Analysis of zz-www.sudokuoftheday.co.uk-20190115-absurd-base.sdk

Contents

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

level: medium

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

position: 7.634..9....87.....8..964..6.....98..3...4..1.95....2.5....8.....7.1.2.8......15. initial

Autosolve

position: 7.634.89....87.....8..964..67....98..3.9.4..1.95.8..2.5....8.....7.1.2.8......15. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # I2: 2,5 => SOL
* DIS # I3: 2,5 => CTR => I3: 3,7
* DIS # F1: 2,5 => CTR => F1: 1
* DIS # C2: 1,4 => CTR => C2: 2,3,9
* DIS # F4: 1,2 => CTR => F4: 3
* DIS # D3: 1,2 => CTR => D3: 5
* DIS # G5: 7 => CTR => G5: 5,6
* PRF # G5: 5 => SOL
* DIS # H7: 6,7 => CTR => H7: 3,4
* PRF # I6: 3,6 => SOL
* PRF # G2: 3,6 => SOL
* DIS # G7: 3,6 => CTR => G7: 7
* DIS # H8: 4,6 => CTR => H8: 3
* CNT  13 HDP CHAINS /  37 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 # I2: 2,5 => SOL
* STA I2: 2,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

7.634..9....87.....8..964..6.....98..3...4..1.95....2.5....8.....7.1.2.8......15. initial
7.634.89....87.....8..964..67....98..3.9.4..1.95.8..2.5....8.....7.1.2.8......15. autosolve
756341892149872365382596417671253984238964571495187623513628749967415238824739156 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
I1: 2,5
C4: 1,4
A5: 2,8
C5: 2,8
A6: 1,4
D4: 1,2
E5: 5,6
H5: 6,7
G6: 3,6
B8: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H2,H3: 1.. / H2 = 1  => 12 pairs (_) / H3 = 1  => 26 pairs (_)
C4,A6: 1.. / C4 = 1  =>  0 pairs (*) / A6 = 1  =>  0 pairs (X)
B7,C7: 1.. / B7 = 1  => 15 pairs (_) / C7 = 1  => 21 pairs (_)
B1,F1: 1.. / B1 = 1  =>  0 pairs (X) / F1 = 1  => 15 pairs (_)
A5,C5: 2.. / A5 = 2  =>  9 pairs (_) / C5 = 2  =>  9 pairs (_)
C4,A6: 4.. / C4 = 4  => 12 pairs (_) / A6 = 4  =>  0 pairs (*)
I4,I6: 4.. / I4 = 4  =>  0 pairs (*) / I6 = 4  =>  0 pairs (X)
H7,H8: 4.. / H7 = 4  => 11 pairs (_) / H8 = 4  =>  0 pairs (X)
C4,I4: 4.. / C4 = 4  => 12 pairs (_) / I4 = 4  =>  0 pairs (*)
A6,I6: 4.. / A6 = 4  =>  0 pairs (*) / I6 = 4  =>  0 pairs (X)
B1,B2: 5.. / B1 = 5  => 13 pairs (_) / B2 = 5  =>  0 pairs (X)
E4,E5: 5.. / E4 = 5  =>  0 pairs (*) / E5 = 5  =>  0 pairs (X)
I4,G5: 5.. / I4 = 5  => 21 pairs (_) / G5 = 5  =>  0 pairs (*)
D8,F8: 5.. / D8 = 5  =>  0 pairs (X) / F8 = 5  => 20 pairs (_)
D3,I3: 5.. / D3 = 5  => 20 pairs (_) / I3 = 5  =>  0 pairs (X)
E4,I4: 5.. / E4 = 5  =>  0 pairs (*) / I4 = 5  =>  0 pairs (X)
E5,G5: 5.. / E5 = 5  => 21 pairs (_) / G5 = 5  =>  0 pairs (*)
D3,D8: 5.. / D3 = 5  => 20 pairs (_) / D8 = 5  =>  0 pairs (X)
G2,G5: 5.. / G2 = 5  => 21 pairs (_) / G5 = 5  =>  0 pairs (*)
E5,D6: 6.. / E5 = 6  =>  0 pairs (*) / D6 = 6  =>  0 pairs (X)
H3,I3: 7.. / H3 = 7  =>  0 pairs (X) / I3 = 7  => 26 pairs (_)
D6,F6: 7.. / D6 = 7  =>  0 pairs (X) / F6 = 7  => 12 pairs (_)
G5,H5: 7.. / G5 = 7  =>  0 pairs (X) / H5 = 7  => 26 pairs (_)
F6,F9: 7.. / F6 = 7  => 12 pairs (_) / F9 = 7  =>  0 pairs (X)
G5,G7: 7.. / G5 = 7  =>  0 pairs (X) / G7 = 7  => 26 pairs (_)
A5,C5: 8.. / A5 = 8  =>  9 pairs (_) / C5 = 8  =>  9 pairs (_)
A9,C9: 8.. / A9 = 8  =>  9 pairs (_) / C9 = 8  =>  9 pairs (_)
A5,A9: 8.. / A5 = 8  =>  9 pairs (_) / A9 = 8  =>  9 pairs (_)
C5,C9: 8.. / C5 = 8  =>  9 pairs (_) / C9 = 8  =>  9 pairs (_)
A2,C2: 9.. / A2 = 9  =>  0 pairs (X) / C2 = 9  => 10 pairs (_)
F8,F9: 9.. / F8 = 9  =>  0 pairs (X) / F9 = 9  => 13 pairs (_)
I7,I9: 9.. / I7 = 9  => 10 pairs (_) / I9 = 9  =>  0 pairs (X)
C7,I7: 9.. / C7 = 9  =>  0 pairs (X) / I7 = 9  => 10 pairs (_)
A8,F8: 9.. / A8 = 9  => 13 pairs (_) / F8 = 9  =>  0 pairs (X)
* DURATION: 0:00:36.362018  START: 02:57:48.019197  END: 02:58:24.381215 2019-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,C4,C5,D4,E5,G6,H5,I1)
* 7.634.89....87.....8..964..67....98..3.9.4..1.95.8..2.5....8.....7.1.2.8......15.
* PAIR I1: 2,5 BLK 3
I2: 2,5,3,6                              # reduction candidate for 2,5
I2: 2,5 => SOLVED
* 756341892149872365382596417671253984238964571495187623513628749967415238824739156
I2: 3,6                                  # 11 pairs
I3: 2,5,3,7                              # reduction candidate for 2,5
I3: 2,5 => CTR
* 7.634.89....87.51..8..9647.67....98..3.9.4761.956873245....86...67.1.2.8....6.15.
I3: 3,7                                  # 23 pairs
* PAIR I1: 2,5 ROW 1
B1: 2,5,1                                # reduction candidate for 2,5
B1: 2,5                                  # 15 pairs
F1: 2,5,1                                # reduction candidate for 2,5
F1: 2,5 => CTR
* 71634.89545987.362.8.596417674152983.3.9645711957836245.1..87.9..7.1.2.8.....7156
F1: 1                                    # 15 pairs
