Analysis of zz-www.sudokuoftheday.co.uk-20060721-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

position: .....7..4..4.3.792.........9...61..8..8..3.51.2....4....1.9452...715........28..7 initial

Autosolve

position: ..2..7..4.14.35792.....2..59...612.8..82.395112...94....179452.2.7156..9...328..7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 6,8 => CTR => A1: 3,5
* DIS # B1: 6,8 => CTR => B1: 3,5,9
* DIS # A3: 6,8 => CTR => A3: 3,7
* DIS # B3: 6,8 => CTR => B3: 3,7,9
* DIS # A7: 3 => CTR => A7: 6,8
* DIS # B1: 6,9 => CTR => B1: 3,5,8
* DIS # D3: 6,9 => CTR => D3: 4,8
* DIS # E3: 1,8 => CTR => E3: 4
* PRF # E3: 4 => SOL
* DIS # D1: 6,8 => CTR => D1: 9
* PRF # D3: 6,8 => SOL
* DIS # B5: 4,7 => CTR => B5: 6
* DIS # B5: 4,7 => CTR => B5: 6
* DIS # H6: 6 => CTR => H6: 3,7
* DIS # H6: 3,6 => CTR => H6: 7
* PRF # H6: 7 => SOL
* DIS # H8: 8 => CTR => H8: 3,4
* DIS # B9: 6,9 => CTR => B9: 4,5
* DIS # B7: 3,6 => CTR => B7: 8
* DIS # H8: 3,8 => CTR => H8: 4
* DIS # H9: 4 => CTR => H9: 1,6
* CNT  21 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 # A1: 6,8 => CTR => A1: 3,5
* DIS A1: 3,5 # B1: 6,8 => CTR => B1: 3,5,9
* DIS A1: 3,5 + B1: 3,5,9 # A3: 6,8 => CTR => A3: 3,7
* DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 # B3: 6,8 => CTR => B3: 3,7,9
* DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 # E3: 1,8 => CTR => E3: 4
* PRF A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4 => SOL
* STA A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4
* CNT   6 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.....7..4..4.3.792.........9...61..8..8..3.51.2....4....1.9452...715........28..7 initial
..2..7..4.14.35792.....2..59...612.8..82.395112...94....179452.2.7156..9...328..7 autosolve
352917684814635792796842315975461238468273951123589476681794523237156849549328167 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A2: 6,8
C3: 6,9
E1: 1,8
D2: 6,8
B4: 4,7
C4: 3,5
C6: 3,5
D4: 4,5
E5: 4,7
D6: 5,8
E6: 7,8
H4: 3,7
I6: 3,6
B8: 3,4
C9: 6,9
I7: 3,6
G8: 3,8
G9: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,E3: 1.. / E1 = 1  => 18 pairs (_) / E3 = 1  =>  0 pairs (X)
G9,H9: 1.. / G9 = 1  => 18 pairs (_) / H9 = 1  => 22 pairs (_)
C4,C6: 3.. / C4 = 3  =>  0 pairs (X) / C6 = 3  =>  0 pairs (_)
C4,H4: 3.. / C4 = 3  =>  0 pairs (X) / H4 = 3  =>  0 pairs (_)
I6,I7: 3.. / I6 = 3  =>  0 pairs (X) / I7 = 3  => 22 pairs (_)
D3,E3: 4.. / D3 = 4  =>  0 pairs (X) / E3 = 4  =>  0 pairs (_)
D4,E5: 4.. / D4 = 4  =>  0 pairs (*) / E5 = 4  =>  0 pairs (X)
H8,H9: 4.. / H8 = 4  => 22 pairs (_) / H9 = 4  =>  0 pairs (X)
B4,D4: 4.. / B4 = 4  =>  0 pairs (X) / D4 = 4  =>  0 pairs (_)
B8,H8: 4.. / B8 = 4  =>  0 pairs (X) / H8 = 4  => 22 pairs (_)
A5,A9: 4.. / A5 = 4  =>  0 pairs (*) / A9 = 4  =>  0 pairs (X)
D3,D4: 4.. / D3 = 4  =>  0 pairs (X) / D4 = 4  =>  0 pairs (_)
E3,E5: 4.. / E3 = 4  =>  0 pairs (*) / E5 = 4  =>  0 pairs (X)
A1,B1: 5.. / A1 = 5  => 20 pairs (_) / B1 = 5  =>  0 pairs (*)
C4,C6: 5.. / C4 = 5  =>  0 pairs (*) / C6 = 5  =>  0 pairs (X)
D4,D6: 5.. / D4 = 5  =>  0 pairs (X) / D6 = 5  =>  0 pairs (_)
