Analysis of zz-www.sudokuoftheday.co.uk-20190225-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: 7.....3....5....84.....8..2.61.49..8.9.....5.82..1...3..6.....94...3..1..7.9.1... initial

Autosolve

position: 782...3...15..3784.43..8..2561349278394....5.827.1.943136....29459.3..172789.143. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E2: 6,9 => CTR => E2: 2
* PRF # E2: 2 => SOL
* DIS # E2: 9 => CTR => E2: 2,6
* DIS # D8: 2,6 => CTR => D8: 8
* PRF # D8: 8 => SOL
* DIS # D3: 5,7 => CTR => D3: 1
* PRF # D3: 1 => SOL
* PRF # E7: 5,7 => SOL
* DIS # E7: 8 => CTR => E7: 5,7
* DIS # E1: 5 => CTR => E1: 6,9
* PRF # D1: 4,6 => SOL
* DIS # D3: 7 => CTR => D3: 1,5
* PRF # D5: 2,7 => SOL
* DIS # D5: 8 => CTR => D5: 2,7
* DIS # E5: 2,7 => CTR => E5: 8
* PRF # E5: 8 => SOL
* DIS # D1: 5,6 => CTR => D1: 1,4
* PRF # F1: 5,6 => SOL
* DIS # D8: 2,6 => CTR => D8: 8
* PRF # D8: 8 => SOL
* DIS # E1: 5,6 => CTR => E1: 9
* DIS # D7: 5,8 => CTR => D7: 4,7
* DIS # D8: 2 => CTR => D8: 6,8
* CNT  23 HDP CHAINS /  33 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 # E2: 6,9 => CTR => E2: 2
* PRF E2: 2 => SOL
* STA E2: 2
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

7.....3....5....84.....8..2.61.49..8.9.....5.82..1...3..6.....94...3..1..7.9.1... initial
782...3...15..3784.43..8..2561349278394....5.827.1.943136....29459.3..172789.143. autosolve
782495361915623784643178592561349278394287156827516943136754829459832617278961435 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A2: 6,9
A3: 6,9
D2: 2,6
E3: 5,7
H1: 6,9
I1: 1,5
G3: 1,5
H3: 6,9
F5: 2,7
D6: 5,6
F6: 5,6
G5: 1,6
I5: 1,6
F8: 2,6
E9: 5,6
G7: 5,8
G8: 6,8
I9: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,D3: 1.. / D1 = 1  =>  0 pairs (X) / D3 = 1  =>  0 pairs (_)
I1,G3: 1.. / I1 = 1  =>  0 pairs (*) / G3 = 1  =>  0 pairs (X)
G5,I5: 1.. / G5 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
D1,I1: 1.. / D1 = 1  =>  0 pairs (X) / I1 = 1  =>  0 pairs (_)
D3,G3: 1.. / D3 = 1  =>  0 pairs (*) / G3 = 1  =>  0 pairs (X)
G3,G5: 1.. / G3 = 1  =>  0 pairs (X) / G5 = 1  =>  0 pairs (_)
I1,I5: 1.. / I1 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
D2,E2: 2.. / D2 = 2  =>  0 pairs (X) / E2 = 2  =>  0 pairs (_)
D8,F8: 2.. / D8 = 2  =>  0 pairs (X) / F8 = 2  => 23 pairs (_)
E2,E5: 2.. / E2 = 2  =>  0 pairs (*) / E5 = 2  =>  0 pairs (X)
