Analysis of zz-www.sudokuoftheday.co.uk-20190414-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

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

level: medium

position: 7....9..2......7.....4.31.6.932......6..4....24........5..2..4.4..98.56..19....7. initial

Autosolve

position: 78...9..213.8.279.925473186.932......6..4..2924..9....358.2.941472981563619534278 autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E1: 1,6 => SOL
* DIS # E1: 5 => CTR => E1: 1,6
* PRF # D6: 1,6 => SOL
* DIS # D6: 3,7 => CTR => D6: 1,6
* DIS # E1: 5,6 => CTR => E1: 1
* PRF # E1: 1 => SOL
* PRF # H6: 3,5 => SOL
* DIS # H6: 1 => CTR => H6: 3,5
* DIS # I4: 4,5 => CTR => I4: 7
* PRF # I4: 7 => SOL
* PRF # F4: 5,8 => SOL
* DIS # F4: 6,7 => CTR => F4: 5,8
* DIS # F5: 5,8 => CTR => F5: 7
* PRF # F5: 7 => SOL
* DIS # D5: 1,7 => CTR => D5: 3
* PRF # D5: 3 => SOL
* PRF # D6: 1,7 => SOL
* PRF # D6: 1,6 => SOL
* DIS # D6: 3,7 => CTR => D6: 1,6
* PRF # E1: 1,6 => SOL
* DIS # E1: 5 => CTR => E1: 1,6
* DIS # H6: 1,5 => CTR => H6: 3
* PRF # H6: 3 => SOL
* DIS # G6: 3,8 => CTR => G6: 6
* PRF # G6: 6 => SOL
* PRF # I4: 5,7 => SOL
* DIS # I4: 4 => CTR => I4: 5,7
* DIS # F6: 5,7 => CTR => F6: 6,8
* PRF # F6: 6,8 => SOL
* DIS # D6: 6,7 => CTR => D6: 1,3
* PRF # D6: 1,3 => SOL
* DIS # F4: 6,7 => CTR => F4: 5,8
* PRF # F4: 5,8 => SOL
* DIS # F6: 6,7 => CTR => F6: 5,8
* CNT  34 HDP CHAINS /  36 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* PRF # E1: 1,6 => SOL
* STA E1: 1,6
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

