Analysis of zz-www.sudokuoftheday.co.uk-20060329-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

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

level: medium

position: 4..91.7.3......4.......7.5...4.8..3.2.67..1......5...2..3..52..8....1.4...7....91 initial

Autosolve

position: 4.591.723...5..41......7.5...4.8..3.256739184....5...2..3..52..8....1.4.5.7....91 autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B2: 6,8 => SOL
* DIS # B3: 6,8 => CTR => B3: 1,2,3,9
* DIS # F2: 6,8 => CTR => F2: 2,3
* DIS # F2: 2,6 => CTR => F2: 3,8
* PRF # D3: 2,6 => SOL
* DIS # E3: 2,6 => CTR => E3: 4
* DIS # B2: 2,6 => CTR => B2: 3,7,8,9
* DIS # E9: 4 => CTR => E9: 2,6
* DIS # D4: 1 => CTR => D4: 2,6
* DIS # F2: 2,6 => CTR => F2: 3,8
* PRF # F9: 2,6 => SOL
* DIS # D6: 4,6 => CTR => D6: 1
* PRF # F9: 4,6 => SOL
* DIS # G4: 6,9 => CTR => G4: 5
* DIS # I4: 6,9 => CTR => I4: 5,7
* DIS # G3: 6,9 => CTR => G3: 8
* DIS # I4: 5,9 => CTR => I4: 6,7
* DIS # B8: 6 => CTR => B8: 2,9
* DIS # C3: 2,9 => CTR => C3: 1,8
* DIS # I7: 6,7 => CTR => I7: 8
* DIS # I8: 6,7 => CTR => I8: 5
* CNT  21 HDP CHAINS /  46 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* PRF # B2: 6,8 => SOL
* STA B2: 6,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

