Analysis of zz-www.sudokuoftheday.co.uk-20190116-absurd-base.sdk

Contents

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

level: medium

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

position: ...34....37...8...294..56.........16.61...3..9...8.......8132.7.2.5........2.7.35 initial

Autosolve

position: ...346...376928...294175683....3..16.61.5.3..93.681......8132.77235.4......2.7.35 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # H1: 7,9 => SOL
* DIS # G4: 7,9 => CTR => G4: 8
* PRF # G4: 8 => SOL
* DIS # H1: 7 => CTR => H1: 2,9
* PRF # I5: 2,9 => SOL
* DIS # I5: 8 => CTR => I5: 2,9
* PRF # G2: 4,5 => SOL
* DIS # G2: 1 => CTR => G2: 4,5
* PRF # H6: 2,7 => SOL
* DIS # G2: 5 => CTR => G2: 1,4
* PRF # H6: 2,7 => SOL
* DIS # H5: 2,9 => CTR => H5: 7
* PRF # H5: 7 => SOL
* PRF # I5: 2,9 => SOL
* DIS # I5: 8 => CTR => I5: 2,9
* DIS # B4: 8 => CTR => B4: 4,5
* PRF # H7: 4 => SOL
* CNT  17 HDP CHAINS /  36 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 # H1: 7,9 => SOL
* STA H1: 7,9
* CNT   1 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