A9,B9: 5.. / A9 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
C4,D4: 5.. / C4 = 5  =>  0 pairs (*) / D4 = 5  =>  0 pairs (X)
C6,D6: 5.. / C6 = 5  =>  0 pairs (X) / D6 = 5  =>  0 pairs (_)
A1,A9: 5.. / A1 = 5  => 20 pairs (_) / A9 = 5  =>  0 pairs (*)
B1,B9: 5.. / B1 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
A5,B5: 6.. / A5 = 6  =>  0 pairs (X) / B5 = 6  => 20 pairs (_)
H6,I6: 6.. / H6 = 6  =>  0 pairs (X) / I6 = 6  => 22 pairs (_)
A2,D2: 6.. / A2 = 6  =>  0 pairs (X) / D2 = 6  => 18 pairs (_)
C3,C9: 6.. / C3 = 6  => 18 pairs (_) / C9 = 6  =>  0 pairs (X)
I6,I7: 6.. / I6 = 6  => 22 pairs (_) / I7 = 6  =>  0 pairs (X)
A3,B3: 7.. / A3 = 7  => 19 pairs (_) / B3 = 7  =>  0 pairs (X)
E5,E6: 7.. / E5 = 7  =>  0 pairs (*) / E6 = 7  =>  0 pairs (X)
H4,H6: 7.. / H4 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
B4,H4: 7.. / B4 = 7  =>  0 pairs (*) / H4 = 7  =>  0 pairs (X)
E6,H6: 7.. / E6 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
A3,A5: 7.. / A3 = 7  => 19 pairs (_) / A5 = 7  =>  0 pairs (X)
D6,E6: 8.. / D6 = 8  =>  0 pairs (X) / E6 = 8  =>  0 pairs (_)
A7,B7: 8.. / A7 = 8  =>  0 pairs (X) / B7 = 8  => 19 pairs (_)
G8,H8: 8.. / G8 = 8  => 18 pairs (_) / H8 = 8  =>  0 pairs (X)
A2,D2: 8.. / A2 = 8  => 18 pairs (_) / D2 = 8  =>  0 pairs (X)
D1,D3: 9.. / D1 = 9  => 18 pairs (_) / D3 = 9  =>  0 pairs (X)
B9,C9: 9.. / B9 = 9  =>  0 pairs (X) / C9 = 9  => 18 pairs (_)
B1,D1: 9.. / B1 = 9  =>  0 pairs (X) / D1 = 9  => 18 pairs (_)
C3,C9: 9.. / C3 = 9  =>  0 pairs (X) / C9 = 9  => 18 pairs (_)
* DURATION: 0:00:49.255870  START: 00:51:47.929202  END: 00:52:37.185072 2019-05-01
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B4,B8,C3,C4,C6,C9,D2,D4,D6,E1,E5,E6,G8,G9,H4,I6,I7)
* ..2..7..4.14.35792.....2..59...612.8..82.395112...94....179452.2.7156..9...328..7
* PAIR A2: 6,8 BLK 1
A1: 6,8,3,5                              # reduction candidate for 6,8
A1: 6,8 => CTR
* .529.7..4.14.35792.....2..59...612.846827395112..89476681794523237156849549328..7
A1: 3,5                                  # 19 pairs
B1: 6,8,3,5,9                            # reduction candidate for 6,8
B1: 6,8 => CTR
* 5.29.7..4.14.35792.96..2..59...612.8..82.395112...94....179452.2.7156..9.59328..7
B1: 3,5,9                                # 18 pairs
A3: 6,8,3,7                              # reduction candidate for 6,8
A3: 6,8 => CTR
* ..2..7..4.14.35792.7...2..594.5612787682439511258794....179452.237156849459328..7
A3: 3,7                                  # 19 pairs
B3: 6,8,3,7,9                            # reduction candidate for 6,8
B3: 6,8 => CTR
* .529.7..4.14.357927.9..2..59...612.846827395112..89476..17945232.7156..9.96328147
B3: 3,7,9                                # 18 pairs
* PAIR A2: 6,8 COL A
A7: 6,8,3                                # reduction candidate for 6,8
A7: 3 => CTR
* ..2..7..4.14.35792.....2..597.461238..82.395112...94..381794526247156..9...328147
A7: 6,8                                  # 24 pairs
* PAIR C3: 6,9 BLK 1
B1: 6,9,3,5,8                            # reduction candidate for 6,9
B1: 6,9 => CTR