* PAIR C4: 1,4 COL C
C2: 1,4,2,3,9                            # reduction candidate for 1,4
C2: 1,4 => CTR
* 7.634.89.9..87.....8..964.567..5.98..3.964571.95.8..2.5....87....75192.8......15.
C2: 2,3,9                                # 10 pairs
C7: 1,4,2,3,9                            # reduction candidate for 1,4
C7: 1,4                                  # 14 pairs
* PAIR A5: 2,8 COL A
A9: 2,8,3,4,9                            # reduction candidate for 2,8
A9: 2,8                                  # 12 pairs
A9: 3,4,9                                # 10 pairs
* PAIR C5: 2,8 COL C
C9: 2,8,3,4,9                            # reduction candidate for 2,8
C9: 2,8                                  # 12 pairs
C9: 3,4,9                                #  9 pairs
* PAIR A6: 1,4 COL A
A2: 1,4,2,3,9                            # reduction candidate for 1,4
A2: 1,4                                  # 14 pairs
A2: 2,3,9                                # 10 pairs
* PAIR D4: 1,2 BLK 5
F4: 1,2,3                                # reduction candidate for 1,2
F4: 1,2 => CTR
* 7.634.89....87.....8..964.5674.5.983.3.9645711957836245....87....75192.8.....715.
F4: 3                                    # 14 pairs
* PAIR D4: 1,2 COL D
D3: 1,2,5                                # reduction candidate for 1,2
D3: 1,2 => CTR
* 7.634.89....87.....8..964.567..5.98..3.964571.95.8..2.5....87....751.2.8......15.
D3: 5                                    # 20 pairs
* PAIR E5: 5,6 ROW 5
G5: 5,6,7                                # reduction candidate for 5,6
G5: 7 => CTR
* 756341892...872516.8.596473674123985.3.95476119568732451.738649967415238.2..69157
G5: 5,6                                  # 26 pairs
* PAIR H5: 6,7 BLK 6
G5: 6,7,5                                # reduction candidate for 6,7
G5: 5 => SOLVED
* 756341892149872365382596417671253984238964571495187623513628749967415238824739156
G5: 6,7                                  # 21 pairs
* PAIR H5: 6,7 COL H
H7: 6,7,3,4                              # reduction candidate for 6,7
H7: 6,7 => CTR
* 7.634.89....87.....8..964.567..5.98..3.964571.95.8..2.5....876..6751.248...6.715.
H7: 3,4                                  # 11 pairs
* PAIR G6: 3,6 BLK 6
I6: 3,6,4                                # reduction candidate for 3,6
I6: 3,6 => SOLVED
* 756341892149872365382596417671253984238964571495187623513628749967415238824739156
I6: 4                                    # 12 pairs
* PAIR G6: 3,6 COL G
G2: 3,6,5                                # reduction candidate for 3,6
G2: 3,6 => SOLVED
* 756341892149872365382596417671253984238964571495187623513628749967415238824739156
G2: 5                                    # 21 pairs
G7: 3,6,7                                # reduction candidate for 3,6
G7: 3,6 => CTR
* 756341892...872516.81596473674123985.3.95476119568732451.738649967415238.2..69157
G7: 7                                    # 26 pairs
* PAIR B8: 4,6 BLK 7
B7: 4,6,1,2                              # reduction candidate for 4,6
B7: 4,6                                  # 24 pairs
B9: 4,6,2                                # reduction candidate for 4,6
B9: 4,6                                  # 16 pairs
* PAIR B8: 4,6 ROW 8
D8: 4,6,5                                # reduction candidate for 4,6
D8: 4,6                                  # 20 pairs
H8: 4,6,3                                # reduction candidate for 4,6
H8: 4,6 => CTR
* 7.634.89....87.....8..964.567..5.98..3.964571.9578..2.5....87....751.2.8.....715.
H8: 3                                    # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190115-absurd-base-pr-000.dot
* REASONING
* PRF # I2: 2,5 => SOL
* DIS # I3: 2,5 => CTR => I3: 3,7
* DIS # F1: 2,5 => CTR => F1: 1
* DIS # C2: 1,4 => CTR => C2: 2,3,9
* DIS # F4: 1,2 => CTR => F4: 3
* DIS # D3: 1,2 => CTR => D3: 5
* DIS # G5: 7 => CTR => G5: 5,6
* PRF # G5: 5 => SOL
* DIS # H7: 6,7 => CTR => H7: 3,4
* PRF # I6: 3,6 => SOL
* PRF # G2: 3,6 => SOL
* DIS # G7: 3,6 => CTR => G7: 7
* DIS # H8: 4,6 => CTR => H8: 3
* CNT  13 HDP CHAINS /  37 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B8,C4,C5,D4,E5,G6,H5,I1)
* 7.634.89....87.....8..964..67....98..3.9.4..1.95.8..2.5....8.....7.1.2.8......15.
* PAIR I1: 2,5 BLK 3
I2: 2,5,3,6                              # reduction candidate for 2,5
I2: 2,5 => SOLVED
* 756341892149872365382596417671253984238964571495187623513628749967415238824739156
* DURATION: 0:00:01.852463  START: 02:58:46.684108  END: 02:58:48.536571 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190115-absurd-base-pr-001.dot
* REASONING
* PRF # I2: 2,5 => SOL
* STA I2: 2,5
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190115, absurd

