Analysis of zz-www.sudokuoftheday.co.uk-20060817-absurd-base.sdk

Contents

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

level: medium

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

position: ....579.8...3...7.6.........8.7.....2...9...49.5...8.......14.97.45....6...6.3.1. initial

Autosolve

position: ....57968...3...7.6..9...4..8.7...9.2...9...49.5...8......714.97145.9..6...643.1. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F2: 2,8 => SOL
* PRF # C3: 2,8 => SOL
* DIS # G4: 3,5 => CTR => G4: 1,2,6
* DIS # G5: 3,5 => CTR => G5: 1,6,7
* DIS # G4: 2,3 => CTR => G4: 1,5,6
* DIS # I6: 2,3 => CTR => I6: 1,7
* DIS # H8: 8 => CTR => H8: 2,3
* DIS # A2: 1,4 => CTR => A2: 5,8
* DIS # H7: 5 => CTR => H7: 2,8
* DIS # H8: 3 => CTR => H8: 2,8
* DIS # H8: 8 => CTR => H8: 2,3
* DIS # G4: 2,3 => CTR => G4: 1,5,6
* CNT  12 HDP CHAINS /  35 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 # F2: 2,8 => SOL
* STA F2: 2,8
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

....579.8...3...7.6.........8.7.....2...9...49.5...8.......14.97.45....6...6.3.1. initial
....57968...3...7.6..9...4..8.7...9.2...9...49.5...8......714.97145.9..6...643.1. autosolve
123457968549368271678912543481735692237896154965124837356271489714589326892643715 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
F3: 2,8
D5: 1,8
H5: 3,5
H6: 2,3
A7: 3,5
A9: 5,8
D7: 2,8
E8: 2,8
G8: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D7,E8: 2.. / D7 = 2  => 23 pairs (_) / E8 = 2  =>  0 pairs (X)
G3,I3: 3.. / G3 = 3  =>  0 pairs (X) / I3 = 3  =>  9 pairs (_)
E4,E6: 3.. / E4 = 3  => 11 pairs (_) / E6 = 3  => 13 pairs (_)
G8,H8: 3.. / G8 = 3  =>  9 pairs (_) / H8 = 3  =>  0 pairs (X)
D1,F2: 4.. / D1 = 4  => 15 pairs (_) / F2 = 4  => 16 pairs (_)
A4,B6: 4.. / A4 = 4  => 11 pairs (_) / B6 = 4  =>  0 pairs (X)
A4,F4: 4.. / A4 = 4  => 11 pairs (_) / F4 = 4  =>  0 pairs (X)
D1,D6: 4.. / D1 = 4  => 15 pairs (_) / D6 = 4  => 16 pairs (_)
F4,F5: 5.. / F4 = 5  => 12 pairs (_) / F5 = 5  =>  0 pairs (X)
H5,H7: 5.. / H5 = 5  => 20 pairs (_) / H7 = 5  =>  0 pairs (X)
E2,F2: 6.. / E2 = 6  =>  9 pairs (_) / F2 = 6  => 19 pairs (_)
G4,G5: 6.. / G4 = 6  => 10 pairs (_) / G5 = 6  =>  0 pairs (X)
B7,C7: 6.. / B7 = 6  => 12 pairs (_) / C7 = 6  => 10 pairs (_)
B3,C3: 7.. / B3 = 7  =>  0 pairs (*) / C3 = 7  =>  0 pairs (X)
G5,I6: 7.. / G5 = 7  => 22 pairs (_) / I6 = 7  => 23 pairs (_)
G9,I9: 7.. / G9 = 7  => 23 pairs (_) / I9 = 7  => 22 pairs (_)
B6,I6: 7.. / B6 = 7  => 22 pairs (_) / I6 = 7  => 23 pairs (_)
C3,C5: 7.. / C3 = 7  => 12 pairs (_) / C5 = 7  =>  0 pairs (*)
G5,G9: 7.. / G5 = 7  => 22 pairs (_) / G9 = 7  => 23 pairs (_)
I6,I9: 7.. / I6 = 7  => 23 pairs (_) / I9 = 7  => 22 pairs (_)
D5,F5: 8.. / D5 = 8  => 23 pairs (_) / F5 = 8  =>  0 pairs (X)
A9,C9: 8.. / A9 = 8  =>  9 pairs (_) / C9 = 8  =>  0 pairs (X)
D7,E8: 8.. / D7 = 8  =>  0 pairs (X) / E8 = 8  => 23 pairs (_)
H7,H8: 8.. / H7 = 8  => 23 pairs (_) / H8 = 8  =>  0 pairs (X)
D7,H7: 8.. / D7 = 8  =>  0 pairs (X) / H7 = 8  => 23 pairs (_)
E8,H8: 8.. / E8 = 8  => 23 pairs (_) / H8 = 8  =>  0 pairs (X)
A2,A9: 8.. / A2 = 8  =>  0 pairs (X) / A9 = 8  =>  9 pairs (_)
D5,D7: 8.. / D5 = 8  => 23 pairs (_) / D7 = 8  =>  0 pairs (X)
B2,C2: 9.. / B2 = 9  =>  9 pairs (_) / C2 = 9  => 10 pairs (_)
B9,C9: 9.. / B9 = 9  => 10 pairs (_) / C9 = 9  =>  9 pairs (_)
B2,B9: 9.. / B2 = 9  =>  9 pairs (_) / B9 = 9  => 10 pairs (_)
C2,C9: 9.. / C2 = 9  => 10 pairs (_) / C9 = 9  =>  9 pairs (_)
* DURATION: 0:00:34.415233  START: 01:51:04.647248  END: 01:51:39.062481 2019-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,D5,D7,E8,F3,G8,H5,H6)
* ....57968...3...7.6..9...4..8.7...9.2...9...49.5...8......714.97145.9..6...643.1.
* PAIR F3: 2,8 BLK 2
E2: 2,8,1,6                              # reduction candidate for 2,8
E2: 2,8                                  # 20 pairs
F2: 2,8,4,6                              # reduction candidate for 2,8
F2: 2,8 => SOLVED
* 123457968549368271678912543481735692237896154965124837356271489714589326892643715
F2: 4,6                                  # 10 pairs
E3: 2,8,1                                # reduction candidate for 2,8
E3: 2,8                                  # 17 pairs
* PAIR F3: 2,8 ROW 3
C3: 2,8,1,7                              # reduction candidate for 2,8
C3: 2,8 => SOLVED
* 123457968549368271678912543481735692237896154965124837356271489714589326892643715
C3: 1,7                                  # 12 pairs
* PAIR H5: 3,5 BLK 6
G4: 3,5,1,2,6                            # reduction candidate for 3,5
G4: 3,5 => CTR
