Analysis of zz-sudoku-de-657771-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ..2...5......9.8.16..31..2....9....7..72.69..5....8....5..64..87.4.2......3...4.. initial

Autosolve

position: ..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 3,4 => CTR => A1: 1,9
* DIS # B1: 3,4 => CTR => B1: 1,9
* DIS # H2: 6 => CTR => H2: 3,4
* DIS # B3: 8,9 => CTR => B3: 4
* DIS # D1: 6 => CTR => D1: 4,8
* DIS # D1: 4,6 => CTR => D1: 8
* PRF # D1: 8 => SOL
* DIS # H2: 3 => CTR => H2: 4,6
* DIS # I1: 4,9 => CTR => I1: 3,6
* DIS # B3: 8 => CTR => B3: 4,9
* DIS # H4: 3,4,5 => CTR => H4: 6,8
* PRF # E6: 4,7 => SOL
* DIS # E6: 3 => CTR => E6: 4,7
* PRF # A7: 1,9 => SOL
* DIS # B8: 1,9 => CTR => B8: 6,8
* DIS # H7: 1,9 => CTR => H7: 3,7
* DIS # C6: 6 => CTR => C6: 1,9
* PRF # D9: 1,7 => SOL
* DIS # H7: 1,7 => CTR => H7: 3,9
* PRF # H7: 3,9 => SOL
* DIS # D9: 7,8 => CTR => D9: 1,5
* DIS # H9: 1,6 => CTR => H9: 5,7
* DIS # B8: 1,6 => CTR => B8: 8,9
* CNT  23 HDP CHAINS /  46 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 # A1: 3,4 => CTR => A1: 1,9
* DIS A1: 1,9 # B1: 3,4 => CTR => B1: 1,9
* DIS A1: 1,9 + B1: 1,9 # D1: 6 => CTR => D1: 4,8
* PRF A1: 1,9 + B1: 1,9 + D1: 4,8 # E6: 4,7 => SOL
* STA A1: 1,9 + B1: 1,9 + D1: 4,8 + E6: 4,7
* CNT   4 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

