Analysis of zz-www.sudokuoftheday.co.uk-20190315-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: ..1.9....6.2...8.......6....7.2..1....6.85.7..24..3.........354..51...6...7....8. initial

Autosolve

position: ..1.97.2.692..18.77...26.1..7.26.1....6.85.7..24713.9.....7.354..51..76...7....81 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B3: 3,8 => SOL
* PRF # D3: 4 => SOL
* PRF # C4: 9 => SOL
* PRF # D2: 3,4 => SOL
* PRF # A5: 1,3 => SOL
* DIS # A5: 9 => CTR => A5: 1,3
* DIS # A4: 3,9 => CTR => A4: 5,8
* DIS # F8: 4,9 => CTR => F8: 2,8
* DIS # D9: 4,9 => CTR => D9: 3,5,6
* DIS # G1: 4 => CTR => G1: 5,6
* PRF # A7: 8,9 => SOL
* DIS # F7: 8,9 => CTR => F7: 2
* DIS # C4: 3 => CTR => C4: 8,9
* DIS # D9: 6,9 => CTR => D9: 3,4,5
* PRF # D9: 3,4,5 => SOL
* DIS # D9: 3,4 => CTR => D9: 5,6,9
* PRF # E9: 3,4 => SOL
* DIS # A8: 3,4 => CTR => A8: 2,8,9
* PRF # E2: 5 => SOL
* DIS # F8: 2,9 => CTR => F8: 4,8
* DIS # A9: 2,9 => CTR => A9: 3,4
* CNT  21 HDP CHAINS /  50 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 # B3: 3,8 => SOL
* STA B3: 3,8
* CNT   1 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

..1.9....6.2...8.......6....7.2..1....6.85.7..24..3.........354..51...6...7....8. initial
..1.97.2.692..18.77...26.1..7.26.1....6.85.7..24713.9.....7.354..51..76...7....81 autosolve
451897623692351847783426915579264138136985472824713596918672354245138769367549281 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
C3: 3,8
H2: 3,4
B5: 1,3
A6: 5,8
F4: 4,9
D5: 4,9
H4: 3,4
G5: 2,4
I5: 2,3
G6: 5,6
C7: 8,9
D7: 6,9
E8: 3,4
I8: 2,9
G9: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A5,B5: 1.. / A5 = 1  =>  0 pairs (*) / B5 = 1  =>  0 pairs (X)
A7,B7: 1.. / A7 = 1  => 19 pairs (_) / B7 = 1  =>  0 pairs (*)
A5,A7: 1.. / A5 = 1  =>  0 pairs (*) / A7 = 1  =>  0 pairs (X)
B5,B7: 1.. / B5 = 1  => 19 pairs (_) / B7 = 1  =>  0 pairs (*)
G5,I5: 2.. / G5 = 2  =>  0 pairs (X) / I5 = 2  =>  0 pairs (_)
I8,G9: 2.. / I8 = 2  =>  0 pairs (X) / G9 = 2  =>  0 pairs (_)
A7,F7: 2.. / A7 = 2  =>  0 pairs (X) / F7 = 2  => 18 pairs (_)
G5,G9: 2.. / G5 = 2  =>  0 pairs (X) / G9 = 2  =>  0 pairs (_)
I5,I8: 2.. / I5 = 2  =>  0 pairs (*) / I8 = 2  =>  0 pairs (X)
C3,C4: 3.. / C3 = 3  => 18 pairs (_) / C4 = 3  =>  0 pairs (X)
H2,H4: 3.. / H2 = 3  =>  0 pairs (X) / H4 = 3  =>  0 pairs (_)
F4,D5: 4.. / F4 = 4  =>  0 pairs (*) / D5 = 4  =>  0 pairs (X)
H4,G5: 4.. / H4 = 4  =>  0 pairs (X) / G5 = 4  =>  0 pairs (_)
F4,H4: 4.. / F4 = 4  =>  0 pairs (*) / H4 = 4  =>  0 pairs (X)
D5,G5: 4.. / D5 = 4  =>  0 pairs (X) / G5 = 4  =>  0 pairs (_)
H2,H4: 4.. / H2 = 4  =>  0 pairs (*) / H4 = 4  =>  0 pairs (X)
B1,B3: 5.. / B1 = 5  => 19 pairs (_) / B3 = 5  => 20 pairs (_)
D2,E2: 5.. / D2 = 5  => 16 pairs (_) / E2 = 5  =>  0 pairs (*)
A4,A6: 5.. / A4 = 5  => 17 pairs (_) / A6 = 5  => 15 pairs (_)
D9,E9: 5.. / D9 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
A4,I4: 5.. / A4 = 5  => 17 pairs (_) / I4 = 5  => 15 pairs (_)
D2,D9: 5.. / D2 = 5  => 16 pairs (_) / D9 = 5  =>  0 pairs (*)
E2,E9: 5.. / E2 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
G1,I1: 6.. / G1 = 6  => 17 pairs (_) / I1 = 6  => 18 pairs (_)
G6,I6: 6.. / G6 = 6  => 18 pairs (_) / I6 = 6  => 17 pairs (_)
B7,B9: 6.. / B7 = 6  =>  0 pairs (X) / B9 = 6  => 15 pairs (_)
D7,D9: 6.. / D7 = 6  => 15 pairs (_) / D9 = 6  =>  0 pairs (X)
B7,D7: 6.. / B7 = 6  =>  0 pairs (X) / D7 = 6  => 15 pairs (_)
