 = 7  => 24 pairs (_) / F6 = 7  =>  6 pairs (_)
F6,G6: 7.. / F6 = 7  =>  6 pairs (_) / G6 = 7  => 24 pairs (_)
H1,H4: 7.. / H1 = 7  => 16 pairs (_) / H4 = 7  => 11 pairs (_)
D5,F5: 8.. / D5 = 8  =>  8 pairs (_) / F5 = 8  =>  7 pairs (_)
D5,F5: 9.. / D5 = 9  =>  7 pairs (_) / F5 = 9  =>  8 pairs (_)
H7,G8: 9.. / H7 = 9  => 11 pairs (_) / G8 = 9  =>  0 pairs (X)
H4,H7: 9.. / H4 = 9  =>  0 pairs (X) / H7 = 9  => 11 pairs (_)
* DURATION: 0:00:33.043706  START: 06:53:32.690690  END: 06:54:05.734396 2017-05-01
* CP COUNT: (25)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B6,D4,D5,E1,F5,F6,H5)
* 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7
* PAIR E1: 7,8 BLK 2
F1: 7,8,1,4                              # reduction candidate for 7,8
F1: 7,8 => CTR
* 254678139.6.9...5.....3..6.6...43.71.17.6..25...217.4..7.1..49..4.....1.19.4.6.87
F1: 1,4                                  #  9 pairs
D2: 7,8,4,9                              # reduction candidate for 7,8
D2: 7,8                                  # 11 pairs
E2: 7,8,2,9                              # reduction candidate for 7,8
E2: 7,8                                  # 13 pairs
F2: 7,8,1,2,4,9                          # reduction candidate for 7,8
F2: 7,8                                  # 12 pairs
D3: 7,8,4,5,9                            # reduction candidate for 7,8
D3: 7,8                                  # 10 pairs
F3: 7,8,1,2,4,5,9                        # reduction candidate for 7,8
F3: 7,8 => CTR
* 25.681379763492.5...15372646.57439..4.7869135..92157463761584925.2.7.61.19..265.7
F3: 1,2,4,5,9                            #  8 pairs
* PAIR E1: 7,8 ROW 1
G1: 7,8,1,3                              # reduction candidate for 7,8
G1: 7,8                                  # 16 pairs
H1: 7,8,3                                # reduction candidate for 7,8
H1: 7,8                                  # 11 pairs
* PAIR E1: 7,8 COL E
E8: 7,8,2,5,9                            # reduction candidate for 7,8
E8: 7,8                                  # 11 pairs
E8: 2,5,9                                # 10 pairs
* PAIR A5: 3,4 BLK 4
B5: 3,4,1,2                              # reduction candidate for 3,4
B5: 3,4                                  # 22 pairs
B5: 1,2                                  #  9 pairs
* PAIR A5: 3,4 COL A
A2: 3,4,7,8,9                            # reduction candidate for 3,4
A2: 3,4                                  # 11 pairs
A8: 3,4,5,8                              # reduction candidate for 3,4
A8: 3,4                                  # 10 pairs
* PAIR B6: 3,8 BLK 4
A6: 3,8,5,9                              # reduction candidate for 3,8
A6: 3,8                                  # 21 pairs
C6: 3,8,5,9                              # reduction candidate for 3,8
C6: 3,8                                  # 19 pairs
* PAIR B6: 3,8 ROW 6
G6: 3,8,6,7,9                            # reduction candidate for 3,8
G6: 3,8                                  # 16 pairs
I6: 3,8,6                                # reduction candidate for 3,8
I6: 3,8                                  # 11 pairs
* PAIR B6: 3,8 COL B
B2: 3,8,1,4,6                            # reduction candidate for 3,8
B2: 3,8                                  # 16 pairs
B8: 3,8,2,4,6                            # reduction candidate for 3,8
B8: 3,8                                  # 11 pairs
* PAIR D4: 5,7 COL D
D3: 5,7,4,8,9                            # reduction candidate for 5,7
D3: 5,7                                  #  9 pairs
D3: 4,8,9                                #  6 pairs
* PAIR D5: 8,9 COL D
D2: 8,9,4,7                              # reduction candidate for 8,9
D2: 8,9                                  # 10 pairs
D3: 8,9,4,5,7                            # reduction candidate for 8,9
D3: 8,9                                  #  9 pairs
D8: 8,9,3,4,7                            # reduction candidate for 8,9
D8: 8,9 => CTR
* 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.......4.1.1943.6..7
