Analysis of zz-www.sudokuoftheday.co.uk-20190310-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: ..31.....8...9.4.1.4....69.39.5.1.6........2...5.7.....5.9....8.2.....3...9...54. initial

Autosolve

position: 9631...8.872.9.451541.8.69339.52186..1.....25285.7..1..5.9...78.28....3..39...54. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E8: 4,5 => CTR => E8: 1,6
* DIS # F8: 7 => CTR => F8: 4,5
* DIS # D6: 4 => CTR => D6: 3,6
* DIS # F6: 3,6 => CTR => F6: 4,9
* PRF # D9: 8 => SOL
* PRF # F9: 2,7 => SOL
* DIS # C5: 6 => CTR => C5: 4,7
* DIS # C5: 4,6 => CTR => C5: 7
* PRF # C5: 7 => SOL
* PRF # A8: 4,6 => SOL
* PRF # D5: 3,4 => SOL
* DIS # F5: 3,4 => CTR => F5: 8,9
* DIS # D6: 3,4 => CTR => D6: 6
* DIS # E7: 1,6 => CTR => E7: 3,4
* PRF # G5: 3,9 => SOL
* DIS # G5: 7 => CTR => G5: 3,9
* PRF # F6: 3,9 => SOL
* DIS # F6: 3,6 => CTR => F6: 4,9
* PRF # A8: 4,6 => SOL
* PRF # E7: 4,6 => SOL
* DIS # C5: 4,6 => CTR => C5: 7
* PRF # C5: 7 => SOL
* DIS # F8: 4,7 => CTR => F8: 5
* DIS # A8: 1,6 => CTR => A8: 4,7
* DIS # E7: 1,6 => CTR => E7: 3,4
* DIS # A9: 1,6 => CTR => A9: 7
* PRF # A9: 7 => SOL
* CNT  27 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 # E8: 4,5 => CTR => E8: 1,6
* PRF E8: 1,6 # D6: 3,6 => SOL
* STA E8: 1,6 + D6: 3,6
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

..31.....8...9.4.1.4....69.39.5.1.6........2...5.7.....5.9....8.2.....3...9...54. initial
9631...8.872.9.451541.8.69339.52186..1.....25285.7..1..5.9...78.28....3..39...54. autosolve
963154782872396451541287693394521867617438925285679314156943278428765139739812546 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (21)
E1: 4,5
F1: 4,5
D2: 3,6
F2: 3,6
D3: 2,7
F3: 2,7
G1: 2,7
I1: 2,7
C4: 4,7
A5: 4,6
E5: 3,4
I4: 4,7
G6: 3,9
I6: 4,9
C7: 4,6
D8: 4,7
E9: 1,6
G7: 1,2
G8: 1,9
I8: 6,9
I9: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G7,G8: 1.. / G7 = 1  =>  0 pairs (X) / G8 = 1  =>  0 pairs (_)
A9,E9: 1.. / A9 = 1  =>  0 pairs (X) / E9 = 1  => 21 pairs (_)
D3,F3: 2.. / D3 = 2  => 23 pairs (_) / F3 = 2  =>  0 pairs (X)
G1,I1: 2.. / G1 = 2  =>  0 pairs (X) / I1 = 2  =>  0 pairs (_)
G7,I9: 2.. / G7 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
F7,G7: 2.. / F7 = 2  =>  0 pairs (X) / G7 = 2  =>  0 pairs (_)
D3,D9: 2.. / D3 = 2  => 23 pairs (_) / D9 = 2  =>  0 pairs (X)
G1,G7: 2.. / G1 = 2  =>  0 pairs (X) / G7 = 2  =>  0 pairs (_)
I1,I9: 2.. / I1 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
D2,F2: 3.. / D2 = 3  => 20 pairs (_) / F2 = 3  =>  0 pairs (X)