`4..91.7.3......4.......7.5...4.8..3.2.67..1......5...2..3..52..8....1.4...7....91`	initial
`4.591.723...5..41......7.5...4.8..3.256739184....5...2..3..52..8....1.4.5.7....91`	autosolve
`465918723782563419931247856194682537256739184378154962613495278829371645547826391`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
B1: 6,8
F1: 6,8
E2: 2,6
F4: 2,6
F6: 4,6
G6: 6,9
H6: 6,7
C8: 2,9
E7: 7,9
E8: 7,9
H7: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,D6: 1.. / D4 = 1  =>  0 pairs (X) / D6 = 1  => 13 pairs (_)
A7,B7: 1.. / A7 = 1  =>  0 pairs (X) / B7 = 1  => 20 pairs (_)
C3,C6: 1.. / C3 = 1  => 12 pairs (_) / C6 = 1  =>  0 pairs (X)
D4,F4: 2.. / D4 = 2  =>  0 pairs (X) / F4 = 2  => 11 pairs (_)
F2,D3: 3.. / F2 = 3  => 11 pairs (_) / D3 = 3  => 18 pairs (_)
A6,B6: 3.. / A6 = 3  => 11 pairs (_) / B6 = 3  => 12 pairs (_)
G8,G9: 3.. / G8 = 3  => 12 pairs (_) / G9 = 3  =>  0 pairs (*)
D8,G8: 3.. / D8 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
F2,F9: 3.. / F2 = 3  => 11 pairs (_) / F9 = 3  => 18 pairs (_)
D3,E3: 4.. / D3 = 4  =>  0 pairs (X) / E3 = 4  => 12 pairs (_)
D6,F6: 4.. / D6 = 4  =>  0 pairs (X) / F6 = 4  => 11 pairs (_)
B7,B9: 4.. / B7 = 4  =>  0 pairs (X) / B9 = 4  => 18 pairs (_)
B7,D7: 4.. / B7 = 4  =>  0 pairs (X) / D7 = 4  => 18 pairs (_)
E3,E9: 4.. / E3 = 4  => 12 pairs (_) / E9 = 4  =>  0 pairs (X)
F6,F9: 4.. / F6 = 4  => 11 pairs (_) / F9 = 4  =>  0 pairs (X)
G4,I4: 5.. / G4 = 5  => 11 pairs (_) / I4 = 5  =>  0 pairs (X)
G8,I8: 5.. / G8 = 5  =>  0 pairs (X) / I8 = 5  => 11 pairs (_)
G4,G8: 5.. / G4 = 5  => 11 pairs (_) / G8 = 5  =>  0 pairs (X)
I4,I8: 5.. / I4 = 5  =>  0 pairs (X) / I8 = 5  => 11 pairs (_)
B1,F1: 6.. / B1 = 6  =>  0 pairs (*) / F1 = 6  =>  0 pairs (X)
H6,H7: 6.. / H6 = 6  => 15 pairs (_) / H7 = 6  =>  0 pairs (X)
A2,B2: 7.. / A2 = 7  => 12 pairs (_) / B2 = 7  => 12 pairs (_)
I4,H6: 7.. / I4 = 7  => 15 pairs (_) / H6 = 7  =>  0 pairs (X)
E7,E8: 7.. / E7 = 7  =>  0 pairs (X) / E8 = 7  => 11 pairs (_)
E8,I8: 7.. / E8 = 7  => 11 pairs (_) / I8 = 7  =>  0 pairs (X)
H6,H7: 7.. / H6 = 7  =>  0 pairs (X) / H7 = 7  => 15 pairs (_)
B6,C6: 8.. / B6 = 8  =>  0 pairs (X) / C6 = 8  => 12 pairs (_)
I7,G9: 8.. / I7 = 8  => 17 pairs (_) / G9 = 8  =>  0 pairs (X)
B1,F1: 8.. / B1 = 8  =>  0 pairs (X) / F1 = 8  =>  0 pairs (_)
D7,I7: 8.. / D7 = 8  =>  0 pairs (X) / I7 = 8  => 17 pairs (_)
G3,G9: 8.. / G3 = 8  => 17 pairs (_) / G9 = 8  =>  0 pairs (X)
E7,E8: 9.. / E7 = 9  => 11 pairs (_) / E8 = 9  =>  0 pairs (X)
* DURATION: 0:00:35.733046  START: 21:59:35.556253  END: 22:00:11.289299 2019-04-30
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C8,E2,E7,E8,F1,F4,F6,G6,H6,H7)
* 4.591.723...5..41......7.5...4.8..3.256739184....5...2..3..52..8....1.4.5.7....91
* PAIR B1: 6,8 BLK 1
B2: 6,8,2,3,7,9                          # reduction candidate for 6,8
B2: 6,8 => SOLVED
* 465918723782563419931247856194682537256739184378154962613495278829371645547826391
B2: 2,3,7,9                              # 11 pairs
B3: 6,8,1,2,3,9                          # reduction candidate for 6,8
B3: 6,8 => CTR
* 4.591.723...5.841.3.1247859..4.82.37256739184.38.54.626134952788..371.45547826.91
B3: 1,2,3,9                              # 11 pairs
* PAIR F1: 6,8 BLK 2
F2: 6,8,2,3                              # reduction candidate for 6,8
F2: 6,8 => CTR
* 4.591.723...52.41....347.5...4.8253.256739184....54..2..38952..869271345527463891
F2: 2,3                                  # 12 pairs
D3: 6,8,2,3,4                            # reduction candidate for 6,8
D3: 6,8                                  # 19 pairs
* PAIR F1: 6,8 COL F
F9: 6,8,2,3,4                            # reduction candidate for 6,8
F9: 6,8                                  # 16 pairs
F9: 2,3,4                                # 11 pairs
* PAIR E2: 2,6 BLK 2
F2: 2,6,3,8                              # reduction candidate for 2,6
F2: 2,6 => CTR
* 465918723...562419...347856..4286537256739184...1549626134952788..671345547823691
F2: 3,8                                  # 12 pairs
D3: 2,6,3,4,8                            # reduction candidate for 2,6
D3: 2,6 => SOLVED
* 465918723782563419931247856194682537256739184378154962613495278829371645547826391
D3: 3,4,8                                # 11 pairs
E3: 2,6,4                                # reduction candidate for 2,6
E3: 2,6 => CTR
* 465918723...5.341....4.7.5...4.8..3.256739184....54..2143.952..8...71.4.527.46.91
E3: 4                                    # 12 pairs
* PAIR E2: 2,6 ROW 2
B2: 2,6,3,7,8,9                          # reduction candidate for 2,6
B2: 2,6 => CTR
* 4.591.7237.85.3419....47856..4.8..37256739184....5...26134952788...71.4.547....91
B2: 3,7,8,9                              # 11 pairs
* PAIR E2: 2,6 COL E
E9: 2,6,4                                # reduction candidate for 2,6