F5,F8: 2.. / F5 = 2  =>  0 pairs (X) / F8 = 2  => 23 pairs (_)
D1,F1: 4.. / D1 = 4  =>  0 pairs (*) / F1 = 4  =>  0 pairs (X)
D7,F7: 4.. / D7 = 4  => 19 pairs (_) / F7 = 4  =>  0 pairs (*)
D1,D7: 4.. / D1 = 4  =>  0 pairs (*) / D7 = 4  =>  0 pairs (X)
F1,F7: 4.. / F1 = 4  => 19 pairs (_) / F7 = 4  =>  0 pairs (*)
I1,G3: 5.. / I1 = 5  =>  0 pairs (X) / G3 = 5  =>  0 pairs (_)
D6,F6: 5.. / D6 = 5  => 20 pairs (_) / F6 = 5  =>  0 pairs (X)
G7,I9: 5.. / G7 = 5  =>  0 pairs (X) / I9 = 5  =>  0 pairs (_)
E9,I9: 5.. / E9 = 5  =>  0 pairs (X) / I9 = 5  =>  0 pairs (_)
G3,G7: 5.. / G3 = 5  =>  0 pairs (*) / G7 = 5  =>  0 pairs (X)
I1,I9: 5.. / I1 = 5  =>  0 pairs (X) / I9 = 5  =>  0 pairs (_)
A2,A3: 6.. / A2 = 6  =>  0 pairs (X) / A3 = 6  => 16 pairs (_)
H1,H3: 6.. / H1 = 6  => 16 pairs (_) / H3 = 6  =>  0 pairs (X)
D6,F6: 6.. / D6 = 6  =>  0 pairs (X) / F6 = 6  => 20 pairs (_)
G5,I5: 6.. / G5 = 6  =>  0 pairs (X) / I5 = 6  =>  0 pairs (_)
G8,I9: 6.. / G8 = 6  =>  0 pairs (*) / I9 = 6  =>  0 pairs (X)
A3,H3: 6.. / A3 = 6  => 16 pairs (_) / H3 = 6  =>  0 pairs (X)
E9,I9: 6.. / E9 = 6  =>  0 pairs (*) / I9 = 6  =>  0 pairs (X)
G5,G8: 6.. / G5 = 6  =>  0 pairs (X) / G8 = 6  =>  0 pairs (_)
I5,I9: 6.. / I5 = 6  =>  0 pairs (*) / I9 = 6  =>  0 pairs (X)
D3,E3: 7.. / D3 = 7  =>  0 pairs (X) / E3 = 7  => 24 pairs (_)
F5,F7: 7.. / F5 = 7  => 23 pairs (_) / F7 = 7  =>  0 pairs (X)
D5,E5: 8.. / D5 = 8  =>  0 pairs (X) / E5 = 8  =>  0 pairs (_)
G7,G8: 8.. / G7 = 8  =>  0 pairs (*) / G8 = 8  =>  0 pairs (X)
D8,G8: 8.. / D8 = 8  =>  0 pairs (*) / G8 = 8  =>  0 pairs (X)
E5,E7: 8.. / E5 = 8  =>  0 pairs (*) / E7 = 8  =>  0 pairs (X)
A2,A3: 9.. / A2 = 9  => 16 pairs (_) / A3 = 9  =>  0 pairs (X)
E1,E2: 9.. / E1 = 9  => 16 pairs (_) / E2 = 9  =>  0 pairs (X)
H1,H3: 9.. / H1 = 9  =>  0 pairs (X) / H3 = 9  => 16 pairs (_)
E1,H1: 9.. / E1 = 9  => 16 pairs (_) / H1 = 9  =>  0 pairs (X)
A2,E2: 9.. / A2 = 9  => 16 pairs (_) / E2 = 9  =>  0 pairs (X)
A3,H3: 9.. / A3 = 9  =>  0 pairs (X) / H3 = 9  => 16 pairs (_)
* DURATION: 0:01:13.003700  START: 04:00:07.909716  END: 04:01:20.913416 2019-05-01
* CP COUNT: (42)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,D2,D6,E3,E9,F5,F6,F8,G3,G5,G7,G8,H1,H3,I1,I5,I9)
* 782...3...15..3784.43..8..2561349278394....5.827.1.943136....29459.3..172789.143.
