Analysis of zz-sudoku-de-772112-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 16..7.5.8..3.....44....6.9...52.8...9...5...3...3.12...8.9....13.....8..5.7.8..62 initial

Autosolve

position: 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A6: 7,8 => CTR => A6: 6
* PRF # A6: 6 => SOL
* PRF # A6: 6,7 => SOL
* DIS # A6: 8 => CTR => A6: 6,7
* DIS # G4: 1,7 => CTR => G4: 9
* PRF # G4: 9 => SOL
* PRF # H7: 5,7 => SOL
* PRF # C8: 4,6 => SOL
* DIS # C8: 1 => CTR => C8: 4,6
* DIS # B8: 4,9 => CTR => B8: 1
* PRF # B8: 1 => SOL
* PRF # F7: 3,4 => SOL
* DIS # H7: 3,7 => CTR => H7: 4,5
* PRF # H7: 4,5 => SOL
* PRF # H7: 4,5 => SOL
* DIS # H7: 3,7 => CTR => H7: 4,5
* PRF # F8: 4,5 => SOL
* DIS # F8: 2 => CTR => F8: 4,5
* CNT  18 HDP CHAINS /  20 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 # A6: 7,8 => CTR => A6: 6
* PRF A6: 6 => SOL
* STA A6: 6
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

