Analysis of zz-sudoku-de-707313-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 93...54..7..41...3.....61....9.6...4.7.....3.5...8.6....86.....4...28..6..39...25 initial

Autosolve

position: 9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C2: 2,6 => SOL
* DIS # C2: 5 => CTR => C2: 2,6
* DIS # C3: 2,4 => CTR => C3: 5
* PRF # C3: 5 => SOL
* DIS # B6: 1 => CTR => B6: 2,4
* DIS # F5: 2,9 => CTR => F5: 1,4
* DIS # F6: 2,9 => CTR => F6: 1,3,4
* PRF # D6: 1,7 => SOL
* PRF # H3: 7 => SOL
* DIS # G5: 5,9 => CTR => G5: 2
* PRF # H3: 7,9 => SOL
* DIS # H3: 5 => CTR => H3: 7,9
* DIS # I6: 7,9 => CTR => I6: 1
* PRF # I6: 1 => SOL
* PRF # I7: 7,9 => SOL
* DIS # I7: 1 => CTR => I7: 7,9
* DIS # C5: 2,4 => CTR => C5: 6
* DIS # F6: 2,4 => CTR => F6: 1,3,9
* DIS # C3: 2,4 => CTR => C3: 5
* PRF # C3: 5 => SOL
* PRF # D4: 1,2 => SOL
* DIS # F5: 1,2 => CTR => F5: 4,9
* DIS # D6: 1,2 => CTR => D6: 3,7
* DIS # F6: 1,2 => CTR => F6: 3,4,9
* DIS # G5: 5,9 => CTR => G5: 2
* PRF # D8: 3,5 => SOL
* DIS # D8: 1 => CTR => D8: 3,5
* PRF # D8: 1,3 => SOL
* DIS # D8: 5 => CTR => D8: 1,3
* PRF # F6: 1,3 => SOL
* DIS # F6: 2,4,9 => CTR => F6: 1,3
* PRF # G7: 3,9 => SOL
* PRF # I7: 7 => SOL
* CNT  33 HDP CHAINS /  52 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C2: 2,6 => SOL
* STA C2: 2,6
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

