Analysis of zz-www.sudokuoftheday.co.uk-20190213-absurd-base.sdk

Contents

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

level: medium

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

position: 5.....9.6...27.3.5.9......1.7.5.3.....6...5..2.......37.13.5..2.6.......83.4....7 initial

Autosolve

position: 527134986618279345493.5...117.5.3...386...5..25......37413.5.92965....3.83249..57 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # D6: 6,8 => SOL
* DIS # D6: 7,9 => CTR => D6: 6,8
* DIS # F6: 6,8 => CTR => F6: 1,7
* PRF # I4: 4,9 => SOL
* DIS # I4: 8 => CTR => I4: 4,9
* DIS # D6: 7,9 => CTR => D6: 6,8
* PRF # D6: 6,8 => SOL
* PRF # I4: 4,9 => SOL
* DIS # I4: 8 => CTR => I4: 4,9
* DIS # F8: 7,8 => CTR => F8: 1,2
* PRF # F8: 1,2 => SOL
* PRF # D6: 7,8 => SOL
* PRF # G8: 4,8 => SOL
* DIS # G8: 1 => CTR => G8: 4,8
* DIS # I4: 4,8 => CTR => I4: 9
* PRF # I4: 9 => SOL
* CNT  16 HDP CHAINS /  26 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 # D6: 6,8 => SOL
* STA D6: 6,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