`7....9..2......7.....4.31.6.932......6..4....24........5..2..4.4..98.56..19....7.`	initial
`78...9..213.8.279.925473186.932......6..4..2924..9....358.2.941472981563619534278`	autosolve
`784619352136852794925473186893265417561347829247198635358726941472981563619534278`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
C1: 4,6
C2: 4,6
D1: 1,6
E2: 5,6
G1: 3,4
H1: 3,5
I2: 4,5
A4: 5,8
A5: 5,8
C5: 1,7
C6: 1,7
E4: 1,6
H4: 1,5
G5: 3,8
I6: 5,7
D7: 6,7
F7: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,E1: 1.. / D1 = 1  =>  0 pairs (X) / E1 = 1  =>  0 pairs (_)
C5,C6: 1.. / C5 = 1  =>  0 pairs (*) / C6 = 1  =>  0 pairs (X)
H4,H6: 1.. / H4 = 1  =>  0 pairs (*) / H6 = 1  =>  0 pairs (X)
E4,H4: 1.. / E4 = 1  =>  0 pairs (X) / H4 = 1  =>  0 pairs (_)
C5,D5: 1.. / C5 = 1  =>  0 pairs (*) / D5 = 1  =>  0 pairs (X)
E1,E4: 1.. / E1 = 1  =>  0 pairs (*) / E4 = 1  =>  0 pairs (X)
G1,H1: 3.. / G1 = 3  =>  0 pairs (*) / H1 = 3  =>  0 pairs (X)
D5,D6: 3.. / D5 = 3  =>  0 pairs (*) / D6 = 3  =>  0 pairs (X)
D5,G5: 3.. / D5 = 3  =>  0 pairs (*) / G5 = 3  =>  0 pairs (X)
H1,H6: 3.. / H1 = 3  =>  0 pairs (X) / H6 = 3  =>  0 pairs (_)
C1,C2: 4.. / C1 = 4  =>  0 pairs (*) / C2 = 4  =>  0 pairs (X)
G1,I2: 4.. / G1 = 4  =>  0 pairs (X) / I2 = 4  =>  0 pairs (_)
G4,I4: 4.. / G4 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
C1,G1: 4.. / C1 = 4  =>  0 pairs (*) / G1 = 4  =>  0 pairs (X)
C2,I2: 4.. / C2 = 4  =>  0 pairs (X) / I2 = 4  =>  0 pairs (_)
G1,G4: 4.. / G1 = 4  =>  0 pairs (X) / G4 = 4  =>  0 pairs (_)
I2,I4: 4.. / I2 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
E1,E2: 5.. / E1 = 5  =>  0 pairs (X) / E2 = 5  =>  0 pairs (_)
H1,I2: 5.. / H1 = 5  =>  0 pairs (*) / I2 = 5  =>  0 pairs (X)
A4,A5: 5.. / A4 = 5  =>  0 pairs (X) / A5 = 5  => 17 pairs (_)
E1,H1: 5.. / E1 = 5  =>  0 pairs (X) / H1 = 5  =>  0 pairs (_)
E2,I2: 5.. / E2 = 5  =>  0 pairs (*) / I2 = 5  =>  0 pairs (X)
A5,F5: 5.. / A5 = 5  => 17 pairs (_) / F5 = 5  =>  0 pairs (X)
C1,C2: 6.. / C1 = 6  =>  0 pairs (X) / C2 = 6  =>  0 pairs (_)
G4,G6: 6.. / G4 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
D7,F7: 6.. / D7 = 6  =>  0 pairs (X) / F7 = 6  => 16 pairs (_)
C2,E2: 6.. / C2 = 6  =>  0 pairs (*) / E2 = 6  =>  0 pairs (X)
C5,C6: 7.. / C5 = 7  =>  0 pairs (X) / C6 = 7  =>  0 pairs (_)
I4,I6: 7.. / I4 = 7  =>  0 pairs (*) / I6 = 7  =>  0 pairs (X)
D7,F7: 7.. / D7 = 7  => 16 pairs (_) / F7 = 7  =>  0 pairs (X)
F4,I4: 7.. / F4 = 7  =>  0 pairs (X) / I4 = 7  =>  0 pairs (_)
A4,A5: 8.. / A4 = 8  => 17 pairs (_) / A5 = 8  =>  0 pairs (X)
F6,G6: 8.. / F6 = 8  =>  0 pairs (*) / G6 = 8  =>  0 pairs (X)
* DURATION: 0:00:39.176070  START: 05:17:35.981262  END: 05:18:15.157332 2019-05-01
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,C1,C2,C5,C6,D1,D7,E2,E4,F7,G1,G5,H1,H4,I2,I6)
* 78...9..213.8.279.925473186.932......6..4..2924..9....358.2.941472981563619534278
* PAIR D1: 1,6 BLK 2
E1: 1,6,5                                # reduction candidate for 1,6
E1: 1,6 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
E1: 5 => CTR
* 78.159.3213.862795925473186.9321..54561.4..29247.9....358.2.941472981563619534278
* PAIR D1: 1,6 COL D
D6: 1,6,3,7                              # reduction candidate for 1,6
D6: 1,6 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
D6: 3,7 => CTR
* 78...9..213.8.279.925473186.932...1..6.14.32924139..57358726941472981563619534278
* PAIR E2: 5,6 BLK 2
E1: 5,6,1                                # reduction candidate for 5,6
E1: 5,6 => CTR
* 78.1.9..213.8.279.925473186.9321..5.561.4..29247.9....358.2.941472981563619534278
E1: 1 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
* PAIR H1: 3,5 COL H
H6: 3,5,1                                # reduction candidate for 3,5
H6: 3,5 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
H6: 1 => CTR
* 78...9.3213.8.2795925473186.932...5456..4..2924..9581.358.2.941472981563619534278
* PAIR I2: 4,5 COL I
I4: 4,5,7                                # reduction candidate for 4,5
I4: 4,5 => CTR
* 78...9..213.8.279.925473186.932.7....6714.32924139..57358726941472981563619534278
I4: 7 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
* PAIR A4: 5,8 ROW 4
F4: 5,8,6,7                              # reduction candidate for 5,8
F4: 5,8 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
F4: 6,7 => CTR
* 78...9432134862795925473186.9321..54561748329247.9....358.2.941472981563619534278
* PAIR A5: 5,8 ROW 5
F5: 5,8,7                                # reduction candidate for 5,8
F5: 5,8 => CTR
