Analysis of zz-www.sudokuoftheday.co.uk-20190212-absurd-base.sdk

Contents

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

level: medium

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

position: ..85...9....81.....5...2....7.428....2...973.....7......7..4.8..63.8.4.7..1...65. initial

Autosolve

position: 7.854..9.9.281.57..5.792...37.428....2...973....37.....97..4.8..6398.4.7..1237659 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A3: 4,6 => SOL
* DIS # A3: 1 => CTR => A3: 4,6
* PRF # C6: 4,6 => SOL
* DIS # I1: 1,2 => CTR => I1: 6
* PRF # I1: 6 => SOL
* PRF # A3: 6 => SOL
* DIS # A6: 4,8 => CTR => A6: 1,6
* PRF # B6: 4,8 => SOL
* DIS # B6: 1 => CTR => B6: 4,8
* CNT   9 HDP CHAINS /  21 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 # A3: 4,6 => SOL
* STA A3: 4,6
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

..85...9....81.....5...2....7.428....2...973.....7......7..4.8..63.8.4.7..1...65. initial
7.854..9.9.281.57..5.792...37.428....2...973....37.....97..4.8..6398.4.7..1237659 autosolve
718543296932816574654792813379428165425169738186375942297654381563981427841237659 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (25)
B1: 1,3
B2: 3,4
C3: 4,6
F1: 3,6
F2: 3,6
G1: 1,2
I2: 4,6
G3: 3,8
H3: 1,4
I3: 3,8
C5: 4,5
D5: 1,6
E5: 5,6
F6: 1,5
G4: 1,9
H4: 1,6
I4: 1,5
A7: 2,5
A8: 2,5
A9: 4,8
B9: 4,8
D7: 1,6
E7: 5,6
F8: 1,5
H8: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,A3: 1.. / B1 = 1  =>  0 pairs (*) / A3 = 1  =>  0 pairs (X)
D5,F6: 1.. / D5 = 1  => 22 pairs (_) / F6 = 1  =>  0 pairs (X)
D7,F8: 1.. / D7 = 1  =>  0 pairs (X) / F8 = 1  => 22 pairs (_)
A3,H3: 1.. / A3 = 1  =>  0 pairs (X) / H3 = 1  =>  0 pairs (_)
A5,D5: 1.. / A5 = 1  =>  0 pairs (X) / D5 = 1  => 22 pairs (_)
F8,H8: 1.. / F8 = 1  => 22 pairs (_) / H8 = 1  =>  0 pairs (X)
B1,B6: 1.. / B1 = 1  =>  0 pairs (*) / B6 = 1  =>  0 pairs (X)
D5,D7: 1.. / D5 = 1  => 22 pairs (_) / D7 = 1  =>  0 pairs (X)
F6,F8: 1.. / F6 = 1  =>  0 pairs (X) / F8 = 1  => 22 pairs (_)
G1,I1: 2.. / G1 = 2  => 27 pairs (_) / I1 = 2  =>  0 pairs (X)
A7,A8: 2.. / A7 = 2  => 22 pairs (_) / A8 = 2  =>  0 pairs (X)
A8,H8: 2.. / A8 = 2  =>  0 pairs (X) / H8 = 2  => 22 pairs (_)
H6,H8: 2.. / H6 = 2  =>  0 pairs (X) / H8 = 2  => 22 pairs (_)
B1,B2: 3.. / B1 = 3  =>  0 pairs (X) / B2 = 3  =>  0 pairs (_)
F1,F2: 3.. / F1 = 3  =>  0 pairs (*) / F2 = 3  =>  0 pairs (X)
G3,I3: 3.. / G3 = 3  => 17 pairs (_) / I3 = 3  => 25 pairs (_)
G7,I7: 3.. / G7 = 3  => 25 pairs (_) / I7 = 3  => 17 pairs (_)
B1,F1: 3.. / B1 = 3  =>  0 pairs (X) / F1 = 3  =>  0 pairs (_)
B2,F2: 3.. / B2 = 3  =>  0 pairs (*) / F2 = 3  =>  0 pairs (X)
G3,G7: 3.. / G3 = 3  => 17 pairs (_) / G7 = 3  => 25 pairs (_)
I3,I7: 3.. / I3 = 3  => 25 pairs (_) / I7 = 3  => 17 pairs (_)
I2,H3: 4.. / I2 = 4  =>  0 pairs (*) / H3 = 4  =>  0 pairs (X)
A9,B9: 4.. / A9 = 4  => 26 pairs (_) / B9 = 4  =>  0 pairs (*)
B2,I2: 4.. / B2 = 4  =>  0 pairs (X) / I2 = 4  =>  0 pairs (_)
H3,H6: 4.. / H3 = 4  =>  0 pairs (X) / H6 = 4  =>  0 pairs (_)
E5,F6: 5.. / E5 = 5  =>  0 pairs (X) / F6 = 5  => 22 pairs (_)
A7,A8: 5.. / A7 = 5  =>  0 pairs (X) / A8 = 5  => 22 pairs (_)
E7,F8: 5.. / E7 = 5  => 22 pairs (_) / F8 = 5  =>  0 pairs (X)
