Analysis of zz-www.sudokuoftheday.co.uk-20190326-absurd-base.sdk

Contents

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

level: medium

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

position: 1...2.........3.8.4.9.........1..6..68...54....1.3...8..32...4..9.4.7..2.5..6.... initial

Autosolve

position: 13852....5679.328.42987...53.51..6..6827954139.163...87132...468964.7..225436.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # H1: 7,9 => SOL
* DIS # H1: 6 => CTR => H1: 7,9
* DIS # I1: 7,9 => CTR => I1: 4
* PRF # I1: 4 => SOL
* DIS # G9: 7,9 => CTR => G9: 1,8
* PRF # G8: 5 => SOL
* DIS # F4: 2 => CTR => F4: 4,8
* PRF # F4: 2,4 => SOL
* DIS # F4: 8 => CTR => F4: 2,4
* DIS # H4: 7,9 => CTR => H4: 2
* DIS # I1: 7,9 => CTR => I1: 4
* PRF # I1: 4 => SOL
* PRF # I9: 7,9 => SOL
* DIS # I9: 1 => CTR => I9: 7,9
* DIS # H6: 2 => CTR => H6: 5,7
* DIS # G7: 9 => CTR => G7: 5,8
* PRF # F9: 8,9 => SOL
* DIS # F9: 1 => CTR => F9: 8,9
* PRF # G7: 8,9 => SOL
* DIS # G7: 5 => CTR => G7: 8,9
* PRF # G8: 1,5 => SOL
* DIS # G8: 3 => CTR => G8: 1,5
* PRF # G8: 3,5 => SOL
* DIS # G8: 1 => CTR => G8: 3,5
* DIS # G9: 7,9 => CTR => G9: 1,8
* PRF # I9: 7,9 => SOL
* DIS # I9: 1 => CTR => I9: 7,9
* PRF # H1: 7,9 => SOL
* DIS # H1: 6 => CTR => H1: 7,9
* DIS # H4: 7,9 => CTR => H4: 2
* CNT  30 HDP CHAINS /  38 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 /   1 HYP OPENED