16..7.5.8..3.....44....6.9...52.8...9...5...3...3.12...8.9....13.....8..5.7.8..62 initial
16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62 autosolve
169472538873519624452836197735248916921657483648391275284963751316725849597184362 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (30)
A2: 7,8
B2: 5,7
B3: 2,5
C3: 2,8
F1: 2,3
D2: 5,8
E2: 1,2
D3: 5,8
E3: 1,3
H1: 2,3
H2: 1,2
G3: 1,3
A4: 6,7
B5: 1,2
C5: 1,2
B6: 4,7
C6: 4,8
H4: 1,7
I4: 6,9
H6: 5,7
I6: 5,6
C7: 4,6
B9: 4,9
E7: 3,6
E8: 2,6
F9: 3,4
G7: 3,7
H8: 4,5
I8: 5,9
G9: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E2,E3: 1.. / E2 = 1  =>  0 pairs (*) / E3 = 1  =>  0 pairs (X)
H2,G3: 1.. / H2 = 1  =>  0 pairs (X) / G3 = 1  =>  0 pairs (_)
B5,C5: 1.. / B5 = 1  =>  0 pairs (X) / C5 = 1  =>  0 pairs (_)
G4,H4: 1.. / G4 = 1  =>  0 pairs (X) / H4 = 1  =>  0 pairs (_)
B8,C8: 1.. / B8 = 1  =>  0 pairs (*) / C8 = 1  =>  0 pairs (X)
E2,H2: 1.. / E2 = 1  =>  0 pairs (*) / H2 = 1  =>  0 pairs (X)
E3,G3: 1.. / E3 = 1  =>  0 pairs (X) / G3 = 1  =>  0 pairs (_)
B5,B8: 1.. / B5 = 1  =>  0 pairs (X) / B8 = 1  =>  0 pairs (_)
C5,C8: 1.. / C5 = 1  =>  0 pairs (*) / C8 = 1  =>  0 pairs (X)
G3,G4: 1.. / G3 = 1  =>  0 pairs (*) / G4 = 1  =>  0 pairs (X)
H2,H4: 1.. / H2 = 1  =>  0 pairs (X) / H4 = 1  =>  0 pairs (_)
B3,C3: 2.. / B3 = 2  =>  0 pairs (X) / C3 = 2  =>  0 pairs (_)
F1,E2: 2.. / F1 = 2  =>  0 pairs (*) / E2 = 2  =>  0 pairs (X)
H1,H2: 2.. / H1 = 2  =>  0 pairs (X) / H2 = 2  =>  0 pairs (_)
B5,C5: 2.. / B5 = 2  =>  0 pairs (*) / C5 = 2  =>  0 pairs (X)
E8,F8: 2.. / E8 = 2  =>  0 pairs (*) / F8 = 2  =>  0 pairs (X)
F1,H1: 2.. / F1 = 2  =>  0 pairs (*) / H1 = 2  =>  0 pairs (X)
E2,H2: 2.. / E2 = 2  =>  0 pairs (X) / H2 = 2  =>  0 pairs (_)
B3,B5: 2.. / B3 = 2  =>  0 pairs (X) / B5 = 2  =>  0 pairs (_)
C3,C5: 2.. / C3 = 2  =>  0 pairs (*) / C5 = 2  =>  0 pairs (X)
E2,E8: 2.. / E2 = 2  =>  0 pairs (X) / E8 = 2  =>  0 pairs (_)
F1,F8: 2.. / F1 = 2  =>  0 pairs (*) / F8 = 2  =>  0 pairs (X)
F1,E3: 3.. / F1 = 3  =>  0 pairs (X) / E3 = 3  =>  0 pairs (_)
H1,G3: 3.. / H1 = 3  =>  0 pairs (*) / G3 = 3  =>  0 pairs (X)
F1,H1: 3.. / F1 = 3  =>  0 pairs (X) / H1 = 3  =>  0 pairs (_)
E3,G3: 3.. / E3 = 3  =>  0 pairs (*) / G3 = 3  =>  0 pairs (X)
F9,G9: 3.. / F9 = 3  =>  0 pairs (X) / G9 = 3  =>  0 pairs (_)
E3,E7: 3.. / E3 = 3  =>  0 pairs (*) / E7 = 3  =>  0 pairs (X)
H1,H7: 3.. / H1 = 3  =>  0 pairs (*) / H7 = 3  =>  0 pairs (X)
B6,C6: 4.. / B6 = 4  =>  0 pairs (*) / C6 = 4  =>  0 pairs (X)
H7,H8: 4.. / H7 = 4  =>  0 pairs (X) / H8 = 4  => 32 pairs (_)
B9,F9: 4.. / B9 = 4  =>  0 pairs (X) / F9 = 4  =>  0 pairs (_)
B2,B3: 5.. / B2 = 5  =>  0 pairs (X) / B3 = 5  =>  0 pairs (_)
D2,D3: 5.. / D2 = 5  =>  0 pairs (*) / D3 = 5  =>  0 pairs (X)
H6,I6: 5.. / H6 = 5  =>  0 pairs (X) / I6 = 5  =>  0 pairs (_)
F7,F8: 5.. / F7 = 5  => 31 pairs (_) / F8 = 5  =>  0 pairs (*)
B2,D2: 5.. / B2 = 5  =>  0 pairs (X) / D2 = 5  =>  0 pairs (_)
B3,D3: 5.. / B3 = 5  =>  0 pairs (*) / D3 = 5  =>  0 pairs (X)
F7,H7: 5.. / F7 = 5  => 31 pairs (_) / H7 = 5  =>  0 pairs (*)
I6,I8: 5.. / I6 = 5  =>  0 pairs (*) / I8 = 5  =>  0 pairs (X)
A4,A6: 6.. / A4 = 6  =>  0 pairs (X) / A6 = 6  =>  0 pairs (_)
I4,I6: 6.. / I4 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
C7,C8: 6.. / C7 = 6  =>  0 pairs (X) / C8 = 6  =>  0 pairs (_)
E7,E8: 6.. / E7 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
A4,I4: 6.. / A4 = 6  =>  0 pairs (X) / I4 = 6  =>  0 pairs (_)
A6,I6: 6.. / A6 = 6  =>  0 pairs (*) / I6 = 6  =>  0 pairs (X)
C7,E7: 6.. / C7 = 6  =>  0 pairs (X) / E7 = 6  =>  0 pairs (_)
C8,E8: 6.. / C8 = 6  =>  0 pairs (*) / E8 = 6  =>  0 pairs (X)
A2,B2: 7.. / A2 = 7  =>  0 pairs (X) / B2 = 7  =>  0 pairs (_)
G7,H7: 7.. / G7 = 7  => 30 pairs (_) / H7 = 7  =>  0 pairs (X)
B2,B6: 7.. / B2 = 7  =>  0 pairs (*) / B6 = 7  =>  0 pairs (X)
G4,G7: 7.. / G4 = 7  =>  0 pairs (X) / G7 = 7  => 30 pairs (_)
A2,C3: 8.. / A2 = 8  =>  0 pairs (*) / C3 = 8  =>  0 pairs (X)
D2,D3: 8.. / D2 = 8  =>  0 pairs (X) / D3 = 8  =>  0 pairs (_)
A6,C6: 8.. / A6 = 8  =>  0 pairs (X) / C6 = 8  =>  0 pairs (_)
A2,D2: 8.. / A2 = 8  =>  0 pairs (*) / D2 = 8  =>  0 pairs (X)
C3,D3: 8.. / C3 = 8  =>  0 pairs (X) / D3 = 8  =>  0 pairs (_)
A2,A6: 8.. / A2 = 8  =>  0 pairs (*) / A6 = 8  =>  0 pairs (X)
C3,C6: 8.. / C3 = 8  =>  0 pairs (X) / C6 = 8  =>  0 pairs (_)
G4,I4: 9.. / G4 = 9  =>  0 pairs (*) / I4 = 9  =>  0 pairs (X)
B8,B9: 9.. / B8 = 9  =>  0 pairs (X) / B9 = 9  =>  0 pairs (_)
I8,G9: 9.. / I8 = 9  =>  0 pairs (*) / G9 = 9  =>  0 pairs (X)
B8,I8: 9.. / B8 = 9  =>  0 pairs (X) / I8 = 9  =>  0 pairs (_)
B9,G9: 9.. / B9 = 9  =>  0 pairs (*) / G9 = 9  =>  0 pairs (X)