C4,I4: 5.. / C4 = 5  => 28 pairs (_) / I4 = 5  => 26 pairs (_)
A7,E7: 5.. / A7 = 5  =>  0 pairs (X) / E7 = 5  => 22 pairs (_)
A8,F8: 5.. / A8 = 5  => 22 pairs (_) / F8 = 5  =>  0 pairs (X)
E5,E7: 5.. / E5 = 5  =>  0 pairs (X) / E7 = 5  => 22 pairs (_)
F6,F8: 5.. / F6 = 5  => 22 pairs (_) / F8 = 5  =>  0 pairs (X)
A3,C3: 6.. / A3 = 6  =>  0 pairs (*) / C3 = 6  =>  0 pairs (X)
F1,F2: 6.. / F1 = 6  =>  0 pairs (X) / F2 = 6  =>  0 pairs (_)
I1,I2: 6.. / I1 = 6  =>  0 pairs (*) / I2 = 6  =>  0 pairs (X)
D5,E5: 6.. / D5 = 6  =>  0 pairs (X) / E5 = 6  => 22 pairs (_)
H4,H6: 6.. / H4 = 6  => 26 pairs (_) / H6 = 6  =>  0 pairs (X)
D7,E7: 6.. / D7 = 6  => 22 pairs (_) / E7 = 6  =>  0 pairs (X)
F1,I1: 6.. / F1 = 6  =>  0 pairs (X) / I1 = 6  =>  0 pairs (_)
F2,I2: 6.. / F2 = 6  =>  0 pairs (*) / I2 = 6  =>  0 pairs (X)
C4,H4: 6.. / C4 = 6  =>  0 pairs (X) / H4 = 6  => 26 pairs (_)
A3,A6: 6.. / A3 = 6  =>  0 pairs (*) / A6 = 6  =>  0 pairs (X)
D5,D7: 6.. / D5 = 6  =>  0 pairs (X) / D7 = 6  => 22 pairs (_)
E5,E7: 6.. / E5 = 6  => 22 pairs (_) / E7 = 6  =>  0 pairs (X)
G3,I3: 8.. / G3 = 8  => 25 pairs (_) / I3 = 8  => 17 pairs (_)
A9,B9: 8.. / A9 = 8  =>  0 pairs (*) / B9 = 8  =>  0 pairs (X)
A5,I5: 8.. / A5 = 8  => 23 pairs (_) / I5 = 8  => 27 pairs (_)
B6,B9: 8.. / B6 = 8  =>  0 pairs (*) / B9 = 8  =>  0 pairs (X)
G3,G6: 8.. / G3 = 8  => 25 pairs (_) / G6 = 8  => 17 pairs (_)
C4,C6: 9.. / C4 = 9  => 23 pairs (_) / C6 = 9  => 26 pairs (_)
G4,G6: 9.. / G4 = 9  => 26 pairs (_) / G6 = 9  => 23 pairs (_)
C4,G4: 9.. / C4 = 9  => 23 pairs (_) / G4 = 9  => 26 pairs (_)
C6,G6: 9.. / C6 = 9  => 26 pairs (_) / G6 = 9  => 23 pairs (_)
* DURATION: 0:01:13.101747  START: 03:40:30.118935  END: 03:41:43.220682 2019-05-01
* CP COUNT: (54)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,A9,B1,B2,B9,C3,C5,D5,D7,E5,E7,F1,F2,F6,F8,G1,G3,G4,H3,H4,H8,I2,I3,I4)
* 7.854..9.9.281.57..5.792...37.428....2...973....37.....97..4.8..6398.4.7..1237659
* PAIR C3: 4,6 BLK 1
A3: 4,6,1                                # reduction candidate for 4,6
A3: 4,6 => SOLVED
* 718543296932816574654792813379428165425169738186375942297654381563981427841237659
A3: 1 => CTR
* 7.854..9.9.281.57.156792.4.37.428.6..2.16973.61.375.2..97654.8..6398.4.7..1237659
* PAIR C3: 4,6 COL C
C6: 4,6,5,9                              # reduction candidate for 4,6
C6: 4,6 => SOLVED
* 718543296932816574654792813379428165425169738186375942297654381563981427841237659
C6: 5,9                                  # 26 pairs
* PAIR G1: 1,2 BLK 3
I1: 1,2,6                                # reduction candidate for 1,2
I1: 1,2 => CTR
* 738546.9.942813576156792.4.37.428.6..2.16973.61.375.2..97654.8..6398.4.7..1237659
I1: 6 => SOLVED
* 718543296932816574654792813379428165425169738186375942297654381563981427841237659
* PAIR G1: 1,2 COL G
G7: 1,2,3                                # reduction candidate for 1,2
G7: 3                                    # 25 pairs
G7: 1,2                                  # 17 pairs
* PAIR H3: 1,4 ROW 3
A3: 1,4,6                                # reduction candidate for 1,4
A3: 6 => SOLVED
* 718543296932816574654792813379428165425169738186375942297654381563981427841237659