5.....9.6...27.3.5.9......1.7.5.3.....6...5..2.......37.13.5..2.6.......83.4....7 initial
527134986618279345493.5...117.5.3...386...5..25......37413.5.92965....3.83249..57 autosolve
527134986618279345493658271174563829386927514259841763741385692965712438832496157 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
D3: 6,8
F3: 6,8
G3: 2,7
H3: 2,7
C4: 4,9
C6: 4,9
D5: 7,9
H4: 2,6
I5: 4,9
E7: 6,8
D8: 7,8
F9: 1,6
G7: 6,8
I8: 4,8
G9: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H5,H6: 1.. / H5 = 1  => 19 pairs (_) / H6 = 1  => 15 pairs (_)
G8,G9: 1.. / G8 = 1  =>  0 pairs (X) / G9 = 1  =>  0 pairs (_)
F9,G9: 1.. / F9 = 1  =>  0 pairs (X) / G9 = 1  =>  0 pairs (_)
G3,H3: 2.. / G3 = 2  => 19 pairs (_) / H3 = 2  => 16 pairs (_)
E8,F8: 2.. / E8 = 2  => 17 pairs (_) / F8 = 2  =>  0 pairs (*)
F5,F8: 2.. / F5 = 2  => 17 pairs (_) / F8 = 2  =>  0 pairs (*)
G3,G4: 2.. / G3 = 2  => 19 pairs (_) / G4 = 2  => 16 pairs (_)
C4,C6: 4.. / C4 = 4  =>  0 pairs (*) / C6 = 4  =>  0 pairs (X)
G8,I8: 4.. / G8 = 4  =>  0 pairs (*) / I8 = 4  =>  0 pairs (X)
E5,I5: 4.. / E5 = 4  =>  0 pairs (X) / I5 = 4  =>  0 pairs (_)
D3,F3: 6.. / D3 = 6  => 13 pairs (_) / F3 = 6  =>  0 pairs (X)
H4,H6: 6.. / H4 = 6  => 15 pairs (_) / H6 = 6  =>  0 pairs (*)
E7,F9: 6.. / E7 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
G7,G9: 6.. / G7 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
E4,H4: 6.. / E4 = 6  =>  0 pairs (*) / H4 = 6  =>  0 pairs (X)
E7,G7: 6.. / E7 = 6  =>  0 pairs (X) / G7 = 6  =>  0 pairs (_)
F9,G9: 6.. / F9 = 6  =>  0 pairs (*) / G9 = 6  =>  0 pairs (X)
D3,D6: 6.. / D3 = 6  => 13 pairs (_) / D6 = 6  =>  0 pairs (X)
G3,H3: 7.. / G3 = 7  => 16 pairs (_) / H3 = 7  => 19 pairs (_)
D8,F8: 7.. / D8 = 7  =>  0 pairs (*) / F8 = 7  =>  0 pairs (X)
G3,G6: 7.. / G3 = 7  => 16 pairs (_) / G6 = 7  => 19 pairs (_)
D3,F3: 8.. / D3 = 8  =>  0 pairs (X) / F3 = 8  => 13 pairs (_)
E7,G7: 8.. / E7 = 8  =>  0 pairs (*) / G7 = 8  =>  0 pairs (X)
I4,I8: 8.. / I4 = 8  =>  0 pairs (X) / I8 = 8  =>  0 pairs (_)
C4,C6: 9.. / C4 = 9  =>  0 pairs (X) / C6 = 9  =>  0 pairs (_)
D5,D6: 9.. / D5 = 9  =>  0 pairs (*) / D6 = 9  =>  0 pairs (X)
I4,I5: 9.. / I4 = 9  =>  0 pairs (*) / I5 = 9  =>  0 pairs (X)
C4,I4: 9.. / C4 = 9  =>  0 pairs (X) / I4 = 9  =>  0 pairs (_)
D5,I5: 9.. / D5 = 9  =>  0 pairs (*) / I5 = 9  =>  0 pairs (X)
C6,D6: 9.. / C6 = 9  =>  0 pairs (*) / D6 = 9  =>  0 pairs (X)
* DURATION: 0:00:36.096453  START: 03:42:11.265638  END: 03:42:47.362091 2019-05-01
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C6,D3,D5,D8,E7,F3,F9,G3,G7,G9,H3,H4,I5,I8)
* 527134986618279345493.5...117.5.3...386...5..25......37413.5.92965....3.83249..57
* PAIR D3: 6,8 COL D
D6: 6,8,7,9                              # reduction candidate for 6,8
D6: 6,8 => SOLVED
* 527134986618279345493658271174563829386927514259841763741385692965712438832496157
D6: 7,9 => CTR
* 527134986618279345493658..117.5.3..8386.4251925.981.63741365.929658.7.3483249..57
* PAIR F3: 6,8 COL F
F6: 6,8,1,7                              # reduction candidate for 6,8
F6: 6,8 => CTR
* 527134986618279345493.5...117.5.3.68386.4.51925.91...3741365892965....34832491657
F6: 1,7                                  # 16 pairs
* PAIR H3: 2,7 COL H
H5: 2,7,1                                # reduction candidate for 2,7
H5: 1                                    # 19 pairs
H5: 2,7                                  # 15 pairs
* PAIR C4: 4,9 ROW 4
I4: 4,9,8                                # reduction candidate for 4,9
I4: 4,9 => SOLVED
* 527134986618279345493658271174563829386927514259841763741385692965712438832496157
I4: 8 => CTR
* 5271349866182793454936582711795.34.838674.5.925498.7.374136589296581..3483249..57
* PAIR D5: 7,9 BLK 5
D6: 7,9,6,8                              # reduction candidate for 7,9
D6: 7,9 => CTR
* 527134986618279345493658..117.5.3..8386.4251925.981.63741365.929658.7.3483249..57
D6: 6,8 => SOLVED
* 527134986618279345493658271174563829386927514259841763741385692965712438832496157
* PAIR H4: 2,6 ROW 4
E4: 2,6,4,8                              # reduction candidate for 2,6
E4: 2,6                                  # 19 pairs
E4: 4,8                                  # 16 pairs
* PAIR I5: 4,9 BLK 6
I4: 4,9,8                                # reduction candidate for 4,9
I4: 4,9 => SOLVED
* 527134986618279345493658271174563829386927514259841763741385692965712438832496157
I4: 8 => CTR
* 5271349866182793454936582711795.34.838674.5.925498.7.374136589296581..3483249..57
* PAIR E7: 6,8 COL E
E4: 6,8,2,4                              # reduction candidate for 6,8
E4: 6,8                                  # 19 pairs
E6: 6,8,1,4                              # reduction candidate for 6,8
E6: 6,8                                  # 19 pairs
* PAIR D8: 7,8 BLK 8
F8: 7,8,1,2                              # reduction candidate for 7,8
F8: 7,8 => CTR
* 527134986618279345493.5...117.5.3..8386.4251925.918.637413.5.92965.2.134832491657
F8: 1,2 => SOLVED
* 527134986618279345493658271174563829386927514259841763741385692965712438832496157
* PAIR D8: 7,8 COL D
D6: 7,8,6,9                              # reduction candidate for 7,8
D6: 7,8 => SOLVED
* 527134986618279345493658271174563829386927514259841763741385692965712438832496157
D6: 6,9                                  # 16 pairs
* PAIR F9: 1,6 COL F
F6: 1,6,7,8                              # reduction candidate for 1,6
F6: 7,8                                  # 16 pairs
F6: 1,6                                  # 16 pairs
* PAIR I8: 4,8 BLK 9
G8: 4,8,1                                # reduction candidate for 4,8
G8: 4,8 => SOLVED
* 527134986618279345493658271174563829386927514259841763741385692965712438832496157
G8: 1 => CTR
* 527134986618279345493.5...117.5.3..8386.4.51925.918.63741365892965.82134832491657
* PAIR I8: 4,8 COL I
I4: 4,8,9                                # reduction candidate for 4,8
I4: 4,8 => CTR
* 527134986618279345493658..11795.34.8386742519254981763741365.929658.7.3483249..57
I4: 9 => SOLVED
* 527134986618279345493658271174563829386927514259841763741385692965712438832496157
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190213-absurd-base-pr-000.dot
* REASONING
* PRF # D6: 6,8 => SOL
* DIS # D6: 7,9 => CTR => D6: 6,8
* DIS # F6: 6,8 => CTR => F6: 1,7
* PRF # I4: 4,9 => SOL
* DIS # I4: 8 => CTR => I4: 4,9
* DIS # D6: 7,9 => CTR => D6: 6,8
* PRF # D6: 6,8 => SOL
* PRF # I4: 4,9 => SOL
* DIS # I4: 8 => CTR => I4: 4,9
* DIS # F8: 7,8 => CTR => F8: 1,2
* PRF # F8: 1,2 => SOL
* PRF # D6: 7,8 => SOL
* PRF # G8: 4,8 => SOL
* DIS # G8: 1 => CTR => G8: 4,8
* DIS # I4: 4,8 => CTR => I4: 9
* PRF # I4: 9 => SOL
* CNT  16 HDP CHAINS /  26 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,C6,D3,D5,D8,E7,F3,F9,G3,G7,G9,H3,H4,I5,I8)
* 527134986618279345493.5...117.5.3...386...5..25......37413.5.92965....3.83249..57
* PAIR D3: 6,8 COL D
D6: 6,8,7,9                              # reduction candidate for 6,8
D6: 6,8 => SOLVED
* 527134986618279345493658271174563829386927514259841763741385692965712438832496157
* DURATION: 0:00:01.496833  START: 03:43:07.527159  END: 03:43:09.023992 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190213-absurd-base-pr-001.dot
* REASONING
* PRF # D6: 6,8 => SOL
* STA D6: 6,8
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190213, absurd