* PAIR A2: 6,9 ROW 2
E2: 6,9,2                                # reduction candidate for 6,9
E2: 6,9 => CTR
* 782...3.5.152.3784.435.8..2561349278394.27.5.827.1.943136.8.529459632817278951436
E2: 2 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
* PAIR D2: 2,6 BLK 2
E2: 2,6,9                                # reduction candidate for 2,6
E2: 9 => CTR
* 782.6.3956152937849435.8.62561349278394.27.5.827.1.943136.8.529459632817278951436
E2: 2,6                                  # 16 pairs
* PAIR D2: 2,6 COL D
D8: 2,6,8                                # reduction candidate for 2,6
D8: 2,6 => CTR
* 7821.43.5.15..3784.435781.2561349278394...65182761594313648752945923.817278951436
D8: 8 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
* PAIR E3: 5,7 BLK 2
D3: 5,7,1                                # reduction candidate for 5,7
D3: 5,7 => CTR
* 7821.43.5.15..3784.435781.2561349278394...651827.1.9431364..529459.3.817278951436
D3: 1 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
* PAIR E3: 5,7 COL E
E7: 5,7,8                                # reduction candidate for 5,7
E7: 5,7 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
E7: 8 => CTR
* 782...3.5.15..3784.435781.2561349278394827651827615943136.8.529459.3.817278951436
* PAIR H1: 6,9 ROW 1
E1: 6,9,5                                # reduction candidate for 6,9
E1: 5 => CTR
* 782.5.391.15.93784943178562561349278394.27156827.1.94313678..29459.3..172789.143.
E1: 6,9                                  # 20 pairs
* PAIR I1: 1,5 ROW 1
D1: 1,5,4,6                              # reduction candidate for 1,5
D1: 4,6 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
D1: 1,5                                  # 21 pairs
* PAIR G3: 1,5 ROW 3
D3: 1,5,7                                # reduction candidate for 1,5
D3: 7 => CTR
* 7821.43.5.15..3784.437581.2561349278394...651827.1.9431364.5829459.3..172789.143.
D3: 1,5                                  # 24 pairs
* PAIR F5: 2,7 BLK 5
D5: 2,7,8                                # reduction candidate for 2,7
D5: 2,7 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
D5: 8 => CTR
* 782...3.5.15..3784.435781.2561349278394827651827615943136.8.529459.3.817278951436
E5: 2,7,8                                # reduction candidate for 2,7
E5: 2,7 => CTR
* 782...3.5.15..3784.435781.2561349278394827651827615943136.8.529459.3.817278951436
E5: 8 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
* PAIR D6: 5,6 COL D
D1: 5,6,1,4                              # reduction candidate for 5,6
D1: 5,6 => CTR
* 782..43.1.15..3784.431785.2561349278394...156827.1.9431364.7829459832.172789.143.
D1: 1,4                                  # 19 pairs
* PAIR F6: 5,6 COL F
F1: 5,6,4                                # reduction candidate for 5,6
F1: 5,6 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
F1: 4                                    # 19 pairs
* PAIR F8: 2,6 BLK 8
D8: 2,6,8                                # reduction candidate for 2,6
D8: 2,6 => CTR
* 7821.43.5.15..3784.435781.2561349278394...65182761594313648752945923.817278951436
D8: 8 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
* PAIR E9: 5,6 COL E
E1: 5,6,9                                # reduction candidate for 5,6
E1: 5,6 => CTR
* 782.6.395615293784943578162561349278394827.5.827.1.943136.8.529459.32817278951436
E1: 9                                    # 16 pairs
* PAIR G7: 5,8 ROW 7
D7: 5,8,4,7                              # reduction candidate for 5,8
D7: 5,8 => CTR
* 7824..3.1.15..3784.431785.2561349278394782.5.827.1.943136....29459.3..172789.143.
