Analysis of zz-www.sudokuwiki.org-0115-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=115

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=115

position: .......4..15..72....8.....75..4....9....3....67...1..89...5.7....43..69..6....... initial

Autosolve

position: 7.6....4..15..72....8.....75..4...79...73....67...14.89...5.7...5437.69..67...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G9: 1,3 => CTR => G9: 5,8
* PRF # H5: 1,5 => SOL
* DIS # I5: 1,5 => CTR => I5: 2,6
* DIS # D7: 2,8 => CTR => D7: 1,6
* DIS # F7: 2,8 => CTR => F7: 4,6
* DIS # F9: 2,8 => CTR => F9: 4,9
* DIS # F1: 2,8 => CTR => F1: 3,5
* DIS # F4: 2,8 => CTR => F4: 6
* PRF # F5: 2,8 => SOL
* DIS # I9: 1,2 => CTR => I9: 3,4,5
* CNT  10 HDP CHAINS /  48 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 # G9: 1,3 => CTR => G9: 5,8
* DIS G9: 5,8 # C4: 2 => CTR => C4: 1,3
* PRF G9: 5,8 + C4: 1,3 # H5: 1,5 => SOL
* STA G9: 5,8 + C4: 1,3 + H5: 1,5
* CNT   3 HDP CHAINS /  22 HYP OPENED

