Analysis of zz-sudoku-de-602142-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 71.8.3.54.3.4.5.9.4.......8...7.1....5.....3....5.6...1.......7.7.3.9.6.56.1.4.23 initial

Autosolve

position: 71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 6 => CTR => C1: 2,9
* DIS # E3: 2,9 => CTR => E3: 6
* DIS # B7: 4,8 => CTR => B7: 2,9
* DIS # E3: 2,9 => CTR => E3: 6
* DIS # C1: 6 => CTR => C1: 2,9
* PRF # E5: 2,9 => SOL
* PRF # C1: 9 => SOL
* PRF # E5: 2,9 => SOL
* DIS # I5: 2,9 => CTR => I5: 1,6
* DIS # D3: 6 => CTR => D3: 2,9
* DIS # E4: 2,8 => CTR => E4: 3,4,9
* DIS # E5: 2,8 => CTR => E5: 4,9
* DIS # G5: 2,8 => CTR => G5: 1,4,6
* DIS # G4: 4,8 => CTR => G4: 2,5,6
* PRF # G5: 4,8 => SOL
* DIS # C4: 4,8 => CTR => C4: 2,6
* DIS # E4: 4,8 => CTR => E4: 2,3,9
* DIS # I4: 2,9 => CTR => I4: 5,6
* DIS # I5: 2,9 => CTR => I5: 1,6
* DIS # C8: 2,8 => CTR => C8: 4
* DIS # E8: 5 => CTR => E8: 2,8
* DIS # A4: 2,8 => CTR => A4: 3,6,9
* DIS # A6: 2,8 => CTR => A6: 3,9
* DIS # B7: 2,4 => CTR => B7: 8,9
* DIS # E7: 2,6 => CTR => E7: 5,8
* PRF # D3: 9 => SOL
* DIS # E7: 2,8 => CTR => E7: 5,6
* PRF # G7: 4,8 => SOL
* DIS # G8: 4,8 => CTR => G8: 1,5
* DIS # B7: 4,8 => CTR => B7: 2,9
* DIS # G8: 4,8 => CTR => G8: 1,5
* DIS # G7: 4,5 => CTR => G7: 8,9
* CNT  32 HDP CHAINS /  89 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # C1: 6 => CTR => C1: 2,9
* DIS C1: 2,9 # E3: 2,9 => CTR => E3: 6
* DIS C1: 2,9 + E3: 6 # B7: 4,8 => CTR => B7: 2,9
* PRF C1: 2,9 + E3: 6 + B7: 2,9 # E5: 2,9 => SOL
* STA C1: 2,9 + E3: 6 + B7: 2,9 + E5: 2,9
* CNT   4 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