Solution

position: 756341892149872365382596417671253984238964571495187623513628749967415238824739156 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 # I2: 2,5 => SOL
* INC # I2: 3,6 => UNS
* DIS # I3: 2,5 => CTR => I3: 3,7
* INC # I3: 3,7 => UNS
* INC # B1: 2,5 => UNS
* DIS # F1: 2,5 => CTR => F1: 1
* INC # F1: 1 => UNS
* DIS # C2: 1,4 => CTR => C2: 2,3,9
* INC # C2: 2,3,9 => UNS
* INC # C7: 1,4 => UNS
* INC # A9: 2,8 => UNS
* INC # A9: 3,4,9 => UNS
* INC # C9: 2,8 => UNS
* INC # C9: 3,4,9 => UNS
* INC # A2: 1,4 => UNS
* INC # A2: 2,3,9 => UNS
* DIS # F4: 1,2 => CTR => F4: 3
* INC # F4: 3 => UNS
* DIS # D3: 1,2 => CTR => D3: 5
* INC # D3: 5 => UNS
* INC # G5: 5,6 => UNS
* DIS # G5: 7 => CTR => G5: 5,6
* INC # G5: 6,7 => UNS
* PRF # G5: 5 => SOL
* DIS # H7: 6,7 => CTR => H7: 3,4
* INC # H7: 3,4 => UNS
* PRF # I6: 3,6 => SOL
* INC # I6: 4 => UNS
* PRF # G2: 3,6 => SOL
* INC # G2: 5 => UNS
* DIS # G7: 3,6 => CTR => G7: 7
* INC # G7: 7 => UNS
* INC # B7: 4,6 => UNS
* INC # B9: 4,6 => UNS
* INC # D8: 4,6 => UNS
* DIS # H8: 4,6 => CTR => H8: 3
* INC # H8: 3 => UNS
* CNT  37 HDP CHAINS /  37 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # I2: 2,5 => SOL
* STA I2: 2,5
* CNT   1 HDP CHAINS /   1 HYP OPENED