Analysis of zz-www.sudokuwiki.org-0012-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=12

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=12

position: 9..851.....79.6.....5.2....82.....3...1...8...4.....27....6.2.....1.53.....782..6 initial

Autosolve

position: 9..8517....79.6.....5.27...82..7..3...12..8...4..18.27....6.2.....1.53.....782..6 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C1: 3,6 => SOL
* DIS # H3: 4,6 => CTR => H3: 1,8,9
* DIS # H5: 5,9 => CTR => H5: 4,6
* PRF # C6: 6,9 => SOL
* DIS # C8: 6,9 => CTR => C8: 2,4,8
* PRF # G4: 4,9 => SOL
* DIS # I4: 4,9 => CTR => I4: 1,5
* PRF # G6: 5,6 => SOL
* DIS # C8: 4,9 => CTR => C8: 2,6,8
* CNT   9 HDP CHAINS /  47 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 # C1: 3,6 => SOL
* STA C1: 3,6
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

9..851.....79.6.....5.2....82.....3...1...8...4.....27....6.2.....1.53.....782..6 initial
9..8517....79.6.....5.27...82..7..3...12..8...4..18.27....6.2.....1.53.....782..6 autosolve
963851742287946153415327698826579431751234869349618527198463275672195384534782916 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
B1: 3,6
E2: 3,4
D3: 3,4
H1: 4,6
C4: 6,9
D4: 5,6
F4: 4,9
D6: 5,6
D7: 3,4
E8: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,I4: 1.. / G4 = 1  => 11 pairs (_) / I4 = 1  => 10 pairs (_)
C1,A2: 2.. / C1 = 2  => 12 pairs (_) / A2 = 2  => 11 pairs (_)
I1,I2: 2.. / I1 = 2  => 11 pairs (_) / I2 = 2  => 12 pairs (_)
A8,C8: 2.. / A8 = 2  => 12 pairs (_) / C8 = 2  => 11 pairs (_)
C1,I1: 2.. / C1 = 2  => 12 pairs (_) / I1 = 2  => 11 pairs (_)
A2,I2: 2.. / A2 = 2  => 11 pairs (_) / I2 = 2  => 12 pairs (_)
A2,A8: 2.. / A2 = 2  => 11 pairs (_) / A8 = 2  => 12 pairs (_)
C1,C8: 2.. / C1 = 2  => 12 pairs (_) / C8 = 2  => 11 pairs (_)
E2,D3: 3.. / E2 = 3  => 12 pairs (_) / D3 = 3  => 13 pairs (_)
A6,C6: 3.. / A6 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
E5,F5: 3.. / E5 = 3  => 13 pairs (_) / F5 = 3  => 12 pairs (_)
D7,F7: 3.. / D7 = 3  => 12 pairs (_) / F7 = 3  => 13 pairs (_)
D3,D7: 3.. / D3 = 3  => 13 pairs (_) / D7 = 3  => 12 pairs (_)
E2,E5: 3.. / E2 = 3  => 12 pairs (_) / E5 = 3  => 13 pairs (_)
F5,F7: 3.. / F5 = 3  => 12 pairs (_) / F7 = 3  => 13 pairs (_)
E2,D3: 4.. / E2 = 4  => 13 pairs (_) / D3 = 4  => 12 pairs (_)
D3,D7: 4.. / D3 = 4  => 12 pairs (_) / D7 = 4  => 13 pairs (_)
D4,D6: 5.. / D4 = 5  => 11 pairs (_) / D6 = 5  =>  0 pairs (X)
D4,D6: 6.. / D4 = 6  =>  0 pairs (X) / D6 = 6  => 11 pairs (_)
A5,B5: 7.. / A5 = 7  => 10 pairs (_) / B5 = 7  => 14 pairs (_)
H7,H8: 7.. / H7 = 7  => 12 pairs (_) / H8 = 7  => 11 pairs (_)
B2,B3: 8.. / B2 = 8  => 10 pairs (_) / B3 = 8  => 11 pairs (_)
C7,C8: 8.. / C7 = 8  => 10 pairs (_) / C8 = 8  =>  0 pairs (X)
F7,E8: 9.. / F7 = 9  => 12 pairs (_) / E8 = 9  => 14 pairs (_)
C6,G6: 9.. / C6 = 9  =>  0 pairs (*) / G6 = 9  =>  0 pairs (X)
E5,E8: 9.. / E5 = 9  => 12 pairs (_) / E8 = 9  => 14 pairs (_)
* DURATION: 0:00:34.672572  START: 03:35:37.370408  END: 03:36:12.042980 2017-05-01
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C4,D3,D4,D6,D7,E2,E8,F4,H1)
* 9..8517....79.6.....5.27...82..7..3...12..8...4..18.27....6.2.....1.53.....782..6
* PAIR B1: 3,6 BLK 1
C1: 3,6,2,4                              # reduction candidate for 3,6
C1: 3,6 => SOLVED
* 963851742287946153415327698826579431751234869349618527198463275672195384534782916
C1: 2,4                                  # 11 pairs
A3: 3,6,1,4                              # reduction candidate for 3,6
A3: 3,6                                  # 15 pairs
B3: 3,6,1,8                              # reduction candidate for 3,6
B3: 3,6                                  # 16 pairs
* PAIR E2: 3,4 ROW 2
A2: 3,4,1,2                              # reduction candidate for 3,4
A2: 3,4                                  # 14 pairs
I2: 3,4,1,2,5,8                          # reduction candidate for 3,4
I2: 3,4                                  # 13 pairs
* PAIR E2: 3,4 COL E
E5: 3,4,9                                # reduction candidate for 3,4
E5: 3,4                                  # 14 pairs
E5: 9                                    # 12 pairs
* PAIR D3: 3,4 ROW 3
A3: 3,4,1,6                              # reduction candidate for 3,4
A3: 3,4                                  # 13 pairs
I3: 3,4,1,8,9                            # reduction candidate for 3,4
I3: 3,4                                  # 14 pairs
* PAIR H1: 4,6 BLK 3
G3: 4,6,1,9                              # reduction candidate for 4,6
G3: 4,6                                  # 13 pairs
H3: 4,6,1,8,9                            # reduction candidate for 4,6
H3: 4,6 => CTR
* 9..8517....79.6.....5.27...829.74.3...12..8.4.43.18927....6.2.....1.53....4782..6
H3: 1,8,9                                # 10 pairs
