Analysis of zz-www.sudokuoftheday.co.uk-20060707-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

position: .6.73.1..9..1.4..57...5.9.....3......4......61.9..........8..51.3....26.45.6..8.9 initial

Autosolve

position: .6.7391..98312467571.8569.3...3.....34......61.9.6.3...9..83.5183....26.45.6..839 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 4 => CTR => C1: 2,5
* DIS # C1: 2,4 => CTR => C1: 5
* DIS # C4: 8 => CTR => C4: 5,6
* PRF # I4: 4,8 => SOL
* DIS # C4: 5,8 => CTR => C4: 6
* PRF # D8: 4,5 => SOL
* DIS # D8: 9 => CTR => D8: 4,5
* DIS # E4: 1,9 => CTR => E4: 4,7
* PRF # G4: 5,7 => SOL
* DIS # G4: 4 => CTR => G4: 5,7
* DIS # E5: 1,9 => CTR => E5: 7
* DIS # C7: 2,6 => CTR => C7: 7
* PRF # C7: 7 => SOL
* DIS # C9: 1,7 => CTR => C9: 2
* PRF # C9: 2 => SOL
* DIS # E8: 1,7 => CTR => E8: 4,9
* DIS # F8: 1,7 => CTR => F8: 5
* PRF # F8: 5 => SOL
* DIS # E8: 1,7 => CTR => E8: 4,9
* DIS # F8: 1,7 => CTR => F8: 5
* PRF # F8: 5 => SOL
* PRF # F9: 1,7 => SOL
* DIS # F9: 2 => CTR => F9: 1,7
* DIS # C9: 1,7 => CTR => C9: 2
* PRF # C9: 2 => SOL
* DIS # E4: 1,7 => CTR => E4: 4,9
* DIS # G4: 5 => CTR => G4: 4,7
* DIS # E8: 4,7 => CTR => E8: 1,9
* PRF # E8: 1,9 => SOL
* DIS # I4: 4,7 => CTR => I4: 2,8
* CNT  30 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:

* DIS # C1: 4 => CTR => C1: 2,5
* DIS C1: 2,5 # C4: 8 => CTR => C4: 5,6
* DIS C1: 2,5 + C4: 5,6 # I4: 2,7 => CTR => I4: 4,8
* PRF C1: 2,5 + C4: 5,6 + I4: 4,8 => SOL
* STA C1: 2,5 + C4: 5,6 + I4: 4,8
* CNT   4 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.6.73.1..9..1.4..57...5.9.....3......4......61.9..........8..51.3....26.45.6..8.9 initial
.6.7391..98312467571.8569.3...3.....34......61.9.6.3...9..83.5183....26.45.6..839 autosolve
265739184983124675714856923526341798348972516179568342697283451831495267452617839 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A1: 2,5
C3: 2,4
H3: 2,4
A4: 5,6
B4: 2,7
C5: 5,8
B6: 2,7
D5: 2,9
D6: 4,5
H4: 1,9
G5: 5,7
H5: 1,9
A7: 2,6
C8: 1,7
D7: 2,4
E9: 1,7
G7: 4,7
I8: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H4,H5: 1.. / H4 = 1  =>  0 pairs (X) / H5 = 1  => 17 pairs (_)
C8,C9: 1.. / C8 = 1  => 19 pairs (_) / C9 = 1  =>  0 pairs (X)
B4,B6: 2.. / B4 = 2  => 17 pairs (_) / B6 = 2  => 21 pairs (_)
D5,F5: 2.. / D5 = 2  =>  0 pairs (X) / F5 = 2  =>  0 pairs (_)
D7,F9: 2.. / D7 = 2  =>  0 pairs (*) / F9 = 2  =>  0 pairs (X)
C3,H3: 2.. / C3 = 2  =>  0 pairs (X) / H3 = 2  => 20 pairs (_)
B4,I4: 2.. / B4 = 2  => 17 pairs (_) / I4 = 2  => 21 pairs (_)
C9,F9: 2.. / C9 = 2  =>  0 pairs (*) / F9 = 2  =>  0 pairs (X)
A1,A7: 2.. / A1 = 2  => 19 pairs (_) / A7 = 2  =>  0 pairs (X)
D5,D7: 2.. / D5 = 2  =>  0 pairs (X) / D7 = 2  =>  0 pairs (_)
F5,F9: 2.. / F5 = 2  =>  0 pairs (*) / F9 = 2  =>  0 pairs (X)
C1,C3: 4.. / C1 = 4  =>  0 pairs (X) / C3 = 4  => 20 pairs (_)
E4,D6: 4.. / E4 = 4  =>  0 pairs (*) / D6 = 4  =>  0 pairs (X)
G7,I8: 4.. / G7 = 4  =>  0 pairs (*) / I8 = 4  =>  0 pairs (X)
C3,H3: 4.. / C3 = 4  => 20 pairs (_) / H3 = 4  =>  0 pairs (X)