* ....57968...3...7.6..9...4..8.7...912.18956349.5...8.7....714.97145.9..6...64371.
G4: 1,2,6                                #  9 pairs
I4: 3,5,1,2                              # reduction candidate for 3,5
I4: 3,5                                  # 15 pairs
G5: 3,5,1,6,7                            # reduction candidate for 3,5
G5: 3,5 => CTR
* ....57968...3...726.79.8.43.837..6912.189...49.5...827..6271489714589236...643715
G5: 1,6,7                                #  9 pairs
* PAIR H6: 2,3 BLK 6
G4: 2,3,1,5,6                            # reduction candidate for 2,3
G4: 2,3 => CTR
* ....57968...3...7.6..9...4..8.7...912.18956349.5...8.7....714.97145.9..6...64371.
G4: 1,5,6                                #  9 pairs
I4: 2,3,1,5                              # reduction candidate for 2,3
I4: 2,3                                  # 26 pairs
I6: 2,3,1,7                              # reduction candidate for 2,3
I6: 2,3 => CTR
* ....57968...3...7.6.79...4.48.7..6912.189.754975...8....6271489714589..6...643517
I6: 1,7                                  # 10 pairs
* PAIR H6: 2,3 ROW 6
E6: 2,3,1,6                              # reduction candidate for 2,3
E6: 2,3                                  # 13 pairs
E6: 1,6                                  # 12 pairs
* PAIR H6: 2,3 COL H
H8: 2,3,8                                # reduction candidate for 2,3
H8: 8 => CTR
* ...457968.493.62756579821434817356922..1987549752648315..8714297145293868..643517
H8: 2,3                                  # 23 pairs
* PAIR A7: 3,5 BLK 7
B7: 3,5,2,6                              # reduction candidate for 3,5
B7: 3,5                                  # 21 pairs
B7: 2,6                                  # 10 pairs
* PAIR A9: 5,8 COL A
A2: 5,8,1,4                              # reduction candidate for 5,8
A2: 1,4 => CTR
* 34215796819836457265792814.48.7.5.9.2..896.549654.28375.6271489714589326829643715
A2: 5,8                                  # 12 pairs
* PAIR D7: 2,8 ROW 7
H7: 2,8,5                                # reduction candidate for 2,8
H7: 5 => CTR
* ....57968...3...7.6..9...43.8.7...9.2..1985349.5...8.....871459714529386...643.1.
H7: 2,8                                  # 20 pairs
* PAIR E8: 2,8 ROW 8
H8: 2,8,3                                # reduction candidate for 2,8
H8: 3 => CTR
* .2.457968.49368.726.8912.4348372569127.896.54965134827..6271489714589236892643715
H8: 2,8                                  #  9 pairs
* PAIR E8: 2,8 COL E
E2: 2,8,1,6                              # reduction candidate for 2,8
E2: 2,8                                  # 20 pairs
E3: 2,8,1                                # reduction candidate for 2,8
E3: 2,8                                  # 17 pairs
* PAIR G8: 2,3 BLK 9
H8: 2,3,8                                # reduction candidate for 2,3
H8: 8 => CTR
* ...457968.493.62756579821434817356922..1987549752648315..8714297145293868..643517
H8: 2,3                                  # 23 pairs
* PAIR G8: 2,3 COL G
G3: 2,3,1,5                              # reduction candidate for 2,3
G3: 2,3                                  # 12 pairs
G4: 2,3,1,5,6                            # reduction candidate for 2,3
G4: 2,3 => CTR
* ....57968...3...7.6..9...4..8.7...912.18956349.5...8.7....714.97145.9..6...64371.
G4: 1,5,6                                #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060817-absurd-base-pr-000.dot
* REASONING
* PRF # F2: 2,8 => SOL
* PRF # C3: 2,8 => SOL
* DIS # G4: 3,5 => CTR => G4: 1,2,6
* DIS # G5: 3,5 => CTR => G5: 1,6,7
* DIS # G4: 2,3 => CTR => G4: 1,5,6
* DIS # I6: 2,3 => CTR => I6: 1,7
* DIS # H8: 8 => CTR => H8: 2,3
* DIS # A2: 1,4 => CTR => A2: 5,8
* DIS # H7: 5 => CTR => H7: 2,8
* DIS # H8: 3 => CTR => H8: 2,8
* DIS # H8: 8 => CTR => H8: 2,3
* DIS # G4: 2,3 => CTR => G4: 1,5,6
* CNT  12 HDP CHAINS /  35 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,D5,D7,E8,F3,G8,H5,H6)
* ....57968...3...7.6..9...4..8.7...9.2...9...49.5...8......714.97145.9..6...643.1.
* PAIR F3: 2,8 BLK 2
E2: 2,8,1,6                              # reduction candidate for 2,8
E2: 2,8                                  # 20 pairs
F2: 2,8,4,6                              # reduction candidate for 2,8
F2: 2,8 => SOLVED
* 123457968549368271678912543481735692237896154965124837356271489714589326892643715
* DURATION: 0:00:02.342330  START: 01:51:59.042000  END: 01:52:01.384330 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060817-absurd-base-pr-001.dot
* REASONING
* PRF # F2: 2,8 => SOL
* STA F2: 2,8
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060817, absurd