* PAIR H1: 4,6 ROW 1
C1: 4,6,2,3                              # reduction candidate for 4,6
C1: 2,3                                  # 12 pairs
C1: 4,6                                  # 11 pairs
* PAIR H1: 4,6 COL H
H5: 4,6,5,9                              # reduction candidate for 4,6
H5: 5,9 => CTR
* 9..85174...79.6.....5.27169829.74631..12..854543618927..84632.5...1.53....4782..6
H5: 4,6                                  # 11 pairs
* PAIR C4: 6,9 BLK 4
B5: 6,9,5,7                              # reduction candidate for 6,9
B5: 6,9                                  # 13 pairs
C6: 6,9,3                                # reduction candidate for 6,9
C6: 6,9 => SOLVED
* 963851742287946153415327698826579431751234869349618527198463275672195384534782916
C6: 3                                    # 13 pairs
* PAIR C4: 6,9 ROW 4
G4: 6,9,1,4,5                            # reduction candidate for 6,9
G4: 6,9                                  # 17 pairs
G4: 1,4,5                                # 10 pairs
* PAIR C4: 6,9 COL C
C8: 6,9,2,4,8                            # reduction candidate for 6,9
C8: 6,9 => CTR
* 962851743..79.6..2..5.276..8265794317912..8655436189271.8.6.2..27914538...4782..6
C8: 2,4,8                                # 10 pairs
* PAIR D4: 5,6 ROW 4
G4: 5,6,1,4,9                            # reduction candidate for 5,6
G4: 5,6                                  # 16 pairs
G4: 1,4,9                                # 10 pairs
* PAIR F4: 4,9 BLK 5
E5: 4,9,3                                # reduction candidate for 4,9
E5: 4,9                                  # 12 pairs
F5: 4,9,3                                # reduction candidate for 4,9
F5: 4,9                                  # 13 pairs
* PAIR F4: 4,9 ROW 4
G4: 4,9,1,5,6                            # reduction candidate for 4,9
G4: 4,9 => SOLVED
* 963851742287946153415327698826579431751234869349618527198463275672195384534782916
G4: 1,5,6                                # 10 pairs
I4: 4,9,1,5                              # reduction candidate for 4,9
I4: 4,9 => CTR
* 96.8517422.79465..4.53276..82657.13...123.865543618.27....6.2..6.21.53.....782..6
I4: 1,5                                  # 11 pairs
* PAIR F4: 4,9 COL F
F7: 4,9,3                                # reduction candidate for 4,9
F7: 3                                    # 13 pairs
F7: 4,9                                  # 12 pairs
* PAIR D6: 5,6 ROW 6
A6: 5,6,3                                # reduction candidate for 5,6
A6: 5,6                                  # 13 pairs
G6: 5,6,9                                # reduction candidate for 5,6
G6: 5,6 => SOLVED
* 963851742287946153415327698826579431751234869349618527198463275672195384534782916
G6: 9                                    # 12 pairs
* PAIR D7: 3,4 BLK 8
F7: 3,4,9                                # reduction candidate for 3,4
F7: 3,4                                  # 14 pairs
F7: 9                                    # 12 pairs
* PAIR E8: 4,9 BLK 8
F7: 4,9,3                                # reduction candidate for 4,9
F7: 3                                    # 13 pairs
F7: 4,9                                  # 12 pairs
* PAIR E8: 4,9 ROW 8
C8: 4,9,2,6,8                            # reduction candidate for 4,9
C8: 4,9 => CTR
* 932851764..7936..26.5427..382..7..3...12.38...4..18.27..836.2..26.1.5378...782..6
C8: 2,6,8                                # 10 pairs
H8: 4,9,7,8                              # reduction candidate for 4,9
H8: 4,9                                  # 13 pairs
I8: 4,9,8                                # reduction candidate for 4,9
I8: 4,9                                  # 13 pairs
* PAIR E8: 4,9 COL E
E5: 4,9,3                                # reduction candidate for 4,9
E5: 3                                    # 13 pairs
E5: 4,9                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0012-base-pr-000.dot
* REASONING
* PRF # C1: 3,6 => SOL
* DIS # H3: 4,6 => CTR => H3: 1,8,9
* DIS # H5: 5,9 => CTR => H5: 4,6
* PRF # C6: 6,9 => SOL
* DIS # C8: 6,9 => CTR => C8: 2,4,8
* PRF # G4: 4,9 => SOL
* DIS # I4: 4,9 => CTR => I4: 1,5
* PRF # G6: 5,6 => SOL
* DIS # C8: 4,9 => CTR => C8: 2,6,8
* CNT   9 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C4,D3,D4,D6,D7,E2,E8,F4,H1)
* 9..8517....79.6.....5.27...82..7..3...12..8...4..18.27....6.2.....1.53.....782..6
* PAIR B1: 3,6 BLK 1
C1: 3,6,2,4                              # reduction candidate for 3,6
C1: 3,6 => SOLVED
* 963851742287946153415327698826579431751234869349618527198463275672195384534782916
* DURATION: 0:00:02.536880  START: 03:36:49.953972  END: 03:36:52.490852 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0012-base-pr-001.dot
* REASONING
* PRF # C1: 3,6 => SOL
* STA C1: 3,6
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=12

