Analysis of zz-www.sudokuoftheday.co.uk-20190114-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

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

level: medium

position: ..8...2...9...3...3...75..1..58....4...91.3..41.....8.......465....9...2.6....... initial

Autosolve

position: ..8..92.3.9..835.63...758919.58..124...91435741....689..9...465....9.7.2.6....9.8 autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C2: 2,4 => CTR => C2: 1,7
* PRF # C3: 2,4 => SOL
* PRF # D3: 6 => SOL
* DIS # D1: 4,6 => CTR => D1: 1
* DIS # B1: 4,7 => CTR => B1: 5
* DIS # C2: 4,7 => CTR => C2: 1,2
* PRF # A5: 2,8 => SOL
* PRF # A5: 8 => SOL
* DIS # C3: 4 => CTR => C3: 2,6
* PRF # D6: 5 => SOL
* DIS # F7: 2,7 => CTR => F7: 1,8
* DIS # F9: 2,7 => CTR => F9: 1
* PRF # D9: 3,7 => SOL
* PRF # D6: 5 => SOL
* DIS # E9: 2,3 => CTR => E9: 4,5
* PRF # E6: 2,3 => SOL
* DIS # C9: 1,3 => CTR => C9: 2,4,7
* CNT  17 HDP CHAINS /  47 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* DIS # C2: 2,4 => CTR => C2: 1,7
* PRF C2: 1,7 # C3: 2,4 => SOL
* STA C2: 1,7 + C3: 2,4
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