D7,G7: 4.. / D7 = 4  =>  0 pairs (X) / G7 = 4  =>  0 pairs (_)
E4,E8: 4.. / E4 = 4  =>  0 pairs (*) / E8 = 4  =>  0 pairs (X)
G4,G7: 4.. / G4 = 4  =>  0 pairs (X) / G7 = 4  =>  0 pairs (_)
A1,C1: 5.. / A1 = 5  =>  0 pairs (X) / C1 = 5  => 19 pairs (_)
D6,F6: 5.. / D6 = 5  =>  0 pairs (*) / F6 = 5  =>  0 pairs (X)
G4,G5: 5.. / G4 = 5  =>  0 pairs (X) / G5 = 5  => 20 pairs (_)
D8,F8: 5.. / D8 = 5  =>  0 pairs (X) / F8 = 5  =>  0 pairs (_)
C5,G5: 5.. / C5 = 5  =>  0 pairs (X) / G5 = 5  => 20 pairs (_)
A1,A4: 5.. / A1 = 5  =>  0 pairs (X) / A4 = 5  => 19 pairs (_)
D6,D8: 5.. / D6 = 5  =>  0 pairs (*) / D8 = 5  =>  0 pairs (X)
F6,F8: 5.. / F6 = 5  =>  0 pairs (X) / F8 = 5  =>  0 pairs (_)
A4,C4: 6.. / A4 = 6  =>  0 pairs (X) / C4 = 6  => 19 pairs (_)
A7,C7: 6.. / A7 = 6  => 19 pairs (_) / C7 = 6  =>  0 pairs (X)
A4,A7: 6.. / A4 = 6  =>  0 pairs (X) / A7 = 6  => 19 pairs (_)
C4,C7: 6.. / C4 = 6  => 19 pairs (_) / C7 = 6  =>  0 pairs (X)
B4,B6: 7.. / B4 = 7  => 21 pairs (_) / B6 = 7  => 17 pairs (_)
G7,I8: 7.. / G7 = 7  =>  0 pairs (X) / I8 = 7  =>  0 pairs (_)
C7,G7: 7.. / C7 = 7  =>  0 pairs (*) / G7 = 7  =>  0 pairs (X)
H1,I1: 8.. / H1 = 8  => 20 pairs (_) / I1 = 8  => 20 pairs (_)
C4,C5: 8.. / C4 = 8  =>  0 pairs (X) / C5 = 8  => 20 pairs (_)
C5,F5: 8.. / C5 = 8  => 20 pairs (_) / F5 = 8  =>  0 pairs (X)
H1,H6: 8.. / H1 = 8  => 20 pairs (_) / H6 = 8  => 20 pairs (_)
H4,H5: 9.. / H4 = 9  => 17 pairs (_) / H5 = 9  =>  0 pairs (X)
D8,E8: 9.. / D8 = 9  =>  0 pairs (X) / E8 = 9  =>  0 pairs (_)
E4,H4: 9.. / E4 = 9  =>  0 pairs (X) / H4 = 9  => 17 pairs (_)
D5,D8: 9.. / D5 = 9  =>  0 pairs (*) / D8 = 9  =>  0 pairs (X)
* DURATION: 0:00:51.823018  START: 00:27:19.718720  END: 00:28:11.541738 2019-05-01
* CP COUNT: (41)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A7,B4,B6,C3,C5,C8,D5,D6,D7,E9,G5,G7,H3,H4,H5,I8)
* .6.7391..98312467571.8569.3...3.....34......61.9.6.3...9..83.5183....26.45.6..839
* PAIR A1: 2,5 BLK 1
C1: 2,5,4                                # reduction candidate for 2,5
C1: 4 => CTR
* 5647391..9831246757128569436..3.....34......61.9.6.3..29648375183....26445.6.2839
C1: 2,5                                  # 20 pairs
* PAIR C3: 2,4 BLK 1
C1: 2,4,5                                # reduction candidate for 2,4
C1: 2,4 => CTR
* 56.7391..98312467571.8569.36..34.5..34......61.9.6.3..29648375183....26445.6.2839
C1: 5                                    # 19 pairs
* PAIR H3: 2,4 BLK 3
H1: 2,4,8                                # reduction candidate for 2,4
H1: 2,4                                  # 20 pairs
I1: 2,4,8                                # reduction candidate for 2,4
I1: 2,4                                  # 20 pairs
* PAIR H3: 2,4 COL H
H6: 2,4,8                                # reduction candidate for 2,4
H6: 8                                    # 20 pairs
H6: 2,4                                  # 20 pairs
* PAIR A4: 5,6 BLK 4
C4: 5,6,8                                # reduction candidate for 5,6
C4: 8 => CTR