71.8.3.54.3.4.5.9.4.......8...7.1....5.....3....5.6...1.......7.7.3.9.6.56.1.4.23 initial
71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23 autosolve
719823654836415792425967318942731586657298431381546279193652847274389165568174923 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B3: 2,9
E1: 2,9
G1: 2,6
I2: 2,6
D5: 2,9
F5: 2,8
H4: 4,8
I6: 2,9
A8: 2,8
C9: 8,9
D7: 2,6
F7: 2,8
H7: 4,8
I8: 1,5
G9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G5,I5: 1.. / G5 = 1  => 16 pairs (_) / I5 = 1  => 15 pairs (_)
G8,I8: 1.. / G8 = 1  => 15 pairs (_) / I8 = 1  => 16 pairs (_)
G5,G8: 1.. / G5 = 1  => 16 pairs (_) / G8 = 1  => 15 pairs (_)
I5,I8: 1.. / I5 = 1  => 15 pairs (_) / I8 = 1  => 16 pairs (_)
G1,I2: 2.. / G1 = 2  =>  0 pairs (X) / I2 = 2  => 19 pairs (_)
F5,F7: 2.. / F5 = 2  =>  0 pairs (X) / F7 = 2  => 15 pairs (_)
A4,A6: 3.. / A4 = 3  => 15 pairs (_) / A6 = 3  => 15 pairs (_)
E4,E6: 3.. / E4 = 3  => 15 pairs (_) / E6 = 3  => 15 pairs (_)
A4,E4: 3.. / A4 = 3  => 15 pairs (_) / E4 = 3  => 15 pairs (_)
A6,E6: 3.. / A6 = 3  => 15 pairs (_) / E6 = 3  => 15 pairs (_)
B7,C8: 4.. / B7 = 4  =>  0 pairs (X) / C8 = 4  => 15 pairs (_)
E5,G5: 4.. / E5 = 4  => 15 pairs (_) / G5 = 4  =>  0 pairs (*)
C8,G8: 4.. / C8 = 4  => 15 pairs (_) / G8 = 4  =>  0 pairs (X)
C4,C8: 4.. / C4 = 4  =>  0 pairs (X) / C8 = 4  => 15 pairs (_)
H4,H7: 4.. / H4 = 4  =>  0 pairs (X) / H7 = 4  => 16 pairs (_)
G4,I4: 5.. / G4 = 5  => 15 pairs (_) / I4 = 5  => 16 pairs (_)
E7,E8: 5.. / E7 = 5  => 17 pairs (_) / E8 = 5  =>  0 pairs (X)
E7,G7: 5.. / E7 = 5  => 17 pairs (_) / G7 = 5  =>  0 pairs (X)
I4,I8: 5.. / I4 = 5  => 16 pairs (_) / I8 = 5  => 15 pairs (_)
D3,E3: 6.. / D3 = 6  =>  0 pairs (X) / E3 = 6  => 15 pairs (_)
G1,I2: 6.. / G1 = 6  => 19 pairs (_) / I2 = 6  =>  0 pairs (X)
D7,E7: 6.. / D7 = 6  => 15 pairs (_) / E7 = 6  =>  0 pairs (X)
C1,G1: 6.. / C1 = 6  =>  0 pairs (X) / G1 = 6  => 19 pairs (_)
D3,D7: 6.. / D3 = 6  =>  0 pairs (X) / D7 = 6  => 15 pairs (_)
E3,E7: 6.. / E3 = 6  => 15 pairs (_) / E7 = 6  =>  0 pairs (X)
A2,C2: 8.. / A2 = 8  => 22 pairs (_) / C2 = 8  => 17 pairs (_)
C9,G9: 8.. / C9 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
F5,F7: 8.. / F5 = 8  => 15 pairs (_) / F7 = 8  =>  0 pairs (X)
H4,H7: 8.. / H4 = 8  => 16 pairs (_) / H7 = 8  =>  0 pairs (X)
C1,B3: 9.. / C1 = 9  =>  0 pairs (*) / B3 = 9  =>  0 pairs (X)
B7,C9: 9.. / B7 = 9  =>  0 pairs (*) / C9 = 9  =>  0 pairs (X)
G7,G9: 9.. / G7 = 9  => 17 pairs (_) / G9 = 9  =>  0 pairs (*)
C1,E1: 9.. / C1 = 9  =>  0 pairs (*) / E1 = 9  =>  0 pairs (X)
B7,G7: 9.. / B7 = 9  =>  0 pairs (*) / G7 = 9  =>  0 pairs (X)
C9,G9: 9.. / C9 = 9  => 17 pairs (_) / G9 = 9  =>  0 pairs (*)
B3,B7: 9.. / B3 = 9  => 17 pairs (_) / B7 = 9  =>  0 pairs (*)
C1,C9: 9.. / C1 = 9  =>  0 pairs (*) / C9 = 9  =>  0 pairs (X)
D3,D5: 9.. / D3 = 9  =>  0 pairs (*) / D5 = 9  =>  0 pairs (X)
* DURATION: 0:01:00.786189  START: 07:15:00.161990  END: 07:16:00.948179 2017-05-01
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,C9,D5,D7,E1,F5,F7,G1,G9,H4,H7,I2,I6,I8)
* 71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23
* PAIR B3: 2,9 BLK 1
C1: 2,9,6                                # reduction candidate for 2,9
C1: 6 => CTR
* 716893254.38415796495.67318.42731.8..5794..3.381526479123.5.947.743.9.6.569174823