A3: 1,4                                  # 28 pairs
* PAIR C5: 4,5 BLK 4
C6: 4,5,6,9                              # reduction candidate for 4,5
C6: 6,9                                  # 26 pairs
C6: 4,5                                  # 26 pairs
* PAIR C5: 4,5 ROW 5
I5: 4,5,8                                # reduction candidate for 4,5
I5: 8                                    # 27 pairs
I5: 4,5                                  # 23 pairs
* PAIR A9: 4,8 COL A
A5: 4,8,1                                # reduction candidate for 4,8
A5: 4,8                                  # 22 pairs
A6: 4,8,1,6                              # reduction candidate for 4,8
A6: 4,8 => CTR
* 7.854..9.9.281.57.654792.1.37.428.6.125..973....37.....97..4.8..6398.4.7..1237659
A6: 1,6                                  # 26 pairs
* PAIR B9: 4,8 COL B
B6: 4,8,1                                # reduction candidate for 4,8
B6: 4,8 => SOLVED
* 718543296932816574654792813379428165425169738186375942297654381563981427841237659
B6: 1 => CTR
* 738546.9.942813576156792.4.37.428....2...973..1.375....97.54.8.563981427.81237659
* PAIR H8: 1,2 BLK 9
G7: 1,2,3                                # reduction candidate for 1,2
G7: 1,2                                  # 17 pairs
I7: 1,2,3                                # reduction candidate for 1,2
I7: 1,2                                  # 25 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190212-absurd-base-pr-000.dot
* REASONING
* PRF # A3: 4,6 => SOL
* DIS # A3: 1 => CTR => A3: 4,6
* PRF # C6: 4,6 => SOL
* DIS # I1: 1,2 => CTR => I1: 6
* PRF # I1: 6 => SOL
* PRF # A3: 6 => SOL
* DIS # A6: 4,8 => CTR => A6: 1,6
* PRF # B6: 4,8 => SOL
* DIS # B6: 1 => CTR => B6: 4,8
* CNT   9 HDP CHAINS /  21 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A8,A9,B1,B2,B9,C3,C5,D5,D7,E5,E7,F1,F2,F6,F8,G1,G3,G4,H3,H4,H8,I2,I3,I4)
* 7.854..9.9.281.57..5.792...37.428....2...973....37.....97..4.8..6398.4.7..1237659
* PAIR C3: 4,6 BLK 1
A3: 4,6,1                                # reduction candidate for 4,6
A3: 4,6 => SOLVED
* 718543296932816574654792813379428165425169738186375942297654381563981427841237659
* DURATION: 0:00:01.673786  START: 03:42:00.809520  END: 03:42:02.483306 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190212-absurd-base-pr-001.dot
* REASONING
* PRF # A3: 4,6 => SOL
* STA A3: 4,6
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190212, absurd

Solution

position: 718543296932816574654792813379428165425169738186375942297654381563981427841237659 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 # A3: 4,6 => SOL
* DIS # A3: 1 => CTR => A3: 4,6
* PRF # C6: 4,6 => SOL
* INC # C6: 5,9 => UNS
* DIS # I1: 1,2 => CTR => I1: 6
* PRF # I1: 6 => SOL
* INC # G7: 1,2 => UNS
* INC # G7: 3 => UNS
* INC # A3: 1,4 => UNS
* PRF # A3: 6 => SOL
* INC # C6: 4,5 => UNS
* INC # C6: 6,9 => UNS
* INC # I5: 4,5 => UNS
* INC # I5: 8 => UNS
* INC # A5: 4,8 => UNS
* DIS # A6: 4,8 => CTR => A6: 1,6
* INC # A6: 1,6 => UNS
* PRF # B6: 4,8 => SOL
* DIS # B6: 1 => CTR => B6: 4,8
* INC # G7: 1,2 => UNS
* INC # I7: 1,2 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A3: 4,6 => SOL
* STA A3: 4,6
* CNT   1 HDP CHAINS /   1 HYP OPENED