Analysis of zz-www.sudokuoftheday.co.uk-20190407-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019

position: ...1...3...4.7...8812..4..5....35....9.78.1..........6..........28..75..1..9....3 initial

Autosolve

position: ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.2.3286.75..1..9.2863 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A6: 5,7 => SOL
* DIS # B9: 5,7 => CTR => B9: 4
* PRF # G4: 7,9 => SOL
* DIS # G4: 4 => CTR => G4: 7,9
* DIS # A6: 4,5 => CTR => A6: 2,7
* PRF # A6: 5,7 => SOL
* PRF # H6: 4 => SOL
* PRF # A4: 2,4 => SOL
* DIS # A4: 7 => CTR => A4: 2,4
* PRF # A6: 5,7 => SOL
* PRF # G4: 7,9 => SOL
* DIS # G4: 4 => CTR => G4: 7,9
* PRF # H6: 4,5 => SOL
* DIS # H6: 7 => CTR => H6: 4,5
* DIS # B9: 7 => CTR => B9: 4,5
* DIS # E7: 4,5 => CTR => E7: 1
* PRF # E7: 1 => SOL
* DIS # B9: 5,7 => CTR => B9: 4
* DIS # E7: 5 => CTR => E7: 1,4
* DIS # E7: 4,5 => CTR => E7: 1
* PRF # E7: 1 => SOL
* DIS # B9: 7 => CTR => B9: 4,5
* PRF # G4: 4,7 => SOL
* DIS # G4: 9 => CTR => G4: 4,7
* CNT  24 HDP CHAINS /  34 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 # A6: 5,7 => SOL
* STA A6: 5,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...1...3...4.7...8812..4..5....35....9.78.1..........6..........28..75..1..9....3 initial
..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.2.3286.75..1..9.2863 autosolve
579128634634579218812364975261435789493786152785291346956813427328647591147952863 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A1: 5,7
B1: 5,7
G3: 7,9
H3: 7,9
A5: 4,5
C6: 5,7
D4: 2,4
D6: 2,4
I4: 7,9
H5: 4,5
B7: 4,5
C9: 5,7
E8: 1,4
E9: 4,5
G7: 4,7
I7: 1,7
H8: 4,9
I8: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E7,E8: 1.. / E7 = 1  =>  0 pairs (*) / E8 = 1  =>  0 pairs (X)
I7,I8: 1.. / I7 = 1  =>  0 pairs (X) / I8 = 1  =>  0 pairs (_)
E7,I7: 1.. / E7 = 1  =>  0 pairs (*) / I7 = 1  =>  0 pairs (X)
E8,I8: 1.. / E8 = 1  =>  0 pairs (X) / I8 = 1  =>  0 pairs (_)
A4,A6: 2.. / A4 = 2  =>  0 pairs (*) / A6 = 2  =>  0 pairs (X)
D4,D6: 2.. / D4 = 2  => 18 pairs (_) / D6 = 2  =>  0 pairs (*)
A4,D4: 2.. / A4 = 2  =>  0 pairs (*) / D4 = 2  =>  0 pairs (X)
A6,D6: 2.. / A6 = 2  => 18 pairs (_) / D6 = 2  =>  0 pairs (*)
D4,D6: 4.. / D4 = 4  =>  0 pairs (*) / D6 = 4  =>  0 pairs (X)
B7,B9: 4.. / B7 = 4  =>  0 pairs (X) / B9 = 4  => 14 pairs (_)
G7,H8: 4.. / G7 = 4  =>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
A5,H5: 4.. / A5 = 4  => 18 pairs (_) / H5 = 4  =>  0 pairs (X)
E8,H8: 4.. / E8 = 4  =>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
B9,E9: 4.. / B9 = 4  => 14 pairs (_) / E9 = 4  =>  0 pairs (X)
G4,G7: 4.. / G4 = 4  =>  0 pairs (X) / G7 = 4  =>  0 pairs (_)
A1,B1: 5.. / A1 = 5  => 16 pairs (_) / B1 = 5  =>  0 pairs (X)
H5,H6: 5.. / H5 = 5  => 18 pairs (_) / H6 = 5  =>  0 pairs (X)
E7,E9: 5.. / E7 = 5  =>  0 pairs (X) / E9 = 5  => 14 pairs (_)
A5,H5: 5.. / A5 = 5  =>  0 pairs (X) / H5 = 5  => 18 pairs (_)
B7,E7: 5.. / B7 = 5  => 14 pairs (_) / E7 = 5  =>  0 pairs (X)
C6,C9: 5.. / C6 = 5  => 16 pairs (_) / C9 = 5  =>  0 pairs (X)
A1,B1: 7.. / A1 = 7  =>  0 pairs (X) / B1 = 7  => 16 pairs (_)
G3,H3: 7.. / G3 = 7  =>  0 pairs (X) / H3 = 7  =>  0 pairs (_)
B9,C9: 7.. / B9 = 7  =>  0 pairs (X) / C9 = 7  => 16 pairs (_)
G7,I7: 7.. / G7 = 7  =>  0 pairs (X) / I7 = 7  =>  0 pairs (_)
B1,B9: 7.. / B1 = 7  => 16 pairs (_) / B9 = 7  =>  0 pairs (X)
C6,C9: 7.. / C6 = 7  =>  0 pairs (X) / C9 = 7  => 16 pairs (_)
H3,H6: 7.. / H3 = 7  =>  0 pairs (*) / H6 = 7  =>  0 pairs (X)
I4,I7: 7.. / I4 = 7  =>  0 pairs (X) / I7 = 7  =>  0 pairs (_)
G3,H3: 9.. / G3 = 9  =>  0 pairs (*) / H3 = 9  =>  0 pairs (X)
G4,I4: 9.. / G4 = 9  =>  0 pairs (X) / I4 = 9  =>  0 pairs (_)
H8,I8: 9.. / H8 = 9  =>  0 pairs (*) / I8 = 9  =>  0 pairs (X)
G3,G4: 9.. / G3 = 9  =>  0 pairs (*) / G4 = 9  =>  0 pairs (X)
H3,H8: 9.. / H3 = 9  =>  0 pairs (X) / H8 = 9  =>  0 pairs (_)
I4,I8: 9.. / I4 = 9  =>  0 pairs (*) / I8 = 9  =>  0 pairs (X)
* DURATION: 0:00:41.025591  START: 05:07:45.165849  END: 05:08:26.191440 2019-05-01
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B1,B7,C6,C9,D4,D6,E8,E9,G3,G7,H3,H5,H8,I4,I7,I8)
* ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.2.3286.75..1..9.2863
* PAIR A1: 5,7 COL A
A6: 5,7,2,4                              # reduction candidate for 5,7
A6: 5,7 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
A6: 2,4                                  # 20 pairs
* PAIR B1: 5,7 COL B
B9: 5,7,4                                # reduction candidate for 5,7
B9: 5,7 => CTR
* ..9128634634579218812364..5.61.35.8..937861.2.8..913.69468537213286175491..942863
B9: 4                                    # 14 pairs
* PAIR G3: 7,9 COL G
G4: 7,9,4                                # reduction candidate for 7,9
G4: 7,9 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
G4: 4 => CTR