93...54..7..41...3.....61....9.6...4.7.....3.5...8.6....86.....4...28..6..39...25 initial
9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825 autosolve
931875462762419583845236179389162754176594238524783691298651347457328916613947825 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
B2: 2,6
B3: 2,4
F2: 2,9
D3: 2,3
E3: 3,9
G2: 5,9
I3: 7,9
A5: 1,6
C6: 2,4
F4: 1,2
E5: 5,9
B7: 5,9
B8: 5,9
A9: 1,6
B9: 1,6
E7: 3,5
F7: 1,3
G8: 3,9
H8: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A5,B6: 1.. / A5 = 1  => 18 pairs (_) / B6 = 1  =>  0 pairs (X)
A9,B9: 1.. / A9 = 1  =>  0 pairs (X) / B9 = 1  => 18 pairs (_)
F7,D8: 1.. / F7 = 1  =>  0 pairs (*) / D8 = 1  =>  0 pairs (X)
I7,H8: 1.. / I7 = 1  =>  0 pairs (X) / H8 = 1  =>  0 pairs (_)
F7,I7: 1.. / F7 = 1  =>  0 pairs (*) / I7 = 1  =>  0 pairs (X)
D8,H8: 1.. / D8 = 1  =>  0 pairs (X) / H8 = 1  =>  0 pairs (_)
A5,A9: 1.. / A5 = 1  => 18 pairs (_) / A9 = 1  =>  0 pairs (X)
B6,B9: 1.. / B6 = 1  =>  0 pairs (X) / B9 = 1  => 18 pairs (_)
I6,I7: 1.. / I6 = 1  =>  0 pairs (*) / I7 = 1  =>  0 pairs (X)
F2,D3: 2.. / F2 = 2  =>  0 pairs (X) / D3 = 2  =>  0 pairs (_)
G4,G5: 2.. / G4 = 2  =>  0 pairs (X) / G5 = 2  => 22 pairs (_)
D3,E3: 3.. / D3 = 3  =>  0 pairs (X) / E3 = 3  =>  0 pairs (_)
D6,F6: 3.. / D6 = 3  =>  0 pairs (X) / F6 = 3  =>  0 pairs (_)
G7,G8: 3.. / G7 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
D8,G8: 3.. / D8 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
E3,E7: 3.. / E3 = 3  =>  0 pairs (*) / E7 = 3  =>  0 pairs (X)
F6,F7: 3.. / F6 = 3  =>  0 pairs (*) / F7 = 3  =>  0 pairs (X)
B3,C3: 4.. / B3 = 4  => 20 pairs (_) / C3 = 4  =>  0 pairs (X)
F5,F6: 4.. / F5 = 4  => 20 pairs (_) / F6 = 4  =>  0 pairs (X)
C5,F5: 4.. / C5 = 4  =>  0 pairs (X) / F5 = 4  => 20 pairs (_)
B3,B6: 4.. / B3 = 4  => 20 pairs (_) / B6 = 4  =>  0 pairs (X)
C2,C3: 5.. / C2 = 5  =>  0 pairs (X) / C3 = 5  =>  0 pairs (_)
G2,H3: 5.. / G2 = 5  =>  0 pairs (*) / H3 = 5  =>  0 pairs (X)
B7,B8: 5.. / B7 = 5  =>  0 pairs (X) / B8 = 5  =>  0 pairs (_)
E7,D8: 5.. / E7 = 5  =>  0 pairs (*) / D8 = 5  =>  0 pairs (X)
C2,G2: 5.. / C2 = 5  =>  0 pairs (X) / G2 = 5  =>  0 pairs (_)
C3,H3: 5.. / C3 = 5  =>  0 pairs (*) / H3 = 5  =>  0 pairs (X)
B7,E7: 5.. / B7 = 5  =>  0 pairs (X) / E7 = 5  =>  0 pairs (_)
B8,D8: 5.. / B8 = 5  =>  0 pairs (*) / D8 = 5  =>  0 pairs (X)
E5,E7: 5.. / E5 = 5  =>  0 pairs (X) / E7 = 5  =>  0 pairs (_)
H3,H4: 5.. / H3 = 5  =>  0 pairs (X) / H4 = 5  =>  0 pairs (_)
B2,C2: 6.. / B2 = 6  => 18 pairs (_) / C2 = 6  =>  0 pairs (X)
A5,C5: 6.. / A5 = 6  =>  0 pairs (X) / C5 = 6  => 18 pairs (_)
A9,B9: 6.. / A9 = 6  => 18 pairs (_) / B9 = 6  =>  0 pairs (X)
A5,A9: 6.. / A5 = 6  =>  0 pairs (X) / A9 = 6  => 18 pairs (_)
B2,B9: 6.. / B2 = 6  => 18 pairs (_) / B9 = 6  =>  0 pairs (X)
C2,C5: 6.. / C2 = 6  =>  0 pairs (X) / C5 = 6  => 18 pairs (_)
H3,I3: 7.. / H3 = 7  =>  0 pairs (*) / I3 = 7  =>  0 pairs (X)
D4,D6: 7.. / D4 = 7  => 23 pairs (_) / D6 = 7  =>  0 pairs (*)
G7,I7: 7.. / G7 = 7  => 21 pairs (_) / I7 = 7  =>  0 pairs (*)
G4,G7: 7.. / G4 = 7  =>  0 pairs (*) / G7 = 7  =>  0 pairs (X)
F2,E3: 9.. / F2 = 9  =>  0 pairs (*) / E3 = 9  =>  0 pairs (X)
B7,B8: 9.. / B7 = 9  =>  0 pairs (*) / B8 = 9  =>  0 pairs (X)
F2,G2: 9.. / F2 = 9  =>  0 pairs (*) / G2 = 9  =>  0 pairs (X)
E3,E5: 9.. / E3 = 9  =>  0 pairs (X) / E5 = 9  =>  0 pairs (_)
* DURATION: 0:01:15.552426  START: 08:05:58.030092  END: 08:07:13.582518 2017-05-01
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B3,B7,B8,B9,C6,D3,E3,E5,E7,F2,F4,F7,G2,G8,H8,I3)
* 9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825
* PAIR B2: 2,6 BLK 1
C2: 2,6,5                                # reduction candidate for 2,6
C2: 2,6 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
C2: 5 => CTR
* 9318754627654129838..396157389.61.74176.5..385...8.6..2.86...4.4.7.28..6..3947825
* PAIR B3: 2,4 BLK 1
