Analysis of zz-www.sudokuoftheday.co.uk-20060905-absurd-base.sdk

Contents

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

level: medium

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

position: ......3..9..8.2.....2....4.......93..1...96....3.7...5.4...7.6.6.....8.45.9.8.7.. initial

Autosolve

position: .8....3929..8.2.76..2....48.....8931.1...96.7.93.7.4.5.4...72696.....854529.8.713 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B3: 3,5 => SOL
* DIS # C2: 1,5 => CTR => C2: 4
* PRF # F3: 1,5 => SOL
* DIS # F3: 3 => CTR => F3: 1,5
* DIS # A7: 1,8 => CTR => A7: 3
* PRF # A7: 3 => SOL
* PRF # B3: 3,7 => SOL
* DIS # F3: 5 => CTR => F3: 1,3
* CNT   8 HDP CHAINS /  20 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 # B3: 3,5 => SOL
* STA B3: 3,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

......3..9..8.2.....2....4.......93..1...96....3.7...5.4...7.6.6.....8.45.9.8.7.. initial
.8....3929..8.2.76..2....48.....8931.1...96.7.93.7.4.5.4...72696.....854529.8.713 autosolve
186745392954832176732961548267458931415329687893176425348517269671293854529684713 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
B2: 3,5
G2: 1,5
G3: 1,5
A6: 2,8
D6: 1,6
F6: 1,6
H5: 2,8
H6: 2,8
C7: 1,8
B8: 3,7
C8: 1,7
D8: 2,9
E8: 2,9
F8: 1,3
D9: 4,6
F9: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,G3: 1.. / G2 = 1  => 15 pairs (_) / G3 = 1  =>  0 pairs (X)
D6,F6: 1.. / D6 = 1  => 15 pairs (_) / F6 = 1  =>  0 pairs (X)
C8,F8: 1.. / C8 = 1  =>  0 pairs (*) / F8 = 1  =>  0 pairs (X)
H5,H6: 2.. / H5 = 2  => 15 pairs (_) / H6 = 2  => 15 pairs (_)
D8,E8: 2.. / D8 = 2  => 16 pairs (_) / E8 = 2  => 16 pairs (_)
A6,H6: 2.. / A6 = 2  => 15 pairs (_) / H6 = 2  => 15 pairs (_)
D5,E5: 3.. / D5 = 3  => 17 pairs (_) / E5 = 3  =>  0 pairs (X)
A7,B8: 3.. / A7 = 3  =>  0 pairs (*) / B8 = 3  =>  0 pairs (X)
B2,E2: 3.. / B2 = 3  =>  0 pairs (X) / E2 = 3  =>  0 pairs (_)
B8,F8: 3.. / B8 = 3  =>  0 pairs (X) / F8 = 3  =>  0 pairs (_)
A3,A7: 3.. / A3 = 3  =>  0 pairs (X) / A7 = 3  =>  0 pairs (_)
F3,F8: 3.. / F3 = 3  =>  0 pairs (X) / F8 = 3  =>  0 pairs (_)
D9,F9: 4.. / D9 = 4  =>  0 pairs (X) / F9 = 4  => 15 pairs (_)
C2,E2: 4.. / C2 = 4  => 19 pairs (_) / E2 = 4  =>  0 pairs (X)
F1,F9: 4.. / F1 = 4  =>  0 pairs (X) / F9 = 4  => 15 pairs (_)
F1,F3: 5.. / F1 = 5  => 15 pairs (_) / F3 = 5  =>  0 pairs (X)
G2,G3: 5.. / G2 = 5  =>  0 pairs (X) / G3 = 5  => 15 pairs (_)
D7,E7: 5.. / D7 = 5  => 18 pairs (_) / E7 = 5  => 21 pairs (_)
C1,F1: 5.. / C1 = 5  =>  0 pairs (X) / F1 = 5  => 15 pairs (_)
C1,B3: 6.. / C1 = 6  => 18 pairs (_) / B3 = 6  => 17 pairs (_)
E1,E3: 6.. / E1 = 6  => 17 pairs (_) / E3 = 6  => 18 pairs (_)
B4,C4: 6.. / B4 = 6  => 18 pairs (_) / C4 = 6  => 17 pairs (_)
D6,F6: 6.. / D6 = 6  =>  0 pairs (X) / F6 = 6  => 15 pairs (_)