D8: 3,4,7                                #  8 pairs
* PAIR F5: 8,9 COL F
F2: 8,9,1,2,4,7                          # reduction candidate for 8,9
F2: 8,9                                  # 11 pairs
F3: 8,9,1,2,4,5,7                        # reduction candidate for 8,9
F3: 8,9 => CTR
* 25.68..79.6.....5.7..539.6.6.57439....7968..5...215746.761.249.......61.19...65.7
F3: 1,2,4,5,7                            #  8 pairs
F7: 8,9,2                                # reduction candidate for 8,9
F7: 8,9                                  #  9 pairs
F8: 8,9,2,4,7                            # reduction candidate for 8,9
F8: 8,9 => CTR
* 25.68...9....2..5.....3..6.6...43.....7869..5...21..4..7.1924......7891.19..56..7
F8: 2,4,7                                #  8 pairs
* PAIR F6: 5,7 COL F
F3: 5,7,1,2,4,8,9                        # reduction candidate for 5,7
F3: 1,2,4,8,9 => SOLVED
* 251684379863971254749532861615743928427869135938215746376158492582497613194326587
F3: 5,7                                  #  9 pairs
* PAIR H5: 2,3 BLK 6
G5: 2,3,1                                # reduction candidate for 2,3
G5: 1                                    # 13 pairs
G5: 2,3                                  # 12 pairs
* PAIR H5: 2,3 ROW 5
B5: 2,3,1,4                              # reduction candidate for 2,3
B5: 2,3                                  # 13 pairs
B5: 1,4                                  # 10 pairs
* PAIR H5: 2,3 COL H
H7: 2,3,8,9                              # reduction candidate for 2,3
H7: 2,3 => CTR
* 25.681379.....2.5.....35.6.6..54379...7.6...5...21764..7.1..4.......491.194.26587
H7: 8,9                                  #  9 pairs
H9: 2,3,8                                # reduction candidate for 2,3
H9: 2,3                                  # 13 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06911894-base-pr-000.dot
* REASONING
* DIS # F1: 7,8 => CTR => F1: 1,4
* DIS # F3: 7,8 => CTR => F3: 1,2,4,5,9
* DIS # D8: 8,9 => CTR => D8: 3,4,7
* DIS # F3: 8,9 => CTR => F3: 1,2,4,5,7
* DIS # F8: 8,9 => CTR => F8: 2,4,7
* PRF # F3: 1,2,4,8,9 => SOL
* DIS # H7: 2,3 => CTR => H7: 8,9
* CNT   7 HDP CHAINS /  43 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B6,D4,D5,E1,F5,F6,H5)
* 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7
* PAIR E1: 7,8 BLK 2
F1: 7,8,1,4                              # reduction candidate for 7,8
F1: 7,8 => CTR
* 254678139.6.9...5.....3..6.6...43.71.17.6..25...217.4..7.1..49..4.....1.19.4.6.87
D2: 7,8,4,9                              # reduction candidate for 7,8
D2: 7,8                                  # 11 pairs
E2: 7,8,2,9                              # reduction candidate for 7,8
E2: 7,8                                  # 13 pairs
F2: 7,8,1,2,4,9                          # reduction candidate for 7,8
F2: 7,8                                  # 12 pairs
D3: 7,8,4,5,9                            # reduction candidate for 7,8
D3: 7,8                                  # 10 pairs
F3: 7,8,1,2,4,5,9                        # reduction candidate for 7,8
F3: 7,8 => CTR
* 25.681379763492.5...15372646.57439..4.7869135..92157463761584925.2.7.61.19..265.7
* PAIR E1: 7,8 ROW 1
G1: 7,8,1,3                              # reduction candidate for 7,8
G1: 7,8                                  # 16 pairs
H1: 7,8,3                                # reduction candidate for 7,8
H1: 7,8                                  # 11 pairs
* PAIR E1: 7,8 COL E
E8: 7,8,2,5,9                            # reduction candidate for 7,8
E8: 7,8                                  # 12 pairs
E8: 2,5,9                                # 11 pairs
* PAIR RESTART
* PAIR E1: 7,8 BLK 2
D2: 7,8,4,9                              # reduction candidate for 7,8
D2: 7,8                                  # 11 pairs
E2: 7,8,2,9                              # reduction candidate for 7,8
E2: 7,8                                  # 13 pairs
F2: 7,8,1,2,4,9                          # reduction candidate for 7,8
