Analysis of zz-www.sudokuoftheday.co.uk-20190330-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: .8.7.4..2.....3...75.....81......436.9.3.5........7...9.....14..7...92....15.2... initial

Autosolve

position: .837.4..22.9..3..4754..6381527..1436.963.5...3.8.675.9932678145.75..926...15.2... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E2: 1,5 => SOL
* DIS # E2: 8 => CTR => E2: 1,5
* PRF # E2: 1,8 => SOL
* DIS # E2: 5 => CTR => E2: 1,8
* DIS # G9: 7,8 => CTR => G9: 9
* PRF # G9: 9 => SOL
* DIS # I9: 3 => CTR => I9: 7,8
* DIS # A9: 4,8 => CTR => A9: 6
* PRF # A9: 6 => SOL
* DIS # A9: 8 => CTR => A9: 4,6
* DIS # E8: 3 => CTR => E8: 1,4
* PRF # E8: 3,4 => SOL
* DIS # E8: 1 => CTR => E8: 3,4
* DIS # I9: 7 => CTR => I9: 3,8
* DIS # G9: 8 => CTR => G9: 7,9
* CNT  15 HDP CHAINS /  20 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 # E2: 1,5 => SOL
* STA E2: 1,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.8.7.4..2.....3...75.....81......436.9.3.5........7...9.....14..7...92....15.2... initial
.837.4..22.9..3..4754..6381527..1436.963.5...3.8.675.9932678145.75..926...15.2... autosolve
183754692269813754754296381527981436496325817318467529932678145875149263641532978 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (26)
A1: 1,6
B2: 1,6
E1: 1,5
D2: 1,8
D3: 2,9
E3: 2,9
G1: 6,9
H1: 5,9
G2: 6,7
H2: 5,7
A5: 1,4
B6: 1,4
D4: 8,9
E4: 8,9
E5: 2,4
D6: 2,4
G5: 7,8
H5: 1,2
I5: 7,8
H6: 1,2
A8: 4,8
B9: 4,6
D8: 1,4
E9: 3,4
I8: 3,8
H9: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B2: 1.. / A1 = 1  =>  0 pairs (*) / B2 = 1  =>  0 pairs (X)
A5,B6: 1.. / A5 = 1  =>  0 pairs (X) / B6 = 1  =>  0 pairs (_)
H5,H6: 1.. / H5 = 1  =>  0 pairs (*) / H6 = 1  =>  0 pairs (X)
D8,E8: 1.. / D8 = 1  =>  0 pairs (*) / E8 = 1  =>  0 pairs (X)
A1,E1: 1.. / A1 = 1  =>  0 pairs (*) / E1 = 1  =>  0 pairs (X)
A5,H5: 1.. / A5 = 1  =>  0 pairs (X) / H5 = 1  =>  0 pairs (_)
B6,H6: 1.. / B6 = 1  =>  0 pairs (*) / H6 = 1  =>  0 pairs (X)
A1,A5: 1.. / A1 = 1  =>  0 pairs (*) / A5 = 1  =>  0 pairs (X)
B2,B6: 1.. / B2 = 1  =>  0 pairs (X) / B6 = 1  =>  0 pairs (_)
D2,D8: 1.. / D2 = 1  =>  0 pairs (X) / D8 = 1  =>  0 pairs (_)
D3,E3: 2.. / D3 = 2  =>  0 pairs (*) / E3 = 2  =>  0 pairs (X)
E5,D6: 2.. / E5 = 2  =>  0 pairs (*) / D6 = 2  =>  0 pairs (X)
H5,H6: 2.. / H5 = 2  =>  0 pairs (X) / H6 = 2  =>  0 pairs (_)
