Analysis of zz-www.sudokuwiki.org-0043-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=43

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=43

position: 62...4..51...6.4.2..8....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 initial

Autosolve

position: 62...4..51...6.4.2.48....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G5: 5,8 => CTR => G5: 1,9
* PRF # E9: 4 => SOL
* DIS # C7: 6,9 => CTR => C7: 3,4,7
* PRF # C9: 6,9 => SOL
* PRF # G9: 5,8 => SOL
* DIS # B6: 6,9 => CTR => B6: 1,3,7,8
* PRF # E9: 4 => SOL
* PRF # G9: 5,8 => SOL
* CNT   8 HDP CHAINS /  29 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 # G5: 5,8 => CTR => G5: 1,9
* PRF G5: 1,9 # E9: 4 => SOL
* STA G5: 1,9 + E9: 4
* CNT   2 HDP CHAINS /  14 HYP OPENED

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

Details

Positions

62...4..51...6.4.2..8....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 initial
62...4..51...6.4.2.48....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17 autosolve
629834175135967482748251396563419728412786953987523641354178269871692534296345817 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
I3: 1,6
E5: 5,8
B9: 6,9
F9: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,B6: 1.. / B5 = 1  =>  4 pairs (_) / B6 = 1  =>  0 pairs (X)
D7,F7: 1.. / D7 = 1  => 14 pairs (_) / F7 = 1  =>  5 pairs (_)
D1,G1: 1.. / D1 = 1  => 12 pairs (_) / G1 = 1  => 16 pairs (_)
B5,G5: 1.. / B5 = 1  =>  4 pairs (_) / G5 = 1  =>  0 pairs (X)
F3,F7: 1.. / F3 = 1  => 14 pairs (_) / F7 = 1  =>  5 pairs (_)
I3,I6: 1.. / I3 = 1  => 12 pairs (_) / I6 = 1  =>  5 pairs (_)
D3,F3: 2.. / D3 = 2  =>  8 pairs (_) / F3 = 2  => 10 pairs (_)
C4,C5: 2.. / C4 = 2  =>  5 pairs (_) / C5 = 2  => 10 pairs (_)
H4,H5: 2.. / H4 = 2  => 10 pairs (_) / H5 = 2  =>  5 pairs (_)
D8,F8: 2.. / D8 = 2  => 10 pairs (_) / F8 = 2  =>  8 pairs (_)
C4,H4: 2.. / C4 = 2  =>  5 pairs (_) / H4 = 2  => 10 pairs (_)
C5,H5: 2.. / C5 = 2  => 10 pairs (_) / H5 = 2  =>  5 pairs (_)
D3,D8: 2.. / D3 = 2  =>  8 pairs (_) / D8 = 2  => 10 pairs (_)
F3,F8: 2.. / F3 = 2  => 10 pairs (_) / F8 = 2  =>  8 pairs (_)
E1,E3: 3.. / E1 = 3  =>  7 pairs (_) / E3 = 3  =>  6 pairs (_)
F4,F6: 3.. / F4 = 3  =>  4 pairs (_) / F6 = 3  =>  4 pairs (_)
D4,D6: 4.. / D4 = 4  =>  4 pairs (_) / D6 = 4  =>  5 pairs (_)
H4,H6: 4.. / H4 = 4  =>  5 pairs (_) / H6 = 4  =>  4 pairs (_)
C7,C9: 4.. / C7 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
E7,E9: 4.. / E7 = 4  => 13 pairs (_) / E9 = 4  =>  0 pairs (*)
D4,H4: 4.. / D4 = 4  =>  4 pairs (_) / H4 = 4  =>  5 pairs (_)
D6,H6: 4.. / D6 = 4  =>  5 pairs (_) / H6 = 4  =>  4 pairs (_)
C7,E7: 4.. / C7 = 4  =>  0 pairs (*) / E7 = 4  =>  0 pairs (X)
C9,E9: 4.. / C9 = 4  => 13 pairs (_) / E9 = 4  =>  0 pairs (*)
C2,A3: 5.. / C2 = 5  =>  7 pairs (_) / A3 = 5  =>  6 pairs (_)
G3,I3: 6.. / G3 = 6  => 12 pairs (_) / I3 = 6  =>  5 pairs (_)
D7,D8: 6.. / D7 = 6  =>  9 pairs (_) / D8 = 6  => 10 pairs (_)
B8,F8: 7.. / B8 = 7  =>  8 pairs (_) / F8 = 7  => 13 pairs (_)
I7,G9: 9.. / I7 = 9  => 10 pairs (_) / G9 = 9  => 14 pairs (_)
C1,D1: 9.. / C1 = 9  => 10 pairs (_) / D1 = 9  => 19 pairs (_)
* DURATION: 0:00:34.967288  START: 04:16:34.266264  END: 04:17:09.233552 2017-05-01
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,E5,F9,I3)
* 62...4..51...6.4.2.48....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17
* PAIR I3: 1,6 BLK 3
G3: 1,6,3,7                              # reduction candidate for 1,6
G3: 3,7                                  # 16 pairs
G3: 1,6                                  # 12 pairs
* PAIR I3: 1,6 COL I
I6: 1,6,8,9                              # reduction candidate for 1,6
I6: 8,9                                  # 13 pairs
I6: 1,6                                  #  7 pairs
* PAIR E5: 5,8 BLK 5
D4: 5,8,4,9                              # reduction candidate for 5,8
D4: 5,8                                  #  8 pairs
F4: 5,8,3,9                              # reduction candidate for 5,8
F4: 5,8                                  # 16 pairs
D6: 5,8,4,9                              # reduction candidate for 5,8
D6: 5,8                                  #  7 pairs
F6: 5,8,3,9                              # reduction candidate for 5,8
F6: 5,8                                  # 16 pairs
* PAIR E5: 5,8 ROW 5
G5: 5,8,1,9                              # reduction candidate for 5,8
G5: 5,8 => CTR
* 62.9.41.5195867432.48...796..2.1...94197.6.23..6.29..195..4.2.88.1.9...42643..917
G5: 1,9                                  #  5 pairs
H5: 5,8,2                                # reduction candidate for 5,8
H5: 5,8                                  # 10 pairs