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

Details

Positions

.......4..15..72....8.....75..4....9....3....67...1..89...5.7....43..69..6....... initial
7.6....4..15..72....8.....75..4...79...73....67...14.89...5.7...5437.69..67...... autosolve
796823145415967283238145967521486379849732516673591428982654731154378692367219854 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A2: 3,4
I2: 3,6
E6: 2,9
G4: 1,3
G5: 1,5
F8: 2,8
I8: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C4,G4: 1.. / C4 = 1  => 10 pairs (_) / G4 = 1  => 20 pairs (_)
A8,I8: 1.. / A8 = 1  => 14 pairs (_) / I8 = 1  =>  8 pairs (_)
F1,F3: 3.. / F1 = 3  =>  9 pairs (_) / F3 = 3  =>  8 pairs (_)
G4,H6: 3.. / G4 = 3  => 10 pairs (_) / H6 = 3  => 20 pairs (_)
C6,H6: 3.. / C6 = 3  => 10 pairs (_) / H6 = 3  => 20 pairs (_)
A5,B5: 4.. / A5 = 4  =>  0 pairs (X) / B5 = 4  =>  7 pairs (_)
I7,I9: 4.. / I7 = 4  => 21 pairs (_) / I9 = 4  =>  8 pairs (_)
A2,E2: 4.. / A2 = 4  =>  8 pairs (_) / E2 = 4  =>  0 pairs (X)
F7,I7: 4.. / F7 = 4  =>  8 pairs (_) / I7 = 4  => 21 pairs (_)
B3,B5: 4.. / B3 = 4  =>  0 pairs (X) / B5 = 4  =>  7 pairs (_)
F5,D6: 5.. / F5 = 5  => 17 pairs (_) / D6 = 5  => 10 pairs (_)
D6,H6: 5.. / D6 = 5  => 10 pairs (_) / H6 = 5  => 17 pairs (_)
E4,F4: 6.. / E4 = 6  =>  0 pairs (X) / F4 = 6  =>  9 pairs (_)
H5,I5: 6.. / H5 = 6  =>  8 pairs (_) / I5 = 6  =>  8 pairs (_)
D7,F7: 6.. / D7 = 6  =>  8 pairs (_) / F7 = 6  =>  0 pairs (X)
I2,I5: 6.. / I2 = 6  =>  8 pairs (_) / I5 = 6  =>  8 pairs (_)
G1,H2: 8.. / G1 = 8  => 14 pairs (_) / H2 = 8  =>  8 pairs (_)
A8,F8: 8.. / A8 = 8  =>  8 pairs (_) / F8 = 8  => 14 pairs (_)
G1,G9: 8.. / G1 = 8  => 14 pairs (_) / G9 = 8  =>  8 pairs (_)
B1,B3: 9.. / B1 = 9  =>  7 pairs (_) / B3 = 9  =>  9 pairs (_)
D2,E2: 9.. / D2 = 9  =>  8 pairs (_) / E2 = 9  =>  0 pairs (X)
G1,G3: 9.. / G1 = 9  =>  9 pairs (_) / G3 = 9  =>  7 pairs (_)
C5,C6: 9.. / C5 = 9  =>  8 pairs (_) / C6 = 9  => 22 pairs (_)
B1,G1: 9.. / B1 = 9  =>  7 pairs (_) / G1 = 9  =>  9 pairs (_)
B3,G3: 9.. / B3 = 9  =>  9 pairs (_) / G3 = 9  =>  7 pairs (_)
C5,F5: 9.. / C5 = 9  =>  8 pairs (_) / F5 = 9  => 22 pairs (_)
F5,F9: 9.. / F5 = 9  => 22 pairs (_) / F9 = 9  =>  8 pairs (_)
* DURATION: 0:00:35.485860  START: 05:34:00.692136  END: 05:34:36.177996 2017-05-01
* CP COUNT: (27)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E6,F8,G4,G5,I2,I8)
* 7.6....4..15..72....8.....75..4...79...73....67...14.89...5.7...5437.69..67......
* PAIR A2: 3,4 BLK 1
A3: 3,4,2                                # reduction candidate for 3,4
A3: 3,4                                  # 12 pairs
B3: 3,4,2,9                              # reduction candidate for 3,4
B3: 3,4                                  #  9 pairs
* PAIR I2: 3,6 BLK 3
H2: 3,6,8                                # reduction candidate for 3,6
H2: 3,6                                  # 14 pairs
H3: 3,6,1,5                              # reduction candidate for 3,6
H3: 3,6                                  # 16 pairs
* PAIR E6: 2,9 BLK 5
F5: 2,9,5,8                              # reduction candidate for 2,9
F5: 2,9                                  # 19 pairs
D6: 2,9,5                                # reduction candidate for 2,9
D6: 2,9                                  # 17 pairs
* PAIR E6: 2,9 ROW 6
C6: 2,9,3                                # reduction candidate for 2,9
C6: 2,9                                  # 20 pairs
C6: 3                                    # 10 pairs
* PAIR E6: 2,9 COL E
E9: 2,9,1,4,8                            # reduction candidate for 2,9
E9: 2,9                                  # 11 pairs
E9: 1,4,8                                #  7 pairs
* PAIR G4: 1,3 ROW 4
C4: 1,3,2                                # reduction candidate for 1,3
C4: 2                                    # 21 pairs
C4: 1,3                                  # 10 pairs
* PAIR G4: 1,3 COL G
G1: 1,3,5,8,9                            # reduction candidate for 1,3
G1: 1,3                                  # 14 pairs
G3: 1,3,5,9                              # reduction candidate for 1,3
G3: 1,3                                  # 12 pairs
G9: 1,3,5,8                              # reduction candidate for 1,3
G9: 1,3 => CTR
* 796213845415..726332864591758.46..79.4.7395..6795214389...56784.54372691.67..4352
G9: 5,8                                  #  8 pairs
* PAIR G5: 1,5 BLK 6
H5: 1,5,2,6                              # reduction candidate for 1,5
H5: 1,5 => SOLVED
* 796823145415967283238145967521486379849732516673591428982654731154378692367219854
H5: 2,6                                  #  8 pairs
I5: 1,5,2,6                              # reduction candidate for 1,5
I5: 1,5 => CTR
* 7.6....4..15947286..8.6...75.14.6379..9732.6.6735914289826547..154378692367..9..4
I5: 2,6                                  #  8 pairs
* PAIR G5: 1,5 COL G
G1: 1,5,3,8,9                            # reduction candidate for 1,5
G1: 1,5                                  # 15 pairs
G3: 1,5,3,9                              # reduction candidate for 1,5
G3: 1,5                                  # 17 pairs
G9: 1,5,3,8                              # reduction candidate for 1,5
G9: 1,5                                  # 19 pairs
* PAIR F8: 2,8 BLK 8
D7: 2,8,1,6                              # reduction candidate for 2,8
D7: 2,8 => CTR
* 7.6....4..15..72....8.....75..468.791..73....67...14.89...567.4854372691.67......
D7: 1,6                                  #  8 pairs
F7: 2,8,4,6                              # reduction candidate for 2,8
F7: 2,8 => CTR
* 7.6....41.15..72....8.....75.24861798417395266795214.89..65.7.4154378692267......
F7: 4,6                                  #  8 pairs
D9: 2,8,1,9                              # reduction candidate for 2,8
D9: 2,8                                  # 11 pairs
E9: 2,8,1,4,9                            # reduction candidate for 2,8
E9: 2,8                                  # 13 pairs