* ..9128634634579218812364975.61.3548..937861.2.8..913.69.68.3.2.3286.75..1..9.2863
* PAIR A5: 4,5 BLK 4
A6: 4,5,2,7                              # reduction candidate for 4,5
A6: 4,5 => CTR
* ..9128634634579218812364..5261435.8..937861.2.872913.69.68.34273286475911..9.2863
A6: 2,7                                  # 19 pairs
* PAIR C6: 5,7 BLK 4
A6: 5,7,2,4                              # reduction candidate for 5,7
A6: 5,7 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
A6: 2,4                                  # 20 pairs
* PAIR C6: 5,7 ROW 6
H6: 5,7,4                                # reduction candidate for 5,7
H6: 4 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
H6: 5,7                                  # 20 pairs
* PAIR D4: 2,4 ROW 4
A4: 2,4,7                                # reduction candidate for 2,4
A4: 2,4 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
A4: 7 => CTR
* ..9128634634579218812364..5761235489493786152.8..913.69.68.3.2.3286.75..1..9.2863
* PAIR D6: 2,4 ROW 6
A6: 2,4,5,7                              # reduction candidate for 2,4
A6: 5,7 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
A6: 2,4                                  # 20 pairs
* PAIR I4: 7,9 BLK 6
G4: 7,9,4                                # reduction candidate for 7,9
G4: 7,9 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
G4: 4 => CTR
* ..9128634634579218812364975.61.3548..937861.2.8..913.69.68.3.2.3286.75..1..9.2863
* PAIR H5: 4,5 BLK 6
H6: 4,5,7                                # reduction candidate for 4,5
H6: 4,5 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
H6: 7 => CTR
* ..9128634634579218812364..5.61.35.8..93786152.8..913769.68.3.273286.754.1..9.2863
* PAIR B7: 4,5 BLK 7
B9: 4,5,7                                # reduction candidate for 4,5
B9: 7 => CTR
* ..9128634634579218812364..5.61.35.8..937861.2.8..913.6946853721328617549175942863
B9: 4,5                                  # 16 pairs
* PAIR B7: 4,5 ROW 7
E7: 4,5,1                                # reduction candidate for 4,5
E7: 4,5 => CTR
* ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.213286175491..9.2863
E7: 1 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
* PAIR C9: 5,7 BLK 7
B9: 5,7,4                                # reduction candidate for 5,7
B9: 5,7 => CTR
* ..9128634634579218812364..5.61.35.8..937861.2.8..913.69468537213286175491..942863
B9: 4                                    # 14 pairs
* PAIR E8: 1,4 BLK 8
E7: 1,4,5                                # reduction candidate for 1,4
E7: 5 => CTR
* ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.6853.213286175491..942863
E7: 1,4                                  # 14 pairs
* PAIR E9: 4,5 BLK 8
E7: 4,5,1                                # reduction candidate for 4,5
E7: 4,5 => CTR
* ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.213286175491..9.2863
E7: 1 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
* PAIR E9: 4,5 ROW 9
B9: 4,5,7                                # reduction candidate for 4,5
B9: 7 => CTR
* ..9128634634579218812364..5.61.35.8..937861.2.8..913.6946853721328617549175942863
B9: 4,5                                  # 16 pairs
* PAIR G7: 4,7 COL G
G4: 4,7,9                                # reduction candidate for 4,7
G4: 4,7 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
G4: 9 => CTR
* ..9128634634579218812364..5.61.35987.937861.2.8..913.69.68.3.2.3286.75..1..9.2863
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190407-absurd-base-pr-000.dot
* REASONING
* PRF # A6: 5,7 => SOL
* DIS # B9: 5,7 => CTR => B9: 4
* PRF # G4: 7,9 => SOL
* DIS # G4: 4 => CTR => G4: 7,9
* DIS # A6: 4,5 => CTR => A6: 2,7
* PRF # A6: 5,7 => SOL
* PRF # H6: 4 => SOL
* PRF # A4: 2,4 => SOL
* DIS # A4: 7 => CTR => A4: 2,4
* PRF # A6: 5,7 => SOL
* PRF # G4: 7,9 => SOL
* DIS # G4: 4 => CTR => G4: 7,9
* PRF # H6: 4,5 => SOL
* DIS # H6: 7 => CTR => H6: 4,5
* DIS # B9: 7 => CTR => B9: 4,5
* DIS # E7: 4,5 => CTR => E7: 1
* PRF # E7: 1 => SOL
* DIS # B9: 5,7 => CTR => B9: 4
* DIS # E7: 5 => CTR => E7: 1,4
* DIS # E7: 4,5 => CTR => E7: 1
* PRF # E7: 1 => SOL
* DIS # B9: 7 => CTR => B9: 4,5
* PRF # G4: 4,7 => SOL
* DIS # G4: 9 => CTR => G4: 4,7
* CNT  24 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,B1,B7,C6,C9,D4,D6,E8,E9,G3,G7,H3,H5,H8,I4,I7,I8)
* ..9128634634579218812364..5.61.35.8..937861.2.8..913.69.68.3.2.3286.75..1..9.2863
* PAIR A1: 5,7 COL A
A6: 5,7,2,4                              # reduction candidate for 5,7
A6: 5,7 => SOLVED
* 579128634634579218812364975261435789493786152785291346956813427328647591147952863
* DURATION: 0:00:01.370291  START: 05:08:51.355830  END: 05:08:52.726121 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190407-absurd-base-pr-001.dot
* REASONING
* PRF # A6: 5,7 => SOL
* STA A6: 5,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190407, absurd