..2...5......9.8.16..31..2....9....7..72.69..5....8....5..64..87.4.2......3...4.. initial
..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94.. autosolve
192847563375692841648315729426951387817236954539478612951764238784523196263189475 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
A2: 3,4
C3: 8,9
E1: 4,8
D2: 4,6
I3: 4,9
C4: 6,8
D6: 4,7
C7: 1,9
D7: 1,7
E9: 7,8
G8: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B1: 1.. / A1 = 1  =>  0 pairs (*) / B1 = 1  =>  0 pairs (X)
C6,C7: 1.. / C6 = 1  =>  0 pairs (X) / C7 = 1  =>  0 pairs (_)
G7,I9: 2.. / G7 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
A7,G7: 2.. / A7 = 2  => 16 pairs (_) / G7 = 2  =>  0 pairs (*)
I6,I9: 2.. / I6 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
G7,H7: 3.. / G7 = 3  =>  0 pairs (X) / H7 = 3  =>  0 pairs (_)
A2,H2: 3.. / A2 = 3  => 11 pairs (_) / H2 = 3  =>  0 pairs (X)
B3,I3: 4.. / B3 = 4  => 13 pairs (_) / I3 = 4  =>  0 pairs (X)
E4,E5: 5.. / E4 = 5  => 12 pairs (_) / E5 = 5  =>  0 pairs (X)
D8,D9: 5.. / D8 = 5  => 19 pairs (_) / D9 = 5  => 13 pairs (_)
E4,H4: 5.. / E4 = 5  => 12 pairs (_) / H4 = 5  =>  0 pairs (X)
D1,D2: 6.. / D1 = 6  =>  0 pairs (X) / D2 = 6  => 12 pairs (_)
C4,C6: 6.. / C4 = 6  => 12 pairs (_) / C6 = 6  =>  0 pairs (X)
B8,B9: 6.. / B8 = 6  =>  0 pairs (X) / B9 = 6  => 12 pairs (_)
D2,H2: 6.. / D2 = 6  => 12 pairs (_) / H2 = 6  =>  0 pairs (X)
D6,E6: 7.. / D6 = 7  =>  0 pairs (X) / E6 = 7  =>  0 pairs (_)
H7,H9: 7.. / H7 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
D7,H7: 7.. / D7 = 7  =>  0 pairs (*) / H7 = 7  =>  0 pairs (X)
E6,E9: 7.. / E6 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
B3,C3: 8.. / B3 = 8  =>  0 pairs (X) / C3 = 8  => 12 pairs (_)
D1,E1: 8.. / D1 = 8  =>  0 pairs (*) / E1 = 8  =>  0 pairs (X)
H4,H5: 8.. / H4 = 8  => 13 pairs (_) / H5 = 8  =>  0 pairs (X)
B8,D8: 8.. / B8 = 8  => 15 pairs (_) / D8 = 8  =>  0 pairs (X)
C3,C4: 8.. / C3 = 8  => 12 pairs (_) / C4 = 8  =>  0 pairs (X)
E1,E9: 8.. / E1 = 8  =>  0 pairs (X) / E9 = 8  =>  0 pairs (_)
B6,C6: 9.. / B6 = 9  => 14 pairs (_) / C6 = 9  =>  0 pairs (*)
A1,A7: 9.. / A1 = 9  => 13 pairs (_) / A7 = 9  =>  0 pairs (*)
* DURATION: 0:00:43.750007  START: 07:40:11.805657  END: 07:40:55.555664 2017-05-01
* CP COUNT: (27)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C3,C4,C7,D2,D6,D7,E1,E9,G8,I3)
* ..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94..
* PAIR A2: 3,4 BLK 1
A1: 3,4,1,9                              # reduction candidate for 3,4
A1: 3,4 => CTR
* .128475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947.
A1: 1,9                                  # 12 pairs
B1: 3,4,1,9                              # reduction candidate for 3,4
B1: 3,4 => CTR
* 1.28475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947.
B1: 1,9                                  # 12 pairs
* PAIR A2: 3,4 ROW 2
H2: 3,4,6                                # reduction candidate for 3,4
H2: 6 => CTR
* 9126875..375492861648315729..69512.7..72.69155.17.8....591643787.4.231....3.79452
H2: 3,4                                  # 12 pairs
* PAIR A2: 3,4 COL A
A4: 3,4,2,8                              # reduction candidate for 3,4
A4: 3,4                                  # 14 pairs
A5: 3,4,1,8                              # reduction candidate for 3,4
A5: 3,4                                  # 16 pairs
* PAIR C3: 8,9 BLK 1
B3: 8,9,4                                # reduction candidate for 8,9
B3: 8,9 => CTR
* ..28475.3.75.928.16..315724...9.1..7..72.69..5....8...9517642387.4.23.....3.8947.
B3: 4                                    # 13 pairs
* PAIR E1: 4,8 BLK 2
D1: 4,8,6                                # reduction candidate for 4,8