G5,G6: 3.. / G5 = 3  =>  0 pairs (X) / G6 = 3  => 22 pairs (_)
E7,F7: 3.. / E7 = 3  =>  0 pairs (X) / F7 = 3  =>  0 pairs (_)
E5,E7: 3.. / E5 = 3  =>  0 pairs (*) / E7 = 3  =>  0 pairs (X)
E1,F1: 4.. / E1 = 4  =>  0 pairs (X) / F1 = 4  => 20 pairs (_)
I4,I6: 4.. / I4 = 4  =>  0 pairs (X) / I6 = 4  =>  0 pairs (_)
C4,I4: 4.. / C4 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
E1,F1: 5.. / E1 = 5  => 20 pairs (_) / F1 = 5  =>  0 pairs (X)
E8,F8: 5.. / E8 = 5  =>  0 pairs (X) / F8 = 5  => 20 pairs (_)
E1,E8: 5.. / E1 = 5  => 20 pairs (_) / E8 = 5  =>  0 pairs (X)
F1,F8: 5.. / F1 = 5  =>  0 pairs (X) / F8 = 5  => 20 pairs (_)
D2,F2: 6.. / D2 = 6  =>  0 pairs (X) / F2 = 6  => 20 pairs (_)
A5,C5: 6.. / A5 = 6  => 22 pairs (_) / C5 = 6  =>  0 pairs (X)
D6,F6: 6.. / D6 = 6  => 20 pairs (_) / F6 = 6  =>  0 pairs (X)
I8,I9: 6.. / I8 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
C5,C7: 6.. / C5 = 6  =>  0 pairs (X) / C7 = 6  => 22 pairs (_)
D2,D6: 6.. / D2 = 6  =>  0 pairs (X) / D6 = 6  => 20 pairs (_)
F2,F6: 6.. / F2 = 6  => 20 pairs (_) / F6 = 6  =>  0 pairs (X)
D3,F3: 7.. / D3 = 7  =>  0 pairs (X) / F3 = 7  => 23 pairs (_)
G1,I1: 7.. / G1 = 7  =>  0 pairs (*) / I1 = 7  =>  0 pairs (X)
C4,C5: 7.. / C4 = 7  =>  0 pairs (X) / C5 = 7  =>  0 pairs (_)
I4,G5: 7.. / I4 = 7  =>  0 pairs (*) / G5 = 7  =>  0 pairs (X)
A8,A9: 7.. / A8 = 7  =>  0 pairs (X) / A9 = 7  =>  0 pairs (_)
C4,I4: 7.. / C4 = 7  =>  0 pairs (X) / I4 = 7  =>  0 pairs (_)
C5,G5: 7.. / C5 = 7  =>  0 pairs (*) / G5 = 7  =>  0 pairs (X)
G1,G5: 7.. / G1 = 7  =>  0 pairs (*) / G5 = 7  =>  0 pairs (X)
I1,I4: 7.. / I1 = 7  =>  0 pairs (X) / I4 = 7  =>  0 pairs (_)
D5,F5: 8.. / D5 = 8  => 24 pairs (_) / F5 = 8  =>  0 pairs (*)
D9,F9: 8.. / D9 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
D5,D9: 8.. / D5 = 8  => 24 pairs (_) / D9 = 8  =>  0 pairs (*)
F5,F9: 8.. / F5 = 8  =>  0 pairs (*) / F9 = 8  =>  0 pairs (X)
F5,F6: 9.. / F5 = 9  => 25 pairs (_) / F6 = 9  =>  0 pairs (*)
G8,I8: 9.. / G8 = 9  =>  0 pairs (X) / I8 = 9  =>  0 pairs (_)
F5,G5: 9.. / F5 = 9  => 25 pairs (_) / G5 = 9  =>  0 pairs (*)
I6,I8: 9.. / I6 = 9  =>  0 pairs (X) / I8 = 9  =>  0 pairs (_)
* DURATION: 0:01:13.105658  START: 04:23:19.762829  END: 04:24:32.868487 2019-05-01
* CP COUNT: (44)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C4,C7,D2,D3,D8,E1,E5,E9,F1,F2,F3,G1,G6,G7,G8,I1,I4,I6,I8,I9)
* 9631...8.872.9.451541.8.69339.52186..1.....25285.7..1..5.9...78.28....3..39...54.