E5,H5: 2.. / E5 = 2  =>  0 pairs (*) / H5 = 2  =>  0 pairs (X)
D6,H6: 2.. / D6 = 2  =>  0 pairs (X) / H6 = 2  =>  0 pairs (_)
D3,D6: 2.. / D3 = 2  =>  0 pairs (*) / D6 = 2  =>  0 pairs (X)
E3,E5: 2.. / E3 = 2  =>  0 pairs (X) / E5 = 2  =>  0 pairs (_)
E8,E9: 3.. / E8 = 3  =>  0 pairs (X) / E9 = 3  => 26 pairs (_)
I8,I9: 3.. / I8 = 3  => 26 pairs (_) / I9 = 3  =>  0 pairs (X)
E8,I8: 3.. / E8 = 3  =>  0 pairs (X) / I8 = 3  => 26 pairs (_)
E9,I9: 3.. / E9 = 3  => 26 pairs (_) / I9 = 3  =>  0 pairs (X)
A5,B6: 4.. / A5 = 4  =>  0 pairs (*) / B6 = 4  =>  0 pairs (X)
E5,D6: 4.. / E5 = 4  =>  0 pairs (X) / D6 = 4  =>  0 pairs (_)
A5,E5: 4.. / A5 = 4  =>  0 pairs (*) / E5 = 4  =>  0 pairs (X)
B6,D6: 4.. / B6 = 4  =>  0 pairs (X) / D6 = 4  =>  0 pairs (_)
B6,B9: 4.. / B6 = 4  =>  0 pairs (X) / B9 = 4  =>  0 pairs (_)
D6,D8: 4.. / D6 = 4  =>  0 pairs (*) / D8 = 4  =>  0 pairs (X)
E1,E2: 5.. / E1 = 5  =>  0 pairs (*) / E2 = 5  =>  0 pairs (X)
H1,H2: 5.. / H1 = 5  =>  0 pairs (X) / H2 = 5  =>  0 pairs (_)
E1,H1: 5.. / E1 = 5  =>  0 pairs (*) / H1 = 5  =>  0 pairs (X)
E2,H2: 5.. / E2 = 5  =>  0 pairs (X) / H2 = 5  =>  0 pairs (_)
A1,B2: 6.. / A1 = 6  =>  0 pairs (X) / B2 = 6  =>  0 pairs (_)
G1,G2: 6.. / G1 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
A9,B9: 6.. / A9 = 6  =>  0 pairs (*) / B9 = 6  =>  0 pairs (X)
A1,G1: 6.. / A1 = 6  =>  0 pairs (X) / G1 = 6  =>  0 pairs (_)
B2,G2: 6.. / B2 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
A1,A9: 6.. / A1 = 6  =>  0 pairs (X) / A9 = 6  =>  0 pairs (_)
B2,B9: 6.. / B2 = 6  =>  0 pairs (*) / B9 = 6  =>  0 pairs (X)
G2,H2: 7.. / G2 = 7  =>  0 pairs (*) / H2 = 7  =>  0 pairs (X)
G5,I5: 7.. / G5 = 7  =>  0 pairs (X) / I5 = 7  => 26 pairs (_)
H2,H9: 7.. / H2 = 7  =>  0 pairs (X) / H9 = 7  =>  0 pairs (_)
I5,I9: 7.. / I5 = 7  => 26 pairs (_) / I9 = 7  =>  0 pairs (X)
D2,E2: 8.. / D2 = 8  =>  0 pairs (*) / E2 = 8  =>  0 pairs (X)
D4,E4: 8.. / D4 = 8  =>  0 pairs (X) / E4 = 8  =>  0 pairs (_)
G5,I5: 8.. / G5 = 8  => 26 pairs (_) / I5 = 8  =>  0 pairs (X)
A8,A9: 8.. / A8 = 8  => 26 pairs (_) / A9 = 8  =>  0 pairs (X)
A8,I8: 8.. / A8 = 8  => 26 pairs (_) / I8 = 8  =>  0 pairs (X)
D2,D4: 8.. / D2 = 8  =>  0 pairs (*) / D4 = 8  =>  0 pairs (X)
E2,E4: 8.. / E2 = 8  =>  0 pairs (X) / E4 = 8  =>  0 pairs (_)
G5,G9: 8.. / G5 = 8  => 26 pairs (_) / G9 = 8  =>  0 pairs (X)
D3,E3: 9.. / D3 = 9  =>  0 pairs (X) / E3 = 9  =>  0 pairs (_)