F2: 7,8                                  # 12 pairs
D3: 7,8,4,5,9                            # reduction candidate for 7,8
D3: 7,8                                  # 10 pairs
* PAIR E1: 7,8 ROW 1
G1: 7,8,1,3                              # reduction candidate for 7,8
G1: 7,8                                  # 16 pairs
H1: 7,8,3                                # reduction candidate for 7,8
H1: 7,8                                  # 11 pairs
* PAIR E1: 7,8 COL E
E8: 7,8,2,5,9                            # reduction candidate for 7,8
E8: 7,8                                  # 12 pairs
E8: 2,5,9                                # 11 pairs
* PAIR A5: 3,4 BLK 4
B5: 3,4,1,2                              # reduction candidate for 3,4
B5: 3,4                                  # 22 pairs
B5: 1,2                                  # 10 pairs
* PAIR A5: 3,4 COL A
A2: 3,4,7,8,9                            # reduction candidate for 3,4
A2: 3,4                                  # 12 pairs
A8: 3,4,5,8                              # reduction candidate for 3,4
A8: 3,4                                  # 11 pairs
* PAIR B6: 3,8 BLK 4
A6: 3,8,5,9                              # reduction candidate for 3,8
A6: 3,8                                  # 22 pairs
C6: 3,8,5,9                              # reduction candidate for 3,8
C6: 3,8                                  # 20 pairs
* PAIR B6: 3,8 ROW 6
G6: 3,8,6,7,9                            # reduction candidate for 3,8
G6: 3,8                                  # 17 pairs
I6: 3,8,6                                # reduction candidate for 3,8
I6: 3,8                                  # 12 pairs
* PAIR B6: 3,8 COL B
B2: 3,8,1,4,6                            # reduction candidate for 3,8
B2: 3,8                                  # 17 pairs
B8: 3,8,2,4,6                            # reduction candidate for 3,8
B8: 3,8                                  # 12 pairs
* PAIR D4: 5,7 COL D
D3: 5,7,4,8,9                            # reduction candidate for 5,7
D3: 5,7                                  # 10 pairs
D3: 4,8,9                                #  7 pairs
* PAIR D5: 8,9 COL D
D2: 8,9,4,7                              # reduction candidate for 8,9
D2: 8,9                                  # 11 pairs
D3: 8,9,4,5,7                            # reduction candidate for 8,9
D3: 8,9                                  # 10 pairs
D8: 8,9,3,4,7                            # reduction candidate for 8,9
D8: 8,9 => CTR
* 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.......4.1.1943.6..7
* PAIR RESTART
* PAIR D5: 8,9 COL D
D2: 8,9,4,7                              # reduction candidate for 8,9
D2: 8,9                                  # 11 pairs
D3: 8,9,4,5,7                            # reduction candidate for 8,9
D3: 8,9                                  # 10 pairs
* PAIR F5: 8,9 COL F
F2: 8,9,1,2,4,7                          # reduction candidate for 8,9
F2: 8,9                                  # 12 pairs
F7: 8,9,2                                # reduction candidate for 8,9
F7: 8,9                                  # 10 pairs
F8: 8,9,2,4,7                            # reduction candidate for 8,9
F8: 8,9 => CTR
* 25.68...9....2..5.....3..6.6...43.....7869..5...21..4..7.1924......7891.19..56..7
* PAIR RESTART
* PAIR F5: 8,9 COL F
F2: 8,9,1,2,4,7                          # reduction candidate for 8,9
F2: 8,9                                  # 12 pairs
F7: 8,9,2                                # reduction candidate for 8,9
F7: 8,9                                  # 10 pairs
* PAIR H5: 2,3 BLK 6
G5: 2,3,1                                # reduction candidate for 2,3
G5: 2,3                                  # 13 pairs
G5: 1                                    # 13 pairs
* PAIR H5: 2,3 ROW 5
B5: 2,3,1,4                              # reduction candidate for 2,3
B5: 2,3                                  # 13 pairs
B5: 1,4                                  # 11 pairs
* PAIR H5: 2,3 COL H
