Analysis of zz-www.sudokuoftheday.co.uk-20190318-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: ..427..1..3.1.4.8.7....6..4....6...83.98...4......1.....6...8.7.1.3.........2.... initial

Autosolve

position: ..427..1..3.19478.7.15.6..41...6...8379852.4...8..1.....6.1.837.173...6...3627... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 2,5 => CTR => A2: 6
* DIS # I2: 6 => CTR => I2: 2,5
* PRF # G3: 2,9 => SOL
* DIS # G3: 3 => CTR => G3: 2,9
* DIS # B3: 2,9 => CTR => B3: 8
* PRF # B3: 8 => SOL
* DIS # B4: 2,5 => CTR => B4: 4
* DIS # B6: 2,5 => CTR => B6: 4,6
* PRF # G4: 2,5 => SOL
* PRF # G4: 2,5 => SOL
* PRF # F8: 5,9 => SOL
* DIS # F8: 8 => CTR => F8: 5,9
* PRF # A7: 5,9 => SOL
* DIS # B7: 5,9 => CTR => B7: 2,4
* DIS # G9: 5,9 => CTR => G9: 1,4
* DIS # I9: 5,9 => CTR => I9: 1
* DIS # A9: 5,9 => CTR => A9: 4,8
* CNT  17 HDP CHAINS /  41 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 # A2: 2,5 => CTR => A2: 6
* PRF A2: 6 # G3: 2,9 => SOL
* STA A2: 6 + G3: 2,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

..427..1..3.1.4.8.7....6..4....6...83.98...4......1.....6...8.7.1.3.........2.... initial
..427..1..3.19478.7.15.6..41...6...8379852.4...8..1.....6.1.837.173...6...3627... autosolve
594278613632194785781536924145963278379852146268741359926415837417389562853627491 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
C2: 2,5
F1: 3,8
E3: 3,8
H3: 2,9
C4: 2,5
F4: 3,9
E6: 3,4
G5: 1,6
I5: 1,6
D7: 4,9
F7: 5,9
E8: 4,8
H9: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G5,I5: 1.. / G5 = 1  => 13 pairs (_) / I5 = 1  =>  0 pairs (X)
G9,I9: 1.. / G9 = 1  =>  0 pairs (X) / I9 = 1  => 13 pairs (_)
G5,G9: 1.. / G5 = 1  => 13 pairs (_) / G9 = 1  =>  0 pairs (X)
I5,I9: 1.. / I5 = 1  =>  0 pairs (X) / I9 = 1  => 13 pairs (_)
A7,B7: 2.. / A7 = 2  => 14 pairs (_) / B7 = 2  => 16 pairs (_)
G8,I8: 2.. / G8 = 2  => 20 pairs (_) / I8 = 2  => 15 pairs (_)
C2,C4: 2.. / C2 = 2  => 15 pairs (_) / C4 = 2  => 14 pairs (_)
F1,E3: 3.. / F1 = 3  =>  0 pairs (X) / E3 = 3  =>  0 pairs (_)
F4,E6: 3.. / F4 = 3  =>  0 pairs (*) / E6 = 3  =>  0 pairs (X)
E3,G3: 3.. / E3 = 3  =>  0 pairs (*) / G3 = 3  =>  0 pairs (X)
F4,G4: 3.. / F4 = 3  =>  0 pairs (*) / G4 = 3  =>  0 pairs (X)
E3,E6: 3.. / E3 = 3  =>  0 pairs (*) / E6 = 3  =>  0 pairs (X)
F1,F4: 3.. / F1 = 3  =>  0 pairs (X) / F4 = 3  =>  0 pairs (_)
I1,I6: 3.. / I1 = 3  =>  0 pairs (*) / I6 = 3  =>  0 pairs (X)
D7,E8: 4.. / D7 = 4  =>  0 pairs (*) / E8 = 4  =>  0 pairs (X)
G8,G9: 4.. / G8 = 4  =>  0 pairs (X) / G9 = 4  => 13 pairs (_)