`..8...2...9...3...3...75..1..58....4...91.3..41.....8.......465....9...2.6.......`	initial
`..8..92.3.9..835.63...758919.58..124...91435741....689..9...465....9.7.2.6....9.8`	autosolve
`658149273791283546342675891935867124826914357417532689179328465583496712264751938`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B3: 2,4
E1: 4,6
H1: 4,7
H2: 4,7
B4: 3,7
B5: 2,8
C5: 2,6
C6: 3,7
E4: 3,6
F4: 6,7
F6: 2,7
D7: 3,7
E7: 2,3
H8: 1,3
H9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,D2: 1.. / D1 = 1  => 16 pairs (_) / D2 = 1  =>  0 pairs (X)
H8,H9: 1.. / H8 = 1  => 16 pairs (_) / H9 = 1  =>  0 pairs (X)
A1,D1: 1.. / A1 = 1  =>  0 pairs (X) / D1 = 1  => 16 pairs (_)
A7,F7: 1.. / A7 = 1  => 19 pairs (_) / F7 = 1  =>  0 pairs (X)
D2,D3: 2.. / D2 = 2  => 17 pairs (_) / D3 = 2  =>  0 pairs (X)
E6,F6: 2.. / E6 = 2  =>  0 pairs (X) / F6 = 2  => 16 pairs (_)
B4,C6: 3.. / B4 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
H8,H9: 3.. / H8 = 3  =>  0 pairs (X) / H9 = 3  => 16 pairs (_)
B4,E4: 3.. / B4 = 3  =>  0 pairs (*) / E4 = 3  =>  0 pairs (X)
H1,H2: 4.. / H1 = 4  =>  0 pairs (X) / H2 = 4  => 15 pairs (_)
E1,E9: 4.. / E1 = 4  =>  0 pairs (*) / E9 = 4  =>  0 pairs (X)
A1,B1: 5.. / A1 = 5  =>  0 pairs (X) / B1 = 5  => 15 pairs (_)
D6,E6: 5.. / D6 = 5  =>  0 pairs (*) / E6 = 5  =>  0 pairs (X)
B1,B8: 5.. / B1 = 5  => 15 pairs (_) / B8 = 5  =>  0 pairs (X)
E6,E9: 5.. / E6 = 5  => 17 pairs (_) / E9 = 5  =>  0 pairs (*)
A1,C3: 6.. / A1 = 6  =>  0 pairs (*) / C3 = 6  =>  0 pairs (X)
A5,C5: 6.. / A5 = 6  => 16 pairs (_) / C5 = 6  =>  0 pairs (*)
E4,F4: 6.. / E4 = 6  =>  0 pairs (*) / F4 = 6  =>  0 pairs (X)
D8,F8: 6.. / D8 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
C3,D3: 6.. / C3 = 6  => 16 pairs (_) / D3 = 6  =>  0 pairs (*)
A1,A5: 6.. / A1 = 6  =>  0 pairs (*) / A5 = 6  =>  0 pairs (X)
C3,C5: 6.. / C3 = 6  => 16 pairs (_) / C5 = 6  =>  0 pairs (*)
E1,E4: 6.. / E1 = 6  =>  0 pairs (X) / E4 = 6  =>  0 pairs (_)
F4,F8: 6.. / F4 = 6  =>  0 pairs (X) / F8 = 6  =>  0 pairs (_)
H1,H2: 7.. / H1 = 7  => 15 pairs (_) / H2 = 7  =>  0 pairs (X)
B4,C6: 7.. / B4 = 7  =>  0 pairs (X) / C6 = 7  =>  0 pairs (_)
B4,F4: 7.. / B4 = 7  =>  0 pairs (X) / F4 = 7  =>  0 pairs (_)
A5,B5: 8.. / A5 = 8  =>  0 pairs (*) / B5 = 8  =>  0 pairs (X)
F7,F8: 8.. / F7 = 8  => 20 pairs (_) / F8 = 8  =>  0 pairs (X)
* DURATION: 0:00:33.502283  START: 02:56:32.979522  END: 02:57:06.481805 2019-05-01
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B5,C5,C6,D7,E1,E4,E7,F4,F6,H1,H2,H8,H9)
* ..8..92.3.9..835.63...758919.58..124...91435741....689..9...465....9.7.2.6....9.8
* PAIR B3: 2,4 BLK 1
C2: 2,4,1,7                              # reduction candidate for 2,4
C2: 2,4 => CTR
* .58.692.3.9..835.63.6.75891975836124682914357413...6898.97214655..6987.2.6....9.8
C2: 1,7                                  # 16 pairs
C3: 2,4,6                                # reduction candidate for 2,4
C3: 2,4 => SOLVED
* 658149273791283546342675891935867124826914357417532689179328465583496712264751938
C3: 6                                    # 16 pairs
* PAIR B3: 2,4 ROW 3
D3: 2,4,6                                # reduction candidate for 2,4
D3: 6 => SOLVED
* 658149273791283546342675891935867124826914357417532689179328465583496712264751938
D3: 2,4                                  # 16 pairs
* PAIR E1: 4,6 BLK 2
D1: 4,6,1                                # reduction candidate for 4,6
D1: 4,6 => CTR
* 158..9273.9.1835463.62758919.58..12468291435741....689.29.31465....987.2.6....9.8
D1: 1                                    # 16 pairs
D3: 4,6,2                                # reduction candidate for 4,6
D3: 4,6                                  # 17 pairs
* PAIR H1: 4,7 ROW 1
B1: 4,7,5                                # reduction candidate for 4,7
B1: 4,7 => CTR
* 5.81692.3.9..835.63.6.758919.5836124682914357413...689..9.2.465.5.69.73226.3..9.8
B1: 5                                    # 15 pairs
* PAIR H2: 4,7 ROW 2
C2: 4,7,1,2                              # reduction candidate for 4,7
C2: 4,7 => CTR
* .58.692.3.9..835.63.6.75891975836124682914357413...6898.97214655..6987.2.6....9.8
C2: 1,2                                  # 16 pairs
* PAIR B4: 3,7 COL B
B7: 3,7,2,8                              # reduction candidate for 3,7
B7: 2,8                                  # 20 pairs
B7: 3,7                                  # 19 pairs
* PAIR B5: 2,8 BLK 4
A5: 2,8,6                                # reduction candidate for 2,8
A5: 2,8 => SOLVED
* 658149273791283546342675891935867124826914357417532689179328465583496712264751938
A5: 6                                    # 16 pairs
* PAIR B5: 2,8 COL B
B7: 2,8,3,7                              # reduction candidate for 2,8
B7: 2,8                                  # 20 pairs