D9,F9: 6.. / D9 = 6  => 15 pairs (_) / F9 = 6  =>  0 pairs (X)
C1,E1: 6.. / C1 = 6  => 18 pairs (_) / E1 = 6  => 17 pairs (_)
B3,E3: 6.. / B3 = 6  => 17 pairs (_) / E3 = 6  => 18 pairs (_)
B3,B4: 6.. / B3 = 6  => 17 pairs (_) / B4 = 6  => 18 pairs (_)
C1,C4: 6.. / C1 = 6  => 18 pairs (_) / C4 = 6  => 17 pairs (_)
D6,D9: 6.. / D6 = 6  =>  0 pairs (X) / D9 = 6  => 15 pairs (_)
F6,F9: 6.. / F6 = 6  => 15 pairs (_) / F9 = 6  =>  0 pairs (X)
D1,D3: 7.. / D1 = 7  => 17 pairs (_) / D3 = 7  => 23 pairs (_)
B8,C8: 7.. / B8 = 7  =>  0 pairs (*) / C8 = 7  =>  0 pairs (X)
H5,H6: 8.. / H5 = 8  => 15 pairs (_) / H6 = 8  => 15 pairs (_)
A7,C7: 8.. / A7 = 8  =>  0 pairs (X) / C7 = 8  => 17 pairs (_)
A6,H6: 8.. / A6 = 8  => 15 pairs (_) / H6 = 8  => 15 pairs (_)
C5,C7: 8.. / C5 = 8  =>  0 pairs (X) / C7 = 8  => 17 pairs (_)
D3,E3: 9.. / D3 = 9  => 16 pairs (_) / E3 = 9  => 16 pairs (_)
D8,E8: 9.. / D8 = 9  => 16 pairs (_) / E8 = 9  => 16 pairs (_)
D3,D8: 9.. / D3 = 9  => 16 pairs (_) / D8 = 9  => 16 pairs (_)
E3,E8: 9.. / E3 = 9  => 16 pairs (_) / E8 = 9  => 16 pairs (_)
* DURATION: 0:00:52.737574  START: 02:22:44.779787  END: 02:23:37.517361 2019-05-01
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,B8,C7,C8,D6,D8,D9,E8,F6,F8,F9,G2,G3,H5,H6)
* .8....3929..8.2.76..2....48.....8931.1...96.7.93.7.4.5.4...72696.....854529.8.713
* PAIR B2: 3,5 BLK 1
B3: 3,5,6,7                              # reduction candidate for 3,5
B3: 3,5 => SOLVED
* 186745392954832176732961548267458931415329687893176425348517269671293854529684713
B3: 6,7                                  # 17 pairs
* PAIR G2: 1,5 ROW 2
C2: 1,5,4                                # reduction candidate for 1,5
C2: 1,5 => CTR
* .8....392935842176.62...548.56.28931.14..96.7.931764.5348517269671293854529684713
C2: 4                                    # 19 pairs
* PAIR G3: 1,5 ROW 3
F3: 1,5,3                                # reduction candidate for 1,5
F3: 1,5 => SOLVED
* 186745392954832176732961548267458931415329687893176425348517269671293854529684713
F3: 3 => CTR
* .8...53929..8.2.76..2..3.48.....8931.1...96.7.93.7.4.5348..7269671...854529.8.713
* PAIR A6: 2,8 BLK 4
A5: 2,8,4                                # reduction candidate for 2,8
A5: 4                                    # 19 pairs
A5: 2,8                                  # 19 pairs
* PAIR H5: 2,8 ROW 5
A5: 2,8,4                                # reduction candidate for 2,8
A5: 4                                    # 19 pairs
A5: 2,8                                  # 19 pairs
* PAIR C7: 1,8 BLK 7
A7: 1,8,3                                # reduction candidate for 1,8
A7: 1,8 => CTR
* .8....3929..8.2.763.2....48.....8931.1...96.7.93.7.4.5.4...7269637..1854529.8.713
A7: 3 => SOLVED