C1: 2,9                                  # 19 pairs
* PAIR B3: 2,9 ROW 3
D3: 2,9,6                                # reduction candidate for 2,9
D3: 2,9                                  # 15 pairs
E3: 2,9,6                                # reduction candidate for 2,9
E3: 2,9 => CTR
* 719823654.3.415792425697318..27.1.85.579.2136.815.6.7.1.3268547.74359.6156.174923
E3: 6                                    # 15 pairs
* PAIR B3: 2,9 COL B
B7: 2,9,4,8                              # reduction candidate for 2,9
B7: 4,8 => CTR
* 712893654638415792495267318..67.1.8.8579...3...15.6.7.183652947274389.6.569174823
B7: 2,9                                  # 19 pairs
* PAIR E1: 2,9 BLK 2
D3: 2,9,6                                # reduction candidate for 2,9
D3: 2,9                                  # 15 pairs
E3: 2,9,6                                # reduction candidate for 2,9
E3: 2,9 => CTR
* 719823654.3.415792425697318..27.1.85.579.2136.815.6.7.1.3268547.74359.6156.174923
E3: 6                                    # 15 pairs
* PAIR E1: 2,9 ROW 1
C1: 2,9,6                                # reduction candidate for 2,9
C1: 6 => CTR
* 716893254.38415796495.67318.42731.8..5794..3.381526479123.5.947.743.9.6.569174823
C1: 2,9                                  # 19 pairs
* PAIR E1: 2,9 COL E
E4: 2,9,3,4,8                            # reduction candidate for 2,9
E4: 2,9                                  # 16 pairs
E5: 2,9,4,8                              # reduction candidate for 2,9
E5: 2,9 => SOLVED
* 719823654836415792425967318942731586657298431381546279193652847274389165568174923
E5: 4,8                                  # 16 pairs
E6: 2,9,3,4,8                            # reduction candidate for 2,9
E6: 2,9                                  # 18 pairs
* PAIR G1: 2,6 ROW 1
C1: 2,6,9                                # reduction candidate for 2,6
C1: 9 => SOLVED
* 719823654836415792425967318942731586657298431381546279193652847274389165568174923
C1: 2,6                                  # 17 pairs
* PAIR G1: 2,6 COL G
G4: 2,6,4,5,8                            # reduction candidate for 2,6
G4: 2,6                                  # 18 pairs
G5: 2,6,1,4,8                            # reduction candidate for 2,6
G5: 2,6                                  # 17 pairs
* PAIR I2: 2,6 ROW 2
A2: 2,6,8                                # reduction candidate for 2,6
A2: 2,6                                  # 17 pairs
C2: 2,6,8                                # reduction candidate for 2,6
C2: 2,6                                  # 22 pairs
* PAIR I2: 2,6 COL I
I4: 2,6,5,9                              # reduction candidate for 2,6
I4: 2,6                                  # 17 pairs
I5: 2,6,1,9                              # reduction candidate for 2,6
I5: 2,6                                  # 16 pairs
* PAIR D5: 2,9 BLK 5
E4: 2,9,3,4,8                            # reduction candidate for 2,9
E4: 2,9                                  # 16 pairs
E5: 2,9,4,8                              # reduction candidate for 2,9
E5: 2,9 => SOLVED
* 719823654836415792425967318942731586657298431381546279193652847274389165568174923
E5: 4,8                                  # 16 pairs
E6: 2,9,3,4,8                            # reduction candidate for 2,9
E6: 2,9                                  # 18 pairs
* PAIR D5: 2,9 ROW 5