B4,D4: 4.. / B4 = 4  => 14 pairs (_) / D4 = 4  =>  0 pairs (X)
E6,E8: 4.. / E6 = 4  =>  0 pairs (*) / E8 = 4  =>  0 pairs (X)
F7,F8: 5.. / F7 = 5  => 13 pairs (_) / F8 = 5  =>  0 pairs (X)
C2,C4: 5.. / C2 = 5  => 14 pairs (_) / C4 = 5  => 15 pairs (_)
A6,B6: 6.. / A6 = 6  =>  0 pairs (X) / B6 = 6  => 13 pairs (_)
G5,I5: 6.. / G5 = 6  =>  0 pairs (X) / I5 = 6  => 13 pairs (_)
A2,I2: 6.. / A2 = 6  => 14 pairs (_) / I2 = 6  =>  0 pairs (X)
B1,B6: 6.. / B1 = 6  =>  0 pairs (X) / B6 = 6  => 13 pairs (_)
G1,G5: 6.. / G1 = 6  => 13 pairs (_) / G5 = 6  =>  0 pairs (X)
D4,D6: 7.. / D4 = 7  => 14 pairs (_) / D6 = 7  => 14 pairs (_)
H4,H6: 7.. / H4 = 7  => 14 pairs (_) / H6 = 7  => 14 pairs (_)
D4,H4: 7.. / D4 = 7  => 14 pairs (_) / H4 = 7  => 14 pairs (_)
D6,H6: 7.. / D6 = 7  => 14 pairs (_) / H6 = 7  => 14 pairs (_)
F1,E3: 8.. / F1 = 8  =>  0 pairs (*) / E3 = 8  =>  0 pairs (X)
A9,B9: 8.. / A9 = 8  => 13 pairs (_) / B9 = 8  =>  0 pairs (X)
E8,F8: 8.. / E8 = 8  =>  0 pairs (*) / F8 = 8  =>  0 pairs (X)
B3,E3: 8.. / B3 = 8  =>  0 pairs (*) / E3 = 8  =>  0 pairs (X)
A1,A9: 8.. / A1 = 8  =>  0 pairs (X) / A9 = 8  => 13 pairs (_)
E3,E8: 8.. / E3 = 8  =>  0 pairs (X) / E8 = 8  =>  0 pairs (_)
F1,F8: 8.. / F1 = 8  =>  0 pairs (*) / F8 = 8  =>  0 pairs (X)
* DURATION: 0:00:38.542114  START: 04:37:09.586650  END: 04:37:48.128764 2019-05-01
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C4,D7,E3,E6,E8,F1,F4,F7,G5,H3,H9,I5)
* ..427..1..3.19478.7.15.6..41...6...8379852.4...8..1.....6.1.837.173...6...3627...
* PAIR C2: 2,5 BLK 1
A2: 2,5,6                                # reduction candidate for 2,5
A2: 2,5 => CTR
* ..427..1..3.1947867.15.6..41...6...8379852641..8.41.....641.837.1738.4624836271..
A2: 6                                    # 14 pairs
* PAIR C2: 2,5 ROW 2
I2: 2,5,6                                # reduction candidate for 2,5
I2: 6 => CTR
* ..427..1..3.1947867.15.6..41...6...8379852641..8.41.....641.837.1738.4624836271..
I2: 2,5                                  # 14 pairs
* PAIR H3: 2,9 BLK 3
G3: 2,9,3                                # reduction candidate for 2,9
G3: 2,9 => SOLVED
* 594278613632194785781536924145963278379852146268741359926415837417389562853627491
G3: 3 => CTR
* ..427..1..3.19478.7.15.63.41...63..8379852.4...8.41..3..641.837.1738..6...3627...
* PAIR H3: 2,9 ROW 3
B3: 2,9,8                                # reduction candidate for 2,9
B3: 2,9 => CTR
* ..427..1..3.19478.7.15863.41...63..8379852.4...8..1.....6.1.837.173...6...3627...