* PAIR E1: 4,5 COL E
E8: 4,5,1,6                              # reduction candidate for 4,5
E8: 4,5 => CTR
* 9631..782872396451541.8.69339.521867.17.3.92528567931415.9.3278.28...139739.1.546
E8: 1,6                                  # 24 pairs
* PAIR F1: 4,5 COL F
F8: 4,5,7                                # reduction candidate for 4,5
F8: 7 => CTR
* 963145.82872.9.45154178269339.521867.17.3.925285.79314.569...78.28.57.3.739.1.546
F8: 4,5                                  # 23 pairs
* PAIR D2: 3,6 COL D
D6: 3,6,4                                # reduction candidate for 3,6
D6: 4 => CTR
* 9631...8.872693451541.8.69339.52186..1.34..25285.7..1..5.9...78.28....3..39...54.
D6: 3,6                                  # 23 pairs
* PAIR F2: 3,6 COL F
F6: 3,6,4,9                              # reduction candidate for 3,6
F6: 3,6 => CTR
* 9631...8.872.9.451541.8.69339.52186..1.849325285.7.914.5.93..78.284..139.39.18546
F6: 4,9                                  # 21 pairs
* PAIR D3: 2,7 COL D
D9: 2,7,8                                # reduction candidate for 2,7
D9: 8 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
D9: 2,7                                  # 24 pairs
* PAIR F3: 2,7 COL F
F9: 2,7,8                                # reduction candidate for 2,7
F9: 2,7 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
F9: 8                                    # 24 pairs
* PAIR C4: 4,7 BLK 4
C5: 4,7,6                                # reduction candidate for 4,7
C5: 6 => CTR
* 9631...8.872.9.451541.8.693397521864416.3.725285.7.319.549.3278.28....3..39...54.
C5: 4,7                                  # 22 pairs
* PAIR A5: 4,6 BLK 4
C5: 4,6,7                                # reduction candidate for 4,6
C5: 4,6 => CTR
* 9631..287872.93451541287693397521864.1...9725285.7.319.5.9.2178.28...936.39..8542
C5: 7 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
* PAIR A5: 4,6 COL A
A7: 4,6,1                                # reduction candidate for 4,6
A7: 4,6                                  # 26 pairs
A8: 4,6,1,7                              # reduction candidate for 4,6
A8: 4,6 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
A8: 1,7                                  # 23 pairs
* PAIR E5: 3,4 BLK 5
D5: 3,4,8                                # reduction candidate for 3,4
D5: 3,4 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
D5: 8                                    # 24 pairs
F5: 3,4,8,9                              # reduction candidate for 3,4
F5: 3,4 => CTR
* 9631..782872396451541.8.6933945218676178..92528567931445691..78.284..139.39..8546
F5: 8,9                                  # 22 pairs
D6: 3,4,6                                # reduction candidate for 3,4
D6: 3,4 => CTR
* 9631...8.872693451541.8.69339.52186..1..49.25285376914.5.93..78.284..139.39.18546
D6: 6                                    # 20 pairs
F6: 3,4,6,9                              # reduction candidate for 3,4
F6: 3,4                                  # 23 pairs
* PAIR E5: 3,4 COL E
E7: 3,4,1,6                              # reduction candidate for 3,4
E7: 1,6 => CTR
* 9631..782872396451541.8.69339.521867.17.3.925285679314.56913278.28...139.39...546
E7: 3,4                                  # 24 pairs
* PAIR G6: 3,9 BLK 6
G5: 3,9,7                                # reduction candidate for 3,9
G5: 3,9 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
G5: 7 => CTR