A5: 2,9,6,8                              # reduction candidate for 2,9
A5: 2,9                                  # 18 pairs
I5: 2,9,1,6                              # reduction candidate for 2,9
I5: 2,9 => CTR
* 716893254.3.41579649526731892.7316856579481323815264791436.29.7.7.3.9561569174823
I5: 1,6                                  # 16 pairs
* PAIR D5: 2,9 COL D
D3: 2,9,6                                # reduction candidate for 2,9
D3: 6 => CTR
* 719823654.3.415792425697318..27.1.85.579.2136.815.6.7.1.3268547.74359.6156.174923
D3: 2,9                                  # 15 pairs
* PAIR F5: 2,8 BLK 5
E4: 2,8,3,4,9                            # reduction candidate for 2,8
E4: 2,8 => CTR
* 71.8.3254.3.4157964.5..73183..7.15.9657.4..319.1536.721.3.5...7.7.3.916556.174.23
E4: 3,4,9                                # 15 pairs
E5: 2,8,4,9                              # reduction candidate for 2,8
E5: 2,8 => CTR
* 71.8.3654.364157924.5.673189.27315866579..431..15.62791.3.5..47.743.916556.174.23
E5: 4,9                                  # 16 pairs
E6: 2,8,3,4,9                            # reduction candidate for 2,8
E6: 2,8                                  # 15 pairs
* PAIR F5: 2,8 ROW 5
A5: 2,8,6,9                              # reduction candidate for 2,8
A5: 2,8                                  # 10 pairs
G5: 2,8,1,4,6                            # reduction candidate for 2,8
G5: 2,8 => CTR
* 71.8936548364157924952673189..7315.66579482313.1526.79183652947274389165569174823
G5: 1,4,6                                # 15 pairs
* PAIR H4: 4,8 BLK 6
G4: 4,8,2,5,6                            # reduction candidate for 4,8
G4: 4,8 => CTR
* 712893654638415792495.27318926731..5.57.4.136.415.6279183..2947274389561569174823
G4: 2,5,6                                # 15 pairs
G5: 4,8,1,2,6                            # reduction candidate for 4,8
G5: 4,8 => SOLVED
* 719823654836415792425967318942731586657298431381546279193652847274389165568174923
G5: 1,2,6                                # 15 pairs
G6: 4,8,2                                # reduction candidate for 4,8
G6: 4,8                                  # 16 pairs
* PAIR H4: 4,8 ROW 4
B4: 4,8,2                                # reduction candidate for 4,8
B4: 4,8                                  # 17 pairs
C4: 4,8,2,6                              # reduction candidate for 4,8
C4: 4,8 => CTR
* 71.893.54.3.41579.495..7318.2.731.8.6579...3.3815.6.79143...9.7.7.3.9.6.569174823
C4: 2,6                                  # 16 pairs
E4: 4,8,2,3,9                            # reduction candidate for 4,8
E4: 4,8 => CTR
* 71.8.3254.3.4157964.5..73183..7.15.9657....319.1536.721.3.5...7.7.3.916556.174.23
E4: 2,3,9                                # 15 pairs
* PAIR I6: 2,9 BLK 6
I4: 2,9,5,6                              # reduction candidate for 2,9
I4: 2,9 => CTR
* 716893254.3.4157964952673186..7315.9.5794.631..15.6.7.1.365...7.743.916556.174.23
I4: 5,6                                  # 18 pairs
I5: 2,9,1,6                              # reduction candidate for 2,9
I5: 2,9 => CTR
* 716893254.3.41579649526731892.7316856579481323815264791436.29.7.7.3.9561569174823
I5: 1,6                                  # 16 pairs
* PAIR I6: 2,9 ROW 6
A6: 2,9,3,8                              # reduction candidate for 2,9