* .6.7391..98312467571.8569.36.83..5..345..87.61.9.6.3..29..83.5183....26.45.6..839
C4: 5,6                                  # 20 pairs
* PAIR B4: 2,7 ROW 4
I4: 2,7,4,8                              # reduction candidate for 2,7
I4: 4,8 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
I4: 2,7                                  # 22 pairs
* PAIR C5: 5,8 BLK 4
C4: 5,8,6                                # reduction candidate for 5,8
C4: 5,8 => CTR
* 56.7391..98312467571.8569.36..34.5..34......61.9.6.3..29648375183....26445.6.2839
C4: 6                                    # 19 pairs
* PAIR B6: 2,7 ROW 6
I6: 2,7,4,8                              # reduction candidate for 2,7
I6: 2,7                                  # 22 pairs
I6: 4,8                                  # 19 pairs
* PAIR D6: 4,5 COL D
D8: 4,5,9                                # reduction candidate for 4,5
D8: 4,5 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
D8: 9 => CTR
* .6.7391..98312467571.8569.3...34.5..34......61.956.3...9.48375183.9.526445.6.2839
* PAIR H4: 1,9 ROW 4
E4: 1,9,4,7                              # reduction candidate for 1,9
E4: 1,9 => CTR
* .6.7391..98312467571.8569.3...3.....34......61.94653...9.28345183.5..26.45.6..839
E4: 4,7                                  # 20 pairs
* PAIR G5: 5,7 BLK 6
G4: 5,7,4                                # reduction candidate for 5,7
G4: 5,7 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
G4: 4 => CTR
* .6.7391..98312467571.8569.3...3..4..34....5.61.94653...9.28375183.5..26.45.6..839
* PAIR H5: 1,9 ROW 5
E5: 1,9,7                                # reduction candidate for 1,9
E5: 1,9 => CTR
* .6.7391..98312467571.8569.3...3415..34.2....61.9.6.3...9.48375183.9.526445.6.2839
E5: 7                                    # 24 pairs
* PAIR A7: 2,6 BLK 7
C7: 2,6,7                                # reduction candidate for 2,6
C7: 2,6 => CTR
* .6.7391..98312467571.8569.3...34.5..34......61.9.6.3...9..8375183....26445.6..839
C7: 7 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
* PAIR C8: 1,7 BLK 7
C9: 1,7,2                                # reduction candidate for 1,7
C9: 1,7 => CTR
* .6.7391..98312467571.8569.3...34.5..34.2....61.9.6.3...9.48375183.9.526445.6.2839
C9: 2 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
* PAIR C8: 1,7 ROW 8
E8: 1,7,4,9                              # reduction candidate for 1,7
E8: 1,7 => CTR
* .6.7391..98312467571.8569.3...34..9.34..9..161.956.3...9..8345183....26.45.6..839
E8: 4,9                                  # 19 pairs
F8: 1,7,5                                # reduction candidate for 1,7
F8: 1,7 => CTR
* .6.7391..98312467571.8569.3...34....34......61.9.653...9..83.5183.59.26445.6..839
F8: 5 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
* PAIR E9: 1,7 BLK 8
E8: 1,7,4,9                              # reduction candidate for 1,7
E8: 1,7 => CTR
* .6.7391..98312467571.8569.3...34..9.34..9..161.956.3...9..8345183....26.45.6..839
E8: 4,9                                  # 19 pairs
F8: 1,7,5                                # reduction candidate for 1,7