* 9631..287872.9.451541287693397521864.1.839725285.7.319.5.9...78.28...936.39..8542
* PAIR G6: 3,9 ROW 6
F6: 3,9,4,6                              # reduction candidate for 3,9
F6: 3,9 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
F6: 4,6                                  # 26 pairs
* PAIR I6: 4,9 ROW 6
F6: 4,9,3,6                              # reduction candidate for 4,9
F6: 3,6 => CTR
* 9631...8.872.9.451541.8.69339.52186..1.849325285.7.914.5.93..78.284..139.39.18546
F6: 4,9                                  # 21 pairs
* PAIR C7: 4,6 BLK 7
A7: 4,6,1                                # reduction candidate for 4,6
A7: 4,6                                  # 26 pairs
A8: 4,6,1,7                              # reduction candidate for 4,6
A8: 4,6 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
A8: 1,7                                  # 23 pairs
* PAIR C7: 4,6 ROW 7
E7: 4,6,1,3                              # reduction candidate for 4,6
E7: 4,6 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
E7: 1,3                                  # 23 pairs
* PAIR C7: 4,6 COL C
C5: 4,6,7                                # reduction candidate for 4,6
C5: 4,6 => CTR
* 9631..287872.93451541287693397521864.1...9725285.7.319.5.9.2178.28...936.39..8542
C5: 7 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
* PAIR D8: 4,7 BLK 8
F8: 4,7,5                                # reduction candidate for 4,7
F8: 4,7 => CTR
* 963145782872396451541.8.69339.521867.17.3.925285679314.56913278.28.5.139.39...546
F8: 5                                    # 20 pairs
* PAIR D8: 4,7 ROW 8
A8: 4,7,1,6                              # reduction candidate for 4,7
A8: 1,6 => CTR
* 9631...82872.9.451541.8.69339.521867.17....25285.7..14.569..278128....3.739.1.546
A8: 4,7                                  # 24 pairs
* PAIR E9: 1,6 BLK 8
E7: 1,6,3,4                              # reduction candidate for 1,6
E7: 1,6 => CTR
* 9631..782872396451541.8.69339.521867.17.3.925285679314.56913278.28...139.39...546
E7: 3,4                                  # 24 pairs
E8: 1,6,4,5                              # reduction candidate for 1,6
E8: 1,6                                  # 24 pairs
* PAIR E9: 1,6 ROW 9
A9: 1,6,7                                # reduction candidate for 1,6
A9: 1,6 => CTR
* 963154.8.872.9.451541.8.69339.52186..1..4..25285.7..1445693217872841593..39...54.
A9: 7 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190310-absurd-base-pr-000.dot
* REASONING
* DIS # E8: 4,5 => CTR => E8: 1,6
* DIS # F8: 7 => CTR => F8: 4,5
* DIS # D6: 4 => CTR => D6: 3,6
* DIS # F6: 3,6 => CTR => F6: 4,9
* PRF # D9: 8 => SOL
* PRF # F9: 2,7 => SOL
* DIS # C5: 6 => CTR => C5: 4,7
* DIS # C5: 4,6 => CTR => C5: 7
* PRF # C5: 7 => SOL
* PRF # A8: 4,6 => SOL
* PRF # D5: 3,4 => SOL
* DIS # F5: 3,4 => CTR => F5: 8,9
* DIS # D6: 3,4 => CTR => D6: 6
* DIS # E7: 1,6 => CTR => E7: 3,4
* PRF # G5: 3,9 => SOL
* DIS # G5: 7 => CTR => G5: 3,9
* PRF # F6: 3,9 => SOL
* DIS # F6: 3,6 => CTR => F6: 4,9
* PRF # A8: 4,6 => SOL
* PRF # E7: 4,6 => SOL
* DIS # C5: 4,6 => CTR => C5: 7
* PRF # C5: 7 => SOL
* DIS # F8: 4,7 => CTR => F8: 5
* DIS # A8: 1,6 => CTR => A8: 4,7
* DIS # E7: 1,6 => CTR => E7: 3,4
* DIS # A9: 1,6 => CTR => A9: 7
* PRF # A9: 7 => SOL
* CNT  27 HDP CHAINS /  50 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,C4,C7,D2,D3,D8,E1,E5,E9,F1,F2,F3,G1,G6,G7,G8,I1,I4,I6,I8,I9)
* 9631...8.872.9.451541.8.69339.52186..1.....25285.7..1..5.9...78.28....3..39...54.