D1: 6 => CTR
* 9126875..375492861648315729..69512.7..72.69155.17.8....591643787.4.231....3.79452
D1: 4,8                                  # 12 pairs
* PAIR D2: 4,6 BLK 2
D1: 4,6,8                                # reduction candidate for 4,6
D1: 4,6 => CTR
* 912.875..375.928.1648315729..69.12.7..72.691.5.17.8....591643787.4.231....3.794.2
D1: 8 => SOLVED
* 192847563375692841648315729426951387817236954539478612951764238784523196263189475
* PAIR D2: 4,6 ROW 2
H2: 4,6,3                                # reduction candidate for 4,6
H2: 3 => CTR
* 9.2..75..4756928316..315724...9.1..7..72.69..5....8...25..643.87.4.23.....3..94.2
H2: 4,6                                  # 11 pairs
* PAIR I3: 4,9 BLK 3
H1: 4,9,3,6                              # reduction candidate for 4,9
H1: 4,9                                  # 14 pairs
I1: 4,9,3,6                              # reduction candidate for 4,9
I1: 4,9 => CTR
* 912..7534375492861648315729..69.12.7..72.69..5297.8...251.643.87.4.23....63..94.2
I1: 3,6                                  # 12 pairs
* PAIR I3: 4,9 ROW 3
B3: 4,9,8                                # reduction candidate for 4,9
B3: 8 => CTR
* ..2..75...75.928.1689315724..89.1..7..72.698.596..8...951764238764823.....3..94..
B3: 4,9                                  # 12 pairs
* PAIR C4: 6,8 ROW 4
H4: 6,8,3,4,5                            # reduction candidate for 6,8
H4: 3,4,5 => CTR
* ..28475...756928.16.831572.8.69.1.57..72569845.9478..2951764238784523...263189475
H4: 6,8                                  # 14 pairs
* PAIR D6: 4,7 BLK 5
E6: 4,7,3                                # reduction candidate for 4,7
E6: 4,7 => SOLVED
* 192847563375692841648315729426951387817236954539478612951764238784523196263189475
E6: 3 => CTR
* 912.875..375.928.1648315729..69.12.7..72.691.5.1738....591643787.4.231....3.794.2
* PAIR C7: 1,9 BLK 7
A7: 1,9,2                                # reduction candidate for 1,9
A7: 1,9 => SOLVED
* 192847563375692841648315729426951387817236954539478612951764238784523196263189475
A7: 2                                    # 16 pairs
B8: 1,9,6,8                              # reduction candidate for 1,9
B8: 1,9 => CTR
* ..2.875...75.928.16..31572....9.1..7..72.69..5..7.81..251.64..87.4823....63579412
B8: 6,8                                  # 12 pairs
* PAIR C7: 1,9 ROW 7
H7: 1,9,3,7                              # reduction candidate for 1,9
H7: 1,9 => CTR
* 9128475..3756928416483157294.69.12878.72.69..5..478...25.7643.8784.23...163589472
H7: 3,7                                  # 12 pairs
* PAIR C7: 1,9 COL C
C6: 1,9,6                                # reduction candidate for 1,9
C6: 6 => CTR
* ..28475...756928.16.9315724..89.1..7..72.698.596478...9517642387.4.23.....3.8947.
C6: 1,9                                  # 12 pairs
* PAIR D7: 1,7 BLK 8
D9: 1,7,5,8                              # reduction candidate for 1,7
D9: 1,7 => SOLVED
* 192847563375692841648315729426951387817236954539478612951764238784523196263189475
D9: 5,8                                  # 12 pairs
* PAIR D7: 1,7 ROW 7
H7: 1,7,3,9                              # reduction candidate for 1,7
H7: 1,7 => CTR
* 912..75..375.928.1648315729..69.12.7..72.69..5....8...259.643.87.4.23.....3..94.2
H7: 3,9 => SOLVED
* 192847563375692841648315729426951387817236954539478612951764238784523196263189475
* PAIR E9: 7,8 BLK 8
D9: 7,8,1,5                              # reduction candidate for 7,8
D9: 7,8 => CTR
* 912..75..375.928.1648315729..69512.7.372.69..5.1..8....591643787845231..163..9452
D9: 1,5                                  # 12 pairs
* PAIR G8: 1,6 BLK 9
H8: 1,6,5,9                              # reduction candidate for 1,6
