Analysis of zz-www.sudokuoftheday.co.uk-20190203-absurd-base.sdk

Contents

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

level: medium

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

position: 6...9...37..5...28.8.4..........8.......3.4....37.1....6..7.3..2.5....6...92...8. initial

Autosolve

position: 65.89..437.451..28.8.4..........823.8...3.4....37.18.646817.3.22.538..6...92...8. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F3: 2,7 => SOL
* DIS # F3: 3,6 => CTR => F3: 2,7
* DIS # F3: 3,6 => CTR => F3: 2,7
* PRF # F3: 2,7 => SOL
* PRF # F3: 2,6 => SOL
* DIS # G8: 1,7 => CTR => G8: 9
* PRF # G8: 9 => SOL
* PRF # G9: 1,7 => SOL
* DIS # G9: 5 => CTR => G9: 1,7
* DIS # G3: 6,9 => CTR => G3: 5
* PRF # G3: 5 => SOL
* DIS # G3: 6 => CTR => G3: 5,9
* PRF # I4: 5,9 => SOL
* DIS # A4: 1 => CTR => A4: 5,9
* PRF # I5: 1,7 => SOL
* PRF # I4: 5,9 => SOL
* DIS # B9: 1,7 => CTR => B9: 3
* DIS # G8: 1,7 => CTR => G8: 9
* PRF # G8: 9 => SOL
* PRF # I8: 1,7 => SOL
* DIS # I8: 4,9 => CTR => I8: 1,7
* DIS # B9: 7 => CTR => B9: 1,3
* DIS # I8: 4,9 => CTR => I8: 1,7
* PRF # I8: 1,7 => SOL
* PRF # F9: 5,6 => SOL
* DIS # F9: 4 => CTR => F9: 5,6
* CNT  26 HDP CHAINS /  37 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 # F3: 2,7 => SOL
* STA F3: 2,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