* 78...9432134862795925473186.9321..54561748329247.9....358.2.941472981563619534278
F5: 7 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
* PAIR C5: 1,7 ROW 5
D5: 1,7,3                                # reduction candidate for 1,7
D5: 1,7 => CTR
* 78...9432134862795925473186.9321..5456174832924739....358.2.941472981563619534278
D5: 3 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
* PAIR C6: 1,7 ROW 6
D6: 1,7,3,6                              # reduction candidate for 1,7
D6: 1,7 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
D6: 3,6                                  # 18 pairs
* PAIR E4: 1,6 BLK 5
D6: 1,6,3,7                              # reduction candidate for 1,6
D6: 1,6 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
D6: 3,7 => CTR
* 78...9..213.8.279.925473186.932...1..6.14.32924139..57358726941472981563619534278
* PAIR E4: 1,6 COL E
E1: 1,6,5                                # reduction candidate for 1,6
E1: 1,6 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
E1: 5 => CTR
* 78.159.3213.862795925473186.9321..54561.4..29247.9....358.2.941472981563619534278
* PAIR H4: 1,5 BLK 6
H6: 1,5,3                                # reduction candidate for 1,5
H6: 1,5 => CTR
* 78..59432134862795925473186.9321765456..4..2924..9...7358.2.941472981563619534278
H6: 3 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
* PAIR G5: 3,8 BLK 6
G6: 3,8,6                                # reduction candidate for 3,8
G6: 3,8 => CTR
* 78...9432134862795925473186.9321765456..4..2924..9...7358.2.941472981563619534278
G6: 6 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
* PAIR I6: 5,7 BLK 6
I4: 5,7,4                                # reduction candidate for 5,7
I4: 5,7 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
I4: 4 => CTR
* 78...9..213.8.279.925473186.932.7..4.6714.32924139..57358726941472981563619534278
* PAIR I6: 5,7 ROW 6
F6: 5,7,6,8                              # reduction candidate for 5,7
F6: 5,7 => CTR
* 78...9..213.8.279.925473186.932..6.4.6..4.32924..9.8..358.2.941472981563619534278
F6: 6,8 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
* PAIR D7: 6,7 COL D
D6: 6,7,1,3                              # reduction candidate for 6,7
D6: 6,7 => CTR
* 78.1.9..213.8.279.92547318689321..5.561347829247.98...358.2.941472981563619534278
D6: 1,3 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
* PAIR F7: 6,7 COL F
F4: 6,7,5,8                              # reduction candidate for 6,7
F4: 6,7 => CTR
* 78...9432134862795925473186.9321..54561748329247.9....358.2.941472981563619534278
F4: 5,8 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
F6: 6,7,5,8                              # reduction candidate for 6,7
F6: 6,7 => CTR
* 78...9..213.8.279.925473186.932..6.4.6..4.32924.3968.7358627941472981563619534278
F6: 5,8                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190414-absurd-base-pr-000.dot
* REASONING
* PRF # E1: 1,6 => SOL
* DIS # E1: 5 => CTR => E1: 1,6
* PRF # D6: 1,6 => SOL
* DIS # D6: 3,7 => CTR => D6: 1,6
* DIS # E1: 5,6 => CTR => E1: 1
* PRF # E1: 1 => SOL
* PRF # H6: 3,5 => SOL
* DIS # H6: 1 => CTR => H6: 3,5
* DIS # I4: 4,5 => CTR => I4: 7
* PRF # I4: 7 => SOL
* PRF # F4: 5,8 => SOL
* DIS # F4: 6,7 => CTR => F4: 5,8
* DIS # F5: 5,8 => CTR => F5: 7
* PRF # F5: 7 => SOL
* DIS # D5: 1,7 => CTR => D5: 3
* PRF # D5: 3 => SOL
* PRF # D6: 1,7 => SOL
* PRF # D6: 1,6 => SOL
* DIS # D6: 3,7 => CTR => D6: 1,6
* PRF # E1: 1,6 => SOL
* DIS # E1: 5 => CTR => E1: 1,6
* DIS # H6: 1,5 => CTR => H6: 3
* PRF # H6: 3 => SOL
* DIS # G6: 3,8 => CTR => G6: 6
* PRF # G6: 6 => SOL
* PRF # I4: 5,7 => SOL
* DIS # I4: 4 => CTR => I4: 5,7
* DIS # F6: 5,7 => CTR => F6: 6,8
* PRF # F6: 6,8 => SOL
* DIS # D6: 6,7 => CTR => D6: 1,3
* PRF # D6: 1,3 => SOL
* DIS # F4: 6,7 => CTR => F4: 5,8
* PRF # F4: 5,8 => SOL
* DIS # F6: 6,7 => CTR => F6: 5,8
* CNT  34 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,C1,C2,C5,C6,D1,D7,E2,E4,F7,G1,G5,H1,H4,I2,I6)
* 78...9..213.8.279.925473186.932......6..4..2924..9....358.2.941472981563619534278
* PAIR D1: 1,6 BLK 2
E1: 1,6,5                                # reduction candidate for 1,6
E1: 1,6 => SOLVED
* 784619352136852794925473186893265417561347829247198635358726941472981563619534278
* DURATION: 0:00:01.616691  START: 05:18:44.945375  END: 05:18:46.562066 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190414-absurd-base-pr-001.dot
* REASONING
* PRF # E1: 1,6 => SOL
* STA E1: 1,6
* 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, 20190414, absurd