E9: 4 => CTR
* 465918723...5.341....4.7.5...4.8..3.256739184....54..2143.952..8...71.4.527.46.91
E9: 2,6                                  # 12 pairs
* PAIR F4: 2,6 BLK 5
D4: 2,6,1                                # reduction candidate for 2,6
D4: 1 => CTR
* 485916723..9523418..1.47.59..4182.3.256739184..8654972..3..526.862391547547268391
D4: 2,6                                  # 13 pairs
* PAIR F4: 2,6 COL F
F2: 2,6,3,8                              # reduction candidate for 2,6
F2: 2,6 => CTR
* 465918723...562419...347856..4286537256739184...1549626134952788..671345547823691
F2: 3,8                                  # 12 pairs
F9: 2,6,3,4,8                            # reduction candidate for 2,6
F9: 2,6 => SOLVED
* 465918723782563419931247856194682537256739184378154962613495278829371645547826391
F9: 3,4,8                                # 11 pairs
* PAIR F6: 4,6 BLK 5
D6: 4,6,1                                # reduction candidate for 4,6
D6: 4,6 => CTR
* 485916723..9523418..1.47.59..4182.3.256739184..8654972..3..526.862391547547268391
D6: 1                                    # 13 pairs
* PAIR F6: 4,6 COL F
F9: 4,6,2,3,8                            # reduction candidate for 4,6
F9: 4,6 => SOLVED
* 465918723782563419931247856194682537256739184378154962613495278829371645547826391
F9: 2,3,8                                # 11 pairs
* PAIR G6: 6,9 BLK 6
G4: 6,9,5                                # reduction candidate for 6,9
G4: 6,9 => CTR
* 4.5918723...5.341......785...4.8..35256739184....5..72..347526886.3915475.78..391
G4: 5                                    # 11 pairs
I4: 6,9,5,7                              # reduction candidate for 6,9
I4: 6,9 => CTR
* 485916723..95284166.1347958..4682539256739184938.54.721438952678...713455.7463891
I4: 5,7                                  # 13 pairs
* PAIR G6: 6,9 COL G
G3: 6,9,8                                # reduction candidate for 6,9
G3: 6,9 => CTR
* 485916723..95284166.1347958..4682539256739184938.54..21438952..8...713455.7463891
G3: 8                                    # 17 pairs
* PAIR H6: 6,7 BLK 6
I4: 6,7,5,9                              # reduction candidate for 6,7
I4: 5,9 => CTR
* 485916723..9523418..1.47.5...4.82.3.256739184..8.54.72..3..526.862391547547268391
I4: 6,7                                  # 13 pairs
* PAIR C8: 2,9 BLK 7
B8: 2,9,6                                # reduction candidate for 2,9
B8: 6 => CTR
* 485916723..9523418.21847.5...4.82.35256739184.38.54.72..347526.862391547547268391
B8: 2,9                                  # 14 pairs
* PAIR C8: 2,9 COL C
C2: 2,9,8                                # reduction candidate for 2,9
C2: 2,9                                  # 14 pairs
C3: 2,9,1,8                              # reduction candidate for 2,9
C3: 2,9 => CTR
* 465918723..85..41......7.5...4182.3.256739184381.5.9726.3..52..8....1.4.5.7....91
C3: 1,8                                  # 12 pairs
* PAIR H7: 6,7 BLK 9
I7: 6,7,8                                # reduction candidate for 6,7
I7: 6,7 => CTR
* 485916723..95284166.1347958..4682539256739184938.54..21438952..8...713455.7463891
I7: 8                                    # 17 pairs
I8: 6,7,5                                # reduction candidate for 6,7
I8: 6,7 => CTR
* 4.5918723...5.341......785...4.8..35256739184....5..72..347526886.3915475.78..391
I8: 5                                    # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060329-absurd-base-pr-000.dot
* REASONING
* PRF # B2: 6,8 => SOL
* DIS # B3: 6,8 => CTR => B3: 1,2,3,9
* DIS # F2: 6,8 => CTR => F2: 2,3
* DIS # F2: 2,6 => CTR => F2: 3,8
* PRF # D3: 2,6 => SOL
* DIS # E3: 2,6 => CTR => E3: 4
* DIS # B2: 2,6 => CTR => B2: 3,7,8,9
* DIS # E9: 4 => CTR => E9: 2,6
* DIS # D4: 1 => CTR => D4: 2,6
* DIS # F2: 2,6 => CTR => F2: 3,8
* PRF # F9: 2,6 => SOL
* DIS # D6: 4,6 => CTR => D6: 1
* PRF # F9: 4,6 => SOL
* DIS # G4: 6,9 => CTR => G4: 5
* DIS # I4: 6,9 => CTR => I4: 5,7
* DIS # G3: 6,9 => CTR => G3: 8
* DIS # I4: 5,9 => CTR => I4: 6,7
* DIS # B8: 6 => CTR => B8: 2,9
* DIS # C3: 2,9 => CTR => C3: 1,8
* DIS # I7: 6,7 => CTR => I7: 8
* DIS # I8: 6,7 => CTR => I8: 5
* CNT  21 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C8,E2,E7,E8,F1,F4,F6,G6,H6,H7)
* 4.591.723...5..41......7.5...4.8..3.256739184....5...2..3..52..8....1.4.5.7....91
* PAIR B1: 6,8 BLK 1
B2: 6,8,2,3,7,9                          # reduction candidate for 6,8
B2: 6,8 => SOLVED
* 465918723782563419931247856194682537256739184378154962613495278829371645547826391
* DURATION: 0:00:01.906827  START: 22:00:40.422940  END: 22:00:42.329767 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060329-absurd-base-pr-001.dot
* REASONING
* PRF # B2: 6,8 => SOL
* STA B2: 6,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060329, absurd