G4,G9: 9.. / G4 = 9  =>  0 pairs (*) / G9 = 9  =>  0 pairs (X)
I4,I8: 9.. / I4 = 9  =>  0 pairs (X) / I8 = 9  =>  0 pairs (_)
* DURATION: 0:01:56.432082  START: 08:42:22.954354  END: 08:44:19.386436 2017-05-01
* CP COUNT: (66)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,B3,B5,B6,B9,C3,C5,C6,C7,D2,D3,E2,E3,E7,E8,F1,F9,G3,G7,G9,H1,H2,H4,H6,H8,I4,I6,I8)
* 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62
* PAIR A2: 7,8 COL A
A6: 7,8,6                                # reduction candidate for 7,8
A6: 7,8 => CTR
* 16947.5.8..3..96.44....6.97635248..99..657483...3912.628.9....1391762845547183.62
A6: 6 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
* PAIR A4: 6,7 BLK 4
A6: 6,7,8                                # reduction candidate for 6,7
A6: 6,7 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
A6: 8 => CTR
* 16947.5.8..3..96.44....6.97635248..99..6574838743912562869357.13..7..8..5.718..62
* PAIR H4: 1,7 BLK 6
G4: 1,7,9                                # reduction candidate for 1,7
G4: 1,7 => CTR
* 16947.5.8..3..96.44....6.97.35248..99..657483...3912.628.9....1391762845547183.62
G4: 9 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
* PAIR H6: 5,7 COL H
H7: 5,7,3,4                              # reduction candidate for 5,7
H7: 5,7 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
H7: 3,4                                  # 32 pairs
* PAIR C7: 4,6 BLK 7
C8: 4,6,1                                # reduction candidate for 4,6
C8: 4,6 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
C8: 1 => CTR
* 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28693.7.13.17628..5.7184362
* PAIR B9: 4,9 BLK 7
B8: 4,9,1                                # reduction candidate for 4,9
B8: 4,9 => CTR
* 169473528..3.29614428516397.352481799126574838743912562869357413.17628..5.718..62
B8: 1 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
* PAIR F9: 3,4 BLK 8
F7: 3,4,5                                # reduction candidate for 3,4
F7: 3,4 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
F7: 5                                    # 31 pairs
* PAIR G7: 3,7 BLK 9
H7: 3,7,4,5                              # reduction candidate for 3,7
H7: 3,7 => CTR
* 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9.5..13..7..8455.7184.62
H7: 4,5 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
* PAIR H8: 4,5 BLK 9
H7: 4,5,3,7                              # reduction candidate for 4,5
H7: 4,5 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
H7: 3,7 => CTR
* 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9.5..13..7..8455.7184.62
* PAIR H8: 4,5 ROW 8
F8: 4,5,2                                # reduction candidate for 4,5
F8: 4,5 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
F8: 2 => CTR
* 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9.5..13..7.28..5.7184362
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-772112-base-pr-000.dot
* REASONING
* DIS # A6: 7,8 => CTR => A6: 6
* PRF # A6: 6 => SOL
* PRF # A6: 6,7 => SOL
* DIS # A6: 8 => CTR => A6: 6,7
* DIS # G4: 1,7 => CTR => G4: 9
* PRF # G4: 9 => SOL
* PRF # H7: 5,7 => SOL
* PRF # C8: 4,6 => SOL
* DIS # C8: 1 => CTR => C8: 4,6
* DIS # B8: 4,9 => CTR => B8: 1
* PRF # B8: 1 => SOL
* PRF # F7: 3,4 => SOL
* DIS # H7: 3,7 => CTR => H7: 4,5
* PRF # H7: 4,5 => SOL
* PRF # H7: 4,5 => SOL
* DIS # H7: 3,7 => CTR => H7: 4,5
* PRF # F8: 4,5 => SOL
* DIS # F8: 2 => CTR => F8: 4,5
* CNT  18 HDP CHAINS /  20 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,B3,B5,B6,B9,C3,C5,C6,C7,D2,D3,E2,E3,E7,E8,F1,F9,G3,G7,G9,H1,H2,H4,H6,H8,I4,I6,I8)
* 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62
* PAIR A2: 7,8 COL A
A6: 7,8,6                                # reduction candidate for 7,8
A6: 7,8 => CTR
* 16947.5.8..3..96.44....6.97635248..99..657483...3912.628.9....1391762845547183.62
A6: 6 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
* DURATION: 0:00:03.089118  START: 08:44:43.741565  END: 08:44:46.830683 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-772112-base-pr-001.dot
* REASONING
* DIS # A6: 7,8 => CTR => A6: 6
* PRF A6: 6 => SOL
* STA A6: 6
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokus.de/772112.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: 16947.5.8..3..96.44....6.97.35248...9..657483...3912..28.9....13..7..8..5.718..62
A2: 7,8
A6: 6,7,8                                # reduction candidate for 7,8
A6: 7,8 => CTR
* 16947.5.8..3..96.44....6.97635248..99..657483...3912.628.9....1391762845547183.62
A6: 6 => SOLVED
* 169472538873519624452836197735248916921657483648391275284963751316725849597184362
* SOLVED!
--------------------------------------------------