A6: 2,9                                  # 18 pairs
E6: 2,9,3,4,8                            # reduction candidate for 2,9
E6: 2,9                                  # 18 pairs
* PAIR A8: 2,8 BLK 7
B7: 2,8,4,9                              # reduction candidate for 2,8
B7: 2,8                                  # 17 pairs
C8: 2,8,4                                # reduction candidate for 2,8
C8: 2,8 => CTR
* 71.8.3.54.3.41579.4.5..7318..47.1.8..57....3...15.6.7.143.....7.7.3.9.6.56.174.23
C8: 4                                    # 15 pairs
* PAIR A8: 2,8 ROW 8
E8: 2,8,5                                # reduction candidate for 2,8
E8: 5 => CTR
* 719823654836415792425..73186.27.1..5.57.4.136..15.6.79193...547.74359861568174923
E8: 2,8                                  # 17 pairs
* PAIR A8: 2,8 COL A
A2: 2,8,6                                # reduction candidate for 2,8
A2: 2,8                                  # 21 pairs
A4: 2,8,3,6,9                            # reduction candidate for 2,8
A4: 2,8 => CTR
* 719823.54.3.41579.4.5..7318...731..9.57....3.3.1596.721.3.....7.7.3.9.6556.174.23
A4: 3,6,9                                # 15 pairs
A5: 2,8,6,9                              # reduction candidate for 2,8
A5: 2,8                                  # 10 pairs
A6: 2,8,3,9                              # reduction candidate for 2,8
A6: 2,8 => CTR
* 71.8.3.546384157924.59673183.6791..5957248.36..1536.791936.2..7.7.3.9.6.56.174.23
A6: 3,9                                  # 16 pairs
* PAIR C9: 8,9 BLK 7
B7: 8,9,2,4                              # reduction candidate for 8,9
B7: 2,4 => CTR
* 71289365463841579.495267318.4.731.8..57982431381546279123658947874329165569174823
B7: 8,9                                  # 17 pairs
* PAIR D7: 2,6 BLK 8
E7: 2,6,5,8                              # reduction candidate for 2,6
E7: 2,6 => CTR
* 719823654836415792425697318...7.1..5.57...136..15.6.79193.68547.74359861568174923
E7: 5,8                                  # 16 pairs
* PAIR D7: 2,6 COL D
D3: 2,6,9                                # reduction candidate for 2,6
D3: 9 => SOLVED
* 719823654836415792425967318942731586657298431381546279193652847274389165568174923
D3: 2,6                                  # 17 pairs
* PAIR F7: 2,8 BLK 8
E7: 2,8,5,6                              # reduction candidate for 2,8
E7: 2,8 => CTR
* 7198236548364157924259673186.27.1..5.572.8136..15.6.79193682547.74359861568174923
E7: 5,6                                  # 16 pairs
E8: 2,8,5                                # reduction candidate for 2,8
E8: 2,8                                  # 17 pairs
* PAIR F7: 2,8 ROW 7
B7: 2,8,4,9                              # reduction candidate for 2,8
B7: 4,9                                  # 17 pairs
B7: 2,8                                  # 17 pairs
* PAIR H7: 4,8 BLK 9
G7: 4,8,5,9                              # reduction candidate for 4,8
G7: 4,8 => SOLVED
* 719823654836415792425967318942731586657298431381546279193652847274389165568174923
G7: 5,9                                  # 16 pairs
G8: 4,8,1,5                              # reduction candidate for 4,8
G8: 4,8 => CTR
* 719823654836415792425..73186.27.1..5.57.4.136..15.6.79193...547.74359861568174923
G8: 1,5                                  # 17 pairs
* PAIR H7: 4,8 ROW 7
B7: 4,8,2,9                              # reduction candidate for 4,8