B9,D9: 6.. / B9 = 6  => 15 pairs (_) / D9 = 6  =>  0 pairs (X)
G1,G6: 6.. / G1 = 6  => 17 pairs (_) / G6 = 6  => 18 pairs (_)
I1,I6: 6.. / I1 = 6  => 18 pairs (_) / I6 = 6  => 17 pairs (_)
D1,D3: 8.. / D1 = 8  => 17 pairs (_) / D3 = 8  => 19 pairs (_)
I4,I6: 8.. / I4 = 8  => 17 pairs (_) / I6 = 8  => 15 pairs (_)
F7,F8: 8.. / F7 = 8  =>  0 pairs (X) / F8 = 8  => 18 pairs (_)
A6,I6: 8.. / A6 = 8  => 17 pairs (_) / I6 = 8  => 15 pairs (_)
G3,I3: 9.. / G3 = 9  =>  0 pairs (*) / I3 = 9  =>  0 pairs (X)
F4,D5: 9.. / F4 = 9  =>  0 pairs (X) / D5 = 9  =>  0 pairs (_)
I8,G9: 9.. / I8 = 9  =>  0 pairs (*) / G9 = 9  =>  0 pairs (X)
A5,D5: 9.. / A5 = 9  =>  0 pairs (X) / D5 = 9  =>  0 pairs (_)
C4,C7: 9.. / C4 = 9  =>  0 pairs (*) / C7 = 9  =>  0 pairs (X)
G3,G9: 9.. / G3 = 9  =>  0 pairs (*) / G9 = 9  =>  0 pairs (X)
I3,I8: 9.. / I3 = 9  =>  0 pairs (X) / I8 = 9  =>  0 pairs (_)
* DURATION: 0:00:49.235633  START: 04:32:29.901979  END: 04:33:19.137612 2019-05-01
* CP COUNT: (42)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B5,C3,C7,D5,D7,E8,F4,G5,G6,G9,H2,H4,I5,I8)
* ..1.97.2.692..18.77...26.1..7.26.1....6.85.7..24713.9.....7.354..51..76...7....81
* PAIR C3: 3,8 BLK 1
A1: 3,8,4                                # reduction candidate for 3,8
A1: 3,8                                  # 21 pairs
B1: 3,8,4,5                              # reduction candidate for 3,8
B1: 3,8                                  # 21 pairs
B3: 3,8,4,5                              # reduction candidate for 3,8
B3: 3,8 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
B3: 4,5                                  # 16 pairs
* PAIR C3: 3,8 ROW 3
D3: 3,8,4                                # reduction candidate for 3,8
D3: 4 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
D3: 3,8                                  # 18 pairs
* PAIR C3: 3,8 COL C
C4: 3,8,9                                # reduction candidate for 3,8
C4: 9 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
C4: 3,8                                  # 16 pairs
* PAIR H2: 3,4 ROW 2
D2: 3,4,5                                # reduction candidate for 3,4
D2: 3,4 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
D2: 5                                    # 16 pairs
E2: 3,4,5                                # reduction candidate for 3,4
E2: 3,4                                  # 16 pairs
* PAIR B5: 1,3 BLK 4
A5: 1,3,9                                # reduction candidate for 1,3
A5: 1,3 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
A5: 9 => CTR
* ..1.97.2.692..18.77...26.1..7.26.1..916485273.24713.9.1.9672354..51.876...7....81
* PAIR A6: 5,8 BLK 4
A4: 5,8,3,9                              # reduction candidate for 5,8
A4: 3,9 => CTR
* ..1.97.26692..18.77.3.26.19.7826.1.5..6.85.73524713698..967.354.35149762467....81
A4: 5,8                                  # 19 pairs
* PAIR A6: 5,8 ROW 6
I6: 5,8,6                                # reduction candidate for 5,8
I6: 5,8                                  # 18 pairs
I6: 6                                    # 17 pairs
* PAIR F4: 4,9 COL F
F8: 4,9,2,8                              # reduction candidate for 4,9
F8: 4,9 => CTR
* ..1.97.2.692..18.77...26.19.7.26.1....6.85273.24713.9.21..78354..51..76...7..2981
F8: 2,8                                  # 16 pairs
F9: 4,9,2                                # reduction candidate for 4,9
