Analysis of zz-www.sudokuoftheday.co.uk-20190421-absurd-base.sdk

Contents

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

level: medium

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

position: ..7.8.6.....12...86........4.28....7....6..93.63....2.8...71.5.....9.3...4.2.3... initial

Autosolve

position: ..7.8.6....4126..86...47...4.283.167....62493.63.1482583..71.5.....983...4.253.8. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A1: 1,2 => SOL
* DIS # B8: 1,2 => CTR => B8: 7
* DIS # A2: 5,9 => CTR => A2: 3
* PRF # C3: 5,9 => SOL
* DIS # G2: 7 => CTR => G2: 5,9
* DIS # G3: 2,9 => CTR => G3: 5
* DIS # G2: 5 => CTR => G2: 7,9
* CNT   7 HDP CHAINS /  40 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 # A1: 1,2 => SOL
* STA A1: 1,2
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

..7.8.6.....12...86........4.28....7....6..93.63....2.8...71.5.....9.3...4.2.3... initial
..7.8.6....4126..86...47...4.283.167....62493.63.1482583..71.5.....983...4.253.8. autosolve
127589634354126978689347512492835167518762493763914825836471259275698341941253786 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B1: 1,2
B2: 5,9
F1: 5,9
H2: 3,7
H3: 1,3
B4: 5,9
A6: 7,9
F4: 5,9
D5: 5,7
D6: 7,9
C7: 6,9
D7: 4,6
D8: 4,6
G7: 2,9
G9: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A8,B8: 2.. / A8 = 2  => 17 pairs (_) / B8 = 2  =>  0 pairs (X)
G7,I7: 2.. / G7 = 2  => 15 pairs (_) / I7 = 2  =>  0 pairs (X)
A1,A8: 2.. / A1 = 2  =>  0 pairs (X) / A8 = 2  => 17 pairs (_)
G3,G7: 2.. / G3 = 2  =>  0 pairs (X) / G7 = 2  => 15 pairs (_)
A1,A2: 3.. / A1 = 3  =>  0 pairs (X) / A2 = 3  => 20 pairs (_)
D1,D3: 3.. / D1 = 3  => 21 pairs (_) / D3 = 3  => 20 pairs (_)
A2,H2: 3.. / A2 = 3  => 20 pairs (_) / H2 = 3  =>  0 pairs (X)
D3,H3: 3.. / D3 = 3  => 20 pairs (_) / H3 = 3  => 21 pairs (_)
H1,I1: 4.. / H1 = 4  => 16 pairs (_) / I1 = 4  => 20 pairs (_)
D7,D8: 4.. / D7 = 4  => 15 pairs (_) / D8 = 4  => 16 pairs (_)
D7,I7: 4.. / D7 = 4  => 15 pairs (_) / I7 = 4  => 16 pairs (_)
H1,H8: 4.. / H1 = 4  => 16 pairs (_) / H8 = 4  => 20 pairs (_)
G2,G3: 5.. / G2 = 5  =>  0 pairs (X) / G3 = 5  => 16 pairs (_)
F4,D5: 5.. / F4 = 5  =>  0 pairs (*) / D5 = 5  =>  0 pairs (X)
A8,C8: 5.. / A8 = 5  =>  0 pairs (X) / C8 = 5  => 16 pairs (_)
B4,F4: 5.. / B4 = 5  => 17 pairs (_) / F4 = 5  =>  0 pairs (*)
B2,B4: 5.. / B2 = 5  =>  0 pairs (*) / B4 = 5  =>  0 pairs (X)
F1,F4: 5.. / F1 = 5  => 17 pairs (_) / F4 = 5  =>  0 pairs (*)
D7,D8: 6.. / D7 = 6  => 16 pairs (_) / D8 = 6  => 15 pairs (_)
C9,I9: 6.. / C9 = 6  => 18 pairs (_) / I9 = 6  => 19 pairs (_)
G2,H2: 7.. / G2 = 7  =>  0 pairs (X) / H2 = 7  => 20 pairs (_)
D5,D6: 7.. / D5 = 7  =>  0 pairs (*) / D6 = 7  =>  0 pairs (X)
H8,G9: 7.. / H8 = 7  =>  0 pairs (X) / G9 = 7  => 20 pairs (_)
A6,D6: 7.. / A6 = 7  =>  0 pairs (*) / D6 = 7  =>  0 pairs (X)
A9,G9: 7.. / A9 = 7  =>  0 pairs (X) / G9 = 7  => 20 pairs (_)
B5,B8: 7.. / B5 = 7  =>  0 pairs (X) / B8 = 7  => 20 pairs (_)
G2,G9: 7.. / G2 = 7  =>  0 pairs (X) / G9 = 7  => 20 pairs (_)
H2,H8: 7.. / H2 = 7  => 20 pairs (_) / H8 = 7  =>  0 pairs (X)
B3,C3: 8.. / B3 = 8  => 16 pairs (_) / C3 = 8  => 21 pairs (_)
B5,C5: 8.. / B5 = 8  => 21 pairs (_) / C5 = 8  => 16 pairs (_)
B3,B5: 8.. / B3 = 8  => 16 pairs (_) / B5 = 8  => 21 pairs (_)
C3,C5: 8.. / C3 = 8  => 21 pairs (_) / C5 = 8  => 16 pairs (_)
B4,A6: 9.. / B4 = 9  =>  0 pairs (*) / A6 = 9  =>  0 pairs (X)
F4,D6: 9.. / F4 = 9  => 17 pairs (_) / D6 = 9  =>  0 pairs (*)
B4,F4: 9.. / B4 = 9  =>  0 pairs (*) / F4 = 9  =>  0 pairs (X)
A6,D6: 9.. / A6 = 9  => 17 pairs (_) / D6 = 9  =>  0 pairs (*)
B2,B4: 9.. / B2 = 9  => 17 pairs (_) / B4 = 9  =>  0 pairs (*)
F1,F4: 9.. / F1 = 9  =>  0 pairs (*) / F4 = 9  =>  0 pairs (X)
* DURATION: 0:00:42.898480  START: 05:29:49.659457  END: 05:30:32.557937 2019-05-01
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,B2,B4,C7,D5,D6,D7,D8,F1,F4,G7,G9,H2,H3)
* ..7.8.6....4126..86...47...4.283.167....62493.63.1482583..71.5.....983...4.253.8.
* PAIR B1: 1,2 BLK 1
A1: 1,2,3,5,9                            # reduction candidate for 1,2
A1: 1,2 => SOLVED
* 127589634354126978689347512492835167518762493763914825836471259275698341941253786
A1: 3,5,9                                # 21 pairs
B3: 1,2,8                                # reduction candidate for 1,2
B3: 1,2                                  # 21 pairs
* PAIR B1: 1,2 ROW 1
I1: 1,2,4,9                              # reduction candidate for 1,2
I1: 1,2                                  # 23 pairs
I1: 4,9                                  # 17 pairs
* PAIR B1: 1,2 COL B
B8: 1,2,7                                # reduction candidate for 1,2
B8: 1,2 => CTR