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

Details

Positions

1...2.........3.8.4.9.........1..6..68...54....1.3...8..32...4..9.4.7..2.5..6.... initial
13852....5679.328.42987...53.51..6..6827954139.163...87132...468964.7..225436.... autosolve
138526974567943281429871365375184629682795413941632758713259846896417532254368197 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
F1: 4,6
E2: 1,4
F3: 1,6
G1: 7,9
I2: 1,4
G3: 1,3
H3: 3,6
B4: 4,7
B6: 4,7
E4: 4,8
F6: 2,4
I4: 7,9
G6: 5,7
E7: 5,8
F7: 8,9
E8: 1,5
H8: 3,5
H9: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E2,F3: 1.. / E2 = 1  =>  0 pairs (X) / F3 = 1  =>  0 pairs (_)
I2,G3: 1.. / I2 = 1  =>  0 pairs (*) / G3 = 1  =>  0 pairs (X)
E8,F9: 1.. / E8 = 1  =>  0 pairs (*) / F9 = 1  =>  0 pairs (X)
E2,I2: 1.. / E2 = 1  =>  0 pairs (X) / I2 = 1  =>  0 pairs (_)
F3,G3: 1.. / F3 = 1  =>  0 pairs (*) / G3 = 1  =>  0 pairs (X)
E8,G8: 1.. / E8 = 1  =>  0 pairs (*) / G8 = 1  =>  0 pairs (X)
E2,E8: 1.. / E2 = 1  =>  0 pairs (X) / E8 = 1  =>  0 pairs (_)
F3,F9: 1.. / F3 = 1  =>  0 pairs (*) / F9 = 1  =>  0 pairs (X)
I2,I9: 1.. / I2 = 1  =>  0 pairs (*) / I9 = 1  =>  0 pairs (X)
F4,F6: 2.. / F4 = 2  =>  0 pairs (X) / F6 = 2  => 18 pairs (_)
H4,H6: 2.. / H4 = 2  => 18 pairs (_) / H6 = 2  =>  0 pairs (X)
F4,H4: 2.. / F4 = 2  =>  0 pairs (X) / H4 = 2  => 18 pairs (_)
F6,H6: 2.. / F6 = 2  => 18 pairs (_) / H6 = 2  =>  0 pairs (X)
G3,H3: 3.. / G3 = 3  =>  0 pairs (*) / H3 = 3  =>  0 pairs (X)
G8,H8: 3.. / G8 = 3  =>  0 pairs (X) / H8 = 3  =>  0 pairs (_)
G3,G8: 3.. / G3 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
H3,H8: 3.. / H3 = 3  =>  0 pairs (X) / H8 = 3  =>  0 pairs (_)
F1,E2: 4.. / F1 = 4  =>  0 pairs (X) / E2 = 4  =>  0 pairs (_)
I1,I2: 4.. / I1 = 4  =>  0 pairs (*) / I2 = 4  =>  0 pairs (X)
B4,B6: 4.. / B4 = 4  =>  0 pairs (X) / B6 = 4  => 18 pairs (_)
F1,I1: 4.. / F1 = 4  =>  0 pairs (X) / I1 = 4  =>  0 pairs (_)
E2,I2: 4.. / E2 = 4  =>  0 pairs (*) / I2 = 4  =>  0 pairs (X)
B6,F6: 4.. / B6 = 4  => 18 pairs (_) / F6 = 4  =>  0 pairs (X)
E2,E4: 4.. / E2 = 4  =>  0 pairs (*) / E4 = 4  =>  0 pairs (X)
G6,H6: 5.. / G6 = 5  =>  0 pairs (X) / H6 = 5  =>  0 pairs (_)
E7,E8: 5.. / E7 = 5  =>  0 pairs (*) / E8 = 5  =>  0 pairs (X)
E7,G7: 5.. / E7 = 5  =>  0 pairs (*) / G7 = 5  =>  0 pairs (X)
H6,H8: 5.. / H6 = 5  =>  0 pairs (*) / H8 = 5  =>  0 pairs (X)
F1,F3: 6.. / F1 = 6  =>  0 pairs (*) / F3 = 6  =>  0 pairs (X)
H1,H3: 6.. / H1 = 6  =>  0 pairs (X) / H3 = 6  =>  0 pairs (_)
F1,H1: 6.. / F1 = 6  =>  0 pairs (*) / H1 = 6  =>  0 pairs (X)
F3,H3: 6.. / F3 = 6  =>  0 pairs (X) / H3 = 6  =>  0 pairs (_)
B4,B6: 7.. / B4 = 7  => 18 pairs (_) / B6 = 7  =>  0 pairs (X)
E4,F4: 8.. / E4 = 8  =>  0 pairs (*) / F4 = 8  =>  0 pairs (X)
G7,G9: 8.. / G7 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
F9,G9: 8.. / F9 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
E4,E7: 8.. / E4 = 8  =>  0 pairs (*) / E7 = 8  =>  0 pairs (X)
H4,I4: 9.. / H4 = 9  =>  0 pairs (X) / I4 = 9  => 20 pairs (_)
F7,F9: 9.. / F7 = 9  => 19 pairs (_) / F9 = 9  =>  0 pairs (X)
F7,G7: 9.. / F7 = 9  => 19 pairs (_) / G7 = 9  =>  0 pairs (X)
* DURATION: 0:00:48.959904  START: 04:48:49.723433  END: 04:49:38.683337 2019-05-01
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,E2,E4,E7,E8,F1,F3,F6,F7,G1,G3,G6,H3,H8,H9,I2,I4)
* 13852....5679.328.42987...53.51..6..6827954139.163...87132...468964.7..225436....
* PAIR G1: 7,9 BLK 3
H1: 7,9,6                                # reduction candidate for 7,9
H1: 7,9 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
H1: 6 => CTR
* 13852..6.5679.328.4298761353.51..6..6827954139.163...87132...4689641735225436...1
I1: 7,9,4                                # reduction candidate for 7,9
I1: 7,9 => CTR
* 138524.6.5679132844298761353.5148629682795413941632..87132895468964.7..225436....
I1: 4 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
* PAIR G1: 7,9 COL G
G9: 7,9,1,8                              # reduction candidate for 7,9
G9: 7,9 => CTR
* 13852....5679132844298761353.51..6..6827954139.163...87132..8468964.7..2254368..1
G9: 1,8                                  # 19 pairs
* PAIR G3: 1,3 COL G
G8: 1,3,5                                # reduction candidate for 1,3
G8: 5 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
G8: 1,3                                  # 19 pairs
* PAIR E4: 4,8 BLK 5
F4: 4,8,2                                # reduction candidate for 4,8
F4: 2 => CTR
* 138526..45679.328.42987...53.51826..6827954139.1634.2871325..46896417.5225436....
F4: 4,8                                  # 18 pairs
* PAIR F6: 2,4 BLK 5
F4: 2,4,8                                # reduction candidate for 2,4
F4: 2,4 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
F4: 8 => CTR
* 13852....5679.328.42987...53.51.86296827954139.1632..8713289546896457132254361897