H8: 1,6                                  # 18 pairs
H9: 1,6,5,7                              # reduction candidate for 1,6
H9: 1,6 => CTR
* 912.875.6375692841648315729..69.12.7..72.691.5.1..8...2591643787.4.231....3579462
H9: 5,7                                  # 12 pairs
* PAIR G8: 1,6 ROW 8
B8: 1,6,8,9                              # reduction candidate for 1,6
B8: 1,6 => CTR
* 912.875.6375692841648315729..69.12.7..72.691.5.17.8....591643787.48231....3579462
B8: 8,9                                  # 13 pairs
* PAIR G8: 1,6 COL G
G6: 1,6,2,3                              # reduction candidate for 1,6
G6: 1,6                                  # 14 pairs
G6: 2,3                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-657771-base-pr-000.dot
* REASONING
* DIS # A1: 3,4 => CTR => A1: 1,9
* DIS # B1: 3,4 => CTR => B1: 1,9
* DIS # H2: 6 => CTR => H2: 3,4
* DIS # B3: 8,9 => CTR => B3: 4
* DIS # D1: 6 => CTR => D1: 4,8
* DIS # D1: 4,6 => CTR => D1: 8
* PRF # D1: 8 => SOL
* DIS # H2: 3 => CTR => H2: 4,6
* DIS # I1: 4,9 => CTR => I1: 3,6
* DIS # B3: 8 => CTR => B3: 4,9
* DIS # H4: 3,4,5 => CTR => H4: 6,8
* PRF # E6: 4,7 => SOL
* DIS # E6: 3 => CTR => E6: 4,7
* PRF # A7: 1,9 => SOL
* DIS # B8: 1,9 => CTR => B8: 6,8
* DIS # H7: 1,9 => CTR => H7: 3,7
* DIS # C6: 6 => CTR => C6: 1,9
* PRF # D9: 1,7 => SOL
* DIS # H7: 1,7 => CTR => H7: 3,9
* PRF # H7: 3,9 => SOL
* DIS # D9: 7,8 => CTR => D9: 1,5
* DIS # H9: 1,6 => CTR => H9: 5,7
* DIS # B8: 1,6 => CTR => B8: 8,9
* CNT  23 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C3,C4,C7,D2,D6,D7,E1,E9,G8,I3)
* ..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94..
* PAIR A2: 3,4 BLK 1
A1: 3,4,1,9                              # reduction candidate for 3,4
A1: 3,4 => CTR
* .128475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947.
B1: 3,4,1,9                              # reduction candidate for 3,4
B1: 3,4 => CTR
* 1.28475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947.
* PAIR E1: 4,8 BLK 2
D1: 4,8,6                                # reduction candidate for 4,8
D1: 6 => CTR
* 9126875..375492861648315729..69512.7..72.69155.17.8....591643787.4.2319...3.79452
* PAIR D6: 4,7 BLK 5
E6: 4,7,3                                # reduction candidate for 4,7
E6: 4,7 => SOLVED
* 192847563375692841648315729426951387817236954539478612951764238784523196263189475
* DURATION: 0:00:06.183469  START: 07:41:33.104888  END: 07:41:39.288357 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-657771-base-pr-001.dot
* REASONING
* DIS # A1: 3,4 => CTR => A1: 1,9
* DIS A1: 1,9 # B1: 3,4 => CTR => B1: 1,9
* DIS A1: 1,9 + B1: 1,9 # D1: 6 => CTR => D1: 4,8
* PRF A1: 1,9 + B1: 1,9 + D1: 4,8 # E6: 4,7 => SOL
* STA A1: 1,9 + B1: 1,9 + D1: 4,8 + E6: 4,7
* CNT   4 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokus.de/657771.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: ..2..75...75.928.16..31572....9.1..7..72.69..5....8....5..64..87.4.23.....3..94..
A2: 3,4
A1: 1,3,4,9                              # reduction candidate for 3,4
A1: 3,4 => CTR
* .128475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947.
B1: 1,3,4,9                              # reduction candidate for 3,4
B1: 3,4 => CTR
* 1.28475.3.75.928.16..31572....9.1..7..72.69..5....8...9517642387.4.23.....3.8947.
E1: 4,8
D1: 4,6,8                                # reduction candidate for 4,8
D1: 6 => CTR
* 9126875..375492861648315729..69512.7..72.69155.17.8....591643787.4.2319...3.79452
D6: 4,7
E6: 3,4,7                                # reduction candidate for 4,7
E6: 4,7 => SOLVED
* 192847563375692841648315729426951387817236954539478612951764238784523196263189475
* SOLVED!