H7: 2,3,8,9                              # reduction candidate for 2,3
H7: 2,3 => CTR
* 25.68..79....7..5.7...35.6.6..54379...7869..5...21764..7.1984.....75491.194326587
H9: 2,3,8                                # reduction candidate for 2,3
H9: 2,3                                  # 13 pairs
* RESTART
* PAIR H5: 2,3 COL H
H9: 2,3,8                                # reduction candidate for 2,3
H9: 8                                    # 18 pairs
H9: 2,3                                  # 13 pairs
* PAIR RESTART
* PAIR H5: 2,3 BLK 6
G5: 2,3,1                                # reduction candidate for 2,3
G5: 2,3                                  # 14 pairs
G5: 1                                    # 14 pairs
* PAIR H5: 2,3 ROW 5
B5: 2,3,1,4                              # reduction candidate for 2,3
B5: 2,3                                  # 14 pairs
B5: 1,4                                  # 12 pairs
* PAIR H5: 2,3 COL H
H9: 2,3,8                                # reduction candidate for 2,3
H9: 8                                    # 18 pairs
H9: 2,3                                  # 13 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,B6,D4,D5,E1,F1,F5,F6,H5,H7)
* 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7
* PAIR E1: 7,8 BLK 2
D2: 7,8,4,9                              # reduction candidate for 7,8
D2: 7,8                                  # 12 pairs
E2: 7,8,2,9                              # reduction candidate for 7,8
E2: 7,8                                  # 14 pairs
F2: 7,8,1,2,4,9                          # reduction candidate for 7,8
F2: 7,8                                  # 13 pairs
D3: 7,8,4,5,9                            # reduction candidate for 7,8
D3: 7,8                                  # 12 pairs
* PAIR E1: 7,8 ROW 1
G1: 7,8,1,3                              # reduction candidate for 7,8
G1: 7,8 => CTR
* 25.6...39.......5.....35.6.6..543.7...7.6..25...217.4..7.1..49....794.1.1943.6.87
H1: 7,8,3                                # reduction candidate for 7,8
H1: 7,8                                  # 12 pairs
* RESTART
* PAIR E1: 7,8 ROW 1
H1: 7,8,3                                # reduction candidate for 7,8
H1: 3 => CTR
* 258674139.......5.....35.6.6..543.71.17.6.325...217.4..7.1..49....792.1.194356287
* PAIR E1: 7,8 COL E
E8: 7,8,2,5,9                            # reduction candidate for 7,8
E8: 7,8 => CTR
* 25.68..79....9..5.....35.6.6..54379.4.7968.25...21764.37.15948....37491.194826537
* PAIR RESTART
* PAIR E1: 7,8 BLK 2
E2: 7,8,2,9                              # reduction candidate for 7,8
E2: 2,9 => CTR
* 25.67..89.......5.....3..6.6...43.7...7.6...5...217.4..7.1..49....794.1.1943.6.27
* PAIR F1: 1,4 BLK 2
F2: 1,4,2                                # reduction candidate for 1,4
F2: 1,4 => SOLVED
* 251684379863971254749532861615743928427869135938215746376158492582497613194326587
* DURATION: 0:00:51.103410  START: 06:54:36.173042  END: 06:55:27.276452 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06911894-base-pr-001.dot
* REASONING
* DIS # F1: 7,8 => CTR => F1: 1,4
* DIS F1: 1,4 # F3: 7,8 => CTR => F3: 1,2,4,5,9
* DIS F1: 1,4 + F3: 1,2,4,5,9 # D8: 8,9 => CTR => D8: 3,4,7
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F8: 8,9 => CTR => F8: 2,4,7
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # H7: 2,3 => CTR => H7: 8,9
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G1: 7,8 => CTR => G1: 1,3
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 3 => CTR => H1: 7,8
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 # E8: 7,8 => CTR => E8: 2,5,9
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 # E2: 2,9 => CTR => E2: 7,8
* PRF F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 # F2: 1,4 => SOL
* STA F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 + F2: 1,4
* CNT  10 HDP CHAINS /  66 HYP OPENED
```

```http://www.menneske.no/sudoku/utskrift.html?number=6911894
umulig

--------------------------------------------------
level: medium

* PAIR REDUCTION ..