B7: 3,7                                  # 19 pairs
* PAIR C5: 2,6 BLK 4
A5: 2,6,8                                # reduction candidate for 2,6
A5: 8 => SOLVED
* 658149273791283546342675891935867124826914357417532689179328465583496712264751938
A5: 2,6                                  # 17 pairs
* PAIR C5: 2,6 COL C
C3: 2,6,4                                # reduction candidate for 2,6
C3: 4 => CTR
* 658149273.9.2835463246758919.5867124.86914357417..2689.793..465....9.7.2.6....9.8
C3: 2,6                                  # 16 pairs
* PAIR C6: 3,7 ROW 6
D6: 3,7,5                                # reduction candidate for 3,7
D6: 5 => SOLVED
* 658149273791283546342675891935867124826914357417532689179328465583496712264751938
D6: 3,7                                  # 17 pairs
* PAIR C6: 3,7 COL C
C9: 3,7,1,2,4                            # reduction candidate for 3,7
C9: 3,7                                  # 17 pairs
C9: 1,2,4                                # 15 pairs
* PAIR F6: 2,7 COL F
F7: 2,7,1,8                              # reduction candidate for 2,7
F7: 2,7 => CTR
* .581.92.3.91.835.63...75891975836124826914357413...689189327465534698712.67..1938
F7: 1,8                                  # 16 pairs
F9: 2,7,1                                # reduction candidate for 2,7
F9: 2,7 => CTR
* ..8.692.3.97.835463.6.75891975836124682914357413752689739.2.465...69.7.2.6..479.8
F9: 1                                    # 18 pairs
* PAIR D7: 3,7 BLK 8
D9: 3,7,4,5                              # reduction candidate for 3,7
D9: 3,7 => SOLVED
* 658149273791283546342675891935867124826914357417532689179328465583496712264751938
D9: 4,5                                  # 16 pairs
* PAIR D7: 3,7 ROW 7
B7: 3,7,2,8                              # reduction candidate for 3,7
B7: 2,8                                  # 20 pairs
B7: 3,7                                  # 19 pairs
* PAIR D7: 3,7 COL D
D6: 3,7,5                                # reduction candidate for 3,7
D6: 5 => SOLVED
* 658149273791283546342675891935867124826914357417532689179328465583496712264751938
D6: 3,7                                  # 17 pairs
* PAIR E7: 2,3 BLK 8
E9: 2,3,4,5                              # reduction candidate for 2,3
E9: 2,3 => CTR
* ..8.49273.9..835463...758919.5867124...914357417.52689.793..465....9.7.2.6....9.8
E9: 4,5                                  # 16 pairs
* PAIR E7: 2,3 ROW 7
B7: 2,3,7,8                              # reduction candidate for 2,3
B7: 2,3                                  # 19 pairs
B7: 7,8                                  # 16 pairs
* PAIR E7: 2,3 COL E
E6: 2,3,5                                # reduction candidate for 2,3
E6: 2,3 => SOLVED
* 658149273791283546342675891935867124826914357417532689179328465583496712264751938
E6: 5                                    # 17 pairs
* PAIR H8: 1,3 ROW 8
C8: 1,3,4                                # reduction candidate for 1,3
C8: 1,3                                  # 18 pairs
C8: 4                                    # 17 pairs
* PAIR H9: 1,3 ROW 9
C9: 1,3,2,4,7                            # reduction candidate for 1,3
C9: 1,3 => CTR
* ..8.692.3.972835463.6475891975836124682914357413752689739.2.465...69.7.2261..7938
C9: 2,4,7                                # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190114-absurd-base-pr-000.dot
* REASONING
* DIS # C2: 2,4 => CTR => C2: 1,7
* PRF # C3: 2,4 => SOL
* PRF # D3: 6 => SOL
* DIS # D1: 4,6 => CTR => D1: 1
* DIS # B1: 4,7 => CTR => B1: 5
* DIS # C2: 4,7 => CTR => C2: 1,2
* PRF # A5: 2,8 => SOL
* PRF # A5: 8 => SOL
* DIS # C3: 4 => CTR => C3: 2,6
* PRF # D6: 5 => SOL
* DIS # F7: 2,7 => CTR => F7: 1,8
* DIS # F9: 2,7 => CTR => F9: 1
* PRF # D9: 3,7 => SOL
* PRF # D6: 5 => SOL
* DIS # E9: 2,3 => CTR => E9: 4,5
* PRF # E6: 2,3 => SOL
* DIS # C9: 1,3 => CTR => C9: 2,4,7
* CNT  17 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B5,C5,C6,D7,E1,E4,E7,F4,F6,H1,H2,H8,H9)
* ..8..92.3.9..835.63...758919.58..124...91435741....689..9...465....9.7.2.6....9.8
* PAIR B3: 2,4 BLK 1
C2: 2,4,1,7                              # reduction candidate for 2,4
C2: 2,4 => CTR
* .58.692.3.9..835.63.6.75891975836124682914357413...6898.97214655..6987.2.6....9.8
C3: 2,4,6                                # reduction candidate for 2,4
C3: 2,4 => SOLVED
* 658149273791283546342675891935867124826914357417532689179328465583496712264751938
* DURATION: 0:00:02.367338  START: 02:57:37.006183  END: 02:57:39.373521 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190114-absurd-base-pr-001.dot
* REASONING
* DIS # C2: 2,4 => CTR => C2: 1,7
* PRF C2: 1,7 # C3: 2,4 => SOL
* STA C2: 1,7 + C3: 2,4
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190114, absurd