F9: 4,9                                  # 18 pairs
* PAIR D5: 4,9 COL D
D9: 4,9,3,5,6                            # reduction candidate for 4,9
D9: 4,9 => CTR
* ..1.97.2.6925418377...26.1..7.26.14...6485273.24713.9....67.354..513.76236795..81
D9: 3,5,6                                # 15 pairs
* PAIR G6: 5,6 BLK 6
I6: 5,6,8                                # reduction candidate for 5,6
I6: 5,6                                  # 17 pairs
I6: 8                                    # 15 pairs
* PAIR G6: 5,6 COL G
G1: 5,6,4                                # reduction candidate for 5,6
G1: 4 => CTR
* .51.9742669254183774..26519.7.26914.916485273.2471369.1.9672354..513.762..7...981
G1: 5,6                                  # 17 pairs
* PAIR C7: 8,9 BLK 7
A7: 8,9,1,2                              # reduction candidate for 8,9
A7: 8,9 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
A7: 1,2                                  # 16 pairs
A8: 8,9,2,3,4                            # reduction candidate for 8,9
A8: 8,9                                  # 27 pairs
* PAIR C7: 8,9 ROW 7
F7: 8,9,2                                # reduction candidate for 8,9
F7: 8,9 => CTR
* ..1.97.2.692..18477.3.269155792641..136985472.24713.9.21.67.354..51.2769.67...281
F7: 2                                    # 18 pairs
* PAIR C7: 8,9 COL C
C4: 8,9,3                                # reduction candidate for 8,9
C4: 3 => CTR
* ..1.97.2.692..18.77...26.1..7326.14..16485273.24713.9.1.9672354..51.876...7....81
C4: 8,9                                  # 18 pairs
* PAIR D7: 6,9 BLK 8
D9: 6,9,3,4,5                            # reduction candidate for 6,9
D9: 6,9 => CTR
* ..1.97.2.6925418377...26.19.7.26914.916485273.24713.9.1.967.354..513.762..7.5.981
D9: 3,4,5 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
* PAIR E8: 3,4 BLK 8
D9: 3,4,5,6,9                            # reduction candidate for 3,4
D9: 3,4 => CTR
* ..1.97.2.6925318477.3.26915579264138..6985472824713.9....67.354..514.769467359281
D9: 5,6,9                                # 16 pairs
E9: 3,4,5                                # reduction candidate for 3,4
E9: 3,4 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
E9: 5                                    # 16 pairs
* PAIR E8: 3,4 ROW 8
A8: 3,4,2,8,9                            # reduction candidate for 3,4
A8: 3,4 => CTR
* ..1.97.2.692..18477.3826915.7.26.1..136985472.24713.9.219678354.851.2769.67..9281
A8: 2,8,9                                # 15 pairs
B8: 3,4,8                                # reduction candidate for 3,4
B8: 3,4                                  # 16 pairs
* PAIR E8: 3,4 COL E
E2: 3,4,5                                # reduction candidate for 3,4
E2: 5 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
E2: 3,4                                  # 16 pairs
* PAIR I8: 2,9 ROW 8
A8: 2,9,3,4,8                            # reduction candidate for 2,9
A8: 2,9                                  # 17 pairs
F8: 2,9,4,8                              # reduction candidate for 2,9
F8: 2,9 => CTR
* ..1.97.2.692..18477.3.26915.7.26.1..136985472.24713.9.219678354..51.2769.67..9281
F8: 4,8                                  # 17 pairs
* PAIR G9: 2,9 ROW 9
A9: 2,9,3,4                              # reduction candidate for 2,9
A9: 2,9 => CTR
* ..1.97.2.692..18.77...26.1..7.26914.916485273.24713.9.....7.354..51..76...7....81