...34....37...8...294..56.........16.61...3..9...8.......8132.7.2.5........2.7.35 initial
...346...376928...294175683....3..16.61.5.3..93.681......8132.77235.4......2.7.35 autosolve
185346792376928451294175683542739816861452379937681524659813247723594168418267935 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
C1: 5,8
G1: 7,9
I1: 2,9
H2: 4,5
I2: 1,4
C4: 2,7
A5: 4,8
C6: 2,7
D4: 4,7
F4: 2,9
D5: 4,7
F5: 2,9
I6: 2,4
B7: 4,5
C7: 5,9
C9: 8,9
E8: 6,9
E9: 6,9
G8: 1,8
H8: 6,9
I8: 1,8
G9: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B1: 1.. / A1 = 1  => 23 pairs (_) / B1 = 1  => 23 pairs (_)
G2,I2: 1.. / G2 = 1  =>  0 pairs (X) / I2 = 1  =>  0 pairs (_)
A9,B9: 1.. / A9 = 1  => 23 pairs (_) / B9 = 1  => 23 pairs (_)
G8,I8: 1.. / G8 = 1  =>  0 pairs (*) / I8 = 1  =>  0 pairs (X)
A1,A9: 1.. / A1 = 1  => 23 pairs (_) / A9 = 1  => 23 pairs (_)
B1,B9: 1.. / B1 = 1  => 23 pairs (_) / B9 = 1  => 23 pairs (_)
G2,G8: 1.. / G2 = 1  =>  0 pairs (X) / G8 = 1  =>  0 pairs (_)
I2,I8: 1.. / I2 = 1  =>  0 pairs (*) / I8 = 1  =>  0 pairs (X)
H1,I1: 2.. / H1 = 2  => 24 pairs (_) / I1 = 2  =>  0 pairs (*)
C4,C6: 2.. / C4 = 2  => 22 pairs (_) / C6 = 2  =>  0 pairs (X)
F4,F5: 2.. / F4 = 2  =>  0 pairs (X) / F5 = 2  => 22 pairs (_)
C4,F4: 2.. / C4 = 2  => 22 pairs (_) / F4 = 2  =>  0 pairs (X)
D4,D5: 4.. / D4 = 4  =>  0 pairs (X) / D5 = 4  =>  0 pairs (_)
H7,G9: 4.. / H7 = 4  =>  0 pairs (*) / G9 = 4  =>  0 pairs (X)
A5,D5: 4.. / A5 = 4  =>  0 pairs (X) / D5 = 4  =>  0 pairs (_)
I2,I6: 4.. / I2 = 4  =>  0 pairs (X) / I6 = 4  =>  0 pairs (_)
G2,H2: 5.. / G2 = 5  =>  0 pairs (X) / H2 = 5  => 22 pairs (_)
A4,B4: 5.. / A4 = 5  => 25 pairs (_) / B4 = 5  => 34 pairs (_)
G6,H6: 5.. / G6 = 5  => 22 pairs (_) / H6 = 5  =>  0 pairs (X)
C1,C7: 5.. / C1 = 5  => 23 pairs (_) / C7 = 5  => 26 pairs (_)
G2,G6: 5.. / G2 = 5  =>  0 pairs (X) / G6 = 5  => 22 pairs (_)
H2,H6: 5.. / H2 = 5  => 22 pairs (_) / H6 = 5  =>  0 pairs (X)
A7,A9: 6.. / A7 = 6  => 20 pairs (_) / A9 = 6  => 24 pairs (_)
E8,E9: 6.. / E8 = 6  => 24 pairs (_) / E9 = 6  => 20 pairs (_)
H7,H8: 6.. / H7 = 6  => 24 pairs (_) / H8 = 6  => 20 pairs (_)
A7,H7: 6.. / A7 = 6  => 20 pairs (_) / H7 = 6  => 24 pairs (_)
E8,H8: 6.. / E8 = 6  => 24 pairs (_) / H8 = 6  => 20 pairs (_)
A9,E9: 6.. / A9 = 6  => 24 pairs (_) / E9 = 6  => 20 pairs (_)
G1,H1: 7.. / G1 = 7  => 24 pairs (_) / H1 = 7  =>  0 pairs (X)
C4,C6: 7.. / C4 = 7  =>  0 pairs (X) / C6 = 7  => 22 pairs (_)
D4,D5: 7.. / D4 = 7  =>  0 pairs (*) / D5 = 7  =>  0 pairs (X)
D5,H5: 7.. / D5 = 7  =>  0 pairs (X) / H5 = 7  =>  0 pairs (_)
G4,I5: 8.. / G4 = 8  =>  0 pairs (*) / I5 = 8  =>  0 pairs (X)
G8,I8: 8.. / G8 = 8  =>  0 pairs (X) / I8 = 8  =>  0 pairs (_)
A5,I5: 8.. / A5 = 8  =>  0 pairs (*) / I5 = 8  =>  0 pairs (X)
C1,C9: 8.. / C1 = 8  => 26 pairs (_) / C9 = 8  => 23 pairs (_)
G4,G8: 8.. / G4 = 8  =>  0 pairs (*) / G8 = 8  =>  0 pairs (X)
I5,I8: 8.. / I5 = 8  =>  0 pairs (X) / I8 = 8  =>  0 pairs (_)
F4,F5: 9.. / F4 = 9  => 22 pairs (_) / F5 = 9  =>  0 pairs (X)
C7,C9: 9.. / C7 = 9  => 23 pairs (_) / C9 = 9  => 26 pairs (_)
E8,E9: 9.. / E8 = 9  => 20 pairs (_) / E9 = 9  => 24 pairs (_)
F4,G4: 9.. / F4 = 9  => 22 pairs (_) / G4 = 9  =>  0 pairs (X)
C7,H7: 9.. / C7 = 9  => 23 pairs (_) / H7 = 9  => 26 pairs (_)
E8,H8: 9.. / E8 = 9  => 20 pairs (_) / H8 = 9  => 24 pairs (_)
I1,I5: 9.. / I1 = 9  => 24 pairs (_) / I5 = 9  =>  0 pairs (*)
* DURATION: 0:00:57.504767  START: 02:58:57.422590  END: 02:59:54.927357 2019-05-01
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B7,C1,C4,C6,C7,C9,D4,D5,E8,E9,F4,F5,G1,G8,G9,H2,H8,I1,I2,I6,I8)
* ...346...376928...294175683....3..16.61.5.3..93.681......8132.77235.4......2.7.35
* PAIR C1: 5,8 BLK 1
A1: 5,8,1                                # reduction candidate for 5,8
A1: 5,8                                  # 23 pairs
B1: 5,8,1                                # reduction candidate for 5,8
B1: 5,8                                  # 23 pairs
* PAIR G1: 7,9 BLK 3
H1: 7,9,2                                # reduction candidate for 7,9
H1: 7,9 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
H1: 2                                    # 24 pairs
* PAIR G1: 7,9 COL G
G4: 7,9,8                                # reduction candidate for 7,9
G4: 7,9 => CTR
* ...346..9376928154294175683....3..1646175.3.893.681542.4.8132.77235.48.1...2.7435
G4: 8 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
* PAIR I1: 2,9 BLK 3
H1: 2,9,7                                # reduction candidate for 2,9
H1: 7 => CTR
* ...346.72376928...294175683....3..16.6175.3.993.681..4...8132.77235.4..8...2.7.35
H1: 2,9                                  # 24 pairs