Solution

position: 123457968549368271678912543481735692237896154965124837356271489714589326892643715 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 # E2: 2,8 => UNS
* PRF # F2: 2,8 => SOL
* INC # F2: 4,6 => UNS
* INC # E3: 2,8 => UNS
* PRF # C3: 2,8 => SOL
* INC # C3: 1,7 => UNS
* DIS # G4: 3,5 => CTR => G4: 1,2,6
* INC # G4: 1,2,6 => UNS
* INC # I4: 3,5 => UNS
* DIS # G5: 3,5 => CTR => G5: 1,6,7
* INC # G5: 1,6,7 => UNS
* DIS # G4: 2,3 => CTR => G4: 1,5,6
* INC # G4: 1,5,6 => UNS
* INC # I4: 2,3 => UNS
* DIS # I6: 2,3 => CTR => I6: 1,7
* INC # I6: 1,7 => UNS
* INC # E6: 2,3 => UNS
* INC # E6: 1,6 => UNS
* INC # H8: 2,3 => UNS
* DIS # H8: 8 => CTR => H8: 2,3
* INC # B7: 3,5 => UNS
* INC # B7: 2,6 => UNS
* INC # A2: 5,8 => UNS
* DIS # A2: 1,4 => CTR => A2: 5,8
* INC # H7: 2,8 => UNS
* DIS # H7: 5 => CTR => H7: 2,8
* INC # H8: 2,8 => UNS
* DIS # H8: 3 => CTR => H8: 2,8
* INC # E2: 2,8 => UNS
* INC # E3: 2,8 => UNS
* INC # H8: 2,3 => UNS
* DIS # H8: 8 => CTR => H8: 2,3
* INC # G3: 2,3 => UNS
* DIS # G4: 2,3 => CTR => G4: 1,5,6
* INC # G4: 1,5,6 => UNS
* CNT  35 HDP CHAINS /  35 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E2: 2,8 => UNS
* PRF # F2: 2,8 => SOL
* STA F2: 2,8
* CNT   2 HDP CHAINS /   2 HYP OPENED