F8: 1,7 => CTR
* .6.7391..98312467571.8569.3...34....34......61.9.653...9..83.5183.59.26445.6..839
F8: 5 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
F9: 1,7,2                                # reduction candidate for 1,7
F9: 1,7 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
F9: 2 => CTR
* .6.7391..98312467571.8569.3...34.5..34.2....61.9.6.3...9.48375183.9.526445.6.2839
* PAIR E9: 1,7 ROW 9
C9: 1,7,2                                # reduction candidate for 1,7
C9: 1,7 => CTR
* .6.7391..98312467571.8569.3...34.5..34.2....61.9.6.3...9.48375183.9.526445.6.2839
C9: 2 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
* PAIR E9: 1,7 COL E
E4: 1,7,4,9                              # reduction candidate for 1,7
E4: 1,7 => CTR
* .6.7391..98312467571.8569.3...3...9.34.....161.94653...9.28345183.5..26.45.6..839
E4: 4,9                                  # 19 pairs
E5: 1,7,9                                # reduction candidate for 1,7
E5: 1,7                                  # 21 pairs
* PAIR G7: 4,7 COL G
G4: 4,7,5                                # reduction candidate for 4,7
G4: 5 => CTR
* .6.7391..98312467571.8569.3...3..5..345..87.61.9.6.3...97.83451831...26.45.6..839
G4: 4,7                                  # 20 pairs
* PAIR I8: 4,7 ROW 8
E8: 4,7,1,9                              # reduction candidate for 4,7
E8: 4,7 => CTR
* .6.7391..98312467571.8569.3...34.5..34.2....61.956.3...9.483751831975264457612839
E8: 1,9 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
* PAIR I8: 4,7 COL I
I4: 4,7,2,8                              # reduction candidate for 4,7
I4: 4,7 => CTR
* .6.7391..98312467571.8569.3.2.34....34......6179.653...9..83.5183.59.26445.6..839
I4: 2,8                                  # 19 pairs
I6: 4,7,2,8                              # reduction candidate for 4,7
I6: 4,7                                  # 22 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060707-absurd-base-pr-000.dot
* REASONING
* DIS # C1: 4 => CTR => C1: 2,5
* DIS # C1: 2,4 => CTR => C1: 5
* DIS # C4: 8 => CTR => C4: 5,6
* PRF # I4: 4,8 => SOL
* DIS # C4: 5,8 => CTR => C4: 6
* PRF # D8: 4,5 => SOL
* DIS # D8: 9 => CTR => D8: 4,5
* DIS # E4: 1,9 => CTR => E4: 4,7
* PRF # G4: 5,7 => SOL
* DIS # G4: 4 => CTR => G4: 5,7
* DIS # E5: 1,9 => CTR => E5: 7
* DIS # C7: 2,6 => CTR => C7: 7
* PRF # C7: 7 => SOL
* DIS # C9: 1,7 => CTR => C9: 2
* PRF # C9: 2 => SOL
* DIS # E8: 1,7 => CTR => E8: 4,9
* DIS # F8: 1,7 => CTR => F8: 5
* PRF # F8: 5 => SOL
* DIS # E8: 1,7 => CTR => E8: 4,9
* DIS # F8: 1,7 => CTR => F8: 5
* PRF # F8: 5 => SOL
* PRF # F9: 1,7 => SOL
* DIS # F9: 2 => CTR => F9: 1,7
* DIS # C9: 1,7 => CTR => C9: 2
* PRF # C9: 2 => SOL
* DIS # E4: 1,7 => CTR => E4: 4,9
* DIS # G4: 5 => CTR => G4: 4,7
* DIS # E8: 4,7 => CTR => E8: 1,9
* PRF # E8: 1,9 => SOL
* DIS # I4: 4,7 => CTR => I4: 2,8
* CNT  30 HDP CHAINS /  50 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,A7,B4,B6,C3,C5,C8,D5,D6,D7,E9,G5,G7,H3,H4,H5,I8)