* PAIR E5: 5,8 COL E
E9: 5,8,4                                # reduction candidate for 5,8
E9: 4 => SOLVED
* 629834175135967482748251396563419728412786953987523641354178269871692534296345817
E9: 5,8                                  # 13 pairs
* PAIR B9: 6,9 BLK 7
C7: 6,9,3,4,7                            # reduction candidate for 6,9
C7: 6,9 => CTR
* 62...4..51...6.4.2.48....96....1...841.7869.3.8..2...1.56147289871692..4294358617
C7: 3,4,7                                #  4 pairs
C9: 6,9,4                                # reduction candidate for 6,9
C9: 6,9 => SOLVED
* 629834175135967482748251396563419728412786953987523641354178269871692534296345817
C9: 4                                    # 13 pairs
* PAIR B9: 6,9 ROW 9
G9: 6,9,5,8                              # reduction candidate for 6,9
G9: 5,8 => SOLVED
* 629834175135967482748251396563419728412786953987523641354178269871692534296345817
G9: 6,9                                  # 13 pairs
* PAIR B9: 6,9 COL B
B4: 6,9,3,7,8                            # reduction candidate for 6,9
B4: 6,9                                  # 14 pairs
B6: 6,9,1,3,7,8                          # reduction candidate for 6,9
B6: 6,9 => CTR
* 629134..5135.6.4.274825.691.8..1...641.7869.3.6..2.1.8.54.712.9871.9...429634..17
B6: 1,3,7,8                              #  4 pairs
* PAIR F9: 5,8 BLK 8
E9: 5,8,4                                # reduction candidate for 5,8
E9: 4 => SOLVED
* 629834175135967482748251396563419728412786953987523641354178269871692534296345817
E9: 5,8                                  # 13 pairs
* PAIR F9: 5,8 ROW 9
G9: 5,8,6,9                              # reduction candidate for 5,8
G9: 5,8 => SOLVED
* 629834175135967482748251396563419728412786953987523641354178269871692534296345817
G9: 6,9                                  # 13 pairs
* PAIR F9: 5,8 COL F
F2: 5,8,7,9                              # reduction candidate for 5,8
F2: 5,8                                  #  9 pairs
F4: 5,8,3,9                              # reduction candidate for 5,8
F4: 5,8                                  # 16 pairs
F6: 5,8,3,9                              # reduction candidate for 5,8
F6: 5,8                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0043-base-pr-000.dot
* REASONING
* DIS # G5: 5,8 => CTR => G5: 1,9
* PRF # E9: 4 => SOL
* DIS # C7: 6,9 => CTR => C7: 3,4,7
* PRF # C9: 6,9 => SOL
* PRF # G9: 5,8 => SOL
* DIS # B6: 6,9 => CTR => B6: 1,3,7,8
* PRF # E9: 4 => SOL
* PRF # G9: 5,8 => SOL
* CNT   8 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B9,E5,F9,I3)
* 62...4..51...6.4.2.48....9.....1....4..7.6..3....2.....5....2..8.1.9...42..3...17
* PAIR I3: 1,6 BLK 3
G3: 1,6,3,7                              # reduction candidate for 1,6
G3: 3,7                                  # 16 pairs
G3: 1,6                                  # 12 pairs
* PAIR I3: 1,6 COL I
I6: 1,6,8,9                              # reduction candidate for 1,6
I6: 8,9                                  # 13 pairs
I6: 1,6                                  #  7 pairs
* PAIR E5: 5,8 BLK 5
D4: 5,8,4,9                              # reduction candidate for 5,8
D4: 5,8                                  #  8 pairs
F4: 5,8,3,9                              # reduction candidate for 5,8
F4: 5,8                                  # 16 pairs
D6: 5,8,4,9                              # reduction candidate for 5,8
D6: 5,8                                  #  7 pairs
F6: 5,8,3,9                              # reduction candidate for 5,8
F6: 5,8                                  # 16 pairs
* PAIR E5: 5,8 ROW 5
G5: 5,8,1,9                              # reduction candidate for 5,8
G5: 5,8 => CTR
* 62.9.41.5195867432.48...796..2.1...94197.6.23..6.29..195..4.2.88.1.9...42643..917
H5: 5,8,2                                # reduction candidate for 5,8
H5: 5,8                                  # 10 pairs
* RESTART
* PAIR E5: 5,8 ROW 5
H5: 5,8,2                                # reduction candidate for 5,8
H5: 5,8                                  # 10 pairs
H5: 2                                    #  6 pairs
* PAIR E5: 5,8 COL E
E9: 5,8,4                                # reduction candidate for 5,8
E9: 4 => SOLVED
* 629834175135967482748251396563419728412786953987523641354178269871692534296345817
* DURATION: 0:00:10.758458  START: 04:17:31.669507  END: 04:17:42.427965 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0043-base-pr-001.dot
* REASONING
* DIS # G5: 5,8 => CTR => G5: 1,9
* PRF G5: 1,9 # E9: 4 => SOL
* STA G5: 1,9 + E9: 4
* CNT   2 HDP CHAINS /  14 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=43