C3: 2,4,5                                # reduction candidate for 2,4
C3: 2,4 => CTR
* 9318754627.541.9838...96157389.6...4.76.5..385...8.6..2.86...4.4.7.28..6..3947825
C3: 5 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
* PAIR B3: 2,4 COL B
B6: 2,4,1                                # reduction candidate for 2,4
B6: 1 => CTR
* 93187546272641958384523617.389.6...4.7.....3851..8.6..2.86...414.7128396163947825
B6: 2,4                                  # 18 pairs
* PAIR F2: 2,9 COL F
F5: 2,9,1,4                              # reduction candidate for 2,9
F5: 2,9 => CTR
* 9318754627..41..838....61..389.6...4.74....385.2.846..2.86.3.414.7128396..3947825
F5: 1,4                                  # 20 pairs
F6: 2,9,1,3,4                            # reduction candidate for 2,9
F6: 2,9 => CTR
* 9318754627..41..838..2361.938976125417...4.385..38.6..2.86.3.414.7128396..3947825
F6: 1,3,4                                # 20 pairs
* PAIR D3: 2,3 COL D
D6: 2,3,1,7                              # reduction candidate for 2,3
D6: 1,7 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
D6: 2,3                                  # 25 pairs
* PAIR G2: 5,9 BLK 3
H3: 5,9,7                                # reduction candidate for 5,9
H3: 7 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
H3: 5,9                                  # 22 pairs
* PAIR G2: 5,9 COL G
G5: 5,9,2                                # reduction candidate for 5,9
G5: 5,9 => CTR
* 93187546276.41..838...361.9389.612.41762.4.385...8.6..2.86.37414.7128396613947825
G5: 2                                    # 22 pairs
* PAIR I3: 7,9 BLK 3
H3: 7,9,5                                # reduction candidate for 7,9
H3: 7,9 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
H3: 5 => CTR
* 9318754627.541.9838...96157389.6...4.76.5..385...8.6..2.86..74.4.7.283.6..3947825
* PAIR I3: 7,9 COL I
I6: 7,9,1                                # reduction candidate for 7,9
I6: 7,9 => CTR
* 9318754627..41..838...361.9389.6...4.7..9..385..38.6.7298653741457128396..3947825
I6: 1 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
I7: 7,9,1                                # reduction candidate for 7,9
I7: 7,9 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
I7: 1 => CTR
* 9318754627..41..838...361.9389.6...4.7..9..385..38.6.7298653741457128396..3947825
* PAIR C6: 2,4 BLK 4
C5: 2,4,6                                # reduction candidate for 2,4
C5: 2,4 => CTR
* 9318754627.641.5838.5..61..389.6..5467.....3851..8.6..2.86...414.7128396163947825
C5: 6                                    # 18 pairs
B6: 2,4,1                                # reduction candidate for 2,4
B6: 2,4                                  # 18 pairs
* PAIR C6: 2,4 ROW 6
F6: 2,4,1,3,9                            # reduction candidate for 2,4
F6: 2,4 => CTR
* 9318754627..41..838..2361.938976...4.7.59.2385..38.6.7298653741457128396..3947825
F6: 1,3,9                                # 20 pairs
* PAIR C6: 2,4 COL C
C3: 2,4,5                                # reduction candidate for 2,4
C3: 2,4 => CTR
* 9318754627.541.9838...96157389.6...4.76.5..385...8.6..2.86...4.4.7.28..6..3947825
C3: 5 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
* PAIR F4: 1,2 BLK 5
D4: 1,2,5,7                              # reduction candidate for 1,2
D4: 1,2 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
D4: 5,7                                  # 20 pairs
D5: 1,2,5                                # reduction candidate for 1,2
D5: 1,2                                  # 24 pairs
F5: 1,2,4,9                              # reduction candidate for 1,2
F5: 1,2 => CTR
* 9318754627.6419583845236179389.6...4.74....385.2.846..2.86.3.414.7128396..3947825
F5: 4,9                                  # 20 pairs
D6: 1,2,3,7                              # reduction candidate for 1,2
D6: 1,2 => CTR
* 9318754627..41..838....61..38976...4.7.....385...836..2.86.1749497528316..3947825