B3: 8 => SOLVED
* 594278613632194785781536924145963278379852146268741359926415837417389562853627491
* PAIR H3: 2,9 COL H
H4: 2,9,5,7                              # reduction candidate for 2,9
H4: 2,9                                  # 17 pairs
H6: 2,9,5,7                              # reduction candidate for 2,9
H6: 2,9                                  # 16 pairs
* PAIR C4: 2,5 BLK 4
B4: 2,5,4                                # reduction candidate for 2,5
B4: 2,5 => CTR
* ..4273.1..3.19478.7.15863.41..469.78379852146..8731.....6915837.17348.6...36274.1
B4: 4                                    # 14 pairs
A6: 2,5,4,6                              # reduction candidate for 2,5
A6: 2,5                                  # 15 pairs
B6: 2,5,4,6                              # reduction candidate for 2,5
B6: 2,5 => CTR
* 864273.1..3.194786791586..414..6...83798526416.8..1.....6.1.837.173..4624836271..
B6: 4,6                                  # 14 pairs
* PAIR C4: 2,5 ROW 4
G4: 2,5,3,9                              # reduction candidate for 2,5
G4: 2,5 => SOLVED
* 594278613632194785781536924145963278379852146268741359926415837417389562853627491
G4: 3,9                                  # 15 pairs
H4: 2,5,7,9                              # reduction candidate for 2,5
H4: 2,5                                  # 16 pairs
* PAIR F4: 3,9 ROW 4
G4: 3,9,2,5                              # reduction candidate for 3,9
G4: 2,5 => SOLVED
* 594278613632194785781536924145963278379852146268741359926415837417389562853627491
G4: 3,9                                  # 15 pairs
* PAIR D7: 4,9 ROW 7
A7: 4,9,2,5                              # reduction candidate for 4,9
A7: 4,9                                  # 17 pairs
B7: 4,9,2,5                              # reduction candidate for 4,9
B7: 4,9                                  # 15 pairs
* PAIR D7: 4,9 COL D
D4: 4,9,7                                # reduction candidate for 4,9
D4: 4,9                                  # 14 pairs
D6: 4,9,7                                # reduction candidate for 4,9
D6: 4,9                                  # 14 pairs
* PAIR F7: 5,9 BLK 8
F8: 5,9,8                                # reduction candidate for 5,9
F8: 5,9 => SOLVED
* 594278613632194785781536924145963278379852146268741359926415837417389562853627491
F8: 8 => CTR
* ..4273.1..3.19478.7.15863.41...69..8379852.4...8.31.....6915837.17348.6...36274.1
* PAIR F7: 5,9 ROW 7
A7: 5,9,2,4                              # reduction candidate for 5,9
A7: 5,9 => SOLVED
* 594278613632194785781536924145963278379852146268741359926415837417389562853627491
A7: 2,4                                  # 14 pairs
B7: 5,9,2,4                              # reduction candidate for 5,9
B7: 5,9 => CTR
* .64278.1.532194786781536..414..63..8379852.4..28.41...2.641.837.1738..6.8.36274.1
B7: 2,4                                  # 14 pairs
* PAIR H9: 5,9 BLK 9
G8: 5,9,2,4                              # reduction candidate for 5,9
G8: 5,9                                  # 16 pairs
I8: 5,9,2                                # reduction candidate for 5,9
I8: 5,9                                  # 20 pairs
G9: 5,9,1,4                              # reduction candidate for 5,9
G9: 5,9 => CTR
* ..427.61.6321947857.15.6..41.5.6...8379852146.68.41.....641.837.1738.462483627..1
G9: 1,4                                  # 14 pairs
I9: 5,9,1                                # reduction candidate for 5,9
I9: 5,9 => CTR
* ..427..1..3.19478.7.15.6..41...6...8379852641..8.41.....641.837.1738.4624836271..