* PAIR I4: 7,9 BLK 6
H4: 7,9,2                                # reduction candidate for 7,9
H4: 7,9 => CTR
* 138526..45679.328.42987...53.51.26..6827954139.1634.287132...468964.7.5225436....
H4: 2                                    # 18 pairs
* PAIR I4: 7,9 COL I
I1: 7,9,4                                # reduction candidate for 7,9
I1: 7,9 => CTR
* 138524.6.5679132844298761353.5148629682795413941632..87132895468964.7..225436....
I1: 4 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
I9: 7,9,1                                # reduction candidate for 7,9
I9: 7,9 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
I9: 1 => CTR
* 13852....5679132844298761353.5148629682795413941632..8713289.468964.7..225436...1
* PAIR G6: 5,7 BLK 6
H6: 5,7,2                                # reduction candidate for 5,7
H6: 2 => CTR
* 13852....56794328142987...53.51..6..6827954139.163.52871325..4689641735225436....
H6: 5,7                                  # 18 pairs
* PAIR E7: 5,8 ROW 7
G7: 5,8,9                                # reduction candidate for 5,8
G7: 9 => CTR
* 13852....5679.328.42987...53.51..6..6827954139.163...8713258946896417..2254369871
G7: 5,8                                  # 19 pairs
* PAIR F7: 8,9 BLK 8
F9: 8,9,1                                # reduction candidate for 8,9
F9: 8,9 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
F9: 1 => CTR
* 13852.9..5679132844298761353.51486296827954139416327587132.9.468964.7..22543618..
* PAIR F7: 8,9 ROW 7
G7: 8,9,5                                # reduction candidate for 8,9
G7: 8,9 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
G7: 5 => CTR
* 13852....5679.328.42987...53.51..6..6827954139.163...87132.95468964571322543618..
* PAIR E8: 1,5 ROW 8
G8: 1,5,3                                # reduction candidate for 1,5
G8: 1,5 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
G8: 3 => CTR
* 13852....56794328142987...53.51..6..6827954139.163...87132...4689641735225436....
* PAIR H8: 3,5 BLK 9
G8: 3,5,1                                # reduction candidate for 3,5
G8: 3,5 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
G8: 1 => CTR
* 13852....5679.328.42987.3653.51..6..6827954139.163...87132...468964.7132254361...
* PAIR H9: 7,9 BLK 9
G9: 7,9,1,8                              # reduction candidate for 7,9
G9: 7,9 => CTR
* 13852....5679132844298761353.51..6..6827954139.163...87132..8468964.7..2254368..1
G9: 1,8                                  # 19 pairs
I9: 7,9,1                                # reduction candidate for 7,9
I9: 7,9 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
I9: 1 => CTR
* 13852....5679132844298761353.5148629682795413941632..8713289.468964.7..225436...1
* PAIR H9: 7,9 COL H
H1: 7,9,6                                # reduction candidate for 7,9
H1: 7,9 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
H1: 6 => CTR
* 13852..6.5679.328.4298761353.51..6..6827954139.163...87132...4689641735225436...1
H4: 7,9,2                                # reduction candidate for 7,9
H4: 7,9 => CTR
* 138526..45679.328.42987...53.51.26..6827954139.1634.287132...468964.7.5225436....
H4: 2                                    # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190326-absurd-base-pr-000.dot
* REASONING
* PRF # H1: 7,9 => SOL
* DIS # H1: 6 => CTR => H1: 7,9
* DIS # I1: 7,9 => CTR => I1: 4
* PRF # I1: 4 => SOL
* DIS # G9: 7,9 => CTR => G9: 1,8
* PRF # G8: 5 => SOL
* DIS # F4: 2 => CTR => F4: 4,8
* PRF # F4: 2,4 => SOL
* DIS # F4: 8 => CTR => F4: 2,4
* DIS # H4: 7,9 => CTR => H4: 2
* DIS # I1: 7,9 => CTR => I1: 4
* PRF # I1: 4 => SOL
* PRF # I9: 7,9 => SOL
* DIS # I9: 1 => CTR => I9: 7,9
* DIS # H6: 2 => CTR => H6: 5,7
* DIS # G7: 9 => CTR => G7: 5,8
* PRF # F9: 8,9 => SOL
* DIS # F9: 1 => CTR => F9: 8,9
* PRF # G7: 8,9 => SOL
* DIS # G7: 5 => CTR => G7: 8,9
* PRF # G8: 1,5 => SOL
* DIS # G8: 3 => CTR => G8: 1,5
* PRF # G8: 3,5 => SOL
* DIS # G8: 1 => CTR => G8: 3,5
* DIS # G9: 7,9 => CTR => G9: 1,8
* PRF # I9: 7,9 => SOL
* DIS # I9: 1 => CTR => I9: 7,9
* PRF # H1: 7,9 => SOL
* DIS # H1: 6 => CTR => H1: 7,9
* DIS # H4: 7,9 => CTR => H4: 2
* CNT  30 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,E2,E4,E7,E8,F1,F3,F6,F7,G1,G3,G6,H3,H8,H9,I2,I4)
* 13852....5679.328.42987...53.51..6..6827954139.163...87132...468964.7..225436....
* PAIR G1: 7,9 BLK 3
H1: 7,9,6                                # reduction candidate for 7,9
H1: 7,9 => SOLVED
* 138526974567943281429871365375184629682795413941632758713259846896417532254368197
* DURATION: 0:00:01.612482  START: 04:50:09.233908  END: 04:50:10.846390 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190326-absurd-base-pr-001.dot
* REASONING
* PRF # H1: 7,9 => SOL
* STA H1: 7,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190326, absurd