* 186745392954832176732961548267458931415329687893176425348517269671293854529684713
* PAIR B8: 3,7 COL B
B3: 3,7,5,6                              # reduction candidate for 3,7
B3: 3,7 => SOLVED
* 186745392954832176732961548267458931415329687893176425348517269671293854529684713
B3: 5,6                                  # 17 pairs
* PAIR C8: 1,7 COL C
C1: 1,7,4,5,6                            # reduction candidate for 1,7
C1: 1,7                                  # 19 pairs
C1: 4,5,6                                # 16 pairs
* PAIR F8: 1,3 BLK 8
D7: 1,3,5                                # reduction candidate for 1,3
D7: 1,3                                  # 21 pairs
E7: 1,3,5                                # reduction candidate for 1,3
E7: 1,3                                  # 18 pairs
* PAIR F8: 1,3 COL F
F3: 1,3,5                                # reduction candidate for 1,3
F3: 5 => CTR
* .85.6.39293.8.2576762..5148.5...8931.1...96.7.93.7.4.5.4...72696....3854529.8.713
F3: 1,3                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060905-absurd-base-pr-000.dot
* REASONING
* PRF # B3: 3,5 => SOL
* DIS # C2: 1,5 => CTR => C2: 4
* PRF # F3: 1,5 => SOL
* DIS # F3: 3 => CTR => F3: 1,5
* DIS # A7: 1,8 => CTR => A7: 3
* PRF # A7: 3 => SOL
* PRF # B3: 3,7 => SOL
* DIS # F3: 5 => CTR => F3: 1,3
* CNT   8 HDP CHAINS /  20 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,B8,C7,C8,D6,D8,D9,E8,F6,F8,F9,G2,G3,H5,H6)
* .8....3929..8.2.76..2....48.....8931.1...96.7.93.7.4.5.4...72696.....854529.8.713
* PAIR B2: 3,5 BLK 1
B3: 3,5,6,7                              # reduction candidate for 3,5
B3: 3,5 => SOLVED
* 186745392954832176732961548267458931415329687893176425348517269671293854529684713
* DURATION: 0:00:01.781611  START: 02:23:53.239307  END: 02:23:55.020918 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060905-absurd-base-pr-001.dot
* REASONING
* PRF # B3: 3,5 => SOL
* STA B3: 3,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060905, absurd

Solution

position: 186745392954832176732961548267458931415329687893176425348517269671293854529684713 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 # B3: 3,5 => SOL
* INC # B3: 6,7 => UNS
* DIS # C2: 1,5 => CTR => C2: 4
* INC # C2: 4 => UNS
* PRF # F3: 1,5 => SOL
* DIS # F3: 3 => CTR => F3: 1,5
* INC # A5: 2,8 => UNS
* INC # A5: 4 => UNS
* INC # A5: 2,8 => UNS
* INC # A5: 4 => UNS
* DIS # A7: 1,8 => CTR => A7: 3
* PRF # A7: 3 => SOL
* PRF # B3: 3,7 => SOL
* INC # B3: 5,6 => UNS
* INC # C1: 1,7 => UNS
* INC # C1: 4,5,6 => UNS
* INC # D7: 1,3 => UNS
* INC # E7: 1,3 => UNS
* INC # F3: 1,3 => UNS
* DIS # F3: 5 => CTR => F3: 1,3
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # B3: 3,5 => SOL
* STA B3: 3,5
* CNT   1 HDP CHAINS /   1 HYP OPENED