Solution

position: 465918723782563419931247856194682537256739184378154962613495278829371645547826391 solved

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 # B2: 6,8 => SOL
* INC # B2: 2,3,7,9 => UNS
* DIS # B3: 6,8 => CTR => B3: 1,2,3,9
* INC # B3: 1,2,3,9 => UNS
* DIS # F2: 6,8 => CTR => F2: 2,3
* INC # F2: 2,3 => UNS
* INC # D3: 6,8 => UNS
* INC # F9: 6,8 => UNS
* INC # F9: 2,3,4 => UNS
* DIS # F2: 2,6 => CTR => F2: 3,8
* INC # F2: 3,8 => UNS
* PRF # D3: 2,6 => SOL
* INC # D3: 3,4,8 => UNS
* DIS # E3: 2,6 => CTR => E3: 4
* INC # E3: 4 => UNS
* DIS # B2: 2,6 => CTR => B2: 3,7,8,9
* INC # B2: 3,7,8,9 => UNS
* INC # E9: 2,6 => UNS
* DIS # E9: 4 => CTR => E9: 2,6
* INC # D4: 2,6 => UNS
* DIS # D4: 1 => CTR => D4: 2,6
* DIS # F2: 2,6 => CTR => F2: 3,8
* INC # F2: 3,8 => UNS
* PRF # F9: 2,6 => SOL
* INC # F9: 3,4,8 => UNS
* DIS # D6: 4,6 => CTR => D6: 1
* INC # D6: 1 => UNS
* PRF # F9: 4,6 => SOL
* INC # F9: 2,3,8 => UNS
* DIS # G4: 6,9 => CTR => G4: 5
* INC # G4: 5 => UNS
* DIS # I4: 6,9 => CTR => I4: 5,7
* INC # I4: 5,7 => UNS
* DIS # G3: 6,9 => CTR => G3: 8
* INC # G3: 8 => UNS
* INC # I4: 6,7 => UNS
* DIS # I4: 5,9 => CTR => I4: 6,7
* INC # B8: 2,9 => UNS
* DIS # B8: 6 => CTR => B8: 2,9
* INC # C2: 2,9 => UNS
* DIS # C3: 2,9 => CTR => C3: 1,8
* INC # C3: 1,8 => UNS
* DIS # I7: 6,7 => CTR => I7: 8
* INC # I7: 8 => UNS
* DIS # I8: 6,7 => CTR => I8: 5
* INC # I8: 5 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # B2: 6,8 => SOL
* STA B2: 6,8
* CNT   1 HDP CHAINS /   1 HYP OPENED