B7: 4,8 => CTR
* 712893654638415792495267318..67.1.8.8579...3...15.6.7.183652947274389.6.569174823
B7: 2,9                                  # 19 pairs
* PAIR I8: 1,5 BLK 9
G8: 1,5,4,8                              # reduction candidate for 1,5
G8: 4,8 => CTR
* 719823654836415792425..73186.27.1..5.57.4.136..15.6.79193...547.74359861568174923
G8: 1,5                                  # 17 pairs
* PAIR G9: 8,9 BLK 9
G7: 8,9,4,5                              # reduction candidate for 8,9
G7: 4,5 => CTR
* 719823654836415792425..73189.27315.6657...8313.1586279193.....72743.9165568174923
G7: 8,9                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-602142-base-pr-000.dot
* REASONING
* DIS # C1: 6 => CTR => C1: 2,9
* DIS # E3: 2,9 => CTR => E3: 6
* DIS # B7: 4,8 => CTR => B7: 2,9
* DIS # E3: 2,9 => CTR => E3: 6
* DIS # C1: 6 => CTR => C1: 2,9
* PRF # E5: 2,9 => SOL
* PRF # C1: 9 => SOL
* PRF # E5: 2,9 => SOL
* DIS # I5: 2,9 => CTR => I5: 1,6
* DIS # D3: 6 => CTR => D3: 2,9
* DIS # E4: 2,8 => CTR => E4: 3,4,9
* DIS # E5: 2,8 => CTR => E5: 4,9
* DIS # G5: 2,8 => CTR => G5: 1,4,6
* DIS # G4: 4,8 => CTR => G4: 2,5,6
* PRF # G5: 4,8 => SOL
* DIS # C4: 4,8 => CTR => C4: 2,6
* DIS # E4: 4,8 => CTR => E4: 2,3,9
* DIS # I4: 2,9 => CTR => I4: 5,6
* DIS # I5: 2,9 => CTR => I5: 1,6
* DIS # C8: 2,8 => CTR => C8: 4
* DIS # E8: 5 => CTR => E8: 2,8
* DIS # A4: 2,8 => CTR => A4: 3,6,9
* DIS # A6: 2,8 => CTR => A6: 3,9
* DIS # B7: 2,4 => CTR => B7: 8,9
* DIS # E7: 2,6 => CTR => E7: 5,8
* PRF # D3: 9 => SOL
* DIS # E7: 2,8 => CTR => E7: 5,6
* PRF # G7: 4,8 => SOL
* DIS # G8: 4,8 => CTR => G8: 1,5
* DIS # B7: 4,8 => CTR => B7: 2,9
* DIS # G8: 4,8 => CTR => G8: 1,5
* DIS # G7: 4,5 => CTR => G7: 8,9
* CNT  32 HDP CHAINS /  89 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B3,C9,D5,D7,E1,F5,F7,G1,G9,H4,H7,I2,I6,I8)
* 71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23
* PAIR B3: 2,9 BLK 1
C1: 2,9,6                                # reduction candidate for 2,9
C1: 6 => CTR
* 716893254.38415796495.67318.42731.8..5794..3.381526479123.5.947.743.9.6.569174823
* PAIR B3: 2,9 ROW 3
D3: 2,9,6                                # reduction candidate for 2,9
D3: 2,9                                  # 19 pairs
E3: 2,9,6                                # reduction candidate for 2,9
E3: 2,9 => CTR
* 719823654.3.4157924256973189.2731....579...3...15.6.791.3268547.74359.6156.174923
* RESTART
* PAIR B3: 2,9 COL B
B7: 2,9,4,8                              # reduction candidate for 2,9
B7: 4,8 => CTR
* 712893654.384157924952673189.6731.858579...3.3.15.6.791.3652947274389.6.569174823
* PAIR RESTART
* PAIR E1: 2,9 COL E
E5: 2,9,4,8                              # reduction candidate for 2,9
E5: 2,9 => SOLVED
* 719823654836415792425967318942731586657298431381546279193652847274389165568174923
* DURATION: 0:00:08.511544  START: 07:17:21.087261  END: 07:17:29.598805 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-602142-base-pr-001.dot
* REASONING
* DIS # C1: 6 => CTR => C1: 2,9
* DIS C1: 2,9 # E3: 2,9 => CTR => E3: 6
* DIS C1: 2,9 + E3: 6 # B7: 4,8 => CTR => B7: 2,9
* PRF C1: 2,9 + E3: 6 + B7: 2,9 # E5: 2,9 => SOL
* STA C1: 2,9 + E3: 6 + B7: 2,9 + E5: 2,9
* CNT   4 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokus.de/602142.html
sehr schwierig