G1,H1: 9.. / G1 = 9  =>  0 pairs (X) / H1 = 9  =>  0 pairs (_)
D4,E4: 9.. / D4 = 9  =>  0 pairs (*) / E4 = 9  =>  0 pairs (X)
G9,H9: 9.. / G9 = 9  =>  0 pairs (*) / H9 = 9  =>  0 pairs (X)
D3,D4: 9.. / D3 = 9  =>  0 pairs (X) / D4 = 9  =>  0 pairs (_)
E3,E4: 9.. / E3 = 9  =>  0 pairs (*) / E4 = 9  =>  0 pairs (X)
G1,G9: 9.. / G1 = 9  =>  0 pairs (X) / G9 = 9  =>  0 pairs (_)
H1,H9: 9.. / H1 = 9  =>  0 pairs (*) / H9 = 9  =>  0 pairs (X)
* DURATION: 0:01:16.935678  START: 04:54:57.501283  END: 04:56:14.436961 2019-05-01
* CP COUNT: (58)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,A8,B2,B6,B9,D2,D3,D4,D6,D8,E1,E3,E4,E5,E9,G1,G2,G5,H1,H2,H5,H6,H9,I5,I8)
* .837.4..22.9..3..4754..6381527..1436.963.5...3.8.675.9932678145.75..926...15.2...
* PAIR E1: 1,5 BLK 2
E2: 1,5,8                                # reduction candidate for 1,5
E2: 1,5 => SOLVED
* 183754692269813754754296381527981436496325817318467529932678145875149263641532978
E2: 8 => CTR
* .83754.922.9183.54754..6381527891436.963.5...3184675.9932678145.75..926...15.2...
* PAIR D2: 1,8 BLK 2
E2: 1,8,5                                # reduction candidate for 1,8
E2: 1,8 => SOLVED
* 183754692269813754754296381527981436496325817318467529932678145875149263641532978
E2: 5 => CTR
* .837149522198536747542963815279814361963.5...3.8.675.9932678145.751.926...15.2.9.
* PAIR G5: 7,8 COL G
G9: 7,8,9                                # reduction candidate for 7,8
G9: 7,8 => CTR
* 683714952219853674754.963815279814361963.5...3.8.675.9932678145.75..926..615.2.9.
G9: 9 => SOLVED
* 183754692269813754754296381527981436496325817318467529932678145875149263641532978
* PAIR I5: 7,8 COL I
I9: 7,8,3                                # reduction candidate for 7,8
I9: 3 => CTR
* 683714952219853674754..6381527981436.963.5..73.8.675.9932678145.75..9268861542..3
I9: 7,8                                  # 26 pairs
* PAIR A8: 4,8 BLK 7
A9: 4,8,6                                # reduction candidate for 4,8
A9: 4,8 => CTR
* 683714952219853674754..6381527981436196345.2.3482675.9932678145.75..926...15.2...
A9: 6 => SOLVED
* 183754692269813754754296381527981436496325817318467529932678145875149263641532978
* PAIR B9: 4,6 BLK 7
A9: 4,6,8                                # reduction candidate for 4,6
A9: 8 => CTR
* 683714952219853674754..6381527981436196345.2.348.675.9932678145.75..926...15.2...