Solution

position: 579128634634579218812364975261435789493786152785291346956813427328647591147952863 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 # A6: 5,7 => SOL
* INC # A6: 2,4 => UNS
* DIS # B9: 5,7 => CTR => B9: 4
* INC # B9: 4 => UNS
* PRF # G4: 7,9 => SOL
* DIS # G4: 4 => CTR => G4: 7,9
* DIS # A6: 4,5 => CTR => A6: 2,7
* INC # A6: 2,7 => UNS
* PRF # A6: 5,7 => SOL
* INC # A6: 2,4 => UNS
* INC # H6: 5,7 => UNS
* PRF # H6: 4 => SOL
* PRF # A4: 2,4 => SOL
* DIS # A4: 7 => CTR => A4: 2,4
* INC # A6: 2,4 => UNS
* PRF # A6: 5,7 => SOL
* PRF # G4: 7,9 => SOL
* DIS # G4: 4 => CTR => G4: 7,9
* PRF # H6: 4,5 => SOL
* DIS # H6: 7 => CTR => H6: 4,5
* INC # B9: 4,5 => UNS
* DIS # B9: 7 => CTR => B9: 4,5
* DIS # E7: 4,5 => CTR => E7: 1
* PRF # E7: 1 => SOL
* DIS # B9: 5,7 => CTR => B9: 4
* INC # B9: 4 => UNS
* INC # E7: 1,4 => UNS
* DIS # E7: 5 => CTR => E7: 1,4
* DIS # E7: 4,5 => CTR => E7: 1
* PRF # E7: 1 => SOL
* INC # B9: 4,5 => UNS
* DIS # B9: 7 => CTR => B9: 4,5
* PRF # G4: 4,7 => SOL
* DIS # G4: 9 => CTR => G4: 4,7
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A6: 5,7 => SOL
* STA A6: 5,7
* CNT   1 HDP CHAINS /   1 HYP OPENED