F9: 2,8,4,9                              # reduction candidate for 2,8
F9: 2,8 => CTR
* 7.6.1..45.15..72....8265.175..486179..17395..6795214389..6547.1154378692267.....4
F9: 4,9                                  #  8 pairs
* PAIR F8: 2,8 ROW 8
A8: 2,8,1                                # reduction candidate for 2,8
A8: 1                                    # 14 pairs
A8: 2,8                                  #  8 pairs
* PAIR F8: 2,8 COL F
F1: 2,8,3,5                              # reduction candidate for 2,8
F1: 2,8 => CTR
* 7.6....45.15..72....85.39175.14.6379..97351..673..14589.26547.1154378692.67..95.4
F1: 3,5                                  #  8 pairs
F4: 2,8,6                                # reduction candidate for 2,8
F4: 2,8 => CTR
* 796....4.315.472.6248.1.9.75..468.7948.73....67...14.89...5.7..854372691167......
F4: 6                                    #  9 pairs
F5: 2,8,5,9                              # reduction candidate for 2,8
F5: 2,8 => SOLVED
* 796823145415967283238145967521486379849732516673591428982654731154378692367219854
F5: 5,9                                  # 19 pairs
* PAIR I8: 1,2 BLK 9
H7: 1,2,3,8                              # reduction candidate for 1,2
H7: 1,2                                  #  9 pairs
I7: 1,2,3,4                              # reduction candidate for 1,2
I7: 1,2                                  # 13 pairs
H9: 1,2,3,5,8                            # reduction candidate for 1,2
H9: 1,2                                  # 10 pairs
I9: 1,2,3,4,5                            # reduction candidate for 1,2
I9: 1,2 => CTR
* 7.6....45.15..72.3..8.....75..4...79...73..2667...14.89..1567.4.54372691167.....2
I9: 3,4,5                                #  7 pairs
* PAIR I8: 1,2 ROW 8
A8: 1,2,8                                # reduction candidate for 1,2
A8: 1,2                                  # 14 pairs
A8: 8                                    #  8 pairs
* PAIR I8: 1,2 COL I
I5: 1,2,5,6                              # reduction candidate for 1,2
I5: 1,2                                  # 11 pairs
I5: 5,6                                  #  8 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0115-base-pr-000.dot
* REASONING
* DIS # G9: 1,3 => CTR => G9: 5,8
* PRF # H5: 1,5 => SOL
* DIS # I5: 1,5 => CTR => I5: 2,6
* DIS # D7: 2,8 => CTR => D7: 1,6
* DIS # F7: 2,8 => CTR => F7: 4,6
* DIS # F9: 2,8 => CTR => F9: 4,9
* DIS # F1: 2,8 => CTR => F1: 3,5
* DIS # F4: 2,8 => CTR => F4: 6
* PRF # F5: 2,8 => SOL
* DIS # I9: 1,2 => CTR => I9: 3,4,5
* CNT  10 HDP CHAINS /  48 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E6,F8,G4,G5,I2,I8)
* 7.6....4..15..72....8.....75..4...79...73....67...14.89...5.7...5437.69..67......
* PAIR A2: 3,4 BLK 1
A3: 3,4,2                                # reduction candidate for 3,4
A3: 3,4                                  # 12 pairs
B3: 3,4,2,9                              # reduction candidate for 3,4
B3: 3,4                                  #  9 pairs
* PAIR I2: 3,6 BLK 3
H2: 3,6,8                                # reduction candidate for 3,6
H2: 3,6                                  # 14 pairs
H3: 3,6,1,5                              # reduction candidate for 3,6
H3: 3,6                                  # 16 pairs
* PAIR E6: 2,9 BLK 5
F5: 2,9,5,8                              # reduction candidate for 2,9
F5: 2,9                                  # 19 pairs
D6: 2,9,5                                # reduction candidate for 2,9
D6: 2,9                                  # 17 pairs
* PAIR E6: 2,9 ROW 6
C6: 2,9,3                                # reduction candidate for 2,9
C6: 2,9                                  # 20 pairs
C6: 3                                    # 10 pairs
* PAIR E6: 2,9 COL E
E9: 2,9,1,4,8                            # reduction candidate for 2,9
E9: 2,9                                  # 11 pairs
E9: 1,4,8                                #  7 pairs
* PAIR G4: 1,3 ROW 4
C4: 1,3,2                                # reduction candidate for 1,3
C4: 2                                    # 21 pairs
C4: 1,3                                  # 10 pairs
* PAIR G4: 1,3 COL G
G1: 1,3,5,8,9                            # reduction candidate for 1,3
G1: 1,3                                  # 14 pairs
G3: 1,3,5,9                              # reduction candidate for 1,3
G3: 1,3                                  # 12 pairs
G9: 1,3,5,8                              # reduction candidate for 1,3
G9: 1,3 => CTR
* 796213845415..726332864591758.46..79.4.7395..6795214389...56784.54372691.67..4352
* PAIR RESTART
* PAIR G4: 1,3 ROW 4
C4: 1,3,2                                # reduction candidate for 1,3
C4: 2 => CTR
* 7.6.13945315947286.98.65317532486179.41739562679521438983.5.724.5437.691167.94853
* PAIR G4: 1,3 COL G
G1: 1,3,5,8,9                            # reduction candidate for 1,3
G1: 1,3                                  # 17 pairs
G3: 1,3,5,9                              # reduction candidate for 1,3
G3: 1,3                                  # 15 pairs
* PAIR RESTART
* PAIR G4: 1,3 COL G
G1: 1,3,5,8,9                            # reduction candidate for 1,3
G1: 1,3                                  # 17 pairs
G3: 1,3,5,9                              # reduction candidate for 1,3
G3: 1,3                                  # 15 pairs
* PAIR G5: 1,5 BLK 6
H5: 1,5,2,6                              # reduction candidate for 1,5
H5: 1,5 => SOLVED
* 796823145415967283238145967521486379849732516673591428982654731154378692367219854
* DURATION: 0:00:19.043941  START: 05:35:13.441094  END: 05:35:32.485035 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0115-base-pr-001.dot
* REASONING
* DIS # G9: 1,3 => CTR => G9: 5,8
* DIS G9: 5,8 # C4: 2 => CTR => C4: 1,3
* PRF G9: 5,8 + C4: 1,3 # H5: 1,5 => SOL
* STA G9: 5,8 + C4: 1,3 + H5: 1,5
* CNT   3 HDP CHAINS /  22 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=115