A9: 3,4                                  # 16 pairs
F9: 2,9,4                                # reduction candidate for 2,9
F9: 2,9                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190315-absurd-base-pr-000.dot
* REASONING
* PRF # B3: 3,8 => SOL
* PRF # D3: 4 => SOL
* PRF # C4: 9 => SOL
* PRF # D2: 3,4 => SOL
* PRF # A5: 1,3 => SOL
* DIS # A5: 9 => CTR => A5: 1,3
* DIS # A4: 3,9 => CTR => A4: 5,8
* DIS # F8: 4,9 => CTR => F8: 2,8
* DIS # D9: 4,9 => CTR => D9: 3,5,6
* DIS # G1: 4 => CTR => G1: 5,6
* PRF # A7: 8,9 => SOL
* DIS # F7: 8,9 => CTR => F7: 2
* DIS # C4: 3 => CTR => C4: 8,9
* DIS # D9: 6,9 => CTR => D9: 3,4,5
* PRF # D9: 3,4,5 => SOL
* DIS # D9: 3,4 => CTR => D9: 5,6,9
* PRF # E9: 3,4 => SOL
* DIS # A8: 3,4 => CTR => A8: 2,8,9
* PRF # E2: 5 => SOL
* DIS # F8: 2,9 => CTR => F8: 4,8
* DIS # A9: 2,9 => CTR => A9: 3,4
* CNT  21 HDP CHAINS /  50 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B5,C3,C7,D5,D7,E8,F4,G5,G6,G9,H2,H4,I5,I8)
* ..1.97.2.692..18.77...26.1..7.26.1....6.85.7..24713.9.....7.354..51..76...7....81
* PAIR C3: 3,8 BLK 1
A1: 3,8,4                                # reduction candidate for 3,8
A1: 3,8                                  # 21 pairs
B1: 3,8,4,5                              # reduction candidate for 3,8
B1: 3,8                                  # 21 pairs
B3: 3,8,4,5                              # reduction candidate for 3,8
B3: 3,8 => SOLVED
* 451897623692351847783426915579264138136985472824713596918672354245138769367549281
* DURATION: 0:00:02.825767  START: 04:33:50.532922  END: 04:33:53.358689 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190315-absurd-base-pr-001.dot
* REASONING
* PRF # B3: 3,8 => SOL
* STA B3: 3,8
* CNT   1 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190315, absurd

Solution

position: 451897623692351847783426915579264138136985472824713596918672354245138769367549281 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: 3,8 => UNS
* INC # B1: 3,8 => UNS
* PRF # B3: 3,8 => SOL
* INC # B3: 4,5 => UNS
* INC # D3: 3,8 => UNS
* PRF # D3: 4 => SOL
* INC # C4: 3,8 => UNS
* PRF # C4: 9 => SOL
* PRF # D2: 3,4 => SOL
* INC # D2: 5 => UNS
* INC # E2: 3,4 => UNS
* PRF # A5: 1,3 => SOL
* DIS # A5: 9 => CTR => A5: 1,3
* INC # A4: 5,8 => UNS
* DIS # A4: 3,9 => CTR => A4: 5,8
* INC # I6: 5,8 => UNS
* INC # I6: 6 => UNS
* DIS # F8: 4,9 => CTR => F8: 2,8
* INC # F8: 2,8 => UNS
* INC # F9: 4,9 => UNS
* DIS # D9: 4,9 => CTR => D9: 3,5,6
* INC # D9: 3,5,6 => UNS
* INC # I6: 5,6 => UNS
* INC # I6: 8 => UNS
* INC # G1: 5,6 => UNS
* DIS # G1: 4 => CTR => G1: 5,6
* PRF # A7: 8,9 => SOL
* INC # A7: 1,2 => UNS
* INC # A8: 8,9 => UNS
* DIS # F7: 8,9 => CTR => F7: 2
* INC # F7: 2 => UNS
* INC # C4: 8,9 => UNS
* DIS # C4: 3 => CTR => C4: 8,9
* DIS # D9: 6,9 => CTR => D9: 3,4,5
* PRF # D9: 3,4,5 => SOL
* DIS # D9: 3,4 => CTR => D9: 5,6,9
* INC # D9: 5,6,9 => UNS
* PRF # E9: 3,4 => SOL
* INC # E9: 5 => UNS
* DIS # A8: 3,4 => CTR => A8: 2,8,9
* INC # A8: 2,8,9 => UNS
* INC # B8: 3,4 => UNS
* INC # E2: 3,4 => UNS
* PRF # E2: 5 => SOL
* INC # A8: 2,9 => UNS
* DIS # F8: 2,9 => CTR => F8: 4,8
* INC # F8: 4,8 => UNS
* DIS # A9: 2,9 => CTR => A9: 3,4
* INC # A9: 3,4 => UNS
* INC # F9: 2,9 => UNS
* CNT  50 HDP CHAINS /  50 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 3,8 => UNS
* INC # B1: 3,8 => UNS
* PRF # B3: 3,8 => SOL
* STA B3: 3,8
* CNT   3 HDP CHAINS /   3 HYP OPENED