D7: 4,7                                  # 19 pairs
E7: 5,8,7                                # reduction candidate for 5,8
E7: 5,8                                  # 24 pairs
* PAIR G8: 6,8 ROW 8
D8: 6,8,2                                # reduction candidate for 6,8
D8: 2 => CTR
* 782...3.5.156237846435.8..2561349278394....5.827.1.943136....29459236817278951436
D8: 6,8                                  # 23 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190225-absurd-base-pr-000.dot
* REASONING
* DIS # E2: 6,9 => CTR => E2: 2
* PRF # E2: 2 => SOL
* DIS # E2: 9 => CTR => E2: 2,6
* DIS # D8: 2,6 => CTR => D8: 8
* PRF # D8: 8 => SOL
* DIS # D3: 5,7 => CTR => D3: 1
* PRF # D3: 1 => SOL
* PRF # E7: 5,7 => SOL
* DIS # E7: 8 => CTR => E7: 5,7
* DIS # E1: 5 => CTR => E1: 6,9
* PRF # D1: 4,6 => SOL
* DIS # D3: 7 => CTR => D3: 1,5
* PRF # D5: 2,7 => SOL
* DIS # D5: 8 => CTR => D5: 2,7
* DIS # E5: 2,7 => CTR => E5: 8
* PRF # E5: 8 => SOL
* DIS # D1: 5,6 => CTR => D1: 1,4
* PRF # F1: 5,6 => SOL
* DIS # D8: 2,6 => CTR => D8: 8
* PRF # D8: 8 => SOL
* DIS # E1: 5,6 => CTR => E1: 9
* DIS # D7: 5,8 => CTR => D7: 4,7
* DIS # D8: 2 => CTR => D8: 6,8
* CNT  23 HDP CHAINS /  33 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,D2,D6,E3,E9,F5,F6,F8,G3,G5,G7,G8,H1,H3,I1,I5,I9)
* 782...3...15..3784.43..8..2561349278394....5.827.1.943136....29459.3..172789.143.
* PAIR A2: 6,9 ROW 2
E2: 6,9,2                                # reduction candidate for 6,9
E2: 6,9 => CTR
* 782...3.5.152.3784.435.8..2561349278394.27.5.827.1.943136.8.529459632817278951436
E2: 2 => SOLVED
* 782495361915623784643178592561349278394287156827516943136754829459832617278961435
* DURATION: 0:00:02.806993  START: 04:01:55.785756  END: 04:01:58.592749 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190225-absurd-base-pr-001.dot
* REASONING
* DIS # E2: 6,9 => CTR => E2: 2
* PRF E2: 2 => SOL
* STA E2: 2
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190225, absurd

Solution

position: 782495361915623784643178592561349278394287156827516943136754829459832617278961435 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 # E2: 6,9 => CTR => E2: 2
* PRF # E2: 2 => SOL
* INC # E2: 2,6 => UNS
* DIS # E2: 9 => CTR => E2: 2,6
* DIS # D8: 2,6 => CTR => D8: 8
* PRF # D8: 8 => SOL
* DIS # D3: 5,7 => CTR => D3: 1
* PRF # D3: 1 => SOL
* PRF # E7: 5,7 => SOL
* DIS # E7: 8 => CTR => E7: 5,7
* INC # E1: 6,9 => UNS
* DIS # E1: 5 => CTR => E1: 6,9
* INC # D1: 1,5 => UNS
* PRF # D1: 4,6 => SOL
* INC # D3: 1,5 => UNS
* DIS # D3: 7 => CTR => D3: 1,5
* PRF # D5: 2,7 => SOL
* DIS # D5: 8 => CTR => D5: 2,7
* DIS # E5: 2,7 => CTR => E5: 8
* PRF # E5: 8 => SOL
* DIS # D1: 5,6 => CTR => D1: 1,4
* INC # D1: 1,4 => UNS
* PRF # F1: 5,6 => SOL
* INC # F1: 4 => UNS
* DIS # D8: 2,6 => CTR => D8: 8
* PRF # D8: 8 => SOL
* DIS # E1: 5,6 => CTR => E1: 9
* INC # E1: 9 => UNS
* DIS # D7: 5,8 => CTR => D7: 4,7
* INC # D7: 4,7 => UNS
* INC # E7: 5,8 => UNS
* INC # D8: 6,8 => UNS
* DIS # D8: 2 => CTR => D8: 6,8
* CNT  33 HDP CHAINS /  33 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E2: 6,9 => CTR => E2: 2
* PRF E2: 2 => SOL
* STA E2: 2
* CNT   2 HDP CHAINS /   1 HYP OPENED