level: medium

* PAIR REDUCTION ..
* ROUND 1: 71.8.3.54.3.41579.4.5..7318...7.1....57....3...15.6.7.1.3.....7.7.3.9.6.56.174.23
B3: 2,9
C1: 2,6,9                                # reduction candidate for 2,9
C1: 6 => CTR
* 716893254.38415796495.67318.42731.8..5794..3.381526479123.5.947.743.9.6.569174823
D3: 2,6,9                                # reduction candidate for 2,9
D3: 6 => CTR
* 719823654.3.4157924256973189.2731....579...3...15.6.791.3268547.74359.6156.174923
B7: 2,4,8,9                              # reduction candidate for 2,9
B7: 4,8 => CTR
* 712893654.384157924952673189.6731.858579...3.3.15.6.791.3652947274389.6.569174823
E1: 2,9
E5: 2,4,8,9                              # reduction candidate for 2,9
E5: 2,9 => SOLVED
* 719823654836415792425967318942731586657298431381546279193652847274389165568174923
* SOLVED!

--------------------------------------------------
* AUTO ..
C3 = 5                # set value
F3 = 7                # set value
H3: 1                 # naked single
G3 = 3                # set value
H3 = 1                # set value
C7 = 3                # set value
E9 = 7                # set value
E2: 1..               # hidden single
G2: 7..               # hidden single
H6: 7..               # hidden single
E2 = 1                # set value
G2 = 7                # set value
H6 = 7                # set value
C5: 7..               # hidden single
C5 = 7                # set value
C6: 1..               # hidden single
C6 = 1                # set value
Q1,Q3: 6.. => E1 != 6
Q1,Q7: 9.. => B4,B6,C4 != 9
Q9: 9.. = G7,G9: 9.. => G4,G5,G6 != 9
* UNSOLVED!

|:step:| 00
--------------------------------------------------

highlight 4
G8 = 4 => H4,B6,B7 = 4 => CTR => G8 != 4

highlight 8
C4 = 8 => A2,B7,E8,G9 = 8 => G4,H4,G5,G6 != 8 => CTR => C4 != 8

highlight 2
A5 = 2 => B7,E8,D3,F7 = 2 => CTR => A5 != 2

C2 = 2 => C4 = 6 => C1 != 6
C2 = 2 => I2 = 6 => G1 = !6 => C1 = 6
=> CTR => C2 != 6

D5: 2,9
E5: 2,4,8,9
* DISABLE VALUE:: E5 != 4
G5: 4..               # hidden single
* DISABLE VALUE:: E5 != 8

|:step:| 01
--------------------------------------------------

Solution

position: 719823654836415792425967318942731586657298431381546279193652847274389165568174923 solved
Solution