Solution

position: 963851742287946153415327698826579431751234869349618527198463275672195384534782916 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 # C1: 3,6 => SOL
* INC # C1: 2,4 => UNS
* INC # A3: 3,6 => UNS
* INC # B3: 3,6 => UNS
* INC # A2: 3,4 => UNS
* INC # I2: 3,4 => UNS
* INC # E5: 3,4 => UNS
* INC # E5: 9 => UNS
* INC # A3: 3,4 => UNS
* INC # I3: 3,4 => UNS
* INC # G3: 4,6 => UNS
* DIS # H3: 4,6 => CTR => H3: 1,8,9
* INC # H3: 1,8,9 => UNS
* INC # C1: 4,6 => UNS
* INC # C1: 2,3 => UNS
* INC # H5: 4,6 => UNS
* DIS # H5: 5,9 => CTR => H5: 4,6
* INC # B5: 6,9 => UNS
* PRF # C6: 6,9 => SOL
* INC # C6: 3 => UNS
* INC # G4: 6,9 => UNS
* INC # G4: 1,4,5 => UNS
* DIS # C8: 6,9 => CTR => C8: 2,4,8
* INC # C8: 2,4,8 => UNS
* INC # G4: 5,6 => UNS
* INC # G4: 1,4,9 => UNS
* INC # E5: 4,9 => UNS
* INC # F5: 4,9 => UNS
* PRF # G4: 4,9 => SOL
* INC # G4: 1,5,6 => UNS
* DIS # I4: 4,9 => CTR => I4: 1,5
* INC # I4: 1,5 => UNS
* INC # F7: 4,9 => UNS
* INC # F7: 3 => UNS
* INC # A6: 5,6 => UNS
* PRF # G6: 5,6 => SOL
* INC # G6: 9 => UNS
* INC # F7: 3,4 => UNS
* INC # F7: 9 => UNS
* INC # F7: 4,9 => UNS
* INC # F7: 3 => UNS
* DIS # C8: 4,9 => CTR => C8: 2,6,8
* INC # C8: 2,6,8 => UNS
* INC # H8: 4,9 => UNS
* INC # I8: 4,9 => UNS
* INC # E5: 4,9 => UNS
* INC # E5: 3 => UNS
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C1: 3,6 => SOL
* STA C1: 3,6
* CNT   1 HDP CHAINS /   1 HYP OPENED