--------------------------------------------------
* AUTO ..
F1 = 7                # set value
F3: 5                 # naked single
C2 = 5                # set value
F2: 2                 # naked single
F2 = 2                # set value
F3 = 5                # set value
G3 = 7                # set value
F8 = 3                # set value
F4: 1                 # naked single
B2: 7..               # hidden single
F9: 9..               # hidden single
B2 = 7                # set value
F4 = 1                # set value
F9: 9                 # naked single
F9 = 9                # set value
Q2: 8.. = D1,E1: 8.. => A1,B1 != 8
Q7: 6.. = B8,B9: 6.. => B4,B6 != 6
Q5: 5.. = E4,E5: 5.. => E9 != 5
* UNSOLVED!

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

* DISABLE VALUE:: E6 != 3

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

Solution

position: 192847563375692841648315729426951387817236954539478612951764238784523196263189475 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:

* DIS # A1: 3,4 => CTR => A1: 1,9
* INC # A1: 1,9 => UNS
* DIS # B1: 3,4 => CTR => B1: 1,9
* INC # B1: 1,9 => UNS
* INC # H2: 3,4 => UNS
* DIS # H2: 6 => CTR => H2: 3,4
* INC # A4: 3,4 => UNS
* INC # A5: 3,4 => UNS
* DIS # B3: 8,9 => CTR => B3: 4
* INC # B3: 4 => UNS
* INC # D1: 4,8 => UNS
* DIS # D1: 6 => CTR => D1: 4,8
* DIS # D1: 4,6 => CTR => D1: 8
* PRF # D1: 8 => SOL
* INC # H2: 4,6 => UNS
* DIS # H2: 3 => CTR => H2: 4,6
* INC # H1: 4,9 => UNS
* DIS # I1: 4,9 => CTR => I1: 3,6
* INC # I1: 3,6 => UNS
* INC # B3: 4,9 => UNS
* DIS # B3: 8 => CTR => B3: 4,9
* INC # H4: 6,8 => UNS
* DIS # H4: 3,4,5 => CTR => H4: 6,8
* PRF # E6: 4,7 => SOL
* DIS # E6: 3 => CTR => E6: 4,7
* PRF # A7: 1,9 => SOL
* INC # A7: 2 => UNS
* DIS # B8: 1,9 => CTR => B8: 6,8
* INC # B8: 6,8 => UNS
* DIS # H7: 1,9 => CTR => H7: 3,7
* INC # H7: 3,7 => UNS
* INC # C6: 1,9 => UNS
* DIS # C6: 6 => CTR => C6: 1,9
* PRF # D9: 1,7 => SOL
* INC # D9: 5,8 => UNS
* DIS # H7: 1,7 => CTR => H7: 3,9
* PRF # H7: 3,9 => SOL
* DIS # D9: 7,8 => CTR => D9: 1,5
* INC # D9: 1,5 => UNS
* INC # H8: 1,6 => UNS
* DIS # H9: 1,6 => CTR => H9: 5,7
* INC # H9: 5,7 => UNS
* DIS # B8: 1,6 => CTR => B8: 8,9
* INC # B8: 8,9 => UNS
* INC # G6: 1,6 => UNS
* INC # G6: 2,3 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 3,4 => CTR => A1: 1,9
* DIS A1: 1,9 # B1: 3,4 => CTR => B1: 1,9
* INC A1: 1,9 + B1: 1,9 # D1: 4,8 => UNS
* DIS A1: 1,9 + B1: 1,9 # D1: 6 => CTR => D1: 4,8
* PRF A1: 1,9 + B1: 1,9 + D1: 4,8 # E6: 4,7 => SOL
* STA A1: 1,9 + B1: 1,9 + D1: 4,8 + E6: 4,7
* CNT   5 HDP CHAINS /   5 HYP OPENED