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

xwing |:guess:| highlight 7
H6 != 7 => A2,B2,A6,B6: 7.. => A4 != 7

H6 != 7 => CTR
=> H6 = 7

* AUTO ..
* SOLVED!

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

Solution

position: 169472538873519624452836197735248916921657483648391275284963751316725849597184362 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 # A6: 7,8 => CTR => A6: 6
* PRF # A6: 6 => SOL
* PRF # A6: 6,7 => SOL
* DIS # A6: 8 => CTR => A6: 6,7
* DIS # G4: 1,7 => CTR => G4: 9
* PRF # G4: 9 => SOL
* PRF # H7: 5,7 => SOL
* INC # H7: 3,4 => UNS
* PRF # C8: 4,6 => SOL
* DIS # C8: 1 => CTR => C8: 4,6
* DIS # B8: 4,9 => CTR => B8: 1
* PRF # B8: 1 => SOL
* PRF # F7: 3,4 => SOL
* INC # F7: 5 => UNS
* DIS # H7: 3,7 => CTR => H7: 4,5
* PRF # H7: 4,5 => SOL
* PRF # H7: 4,5 => SOL
* DIS # H7: 3,7 => CTR => H7: 4,5
* PRF # F8: 4,5 => SOL
* DIS # F8: 2 => CTR => F8: 4,5
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A6: 7,8 => CTR => A6: 6
* PRF A6: 6 => SOL
* STA A6: 6
* CNT   2 HDP CHAINS /   1 HYP OPENED