Solution

position: 796823145415967283238145967521486379849732516673591428982654731154378692367219854 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 # A3: 3,4 => UNS
* INC # B3: 3,4 => UNS
* INC # H2: 3,6 => UNS
* INC # H3: 3,6 => UNS
* INC # F5: 2,9 => UNS
* INC # D6: 2,9 => UNS
* INC # C6: 2,9 => UNS
* INC # C6: 3 => UNS
* INC # E9: 2,9 => UNS
* INC # E9: 1,4,8 => UNS
* INC # C4: 1,3 => UNS
* INC # C4: 2 => UNS
* INC # G1: 1,3 => UNS
* INC # G3: 1,3 => UNS
* DIS # G9: 1,3 => CTR => G9: 5,8
* INC # G9: 5,8 => UNS
* PRF # H5: 1,5 => SOL
* INC # H5: 2,6 => UNS
* DIS # I5: 1,5 => CTR => I5: 2,6
* INC # I5: 2,6 => UNS
* INC # G1: 1,5 => UNS
* INC # G3: 1,5 => UNS
* INC # G9: 1,5 => UNS
* DIS # D7: 2,8 => CTR => D7: 1,6
* INC # D7: 1,6 => UNS
* DIS # F7: 2,8 => CTR => F7: 4,6
* INC # F7: 4,6 => UNS
* INC # D9: 2,8 => UNS
* INC # E9: 2,8 => UNS
* DIS # F9: 2,8 => CTR => F9: 4,9
* INC # F9: 4,9 => UNS
* INC # A8: 2,8 => UNS
* INC # A8: 1 => UNS
* DIS # F1: 2,8 => CTR => F1: 3,5
* INC # F1: 3,5 => UNS
* DIS # F4: 2,8 => CTR => F4: 6
* INC # F4: 6 => UNS
* PRF # F5: 2,8 => SOL
* INC # F5: 5,9 => UNS
* INC # H7: 1,2 => UNS
* INC # I7: 1,2 => UNS
* INC # H9: 1,2 => UNS
* DIS # I9: 1,2 => CTR => I9: 3,4,5
* INC # I9: 3,4,5 => UNS
* INC # A8: 1,2 => UNS
* INC # A8: 8 => UNS
* INC # I5: 1,2 => UNS
* INC # I5: 5,6 => UNS
* CNT  48 HDP CHAINS /  48 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 3,4 => UNS
* INC # B3: 3,4 => UNS
* INC # H2: 3,6 => UNS
* INC # H3: 3,6 => UNS
* INC # F5: 2,9 => UNS
* INC # D6: 2,9 => UNS
* INC # C6: 2,9 => UNS
* INC # C6: 3 => UNS
* INC # E9: 2,9 => UNS
* INC # E9: 1,4,8 => UNS
* INC # C4: 1,3 => UNS
* INC # C4: 2 => UNS
* INC # G1: 1,3 => UNS
* INC # G3: 1,3 => UNS
* DIS # G9: 1,3 => CTR => G9: 5,8
* INC G9: 5,8 # C4: 1,3 => UNS
* DIS G9: 5,8 # C4: 2 => CTR => C4: 1,3
* INC G9: 5,8 + C4: 1,3 # G1: 1,3 => UNS
* INC G9: 5,8 + C4: 1,3 # G3: 1,3 => UNS
* INC G9: 5,8 + C4: 1,3 # G1: 1,3 => UNS
* INC G9: 5,8 + C4: 1,3 # G3: 1,3 => UNS
* PRF G9: 5,8 + C4: 1,3 # H5: 1,5 => SOL
* STA G9: 5,8 + C4: 1,3 + H5: 1,5
* CNT  22 HDP CHAINS /  22 HYP OPENED