A9: 4,6                                  # 26 pairs
* PAIR D8: 1,4 BLK 8
E8: 1,4,3                                # reduction candidate for 1,4
E8: 3 => CTR
* 683714952219853674754..6381527981436.963.5...3.8.675.9932678145.75139268861542..3
E8: 1,4                                  # 26 pairs
* PAIR E9: 3,4 BLK 8
E8: 3,4,1                                # reduction candidate for 3,4
E8: 3,4 => SOLVED
* 183754692269813754754296381527981436496325817318467529932678145875149263641532978
E8: 1 => CTR
* 183754692269183754754..6381527891436496325...3.8.675.9932678145.75.19263..1532...
* PAIR I8: 3,8 BLK 9
I9: 3,8,7                                # reduction candidate for 3,8
I9: 7 => CTR
* 683714952219853674754.963815279814361963.57.83.8.675.9932678145875..9263.61532897
I9: 3,8                                  # 26 pairs
* PAIR H9: 7,9 BLK 9
G9: 7,9,8                                # reduction candidate for 7,9
G9: 8 => CTR
* 683714952219853674754.963815279814361963.57.83.8.675.9932678145875..9263.61532897
G9: 7,9                                  # 26 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190330-absurd-base-pr-000.dot
* REASONING
* PRF # E2: 1,5 => SOL
* DIS # E2: 8 => CTR => E2: 1,5
* PRF # E2: 1,8 => SOL
* DIS # E2: 5 => CTR => E2: 1,8
* DIS # G9: 7,8 => CTR => G9: 9
* PRF # G9: 9 => SOL
* DIS # I9: 3 => CTR => I9: 7,8
* DIS # A9: 4,8 => CTR => A9: 6
* PRF # A9: 6 => SOL
* DIS # A9: 8 => CTR => A9: 4,6
* DIS # E8: 3 => CTR => E8: 1,4
* PRF # E8: 3,4 => SOL
* DIS # E8: 1 => CTR => E8: 3,4
* DIS # I9: 7 => CTR => I9: 3,8
* DIS # G9: 8 => CTR => G9: 7,9
* CNT  15 HDP CHAINS /  20 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A5,A8,B2,B6,B9,D2,D3,D4,D6,D8,E1,E3,E4,E5,E9,G1,G2,G5,H1,H2,H5,H6,H9,I5,I8)
* .837.4..22.9..3..4754..6381527..1436.963.5...3.8.675.9932678145.75..926...15.2...
* PAIR E1: 1,5 BLK 2
E2: 1,5,8                                # reduction candidate for 1,5
E2: 1,5 => SOLVED
* 183754692269813754754296381527981436496325817318467529932678145875149263641532978
* DURATION: 0:00:01.630311  START: 04:56:32.129912  END: 04:56:33.760223 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190330-absurd-base-pr-001.dot
* REASONING
* PRF # E2: 1,5 => SOL
* STA E2: 1,5
* 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, 20190330, absurd

Solution

position: 183754692269813754754296381527981436496325817318467529932678145875149263641532978 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 # E2: 1,5 => SOL
* DIS # E2: 8 => CTR => E2: 1,5
* PRF # E2: 1,8 => SOL
* DIS # E2: 5 => CTR => E2: 1,8
* DIS # G9: 7,8 => CTR => G9: 9
* PRF # G9: 9 => SOL
* INC # I9: 7,8 => UNS
* DIS # I9: 3 => CTR => I9: 7,8
* DIS # A9: 4,8 => CTR => A9: 6
* PRF # A9: 6 => SOL
* INC # A9: 4,6 => UNS
* DIS # A9: 8 => CTR => A9: 4,6
* INC # E8: 1,4 => UNS
* DIS # E8: 3 => CTR => E8: 1,4
* PRF # E8: 3,4 => SOL
* DIS # E8: 1 => CTR => E8: 3,4
* INC # I9: 3,8 => UNS
* DIS # I9: 7 => CTR => I9: 3,8
* INC # G9: 7,9 => UNS
* DIS # G9: 8 => CTR => G9: 7,9
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # E2: 1,5 => SOL
* STA E2: 1,5
* CNT   1 HDP CHAINS /   1 HYP OPENED