* ..7.856...9412673868.34751.45283916717856249396371482583..71.5.....983..74.25398.
B8: 7                                    # 20 pairs
* PAIR B2: 5,9 BLK 1
A1: 5,9,1,2,3                            # reduction candidate for 5,9
A1: 5,9                                  # 23 pairs
A2: 5,9,3                                # reduction candidate for 5,9
A2: 5,9 => CTR
* 317.8.6....4126.386..347.1.4.283.167....62493.63.1482583..71.5.2.5.9837.74.25398.
A2: 3                                    # 20 pairs
C3: 5,9,1,8                              # reduction candidate for 5,9
C3: 5,9 => SOLVED
* 127589634354126978689347512492835167518762493763914825836471259275698341941253786
C3: 1,8                                  # 21 pairs
* PAIR B2: 5,9 ROW 2
G2: 5,9,7                                # reduction candidate for 5,9
G2: 7 => CTR
* 317.8.642..412673862.34751.4.283.167....62493.63.1482583..7125.....9837.74.25398.
G2: 5,9                                  # 20 pairs
* PAIR F1: 5,9 BLK 2
D1: 5,9,3                                # reduction candidate for 5,9
D1: 5,9                                  # 20 pairs
D3: 5,9,3                                # reduction candidate for 5,9
D3: 5,9                                  # 21 pairs
* PAIR F1: 5,9 ROW 1
A1: 5,9,1,2,3                            # reduction candidate for 5,9
A1: 5,9                                  # 23 pairs
A1: 1,2,3                                # 16 pairs
* PAIR H3: 1,3 BLK 3
H1: 1,3,4                                # reduction candidate for 1,3
H1: 1,3                                  # 20 pairs
H1: 4                                    # 16 pairs
* PAIR A6: 7,9 COL A
A9: 7,9,1                                # reduction candidate for 7,9
A9: 1                                    # 23 pairs
A9: 7,9                                  # 20 pairs
* PAIR D5: 5,7 ROW 5
A5: 5,7,1                                # reduction candidate for 5,7
A5: 1                                    # 22 pairs
A5: 5,7                                  # 20 pairs
* PAIR C7: 6,9 BLK 7
C9: 6,9,1                                # reduction candidate for 6,9
C9: 1                                    # 23 pairs
C9: 6,9                                  # 18 pairs
* PAIR C7: 6,9 ROW 7
I7: 6,9,2,4                              # reduction candidate for 6,9
I7: 6,9                                  # 16 pairs
I7: 2,4                                  # 16 pairs
* PAIR D7: 4,6 ROW 7
I7: 4,6,2,9                              # reduction candidate for 4,6
I7: 2,9                                  # 19 pairs
I7: 4,6                                  # 17 pairs
* PAIR D8: 4,6 ROW 8
I8: 4,6,1                                # reduction candidate for 4,6
I8: 1                                    # 20 pairs
I8: 4,6                                  # 18 pairs
* PAIR G7: 2,9 BLK 9
I7: 2,9,4,6                              # reduction candidate for 2,9
I7: 2,9                                  # 19 pairs
I7: 4,6                                  # 17 pairs
* PAIR G7: 2,9 COL G
G3: 2,9,5                                # reduction candidate for 2,9
G3: 2,9 => CTR
* ..7.856..3941265786.5.47...452839167..856249396371482583..71.5.5...983...4.25378.
G3: 5                                    # 16 pairs
* PAIR G9: 7,9 ROW 9
A9: 7,9,1                                # reduction candidate for 7,9
A9: 1                                    # 23 pairs
A9: 7,9                                  # 20 pairs
* PAIR G9: 7,9 COL G
G2: 7,9,5                                # reduction candidate for 7,9
G2: 5 => CTR
* ..7.856..3941265786.5.47...452839167..856249396371482583..71.5.5...983...4.25378.
G2: 7,9                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190421-absurd-base-pr-000.dot
* REASONING
* PRF # A1: 1,2 => SOL
* DIS # B8: 1,2 => CTR => B8: 7
* DIS # A2: 5,9 => CTR => A2: 3
* PRF # C3: 5,9 => SOL
* DIS # G2: 7 => CTR => G2: 5,9
* DIS # G3: 2,9 => CTR => G3: 5
* DIS # G2: 5 => CTR => G2: 7,9
* CNT   7 HDP CHAINS /  40 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B1,B2,B4,C7,D5,D6,D7,D8,F1,F4,G7,G9,H2,H3)
* ..7.8.6....4126..86...47...4.283.167....62493.63.1482583..71.5.....983...4.253.8.
* PAIR B1: 1,2 BLK 1
A1: 1,2,3,5,9                            # reduction candidate for 1,2
A1: 1,2 => SOLVED
* 127589634354126978689347512492835167518762493763914825836471259275698341941253786
* DURATION: 0:00:01.820717  START: 05:30:57.868098  END: 05:30:59.688815 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190421-absurd-base-pr-001.dot
* REASONING
* PRF # A1: 1,2 => SOL
* STA A1: 1,2
* 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, 20190421, absurd