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 # C1: 2,9 => UNS
* DIS # C1: 6 => CTR => C1: 2,9
* INC # D3: 2,9 => UNS
* DIS # E3: 2,9 => CTR => E3: 6
* INC # E3: 6 => UNS
* INC # B7: 2,9 => UNS
* DIS # B7: 4,8 => CTR => B7: 2,9
* INC # D3: 2,9 => UNS
* DIS # E3: 2,9 => CTR => E3: 6
* INC # E3: 6 => UNS
* INC # C1: 2,9 => UNS
* DIS # C1: 6 => CTR => C1: 2,9
* INC # E4: 2,9 => UNS
* PRF # E5: 2,9 => SOL
* INC # E5: 4,8 => UNS
* INC # E6: 2,9 => UNS
* INC # C1: 2,6 => UNS
* PRF # C1: 9 => SOL
* INC # G4: 2,6 => UNS
* INC # G5: 2,6 => UNS
* INC # A2: 2,6 => UNS
* INC # C2: 2,6 => UNS
* INC # I4: 2,6 => UNS
* INC # I5: 2,6 => UNS
* INC # E4: 2,9 => UNS
* PRF # E5: 2,9 => SOL
* INC # E5: 4,8 => UNS
* INC # E6: 2,9 => UNS
* INC # A5: 2,9 => UNS
* DIS # I5: 2,9 => CTR => I5: 1,6
* INC # I5: 1,6 => UNS
* INC # D3: 2,9 => UNS
* DIS # D3: 6 => CTR => D3: 2,9
* DIS # E4: 2,8 => CTR => E4: 3,4,9
* INC # E4: 3,4,9 => UNS
* DIS # E5: 2,8 => CTR => E5: 4,9
* INC # E5: 4,9 => UNS
* INC # E6: 2,8 => UNS
* INC # A5: 2,8 => UNS
* DIS # G5: 2,8 => CTR => G5: 1,4,6
* INC # G5: 1,4,6 => UNS
* DIS # G4: 4,8 => CTR => G4: 2,5,6
* INC # G4: 2,5,6 => UNS
* PRF # G5: 4,8 => SOL
* INC # G5: 1,2,6 => UNS
* INC # G6: 4,8 => UNS
* INC # B4: 4,8 => UNS
* DIS # C4: 4,8 => CTR => C4: 2,6
* INC # C4: 2,6 => UNS
* DIS # E4: 4,8 => CTR => E4: 2,3,9
* INC # E4: 2,3,9 => UNS
* DIS # I4: 2,9 => CTR => I4: 5,6
* INC # I4: 5,6 => UNS
* DIS # I5: 2,9 => CTR => I5: 1,6
* INC # I5: 1,6 => UNS
* INC # A6: 2,9 => UNS
* INC # E6: 2,9 => UNS
* INC # B7: 2,8 => UNS
* DIS # C8: 2,8 => CTR => C8: 4
* INC # C8: 4 => UNS
* INC # E8: 2,8 => UNS
* DIS # E8: 5 => CTR => E8: 2,8
* INC # A2: 2,8 => UNS
* DIS # A4: 2,8 => CTR => A4: 3,6,9
* INC # A4: 3,6,9 => UNS
* INC # A5: 2,8 => UNS
* DIS # A6: 2,8 => CTR => A6: 3,9
* INC # A6: 3,9 => UNS
* INC # B7: 8,9 => UNS
* DIS # B7: 2,4 => CTR => B7: 8,9
* DIS # E7: 2,6 => CTR => E7: 5,8
* INC # E7: 5,8 => UNS
* INC # D3: 2,6 => UNS
* PRF # D3: 9 => SOL
* DIS # E7: 2,8 => CTR => E7: 5,6
* INC # E7: 5,6 => UNS
* INC # E8: 2,8 => UNS
* INC # B7: 2,8 => UNS
* INC # B7: 4,9 => UNS
* PRF # G7: 4,8 => SOL
* INC # G7: 5,9 => UNS
* DIS # G8: 4,8 => CTR => G8: 1,5
* INC # G8: 1,5 => UNS
* DIS # B7: 4,8 => CTR => B7: 2,9
* INC # B7: 2,9 => UNS
* INC # G8: 1,5 => UNS
* DIS # G8: 4,8 => CTR => G8: 1,5
* INC # G7: 8,9 => UNS
* DIS # G7: 4,5 => CTR => G7: 8,9
* CNT  89 HDP CHAINS /  89 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 2,9 => UNS
* DIS # C1: 6 => CTR => C1: 2,9
* INC C1: 2,9 # D3: 2,9 => UNS
* DIS C1: 2,9 # E3: 2,9 => CTR => E3: 6
* INC C1: 2,9 + E3: 6 # B7: 2,9 => UNS
* DIS C1: 2,9 + E3: 6 # B7: 4,8 => CTR => B7: 2,9
* PRF C1: 2,9 + E3: 6 + B7: 2,9 # E5: 2,9 => SOL
* STA C1: 2,9 + E3: 6 + B7: 2,9 + E5: 2,9
* CNT   7 HDP CHAINS /   7 HYP OPENED