* PAIR I1: 2,9 COL I
I5: 2,9,8                                # reduction candidate for 2,9
I5: 2,9 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
I5: 8 => CTR
* ...346729376928154294175683..2739.16.61.5.3.893.681..2...8132.77235.48.1...2.7.35
* PAIR H2: 4,5 BLK 3
G2: 4,5,1                                # reduction candidate for 4,5
G2: 4,5 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
G2: 1 => CTR
* ...346.29376928154294175683..2.39716.61.5.3..93.681542...8132.77235.48.1...2.7435
* PAIR H2: 4,5 COL H
H6: 4,5,2,7                              # reduction candidate for 4,5
H6: 2,7 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
H6: 4,5                                  # 30 pairs
* PAIR I2: 1,4 BLK 3
G2: 1,4,5                                # reduction candidate for 1,4
G2: 5 => CTR
* ...346...376928541294175683....3.81686145.37.93.681.54...8132.77235.41.8...2.7435
G2: 1,4                                  # 22 pairs
* PAIR A5: 4,8 BLK 4
A4: 4,8,5                                # reduction candidate for 4,8
A4: 4,8                                  # 34 pairs
B4: 4,8,5                                # reduction candidate for 4,8
B4: 4,8                                  # 25 pairs
* PAIR A5: 4,8 COL A
A9: 4,8,1,6                              # reduction candidate for 4,8
A9: 4,8                                  # 23 pairs
A9: 1,6                                  # 23 pairs
* PAIR C6: 2,7 ROW 6
H6: 2,7,4,5                              # reduction candidate for 2,7
H6: 2,7 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
H6: 4,5                                  # 30 pairs
* PAIR F5: 2,9 ROW 5
H5: 2,9,7                                # reduction candidate for 2,9
H5: 2,9 => CTR
* ...346..9376928154294175683...43..1646175.3.893.681542.4.8132.77235.48.1...2.7435
H5: 7 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
I5: 2,9,8                                # reduction candidate for 2,9
I5: 2,9 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
I5: 8 => CTR
* ...346729376928154294175683..2739.16.61.5.3.893.681..2...8132.77235.48.1...2.7.35
* PAIR I6: 2,4 BLK 6
H6: 2,4,5,7                              # reduction candidate for 2,4
H6: 5,7                                  # 23 pairs
H6: 2,4                                  # 22 pairs
* PAIR B7: 4,5 BLK 7
A7: 4,5,6                                # reduction candidate for 4,5
A7: 4,5                                  # 24 pairs
A7: 6                                    # 20 pairs
* PAIR B7: 4,5 COL B
B4: 4,5,8                                # reduction candidate for 4,5
B4: 8 => CTR
* ...346..937692815429417568358.43..1646175.3.893.6815426458132977235.4861...267.35
B4: 4,5                                  # 26 pairs
* PAIR H8: 6,9 BLK 9
H7: 6,9,4                                # reduction candidate for 6,9
H7: 4 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
H7: 6,9                                  # 30 pairs
* PAIR G9: 4,9 BLK 9
H7: 4,9,6                                # reduction candidate for 4,9
H7: 6                                    # 24 pairs
H7: 4,9                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190116-absurd-base-pr-000.dot
* REASONING
* PRF # H1: 7,9 => SOL
* DIS # G4: 7,9 => CTR => G4: 8
* PRF # G4: 8 => SOL
* DIS # H1: 7 => CTR => H1: 2,9
* PRF # I5: 2,9 => SOL
* DIS # I5: 8 => CTR => I5: 2,9
* PRF # G2: 4,5 => SOL
* DIS # G2: 1 => CTR => G2: 4,5
* PRF # H6: 2,7 => SOL
* DIS # G2: 5 => CTR => G2: 1,4
* PRF # H6: 2,7 => SOL
* DIS # H5: 2,9 => CTR => H5: 7
* PRF # H5: 7 => SOL
* PRF # I5: 2,9 => SOL
* DIS # I5: 8 => CTR => I5: 2,9
* DIS # B4: 8 => CTR => B4: 4,5
* PRF # H7: 4 => SOL
* CNT  17 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B7,C1,C4,C6,C7,C9,D4,D5,E8,E9,F4,F5,G1,G8,G9,H2,H8,I1,I2,I6,I8)
* ...346...376928...294175683....3..16.61.5.3..93.681......8132.77235.4......2.7.35
* PAIR C1: 5,8 BLK 1
A1: 5,8,1                                # reduction candidate for 5,8
A1: 5,8                                  # 23 pairs
B1: 5,8,1                                # reduction candidate for 5,8
B1: 5,8                                  # 23 pairs
* PAIR G1: 7,9 BLK 3
H1: 7,9,2                                # reduction candidate for 7,9
H1: 7,9 => SOLVED
* 185346792376928451294175683542739816861452379937681524659813247723594168418267935
* DURATION: 0:00:02.952526  START: 03:00:22.683042  END: 03:00:25.635568 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190116-absurd-base-pr-001.dot
* REASONING
* PRF # H1: 7,9 => SOL
* STA H1: 7,9
* CNT   1 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190116, absurd