D6: 3,7                                  # 20 pairs
F6: 1,2,3,4,9                            # reduction candidate for 1,2
F6: 1,2 => CTR
* 9318754627..4195838.5236179389.6...4.7...4.385..38.6..2.86.3.414.7128396..3947825
F6: 3,4,9                                # 19 pairs
* PAIR E5: 5,9 ROW 5
G5: 5,9,2                                # reduction candidate for 5,9
G5: 5,9 => CTR
* 93187546276.41..838...361.9389.612.41762.4.385...8.6..2.86.37414.7128396613947825
G5: 2                                    # 22 pairs
* PAIR E7: 3,5 BLK 8
D8: 3,5,1                                # reduction candidate for 3,5
D8: 3,5 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
D8: 1 => CTR
* 9318754627..41..838...361.9389.6...4.7..9..385..38.6.7298653741457128396..3947825
* PAIR F7: 1,3 BLK 8
D8: 1,3,5                                # reduction candidate for 1,3
D8: 1,3 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
D8: 5 => CTR
* 9318754627..41..838....61..389162..4.7.....385...8.6..2.86.1.4.4.7528316..3947825
* PAIR F7: 1,3 COL F
F6: 1,3,2,4,9                            # reduction candidate for 1,3
F6: 1,3 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
F6: 2,4,9 => CTR
* 9318754627..41..838..2361.938976...4.7.59.2385..38.6.7298653741457128396..3947825
* PAIR G8: 3,9 BLK 9
G7: 3,9,7                                # reduction candidate for 3,9
G7: 3,9 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
G7: 7                                    # 21 pairs
* PAIR H8: 1,9 BLK 9
I7: 1,9,7                                # reduction candidate for 1,9
I7: 7 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
I7: 1,9                                  # 21 pairs
* PAIR H8: 1,9 COL H
H6: 1,9,7                                # reduction candidate for 1,9
H6: 7                                    # 24 pairs
H6: 1,9                                  # 23 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-707313-base-pr-000.dot
* REASONING
* PRF # C2: 2,6 => SOL
* DIS # C2: 5 => CTR => C2: 2,6
* DIS # C3: 2,4 => CTR => C3: 5
* PRF # C3: 5 => SOL
* DIS # B6: 1 => CTR => B6: 2,4
* DIS # F5: 2,9 => CTR => F5: 1,4
* DIS # F6: 2,9 => CTR => F6: 1,3,4
* PRF # D6: 1,7 => SOL
* PRF # H3: 7 => SOL
* DIS # G5: 5,9 => CTR => G5: 2
* PRF # H3: 7,9 => SOL
* DIS # H3: 5 => CTR => H3: 7,9
* DIS # I6: 7,9 => CTR => I6: 1
* PRF # I6: 1 => SOL
* PRF # I7: 7,9 => SOL
* DIS # I7: 1 => CTR => I7: 7,9
* DIS # C5: 2,4 => CTR => C5: 6
* DIS # F6: 2,4 => CTR => F6: 1,3,9
* DIS # C3: 2,4 => CTR => C3: 5
* PRF # C3: 5 => SOL
* PRF # D4: 1,2 => SOL
* DIS # F5: 1,2 => CTR => F5: 4,9
* DIS # D6: 1,2 => CTR => D6: 3,7
* DIS # F6: 1,2 => CTR => F6: 3,4,9
* DIS # G5: 5,9 => CTR => G5: 2
* PRF # D8: 3,5 => SOL
* DIS # D8: 1 => CTR => D8: 3,5
* PRF # D8: 1,3 => SOL
* DIS # D8: 5 => CTR => D8: 1,3
* PRF # F6: 1,3 => SOL
* DIS # F6: 2,4,9 => CTR => F6: 1,3
* PRF # G7: 3,9 => SOL
* PRF # I7: 7 => SOL
* CNT  33 HDP CHAINS /  52 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A9,B2,B3,B7,B8,B9,C6,D3,E3,E5,E7,F2,F4,F7,G2,G8,H8,I3)
* 9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825
* PAIR B2: 2,6 BLK 1
C2: 2,6,5                                # reduction candidate for 2,6
C2: 2,6 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
* DURATION: 0:00:02.237609  START: 08:08:04.802055  END: 08:08:07.039664 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-707313-base-pr-001.dot
* REASONING
* PRF # C2: 2,6 => SOL
* STA C2: 2,6
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokus.de/707313.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: 9318754627..41..838....61..389.6...4.7.....385...8.6..2.86...4.4.7.28..6..3947825
B2: 2,6
C2: 2,5,6                                # reduction candidate for 2,6
C2: 2,6 => SOLVED
* 931875462762419583845236179389162754176594238524783691298651347457328916613947825
* SOLVED!
--------------------------------------------------