Solution

position: 629834175135967482748251396563419728412786953987523641354178269871692534296345817 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 # G3: 1,6 => UNS
* INC # G3: 3,7 => UNS
* INC # I6: 1,6 => UNS
* INC # I6: 8,9 => UNS
* INC # D4: 5,8 => UNS
* INC # F4: 5,8 => UNS
* INC # D6: 5,8 => UNS
* INC # F6: 5,8 => UNS
* DIS # G5: 5,8 => CTR => G5: 1,9
* INC # G5: 1,9 => UNS
* INC # H5: 5,8 => UNS
* INC # E9: 5,8 => UNS
* PRF # E9: 4 => SOL
* DIS # C7: 6,9 => CTR => C7: 3,4,7
* INC # C7: 3,4,7 => UNS
* PRF # C9: 6,9 => SOL
* INC # C9: 4 => UNS
* INC # G9: 6,9 => UNS
* PRF # G9: 5,8 => SOL
* INC # B4: 6,9 => UNS
* DIS # B6: 6,9 => CTR => B6: 1,3,7,8
* INC # B6: 1,3,7,8 => UNS
* INC # E9: 5,8 => UNS
* PRF # E9: 4 => SOL
* PRF # G9: 5,8 => SOL
* INC # G9: 6,9 => UNS
* INC # F2: 5,8 => UNS
* INC # F4: 5,8 => UNS
* INC # F6: 5,8 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 1,6 => UNS
* INC # G3: 3,7 => UNS
* INC # I6: 1,6 => UNS
* INC # I6: 8,9 => UNS
* INC # D4: 5,8 => UNS
* INC # F4: 5,8 => UNS
* INC # D6: 5,8 => UNS
* INC # F6: 5,8 => UNS
* DIS # G5: 5,8 => CTR => G5: 1,9
* INC G5: 1,9 # H5: 5,8 => UNS
* INC G5: 1,9 # H5: 5,8 => UNS
* INC G5: 1,9 # H5: 2 => UNS
* INC G5: 1,9 # E9: 5,8 => UNS
* PRF G5: 1,9 # E9: 4 => SOL
* STA G5: 1,9 + E9: 4
* CNT  14 HDP CHAINS /  14 HYP OPENED