Solution

position: 658149273791283546342675891935867124826914357417532689179328465583496712264751938 solved

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 # C2: 2,4 => CTR => C2: 1,7
* INC # C2: 1,7 => UNS
* PRF # C3: 2,4 => SOL
* INC # C3: 6 => UNS
* INC # D3: 2,4 => UNS
* PRF # D3: 6 => SOL
* DIS # D1: 4,6 => CTR => D1: 1
* INC # D1: 1 => UNS
* INC # D3: 4,6 => UNS
* DIS # B1: 4,7 => CTR => B1: 5
* INC # B1: 5 => UNS
* DIS # C2: 4,7 => CTR => C2: 1,2
* INC # C2: 1,2 => UNS
* INC # B7: 3,7 => UNS
* INC # B7: 2,8 => UNS
* PRF # A5: 2,8 => SOL
* INC # A5: 6 => UNS
* INC # B7: 2,8 => UNS
* INC # B7: 3,7 => UNS
* INC # A5: 2,6 => UNS
* PRF # A5: 8 => SOL
* INC # C3: 2,6 => UNS
* DIS # C3: 4 => CTR => C3: 2,6
* INC # D6: 3,7 => UNS
* PRF # D6: 5 => SOL
* INC # C9: 3,7 => UNS
* INC # C9: 1,2,4 => UNS
* DIS # F7: 2,7 => CTR => F7: 1,8
* INC # F7: 1,8 => UNS
* DIS # F9: 2,7 => CTR => F9: 1
* INC # F9: 1 => UNS
* PRF # D9: 3,7 => SOL
* INC # D9: 4,5 => UNS
* INC # B7: 3,7 => UNS
* INC # B7: 2,8 => UNS
* INC # D6: 3,7 => UNS
* PRF # D6: 5 => SOL
* DIS # E9: 2,3 => CTR => E9: 4,5
* INC # E9: 4,5 => UNS
* INC # B7: 2,3 => UNS
* INC # B7: 7,8 => UNS
* PRF # E6: 2,3 => SOL
* INC # E6: 5 => UNS
* INC # C8: 1,3 => UNS
* INC # C8: 4 => UNS
* DIS # C9: 1,3 => CTR => C9: 2,4,7
* INC # C9: 2,4,7 => UNS
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C2: 2,4 => CTR => C2: 1,7
* PRF C2: 1,7 # C3: 2,4 => SOL
* STA C2: 1,7 + C3: 2,4
* CNT   2 HDP CHAINS /   2 HYP OPENED