* 592..7..4814635792..6942..59..4612.8..827395112.589476.81794523237156849459328..7
B1: 3,5,8                                # 18 pairs
B3: 6,9,3,7,8                            # reduction candidate for 6,9
B3: 6,9                                  # 22 pairs
* PAIR C3: 6,9 ROW 3
D3: 6,9,4,8                              # reduction candidate for 6,9
D3: 6,9 => CTR
* 352917684.14835792789642315975461238..8273951123589476861794523237156849...328..7
D3: 4,8                                  # 18 pairs
* PAIR E1: 1,8 BLK 2
E3: 1,8,4                                # reduction candidate for 1,8
E3: 1,8 => CTR
* 5.29.7..48146357923..4.2..594.561278..82439511258794....179452.237156849459328..7
E3: 4 => SOLVED
* 352917684814635792796842315975461238468273951123589476681794523237156849549328167
* PAIR E1: 1,8 ROW 1
G1: 1,8,3,6                              # reduction candidate for 1,8
G1: 1,8                                  # 25 pairs
H1: 1,8,3,6                              # reduction candidate for 1,8
H1: 1,8                                  # 21 pairs
* PAIR D2: 6,8 BLK 2
D1: 6,8,9                                # reduction candidate for 6,8
D1: 6,8 => CTR
* 592.17..4814.35792..6942..59..4612.8..827395112.589476..1794523237156849.59328..7
D1: 9                                    # 18 pairs
D3: 6,8,4,9                              # reduction candidate for 6,8
D3: 6,8 => SOLVED
* 352917684814635792796842315975461238468273951123589476681794523237156849549328167
D3: 4,9                                  # 19 pairs
* PAIR B4: 4,7 BLK 4
A5: 4,7,6                                # reduction candidate for 4,7
A5: 4,7                                  # 20 pairs
B5: 4,7,6                                # reduction candidate for 4,7
B5: 4,7 => CTR
* 5.2..7..48146357927.6..2..59...612.86.82.395112...94..3.179452.2.7156..9459328..7
B5: 6                                    # 20 pairs
* PAIR E5: 4,7 ROW 5
A5: 4,7,6                                # reduction candidate for 4,7
A5: 4,7                                  # 20 pairs
B5: 4,7,6                                # reduction candidate for 4,7
B5: 4,7 => CTR
* 5.2..7..48146357927.6..2..59...612.86.82.395112...94..3.179452.2.7156..9459328..7
B5: 6                                    # 20 pairs
* PAIR H4: 3,7 BLK 6
H6: 3,7,6                                # reduction candidate for 3,7
H6: 6 => CTR
* ..2..7..4.14.35792.....2..5943561278..8243951125879463..17945262371568.9...328147
H6: 3,7                                  # 22 pairs
* PAIR I6: 3,6 BLK 6
H6: 3,6,7                                # reduction candidate for 3,6
H6: 3,6 => CTR
* 5.2..7..4814635792376..2..5943561278..82439511258794....179452.237156849459328..7
H6: 7 => SOLVED
* 352917684814635792796842315975461238468273951123589476681794523237156849549328167
* PAIR B8: 3,4 ROW 8
H8: 3,4,8                                # reduction candidate for 3,4
H8: 8 => CTR
* ..2..7..4.14.35792.....2..597.461238468273951123589476..179452.247156389...328.47
H8: 3,4                                  # 18 pairs
* PAIR C9: 6,9 BLK 7
B9: 6,9,4,5                              # reduction candidate for 6,9