* ROUND 1: 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7
E1: 7,8
F1: 1,4,7,8                              # reduction candidate for 7,8
F1: 7,8 => CTR
* 254678139.6.9...5.....3..6.6...43.71.17.6..25...217.4..7.1..49..4.....1.19.4.6.87
D2: 4,7,8,9                              # reduction candidate for 7,8
E2: 2,7,8,9                              # reduction candidate for 7,8
F2: 1,2,4,7,8,9                          # reduction candidate for 7,8
D3: 4,5,7,8,9                            # reduction candidate for 7,8
F3: 1,2,4,5,7,8,9                        # reduction candidate for 7,8
F3: 7,8 => CTR
* 25.681379763492.5...15372646.57439..4.7869135..92157463761584925.2.7.61.19..265.7
G1: 1,3,7,8                              # reduction candidate for 7,8
H1: 3,7,8                                # reduction candidate for 7,8
E8: 2,5,7,8,9                            # reduction candidate for 7,8
A5: 3,4
B5: 1,2,3,4                              # reduction candidate for 3,4
A2: 3,4,7,8,9                            # reduction candidate for 3,4
A8: 3,4,5,8                              # reduction candidate for 3,4
B6: 3,8
A6: 3,5,8,9                              # reduction candidate for 3,8
C6: 3,5,8,9                              # reduction candidate for 3,8
G6: 3,6,7,8,9                            # reduction candidate for 3,8
I6: 3,6,8                                # reduction candidate for 3,8
B2: 1,3,4,6,8                            # reduction candidate for 3,8
B8: 2,3,4,6,8                            # reduction candidate for 3,8
D4: 5,7
D3: 4,5,7,8,9                            # reduction candidate for 5,7
D5: 8,9
D2: 4,7,8,9                              # reduction candidate for 8,9
D3: 4,5,7,8,9                            # reduction candidate for 8,9
D8: 3,4,7,8,9                            # reduction candidate for 8,9
D8: 8,9 => CTR
* 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.......4.1.1943.6..7
F5: 8,9
F2: 1,2,4,7,8,9                          # reduction candidate for 8,9
F7: 2,8,9                                # reduction candidate for 8,9
F8: 2,4,7,8,9                            # reduction candidate for 8,9
F8: 8,9 => CTR
* 25.68...9....2..5.....3..6.6...43.....7869..5...21..4..7.1924......7891.19..56..7
F6: 5,7
H5: 2,3
G5: 1,2,3                                # reduction candidate for 2,3
B5: 1,2,3,4                              # reduction candidate for 2,3
H7: 2,3,8,9                              # reduction candidate for 2,3
H7: 2,3 => CTR
* 25.68..79....7..5.7...35.6.6..54379...7869..5...21764..7.1984.....75491.194326587
H9: 2,3,8                                # reduction candidate for 2,3
* ROUND 2: 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7
E1: 7,8
D2: 4,7,8,9                              # reduction candidate for 7,8
E2: 2,7,8,9                              # reduction candidate for 7,8
F2: 1,2,4,7,8,9                          # reduction candidate for 7,8
D3: 4,5,7,8,9                            # reduction candidate for 7,8
G1: 1,3,7,8                              # reduction candidate for 7,8
G1: 7,8 => CTR
* 25.6...39.......5.....35.6.6..543.7...7.6..25...217.4..7.1..49....794.1.1943.6.87
H1: 3,7,8                                # reduction candidate for 7,8
H1: 3 => CTR
* 258674139.......5.....35.6.6..543.71.17.6.325...217.4..7.1..49....792.1.194356287
E8: 2,5,7,8,9                            # reduction candidate for 7,8
E8: 7,8 => CTR
* 25.68..79....9..5.....35.6.6..54379.4.7968.25...21764.37.15948....37491.194826537
F1: 1,4
F2: 1,2,4,8,9                            # reduction candidate for 1,4
F2: 1,4 => SOLVED
* 251684379863971254749532861615743928427869135938215746376158492582497613194326587
* SOLVED!