* .6.7391..98312467571.8569.3...3.....34......61.9.6.3...9..83.5183....26.45.6..839
* PAIR A1: 2,5 BLK 1
C1: 2,5,4                                # reduction candidate for 2,5
C1: 4 => CTR
* 5647391..9831246757128569436..3.....34......61.9.6.3..29648375183....26445.6.2839
* PAIR A4: 5,6 BLK 4
C4: 5,6,8                                # reduction candidate for 5,6
C4: 8 => CTR
* .6.7391..9831246757148569236.83..5..345..87.61.9.6.3..29..83.5183....26.45.6..839
* PAIR B4: 2,7 ROW 4
I4: 2,7,4,8                              # reduction candidate for 2,7
I4: 2,7 => CTR
* .6.739148983124675714856923...348...348...5.61.9.6538..9..83.5183.59.26445.6..839
I4: 4,8 => SOLVED
* 265739184983124675714856923526341798348972516179568342697283451831495267452617839
* DURATION: 0:00:05.628328  START: 00:28:48.679686  END: 00:28:54.308014 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060707-absurd-base-pr-001.dot
* REASONING
* DIS # C1: 4 => CTR => C1: 2,5
* DIS C1: 2,5 # C4: 8 => CTR => C4: 5,6
* DIS C1: 2,5 + C4: 5,6 # I4: 2,7 => CTR => I4: 4,8
* PRF C1: 2,5 + C4: 5,6 + I4: 4,8 => SOL
* STA C1: 2,5 + C4: 5,6 + I4: 4,8
* CNT   4 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060707, absurd

Solution

position: 265739184983124675714856923526341798348972516179568342697283451831495267452617839 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 # C1: 2,5 => UNS
* DIS # C1: 4 => CTR => C1: 2,5
* DIS # C1: 2,4 => CTR => C1: 5
* INC # C1: 5 => UNS
* INC # H1: 2,4 => UNS
* INC # I1: 2,4 => UNS
* INC # H6: 2,4 => UNS
* INC # H6: 8 => UNS
* INC # C4: 5,6 => UNS
* DIS # C4: 8 => CTR => C4: 5,6
* INC # I4: 2,7 => UNS
* PRF # I4: 4,8 => SOL
* DIS # C4: 5,8 => CTR => C4: 6
* INC # C4: 6 => UNS
* INC # I6: 2,7 => UNS
* INC # I6: 4,8 => UNS
* PRF # D8: 4,5 => SOL
* DIS # D8: 9 => CTR => D8: 4,5
* DIS # E4: 1,9 => CTR => E4: 4,7
* INC # E4: 4,7 => UNS
* PRF # G4: 5,7 => SOL
* DIS # G4: 4 => CTR => G4: 5,7
* DIS # E5: 1,9 => CTR => E5: 7
* INC # E5: 7 => UNS
* DIS # C7: 2,6 => CTR => C7: 7
* PRF # C7: 7 => SOL
* DIS # C9: 1,7 => CTR => C9: 2
* PRF # C9: 2 => SOL
* DIS # E8: 1,7 => CTR => E8: 4,9
* INC # E8: 4,9 => UNS
* DIS # F8: 1,7 => CTR => F8: 5
* PRF # F8: 5 => SOL
* DIS # E8: 1,7 => CTR => E8: 4,9
* INC # E8: 4,9 => UNS
* DIS # F8: 1,7 => CTR => F8: 5
* PRF # F8: 5 => SOL
* PRF # F9: 1,7 => SOL
* DIS # F9: 2 => CTR => F9: 1,7
* DIS # C9: 1,7 => CTR => C9: 2
* PRF # C9: 2 => SOL
* DIS # E4: 1,7 => CTR => E4: 4,9
* INC # E4: 4,9 => UNS
* INC # E5: 1,7 => UNS
* INC # G4: 4,7 => UNS
* DIS # G4: 5 => CTR => G4: 4,7
* DIS # E8: 4,7 => CTR => E8: 1,9
* PRF # E8: 1,9 => SOL
* DIS # I4: 4,7 => CTR => I4: 2,8
* INC # I4: 2,8 => UNS
* INC # I6: 4,7 => UNS
* CNT  50 HDP CHAINS /  50 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 2,5 => UNS
* DIS # C1: 4 => CTR => C1: 2,5
* INC C1: 2,5 # C4: 5,6 => UNS
* DIS C1: 2,5 # C4: 8 => CTR => C4: 5,6
* DIS C1: 2,5 + C4: 5,6 # I4: 2,7 => CTR => I4: 4,8
* PRF C1: 2,5 + C4: 5,6 + I4: 4,8 => SOL
* STA C1: 2,5 + C4: 5,6 + I4: 4,8
* CNT   6 HDP CHAINS /   5 HYP OPENED