B9: 6,9 => CTR
* .529.7..4.14.35792.....2..59...612.846827395112..894766817945232.7156..95..328.47
B9: 4,5                                  # 20 pairs
* PAIR I7: 3,6 ROW 7
A7: 3,6,8                                # reduction candidate for 3,6
A7: 3,6                                  # 19 pairs
B7: 3,6,8                                # reduction candidate for 3,6
B7: 3,6 => CTR
* ..2..7..4614835792..9..2..59...612.8.682.395112.58947683179452.2.7156..9...328..7
B7: 8                                    # 19 pairs
* PAIR G8: 3,8 BLK 9
H8: 3,8,4                                # reduction candidate for 3,8
H8: 3,8 => CTR
* ..2..7..4.14.35792.....2..597.4612384682739511235894766.179452.247156..9...328.47
H8: 4                                    # 22 pairs
* PAIR G8: 3,8 COL G
G1: 3,8,1,6                              # reduction candidate for 3,8
G1: 3,8                                  # 20 pairs
G3: 3,8,1,6                              # reduction candidate for 3,8
G3: 3,8                                  # 20 pairs
* PAIR G9: 1,6 BLK 9
H9: 1,6,4                                # reduction candidate for 1,6
H9: 4 => CTR
* ..2..7..4.14.35792.....2..59...612.846827395112..894766817945232.7156..9...328147
H9: 1,6                                  # 22 pairs
* PAIR G9: 1,6 COL G
G1: 1,6,3,8                              # reduction candidate for 1,6
G1: 1,6                                  # 20 pairs
G3: 1,6,3,8                              # reduction candidate for 1,6
G3: 1,6                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060721-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 6,8 => CTR => A1: 3,5
* DIS # B1: 6,8 => CTR => B1: 3,5,9
* DIS # A3: 6,8 => CTR => A3: 3,7
* DIS # B3: 6,8 => CTR => B3: 3,7,9
* DIS # A7: 3 => CTR => A7: 6,8
* DIS # B1: 6,9 => CTR => B1: 3,5,8
* DIS # D3: 6,9 => CTR => D3: 4,8
* DIS # E3: 1,8 => CTR => E3: 4
* PRF # E3: 4 => SOL
* DIS # D1: 6,8 => CTR => D1: 9
* PRF # D3: 6,8 => SOL
* DIS # B5: 4,7 => CTR => B5: 6
* DIS # B5: 4,7 => CTR => B5: 6
* DIS # H6: 6 => CTR => H6: 3,7
* DIS # H6: 3,6 => CTR => H6: 7
* PRF # H6: 7 => SOL
* DIS # H8: 8 => CTR => H8: 3,4
* DIS # B9: 6,9 => CTR => B9: 4,5
* DIS # B7: 3,6 => CTR => B7: 8
* DIS # H8: 3,8 => CTR => H8: 4
* DIS # H9: 4 => CTR => H9: 1,6
* CNT  21 HDP CHAINS /  48 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,B4,B8,C3,C4,C6,C9,D2,D4,D6,E1,E5,E6,G8,G9,H4,I6,I7)
* ..2..7..4.14.35792.....2..59...612.8..82.395112...94....179452.2.7156..9...328..7
* PAIR A2: 6,8 BLK 1
A1: 6,8,3,5                              # reduction candidate for 6,8
A1: 6,8 => CTR
* .529.7..4.14.35792.....2..59...612.846827395112..89476681794523237156849549328..7
B1: 6,8,3,5,9                            # reduction candidate for 6,8
B1: 6,8 => CTR
* 5.29.7..4.14.35792.96..2..59...612.8..82.395112...94....179452.2.7156..9.59328..7
A3: 6,8,3,7                              # reduction candidate for 6,8
A3: 6,8 => CTR
* ..2..7..4.14.35792.7...2..594.5612787682439511258794...8179452.237156849459328..7