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

* DISABLE VALUE:: H3 != 5

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

Solution

position: 931875462762419583845236179389162754176594238524783691298651347457328916613947825 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:

* PRF # C2: 2,6 => SOL
* DIS # C2: 5 => CTR => C2: 2,6
* DIS # C3: 2,4 => CTR => C3: 5
* PRF # C3: 5 => SOL
* INC # B6: 2,4 => UNS
* DIS # B6: 1 => CTR => B6: 2,4
* DIS # F5: 2,9 => CTR => F5: 1,4
* INC # F5: 1,4 => UNS
* DIS # F6: 2,9 => CTR => F6: 1,3,4
* INC # F6: 1,3,4 => UNS
* INC # D6: 2,3 => UNS
* PRF # D6: 1,7 => SOL
* INC # H3: 5,9 => UNS
* PRF # H3: 7 => SOL
* DIS # G5: 5,9 => CTR => G5: 2
* INC # G5: 2 => UNS
* PRF # H3: 7,9 => SOL
* DIS # H3: 5 => CTR => H3: 7,9
* DIS # I6: 7,9 => CTR => I6: 1
* PRF # I6: 1 => SOL
* PRF # I7: 7,9 => SOL
* DIS # I7: 1 => CTR => I7: 7,9
* DIS # C5: 2,4 => CTR => C5: 6
* INC # C5: 6 => UNS
* INC # B6: 2,4 => UNS
* DIS # F6: 2,4 => CTR => F6: 1,3,9
* INC # F6: 1,3,9 => UNS
* DIS # C3: 2,4 => CTR => C3: 5
* PRF # C3: 5 => SOL
* PRF # D4: 1,2 => SOL
* INC # D4: 5,7 => UNS
* INC # D5: 1,2 => UNS
* DIS # F5: 1,2 => CTR => F5: 4,9
* INC # F5: 4,9 => UNS
* DIS # D6: 1,2 => CTR => D6: 3,7
* INC # D6: 3,7 => UNS
* DIS # F6: 1,2 => CTR => F6: 3,4,9
* INC # F6: 3,4,9 => UNS
* DIS # G5: 5,9 => CTR => G5: 2
* INC # G5: 2 => UNS
* PRF # D8: 3,5 => SOL
* DIS # D8: 1 => CTR => D8: 3,5
* PRF # D8: 1,3 => SOL
* DIS # D8: 5 => CTR => D8: 1,3
* PRF # F6: 1,3 => SOL
* DIS # F6: 2,4,9 => CTR => F6: 1,3
* PRF # G7: 3,9 => SOL
* INC # G7: 7 => UNS
* INC # I7: 1,9 => UNS
* PRF # I7: 7 => SOL
* INC # H6: 1,9 => UNS
* INC # H6: 7 => UNS
* CNT  52 HDP CHAINS /  52 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C2: 2,6 => SOL
* STA C2: 2,6
* CNT   1 HDP CHAINS /   1 HYP OPENED