6...9...37..5...28.8.4..........8.......3.4....37.1....6..7.3..2.5....6...92...8. initial
65.89..437.451..28.8.4..........823.8...3.4....37.18.646817.3.22.538..6...92...8. autosolve
652897143794513628381462579917648235826935417543721896468179352275384961139256784 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (28)
C1: 1,2
B2: 3,9
A3: 3,9
C3: 1,2
F1: 2,7
F2: 3,6
E3: 2,6
G1: 1,7
G2: 6,9
H3: 1,7
I3: 5,9
C4: 6,7
C5: 6,7
A6: 5,9
B6: 2,4
D4: 6,9
E4: 4,5
D5: 6,9
F5: 2,5
E6: 2,4
H5: 1,7
H6: 5,9
B8: 1,7
A9: 1,3
F7: 5,9
F8: 4,9
E9: 5,6
H7: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,C3: 1.. / C1 = 1  =>  0 pairs (X) / C3 = 1  => 27 pairs (_)
G1,H3: 1.. / G1 = 1  => 27 pairs (_) / H3 = 1  =>  0 pairs (X)
C1,G1: 1.. / C1 = 1  =>  0 pairs (X) / G1 = 1  => 27 pairs (_)
C3,H3: 1.. / C3 = 1  => 27 pairs (_) / H3 = 1  =>  0 pairs (X)
A4,A9: 1.. / A4 = 1  =>  0 pairs (X) / A9 = 1  => 28 pairs (_)
H3,H5: 1.. / H3 = 1  =>  0 pairs (X) / H5 = 1  => 27 pairs (_)
C1,C3: 2.. / C1 = 2  => 27 pairs (_) / C3 = 2  =>  0 pairs (X)
B5,B6: 2.. / B5 = 2  =>  0 pairs (*) / B6 = 2  =>  0 pairs (X)
F5,E6: 2.. / F5 = 2  =>  0 pairs (X) / E6 = 2  =>  0 pairs (_)
C1,F1: 2.. / C1 = 2  => 27 pairs (_) / F1 = 2  =>  0 pairs (X)
B5,F5: 2.. / B5 = 2  =>  0 pairs (*) / F5 = 2  =>  0 pairs (X)
B6,E6: 2.. / B6 = 2  =>  0 pairs (X) / E6 = 2  =>  0 pairs (_)
E3,E6: 2.. / E3 = 2  =>  0 pairs (X) / E6 = 2  =>  0 pairs (_)
B2,A3: 3.. / B2 = 3  =>  0 pairs (X) / A3 = 3  => 28 pairs (_)
F2,F3: 3.. / F2 = 3  => 28 pairs (_) / F3 = 3  =>  0 pairs (X)
A9,B9: 3.. / A9 = 3  =>  0 pairs (X) / B9 = 3  => 28 pairs (_)
B2,F2: 3.. / B2 = 3  =>  0 pairs (X) / F2 = 3  => 28 pairs (_)
A3,F3: 3.. / A3 = 3  => 28 pairs (_) / F3 = 3  =>  0 pairs (X)
A3,A9: 3.. / A3 = 3  => 28 pairs (_) / A9 = 3  =>  0 pairs (X)
B2,B9: 3.. / B2 = 3  =>  0 pairs (X) / B9 = 3  => 28 pairs (_)
B4,B6: 4.. / B4 = 4  =>  0 pairs (X) / B6 = 4  =>  0 pairs (_)
E4,E6: 4.. / E4 = 4  =>  0 pairs (*) / E6 = 4  =>  0 pairs (X)
F8,F9: 4.. / F8 = 4  =>  0 pairs (*) / F9 = 4  =>  0 pairs (X)
I8,I9: 4.. / I8 = 4  =>  0 pairs (X) / I9 = 4  =>  0 pairs (_)
B4,E4: 4.. / B4 = 4  =>  0 pairs (X) / E4 = 4  =>  0 pairs (_)
B6,E6: 4.. / B6 = 4  =>  0 pairs (*) / E6 = 4  =>  0 pairs (X)
F8,I8: 4.. / F8 = 4  =>  0 pairs (*) / I8 = 4  =>  0 pairs (X)
F9,I9: 4.. / F9 = 4  =>  0 pairs (X) / I9 = 4  =>  0 pairs (_)
G3,I3: 5.. / G3 = 5  =>  0 pairs (*) / I3 = 5  =>  0 pairs (X)
A4,A6: 5.. / A4 = 5  =>  0 pairs (X) / A6 = 5  =>  0 pairs (_)
E4,F5: 5.. / E4 = 5  =>  0 pairs (X) / F5 = 5  =>  0 pairs (_)
F5,I5: 5.. / F5 = 5  =>  0 pairs (*) / I5 = 5  =>  0 pairs (X)
A6,H6: 5.. / A6 = 5  =>  0 pairs (*) / H6 = 5  =>  0 pairs (X)
F7,H7: 5.. / F7 = 5  =>  0 pairs (X) / H7 = 5  =>  0 pairs (_)
E4,E9: 5.. / E4 = 5  =>  0 pairs (X) / E9 = 5  =>  0 pairs (_)
G3,G9: 5.. / G3 = 5  =>  0 pairs (*) / G9 = 5  =>  0 pairs (X)
H6,H7: 5.. / H6 = 5  =>  0 pairs (X) / H7 = 5  =>  0 pairs (_)
G2,G3: 6.. / G2 = 6  => 28 pairs (_) / G3 = 6  =>  0 pairs (X)
C4,C5: 6.. / C4 = 6  => 26 pairs (_) / C5 = 6  => 25 pairs (_)
D4,D5: 6.. / D4 = 6  => 25 pairs (_) / D5 = 6  => 26 pairs (_)
E9,F9: 6.. / E9 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
F2,G2: 6.. / F2 = 6  =>  0 pairs (X) / G2 = 6  => 28 pairs (_)
C4,D4: 6.. / C4 = 6  => 26 pairs (_) / D4 = 6  => 25 pairs (_)
C5,D5: 6.. / C5 = 6  => 25 pairs (_) / D5 = 6  => 26 pairs (_)
E3,E9: 6.. / E3 = 6  =>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
F1,F3: 7.. / F1 = 7  => 27 pairs (_) / F3 = 7  =>  0 pairs (X)
G1,H3: 7.. / G1 = 7  =>  0 pairs (X) / H3 = 7  => 27 pairs (_)
C4,C5: 7.. / C4 = 7  => 25 pairs (_) / C5 = 7  => 26 pairs (_)
B8,B9: 7.. / B8 = 7  => 30 pairs (_) / B9 = 7  =>  0 pairs (X)
F1,G1: 7.. / F1 = 7  => 27 pairs (_) / G1 = 7  =>  0 pairs (X)
F3,H3: 7.. / F3 = 7  =>  0 pairs (X) / H3 = 7  => 27 pairs (_)
C4,I4: 7.. / C4 = 7  => 25 pairs (_) / I4 = 7  => 26 pairs (_)
H3,H5: 7.. / H3 = 7  => 27 pairs (_) / H5 = 7  =>  0 pairs (X)
B2,A3: 9.. / B2 = 9  => 28 pairs (_) / A3 = 9  =>  0 pairs (X)
D4,D5: 9.. / D4 = 9  => 26 pairs (_) / D5 = 9  => 25 pairs (_)
F7,F8: 9.. / F7 = 9  =>  0 pairs (*) / F8 = 9  =>  0 pairs (X)
B2,G2: 9.. / B2 = 9  => 28 pairs (_) / G2 = 9  =>  0 pairs (X)
A6,H6: 9.. / A6 = 9  =>  0 pairs (X) / H6 = 9  =>  0 pairs (_)
F7,H7: 9.. / F7 = 9  =>  0 pairs (*) / H7 = 9  =>  0 pairs (X)
H6,H7: 9.. / H6 = 9  =>  0 pairs (*) / H7 = 9  =>  0 pairs (X)
* DURATION: 0:01:33.788096  START: 03:25:42.490613  END: 03:27:16.278709 2019-05-01
* CP COUNT: (60)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A9,B2,B6,B8,C1,C3,C4,C5,D4,D5,E3,E4,E6,E9,F1,F2,F5,F7,F8,G1,G2,H3,H5,H6,H7,I3)
* 65.89..437.451..28.8.4..........823.8...3.4....37.18.646817.3.22.538..6...92...8.
* PAIR F1: 2,7 BLK 2
F3: 2,7,3,6                              # reduction candidate for 2,7
F3: 2,7 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
F3: 3,6 => CTR
* 6528971437.451..28.8142.5799....823.8...324155237418964681793522.5384.6...9265784
* PAIR F2: 3,6 BLK 2
F3: 3,6,2,7                              # reduction candidate for 3,6
F3: 3,6 => CTR
* 6528971437.451..28.8142.5799....823.8...324155237418964681793522.5384.6...9265784
F3: 2,7 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
* PAIR E3: 2,6 BLK 2