Solution

position: 185346792376928451294175683542739816861452379937681524659813247723594168418267935 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:

* INC # A1: 5,8 => UNS
* INC # B1: 5,8 => UNS
* PRF # H1: 7,9 => SOL
* INC # H1: 2 => UNS
* DIS # G4: 7,9 => CTR => G4: 8
* PRF # G4: 8 => SOL
* INC # H1: 2,9 => UNS
* DIS # H1: 7 => CTR => H1: 2,9
* PRF # I5: 2,9 => SOL
* DIS # I5: 8 => CTR => I5: 2,9
* PRF # G2: 4,5 => SOL
* DIS # G2: 1 => CTR => G2: 4,5
* INC # H6: 4,5 => UNS
* PRF # H6: 2,7 => SOL
* INC # G2: 1,4 => UNS
* DIS # G2: 5 => CTR => G2: 1,4
* INC # A4: 4,8 => UNS
* INC # B4: 4,8 => UNS
* INC # A9: 4,8 => UNS
* INC # A9: 1,6 => UNS
* PRF # H6: 2,7 => SOL
* INC # H6: 4,5 => UNS
* DIS # H5: 2,9 => CTR => H5: 7
* PRF # H5: 7 => SOL
* PRF # I5: 2,9 => SOL
* DIS # I5: 8 => CTR => I5: 2,9
* INC # H6: 2,4 => UNS
* INC # H6: 5,7 => UNS
* INC # A7: 4,5 => UNS
* INC # A7: 6 => UNS
* INC # B4: 4,5 => UNS
* DIS # B4: 8 => CTR => B4: 4,5
* INC # H7: 6,9 => UNS
* PRF # H7: 4 => SOL
* INC # H7: 4,9 => UNS
* INC # H7: 6 => UNS
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 5,8 => UNS
* INC # B1: 5,8 => UNS
* PRF # H1: 7,9 => SOL
* STA H1: 7,9
* CNT   3 HDP CHAINS /   3 HYP OPENED