B3: 6,8,3,7,9                            # reduction candidate for 6,8
B3: 6,8 => CTR
* .529.7..4.14.357927.9..2..59...612.846827395112..89476..17945232.7156..9.96328147
* PAIR E1: 1,8 BLK 2
E3: 1,8,4                                # reduction candidate for 1,8
E3: 1,8 => CTR
* ..2..7..4814635792..64.2..594.561278..82439511258794...8179452.237156849459328..7
E3: 4 => SOLVED
* 352917684814635792796842315975461238468273951123589476681794523237156849549328167
* DURATION: 0:00:05.327898  START: 00:53:08.360477  END: 00:53:13.688375 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060721-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 6,8 => CTR => A1: 3,5
* DIS A1: 3,5 # B1: 6,8 => CTR => B1: 3,5,9
* DIS A1: 3,5 + B1: 3,5,9 # A3: 6,8 => CTR => A3: 3,7
* DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 # B3: 6,8 => CTR => B3: 3,7,9
* DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 # E3: 1,8 => CTR => E3: 4
* PRF A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4 => SOL
* STA A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4
* CNT   6 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060721, absurd

Solution

position: 352917684814635792796842315975461238468273951123589476681794523237156849549328167 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 # A1: 6,8 => CTR => A1: 3,5
* INC # A1: 3,5 => UNS
* DIS # B1: 6,8 => CTR => B1: 3,5,9
* INC # B1: 3,5,9 => UNS
* DIS # A3: 6,8 => CTR => A3: 3,7
* INC # A3: 3,7 => UNS
* DIS # B3: 6,8 => CTR => B3: 3,7,9
* INC # B3: 3,7,9 => UNS
* INC # A7: 6,8 => UNS
* DIS # A7: 3 => CTR => A7: 6,8
* DIS # B1: 6,9 => CTR => B1: 3,5,8
* INC # B1: 3,5,8 => UNS
* INC # B3: 6,9 => UNS
* DIS # D3: 6,9 => CTR => D3: 4,8
* INC # D3: 4,8 => UNS
* DIS # E3: 1,8 => CTR => E3: 4
* PRF # E3: 4 => SOL
* INC # G1: 1,8 => UNS
* INC # H1: 1,8 => UNS
* DIS # D1: 6,8 => CTR => D1: 9
* INC # D1: 9 => UNS
* PRF # D3: 6,8 => SOL
* INC # D3: 4,9 => UNS
* INC # A5: 4,7 => UNS
* DIS # B5: 4,7 => CTR => B5: 6
* INC # B5: 6 => UNS
* INC # A5: 4,7 => UNS
* DIS # B5: 4,7 => CTR => B5: 6
* INC # B5: 6 => UNS
* INC # H6: 3,7 => UNS
* DIS # H6: 6 => CTR => H6: 3,7
* DIS # H6: 3,6 => CTR => H6: 7
* PRF # H6: 7 => SOL
* INC # H8: 3,4 => UNS
* DIS # H8: 8 => CTR => H8: 3,4
* DIS # B9: 6,9 => CTR => B9: 4,5
* INC # B9: 4,5 => UNS
* INC # A7: 3,6 => UNS
* DIS # B7: 3,6 => CTR => B7: 8
* INC # B7: 8 => UNS
* DIS # H8: 3,8 => CTR => H8: 4
* INC # H8: 4 => UNS
* INC # G1: 3,8 => UNS
* INC # G3: 3,8 => UNS
* INC # H9: 1,6 => UNS
* DIS # H9: 4 => CTR => H9: 1,6
* INC # G1: 1,6 => UNS
* INC # G3: 1,6 => UNS
* CNT  48 HDP CHAINS /  48 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 6,8 => CTR => A1: 3,5
* DIS A1: 3,5 # B1: 6,8 => CTR => B1: 3,5,9
* DIS A1: 3,5 + B1: 3,5,9 # A3: 6,8 => CTR => A3: 3,7
* DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 # B3: 6,8 => CTR => B3: 3,7,9
* DIS A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 # E3: 1,8 => CTR => E3: 4
* PRF A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4 => SOL
* STA A1: 3,5 + B1: 3,5,9 + A3: 3,7 + B3: 3,7,9 + E3: 4
* CNT   6 HDP CHAINS /   5 HYP OPENED