F3: 2,6,3,7                              # reduction candidate for 2,6
F3: 2,6 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
F3: 3,7                                  # 29 pairs
* PAIR G1: 1,7 COL G
G8: 1,7,9                                # reduction candidate for 1,7
G8: 1,7 => CTR
* 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8.
G8: 9 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
G9: 1,7,5                                # reduction candidate for 1,7
G9: 1,7 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
G9: 5 => CTR
* 65.89..437.451..28.8.4....5....5823.8...324..52374189646817.3.22.538..6...92..58.
* PAIR G2: 6,9 BLK 3
G3: 6,9,5                                # reduction candidate for 6,9
G3: 6,9 => CTR
* 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8.
G3: 5 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
* PAIR I3: 5,9 BLK 3
G3: 5,9,6                                # reduction candidate for 5,9
G3: 6 => CTR
* 65.89..437.451..28.8.4..6.5.....823.8...354....37218.646817.3.22.538..6...92...8.
G3: 5,9                                  # 28 pairs
* PAIR I3: 5,9 COL I
I4: 5,9,1,7                              # reduction candidate for 5,9
I4: 5,9 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
I4: 1,7                                  # 30 pairs
I5: 5,9,1,7                              # reduction candidate for 5,9
I5: 5,9                                  # 30 pairs
* PAIR A6: 5,9 BLK 4
A4: 5,9,1                                # reduction candidate for 5,9
A4: 1 => CTR
* 65.89..43734516928.8.4.....1....823.8...3.4..5.37.18964681793522.5384.6.3.92...84
A4: 5,9                                  # 28 pairs
* PAIR H5: 1,7 BLK 6
I4: 1,7,5,9                              # reduction candidate for 1,7
I4: 1,7                                  # 30 pairs
I5: 1,7,5,9                              # reduction candidate for 1,7
I5: 1,7 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
I5: 5,9                                  # 30 pairs
* PAIR H6: 5,9 BLK 6
I4: 5,9,1,7                              # reduction candidate for 5,9
I4: 5,9 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
I4: 1,7                                  # 30 pairs
I5: 5,9,1,7                              # reduction candidate for 5,9
I5: 5,9                                  # 30 pairs
* PAIR B8: 1,7 BLK 7
B9: 1,7,3                                # reduction candidate for 1,7
B9: 1,7 => CTR
* 65.89..4373451692898.423675.....823.8...3.4....37.18.646817.3.22.538..6...92...8.
B9: 3                                    # 28 pairs
* PAIR B8: 1,7 ROW 8
G8: 1,7,9                                # reduction candidate for 1,7
G8: 1,7 => CTR
* 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8.
G8: 9 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
I8: 1,7,4,9                              # reduction candidate for 1,7
I8: 1,7 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
I8: 4,9 => CTR
* 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8.
* PAIR A9: 1,3 BLK 7
B9: 1,3,7                                # reduction candidate for 1,3
B9: 7 => CTR
* 65.89..4373451692898.423675.....823.8...3.4....37.18.646817.3.22.538..6...92...8.
B9: 1,3                                  # 30 pairs
* PAIR F8: 4,9 ROW 8
I8: 4,9,1,7                              # reduction candidate for 4,9
I8: 4,9 => CTR
* 65.89..437.451..28.8.4....5.....823.8...354....37218564681793.22.538..6...92...8.
I8: 1,7 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
* PAIR E9: 5,6 BLK 8
F9: 5,6,4                                # reduction candidate for 5,6
F9: 5,6 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
F9: 4 => CTR
* 65.89..437.451..28.8.42........5823.8...324.552374189646817.3.22.538..6...9264.8.
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190203-absurd-base-pr-000.dot
* REASONING
* PRF # F3: 2,7 => SOL
* DIS # F3: 3,6 => CTR => F3: 2,7
* DIS # F3: 3,6 => CTR => F3: 2,7
* PRF # F3: 2,7 => SOL
* PRF # F3: 2,6 => SOL
* DIS # G8: 1,7 => CTR => G8: 9
* PRF # G8: 9 => SOL
* PRF # G9: 1,7 => SOL
* DIS # G9: 5 => CTR => G9: 1,7
* DIS # G3: 6,9 => CTR => G3: 5
* PRF # G3: 5 => SOL
* DIS # G3: 6 => CTR => G3: 5,9
* PRF # I4: 5,9 => SOL
* DIS # A4: 1 => CTR => A4: 5,9
* PRF # I5: 1,7 => SOL
* PRF # I4: 5,9 => SOL
* DIS # B9: 1,7 => CTR => B9: 3
* DIS # G8: 1,7 => CTR => G8: 9
* PRF # G8: 9 => SOL
* PRF # I8: 1,7 => SOL
* DIS # I8: 4,9 => CTR => I8: 1,7
* DIS # B9: 7 => CTR => B9: 1,3
* DIS # I8: 4,9 => CTR => I8: 1,7
* PRF # I8: 1,7 => SOL
* PRF # F9: 5,6 => SOL
* DIS # F9: 4 => CTR => F9: 5,6
* CNT  26 HDP CHAINS /  37 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A9,B2,B6,B8,C1,C3,C4,C5,D4,D5,E3,E4,E6,E9,F1,F2,F5,F7,F8,G1,G2,H3,H5,H6,H7,I3)
* 65.89..437.451..28.8.4..........823.8...3.4....37.18.646817.3.22.538..6...92...8.
* PAIR F1: 2,7 BLK 2
F3: 2,7,3,6                              # reduction candidate for 2,7
F3: 2,7 => SOLVED
* 652897143794513628381462579917648235826935417543721896468179352275384961139256784
* DURATION: 0:00:02.011539  START: 03:27:51.992296  END: 03:27:54.003835 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190203-absurd-base-pr-001.dot
* REASONING
* PRF # F3: 2,7 => SOL
* STA F3: 2,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190203, absurd