```

# Solution

position: 251684379863971254749532861615743928427869135938215746376158492582497613194326587 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:

```* DIS # F1: 7,8 => CTR => F1: 1,4
* INC # F1: 1,4 => UNS
* INC # D2: 7,8 => UNS
* INC # E2: 7,8 => UNS
* INC # F2: 7,8 => UNS
* INC # D3: 7,8 => UNS
* DIS # F3: 7,8 => CTR => F3: 1,2,4,5,9
* INC # F3: 1,2,4,5,9 => UNS
* INC # G1: 7,8 => UNS
* INC # H1: 7,8 => UNS
* INC # E8: 7,8 => UNS
* INC # E8: 2,5,9 => UNS
* INC # B5: 3,4 => UNS
* INC # B5: 1,2 => UNS
* INC # A2: 3,4 => UNS
* INC # A8: 3,4 => UNS
* INC # A6: 3,8 => UNS
* INC # C6: 3,8 => UNS
* INC # G6: 3,8 => UNS
* INC # I6: 3,8 => UNS
* INC # B2: 3,8 => UNS
* INC # B8: 3,8 => UNS
* INC # D3: 5,7 => UNS
* INC # D3: 4,8,9 => UNS
* INC # D2: 8,9 => UNS
* INC # D3: 8,9 => UNS
* DIS # D8: 8,9 => CTR => D8: 3,4,7
* INC # D8: 3,4,7 => UNS
* INC # F2: 8,9 => UNS
* DIS # F3: 8,9 => CTR => F3: 1,2,4,5,7
* INC # F3: 1,2,4,5,7 => UNS
* INC # F7: 8,9 => UNS
* DIS # F8: 8,9 => CTR => F8: 2,4,7
* INC # F8: 2,4,7 => UNS
* INC # F3: 5,7 => UNS
* PRF # F3: 1,2,4,8,9 => SOL
* INC # G5: 2,3 => UNS
* INC # G5: 1 => UNS
* INC # B5: 2,3 => UNS
* INC # B5: 1,4 => UNS
* DIS # H7: 2,3 => CTR => H7: 8,9
* INC # H7: 8,9 => UNS
* INC # H9: 2,3 => UNS
* CNT  43 HDP CHAINS /  43 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* DIS # F1: 7,8 => CTR => F1: 1,4
* INC F1: 1,4 # D2: 7,8 => UNS
* INC F1: 1,4 # E2: 7,8 => UNS
* INC F1: 1,4 # F2: 7,8 => UNS
* INC F1: 1,4 # D3: 7,8 => UNS
* DIS F1: 1,4 # F3: 7,8 => CTR => F3: 1,2,4,5,9
* INC F1: 1,4 + F3: 1,2,4,5,9 # G1: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # H1: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # E8: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # E8: 2,5,9 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # D2: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # E2: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # F2: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # D3: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # G1: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # H1: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # E8: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # E8: 2,5,9 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # B5: 3,4 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # B5: 1,2 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # A2: 3,4 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # A8: 3,4 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # A6: 3,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # C6: 3,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # G6: 3,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # I6: 3,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # B2: 3,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # B8: 3,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # D3: 5,7 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # D3: 4,8,9 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # D2: 8,9 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 # D3: 8,9 => UNS
* DIS F1: 1,4 + F3: 1,2,4,5,9 # D8: 8,9 => CTR => D8: 3,4,7
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # D2: 8,9 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # D3: 8,9 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F2: 8,9 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F7: 8,9 => UNS
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F8: 8,9 => CTR => F8: 2,4,7
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # F2: 8,9 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # F7: 8,9 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # G5: 2,3 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # G5: 1 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # B5: 2,3 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # B5: 1,4 => UNS
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # H7: 2,3 => CTR => H7: 8,9
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 2,3 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 2,3 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G5: 2,3 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G5: 1 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # B5: 2,3 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # B5: 1,4 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 2,3 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # D2: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # E2: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # F2: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # D3: 7,8 => UNS
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G1: 7,8 => CTR => G1: 1,3
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 7,8 => UNS
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 7,8 => UNS
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 3 => CTR => H1: 7,8
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 # E8: 7,8 => CTR => E8: 2,5,9
* INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 # E2: 7,8 => UNS
* DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 # E2: 2,9 => CTR => E2: 7,8
* PRF F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 # F2: 1,4 => SOL
* STA F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 + F2: 1,4
* CNT  66 HDP CHAINS /  66 HYP OPENED
```