Solution

position: 138526974567943281429871365375184629682795413941632758713259846896417532254368197 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 # H1: 7,9 => SOL
* DIS # H1: 6 => CTR => H1: 7,9
* DIS # I1: 7,9 => CTR => I1: 4
* PRF # I1: 4 => SOL
* DIS # G9: 7,9 => CTR => G9: 1,8
* INC # G9: 1,8 => UNS
* INC # G8: 1,3 => UNS
* PRF # G8: 5 => SOL
* INC # F4: 4,8 => UNS
* DIS # F4: 2 => CTR => F4: 4,8
* PRF # F4: 2,4 => SOL
* DIS # F4: 8 => CTR => F4: 2,4
* DIS # H4: 7,9 => CTR => H4: 2
* INC # H4: 2 => UNS
* DIS # I1: 7,9 => CTR => I1: 4
* PRF # I1: 4 => SOL
* PRF # I9: 7,9 => SOL
* DIS # I9: 1 => CTR => I9: 7,9
* INC # H6: 5,7 => UNS
* DIS # H6: 2 => CTR => H6: 5,7
* INC # G7: 5,8 => UNS
* DIS # G7: 9 => CTR => G7: 5,8
* PRF # F9: 8,9 => SOL
* DIS # F9: 1 => CTR => F9: 8,9
* PRF # G7: 8,9 => SOL
* DIS # G7: 5 => CTR => G7: 8,9
* PRF # G8: 1,5 => SOL
* DIS # G8: 3 => CTR => G8: 1,5
* PRF # G8: 3,5 => SOL
* DIS # G8: 1 => CTR => G8: 3,5
* DIS # G9: 7,9 => CTR => G9: 1,8
* INC # G9: 1,8 => UNS
* PRF # I9: 7,9 => SOL
* DIS # I9: 1 => CTR => I9: 7,9
* PRF # H1: 7,9 => SOL
* DIS # H1: 6 => CTR => H1: 7,9
* DIS # H4: 7,9 => CTR => H4: 2
* INC # H4: 2 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # H1: 7,9 => SOL
* STA H1: 7,9
* CNT   1 HDP CHAINS /   1 HYP OPENED