Solution

position: 784619352136852794925473186893265417561347829247198635358726941472981563619534278 solved

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 # E1: 1,6 => SOL
* DIS # E1: 5 => CTR => E1: 1,6
* PRF # D6: 1,6 => SOL
* DIS # D6: 3,7 => CTR => D6: 1,6
* DIS # E1: 5,6 => CTR => E1: 1
* PRF # E1: 1 => SOL
* PRF # H6: 3,5 => SOL
* DIS # H6: 1 => CTR => H6: 3,5
* DIS # I4: 4,5 => CTR => I4: 7
* PRF # I4: 7 => SOL
* PRF # F4: 5,8 => SOL
* DIS # F4: 6,7 => CTR => F4: 5,8
* DIS # F5: 5,8 => CTR => F5: 7
* PRF # F5: 7 => SOL
* DIS # D5: 1,7 => CTR => D5: 3
* PRF # D5: 3 => SOL
* PRF # D6: 1,7 => SOL
* INC # D6: 3,6 => UNS
* PRF # D6: 1,6 => SOL
* DIS # D6: 3,7 => CTR => D6: 1,6
* PRF # E1: 1,6 => SOL
* DIS # E1: 5 => CTR => E1: 1,6
* DIS # H6: 1,5 => CTR => H6: 3
* PRF # H6: 3 => SOL
* DIS # G6: 3,8 => CTR => G6: 6
* PRF # G6: 6 => SOL
* PRF # I4: 5,7 => SOL
* DIS # I4: 4 => CTR => I4: 5,7
* DIS # F6: 5,7 => CTR => F6: 6,8
* PRF # F6: 6,8 => SOL
* DIS # D6: 6,7 => CTR => D6: 1,3
* PRF # D6: 1,3 => SOL
* DIS # F4: 6,7 => CTR => F4: 5,8
* PRF # F4: 5,8 => SOL
* DIS # F6: 6,7 => CTR => F6: 5,8
* INC # F6: 5,8 => UNS
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # E1: 1,6 => SOL
* STA E1: 1,6
* CNT   1 HDP CHAINS /   1 HYP OPENED