Solution

position: 652897143794513628381462579917648235826935417543721896468179352275384961139256784 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 # F3: 2,7 => SOL
* DIS # F3: 3,6 => CTR => F3: 2,7
* DIS # F3: 3,6 => CTR => F3: 2,7
* PRF # F3: 2,7 => SOL
* PRF # F3: 2,6 => SOL
* INC # F3: 3,7 => UNS
* DIS # G8: 1,7 => CTR => G8: 9
* PRF # G8: 9 => SOL
* PRF # G9: 1,7 => SOL
* DIS # G9: 5 => CTR => G9: 1,7
* DIS # G3: 6,9 => CTR => G3: 5
* PRF # G3: 5 => SOL
* INC # G3: 5,9 => UNS
* DIS # G3: 6 => CTR => G3: 5,9
* PRF # I4: 5,9 => SOL
* INC # I4: 1,7 => UNS
* INC # I5: 5,9 => UNS
* INC # A4: 5,9 => UNS
* DIS # A4: 1 => CTR => A4: 5,9
* INC # I4: 1,7 => UNS
* PRF # I5: 1,7 => SOL
* INC # I5: 5,9 => UNS
* PRF # I4: 5,9 => SOL
* INC # I4: 1,7 => UNS
* INC # I5: 5,9 => UNS
* DIS # B9: 1,7 => CTR => B9: 3
* INC # B9: 3 => UNS
* DIS # G8: 1,7 => CTR => G8: 9
* PRF # G8: 9 => SOL
* PRF # I8: 1,7 => SOL
* DIS # I8: 4,9 => CTR => I8: 1,7
* INC # B9: 1,3 => UNS
* DIS # B9: 7 => CTR => B9: 1,3
* DIS # I8: 4,9 => CTR => I8: 1,7
* PRF # I8: 1,7 => SOL
* PRF # F9: 5,6 => SOL
* DIS # F9: 4 => CTR => F9: 5,6
* CNT  37 HDP CHAINS /  37 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # F3: 2,7 => SOL
* STA F3: 2,7
* CNT   1 HDP CHAINS /   1 HYP OPENED