* PAIR E1: 4,5 COL E
E8: 4,5,1,6                              # reduction candidate for 4,5
E8: 4,5 => CTR
* 9631..782872396451541.8.69339.521867.17.3.92528567931415.9.3278.28...139739.1.546
* PAIR RESTART
* PAIR D2: 3,6 COL D
D6: 3,6,4                                # reduction candidate for 3,6
D6: 3,6 => SOLVED
* 963154782872396451541287693394521867617438925285679314156943278428765139739812546
* DURATION: 0:00:03.946592  START: 04:25:19.276425  END: 04:25:23.223017 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190310-absurd-base-pr-001.dot
* REASONING
* DIS # E8: 4,5 => CTR => E8: 1,6
* PRF E8: 1,6 # D6: 3,6 => SOL
* STA E8: 1,6 + D6: 3,6
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190310, absurd

Solution

position: 963154782872396451541287693394521867617438925285679314156943278428765139739812546 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:

* DIS # E8: 4,5 => CTR => E8: 1,6
* INC # E8: 1,6 => UNS
* INC # F8: 4,5 => UNS
* DIS # F8: 7 => CTR => F8: 4,5
* INC # D6: 3,6 => UNS
* DIS # D6: 4 => CTR => D6: 3,6
* DIS # F6: 3,6 => CTR => F6: 4,9
* INC # F6: 4,9 => UNS
* INC # D9: 2,7 => UNS
* PRF # D9: 8 => SOL
* PRF # F9: 2,7 => SOL
* INC # F9: 8 => UNS
* INC # C5: 4,7 => UNS
* DIS # C5: 6 => CTR => C5: 4,7
* DIS # C5: 4,6 => CTR => C5: 7
* PRF # C5: 7 => SOL
* INC # A7: 4,6 => UNS
* PRF # A8: 4,6 => SOL
* INC # A8: 1,7 => UNS
* PRF # D5: 3,4 => SOL
* INC # D5: 8 => UNS
* DIS # F5: 3,4 => CTR => F5: 8,9
* INC # F5: 8,9 => UNS
* DIS # D6: 3,4 => CTR => D6: 6
* INC # D6: 6 => UNS
* INC # F6: 3,4 => UNS
* INC # E7: 3,4 => UNS
* DIS # E7: 1,6 => CTR => E7: 3,4
* PRF # G5: 3,9 => SOL
* DIS # G5: 7 => CTR => G5: 3,9
* PRF # F6: 3,9 => SOL
* INC # F6: 4,6 => UNS
* INC # F6: 4,9 => UNS
* DIS # F6: 3,6 => CTR => F6: 4,9
* INC # A7: 4,6 => UNS
* PRF # A8: 4,6 => SOL
* INC # A8: 1,7 => UNS
* PRF # E7: 4,6 => SOL
* INC # E7: 1,3 => UNS
* DIS # C5: 4,6 => CTR => C5: 7
* PRF # C5: 7 => SOL
* DIS # F8: 4,7 => CTR => F8: 5
* INC # F8: 5 => UNS
* INC # A8: 4,7 => UNS
* DIS # A8: 1,6 => CTR => A8: 4,7
* DIS # E7: 1,6 => CTR => E7: 3,4
* INC # E7: 3,4 => UNS
* INC # E8: 1,6 => UNS
* DIS # A9: 1,6 => CTR => A9: 7
* PRF # A9: 7 => SOL
* CNT  50 HDP CHAINS /  50 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E8: 4,5 => CTR => E8: 1,6
* PRF E8: 1,6 # D6: 3,6 => SOL
* STA E8: 1,6 + D6: 3,6
* CNT   2 HDP CHAINS /   2 HYP OPENED