I9: 1                                    # 13 pairs
* PAIR H9: 5,9 ROW 9
A9: 5,9,4,8                              # reduction candidate for 5,9
A9: 5,9 => CTR
* 8.4273.1..3.19478.7.15863.41...69..8379852.4...8.31.....6915837.17348.6..836274.1
A9: 4,8                                  # 14 pairs
B9: 5,9,4,8                              # reduction candidate for 5,9
B9: 5,9                                  # 15 pairs
* PAIR H9: 5,9 COL H
H4: 5,9,2,7                              # reduction candidate for 5,9
H4: 5,9                                  # 17 pairs
H6: 5,9,2,7                              # reduction candidate for 5,9
H6: 5,9                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190318-absurd-base-pr-000.dot
* REASONING
* DIS # A2: 2,5 => CTR => A2: 6
* DIS # I2: 6 => CTR => I2: 2,5
* PRF # G3: 2,9 => SOL
* DIS # G3: 3 => CTR => G3: 2,9
* DIS # B3: 2,9 => CTR => B3: 8
* PRF # B3: 8 => SOL
* DIS # B4: 2,5 => CTR => B4: 4
* DIS # B6: 2,5 => CTR => B6: 4,6
* PRF # G4: 2,5 => SOL
* PRF # G4: 2,5 => SOL
* PRF # F8: 5,9 => SOL
* DIS # F8: 8 => CTR => F8: 5,9
* PRF # A7: 5,9 => SOL
* DIS # B7: 5,9 => CTR => B7: 2,4
* DIS # G9: 5,9 => CTR => G9: 1,4
* DIS # I9: 5,9 => CTR => I9: 1
* DIS # A9: 5,9 => CTR => A9: 4,8
* CNT  17 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C2,C4,D7,E3,E6,E8,F1,F4,F7,G5,H3,H9,I5)
* ..427..1..3.19478.7.15.6..41...6...8379852.4...8..1.....6.1.837.173...6...3627...
* PAIR C2: 2,5 BLK 1
A2: 2,5,6                                # reduction candidate for 2,5
A2: 2,5 => CTR
* ..427..1..3.1947867.15.6..41...6...8379852641..8.41.....641.837.1738.4624836271..
* PAIR H3: 2,9 BLK 3
G3: 2,9,3                                # reduction candidate for 2,9
G3: 2,9 => SOLVED
* 594278613632194785781536924145963278379852146268741359926415837417389562853627491
* DURATION: 0:00:02.938940  START: 04:38:14.747154  END: 04:38:17.686094 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190318-absurd-base-pr-001.dot
* REASONING
* DIS # A2: 2,5 => CTR => A2: 6
* PRF A2: 6 # G3: 2,9 => SOL
* STA A2: 6 + G3: 2,9
* 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, 20190318, absurd

Solution

position: 594278613632194785781536924145963278379852146268741359926415837417389562853627491 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 # A2: 2,5 => CTR => A2: 6
* INC # A2: 6 => UNS
* INC # I2: 2,5 => UNS
* DIS # I2: 6 => CTR => I2: 2,5
* PRF # G3: 2,9 => SOL
* DIS # G3: 3 => CTR => G3: 2,9
* DIS # B3: 2,9 => CTR => B3: 8
* PRF # B3: 8 => SOL
* INC # H4: 2,9 => UNS
* INC # H6: 2,9 => UNS
* DIS # B4: 2,5 => CTR => B4: 4
* INC # B4: 4 => UNS
* INC # A6: 2,5 => UNS
* DIS # B6: 2,5 => CTR => B6: 4,6
* INC # B6: 4,6 => UNS
* PRF # G4: 2,5 => SOL
* INC # G4: 3,9 => UNS
* INC # H4: 2,5 => UNS
* INC # G4: 3,9 => UNS
* PRF # G4: 2,5 => SOL
* INC # A7: 4,9 => UNS
* INC # B7: 4,9 => UNS
* INC # D4: 4,9 => UNS
* INC # D6: 4,9 => UNS
* PRF # F8: 5,9 => SOL
* DIS # F8: 8 => CTR => F8: 5,9
* PRF # A7: 5,9 => SOL
* INC # A7: 2,4 => UNS
* DIS # B7: 5,9 => CTR => B7: 2,4
* INC # B7: 2,4 => UNS
* INC # G8: 5,9 => UNS
* INC # I8: 5,9 => UNS
* DIS # G9: 5,9 => CTR => G9: 1,4
* INC # G9: 1,4 => UNS
* DIS # I9: 5,9 => CTR => I9: 1
* INC # I9: 1 => UNS
* DIS # A9: 5,9 => CTR => A9: 4,8
* INC # A9: 4,8 => UNS
* INC # B9: 5,9 => UNS
* INC # H4: 5,9 => UNS
* INC # H6: 5,9 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A2: 2,5 => CTR => A2: 6
* PRF A2: 6 # G3: 2,9 => SOL
* STA A2: 6 + G3: 2,9
* CNT   2 HDP CHAINS /   2 HYP OPENED