Solution

position: 127589634354126978689347512492835167518762493763914825836471259275698341941253786 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 # A1: 1,2 => SOL
* INC # A1: 3,5,9 => UNS
* INC # B3: 1,2 => UNS
* INC # I1: 1,2 => UNS
* INC # I1: 4,9 => UNS
* DIS # B8: 1,2 => CTR => B8: 7
* INC # B8: 7 => UNS
* INC # A1: 5,9 => UNS
* DIS # A2: 5,9 => CTR => A2: 3
* INC # A2: 3 => UNS
* PRF # C3: 5,9 => SOL
* INC # C3: 1,8 => UNS
* INC # G2: 5,9 => UNS
* DIS # G2: 7 => CTR => G2: 5,9
* INC # D1: 5,9 => UNS
* INC # D3: 5,9 => UNS
* INC # A1: 5,9 => UNS
* INC # A1: 1,2,3 => UNS
* INC # H1: 1,3 => UNS
* INC # H1: 4 => UNS
* INC # A9: 7,9 => UNS
* INC # A9: 1 => UNS
* INC # A5: 5,7 => UNS
* INC # A5: 1 => UNS
* INC # C9: 6,9 => UNS
* INC # C9: 1 => UNS
* INC # I7: 6,9 => UNS
* INC # I7: 2,4 => UNS
* INC # I7: 4,6 => UNS
* INC # I7: 2,9 => UNS
* INC # I8: 4,6 => UNS
* INC # I8: 1 => UNS
* INC # I7: 2,9 => UNS
* INC # I7: 4,6 => UNS
* DIS # G3: 2,9 => CTR => G3: 5
* INC # G3: 5 => UNS
* INC # A9: 7,9 => UNS
* INC # A9: 1 => UNS
* INC # G2: 7,9 => UNS
* DIS # G2: 5 => CTR => G2: 7,9
* CNT  40 HDP CHAINS /  40 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A1: 1,2 => SOL
* STA A1: 1,2
* CNT   1 HDP CHAINS /   1 HYP OPENED