Solution

position: 527134986618279345493658271174563829386927514259841763741385692965712438832496157 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 # D6: 6,8 => SOL
* DIS # D6: 7,9 => CTR => D6: 6,8
* DIS # F6: 6,8 => CTR => F6: 1,7
* INC # F6: 1,7 => UNS
* INC # H5: 2,7 => UNS
* INC # H5: 1 => UNS
* PRF # I4: 4,9 => SOL
* DIS # I4: 8 => CTR => I4: 4,9
* DIS # D6: 7,9 => CTR => D6: 6,8
* PRF # D6: 6,8 => SOL
* INC # E4: 2,6 => UNS
* INC # E4: 4,8 => UNS
* PRF # I4: 4,9 => SOL
* DIS # I4: 8 => CTR => I4: 4,9
* INC # E4: 6,8 => UNS
* INC # E6: 6,8 => UNS
* DIS # F8: 7,8 => CTR => F8: 1,2
* PRF # F8: 1,2 => SOL
* PRF # D6: 7,8 => SOL
* INC # D6: 6,9 => UNS
* INC # F6: 1,6 => UNS
* INC # F6: 7,8 => UNS
* PRF # G8: 4,8 => SOL
* DIS # G8: 1 => CTR => G8: 4,8
* DIS # I4: 4,8 => CTR => I4: 9
* PRF # I4: 9 => SOL
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # D6: 6,8 => SOL
* STA D6: 6,8
* CNT   1 HDP CHAINS /   1 HYP OPENED