Analysis of zz-www.sudokuoftheday.co.uk-20060719-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006

position: ....1........9258...8..549.54.3..6.....6..3.8.......4..7..6.1..1..5....2..91.7... initial

Autosolve

position: ...816......49258...873549.54.3..6.....6.43.8.....1.4..7..6.1..1..5....2..91.78.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C7: 4,5 => CTR => C7: 2,3
* PRF # C7: 2,3 => SOL
* PRF # H1: 3 => SOL
* DIS # G6: 9 => CTR => G6: 2,7
* DIS # H1: 2 => CTR => H1: 3,7
* DIS # B6: 3,6 => CTR => B6: 8
* DIS # C2: 3,6 => CTR => C2: 1,7
* DIS # C8: 3,6 => CTR => C8: 4
* PRF # C8: 4 => SOL
* PRF # G6: 7 => SOL
* DIS # I6: 7,9 => CTR => I6: 5
* DIS # I7: 3,5 => CTR => I7: 4,9
* DIS # H9: 3,5 => CTR => H9: 6
* DIS # G6: 2 => CTR => G6: 7,9
* CNT  14 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 # C7: 4,5 => CTR => C7: 2,3
* PRF C7: 2,3 => SOL
* STA C7: 2,3
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

....1........9258...8..549.54.3..6.....6..3.8.......4..7..6.1..1..5....2..91.7... initial
...816......49258...873549.54.3..6.....6.43.8.....1.4..7..6.1..1..5....2..91.78.. autosolve
495816237731492586628735491542378619917654328386921745873269154164583972259147863 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
A1: 4,9
B1: 5,9
C1: 4,5
A3: 2,6
G1: 2,7
I1: 3,7
I2: 1,6
I3: 1,6
C6: 3,6
F4: 8,9
D6: 2,9
I4: 7,9
D7: 2,9
E8: 4,8
E9: 2,4
H7: 3,5
G8: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I2,I3: 1.. / I2 = 1  => 19 pairs (_) / I3 = 1  => 18 pairs (_)
H4,H5: 1.. / H4 = 1  => 18 pairs (_) / H5 = 1  => 22 pairs (_)
B3,I3: 1.. / B3 = 1  => 19 pairs (_) / I3 = 1  => 18 pairs (_)
C4,H4: 1.. / C4 = 1  => 22 pairs (_) / H4 = 1  => 18 pairs (_)
A3,B3: 2.. / A3 = 2  => 21 pairs (_) / B3 = 2  => 18 pairs (_)
G1,H1: 2.. / G1 = 2  => 24 pairs (_) / H1 = 2  =>  0 pairs (X)
D7,E9: 2.. / D7 = 2  =>  0 pairs (*) / E9 = 2  =>  0 pairs (X)
D6,D7: 2.. / D6 = 2  =>  0 pairs (X) / D7 = 2  =>  0 pairs (_)
G1,G6: 2.. / G1 = 2  => 24 pairs (_) / G6 = 2  =>  0 pairs (X)
H1,I1: 3.. / H1 = 3  =>  0 pairs (*) / I1 = 3  =>  0 pairs (X)
F7,F8: 3.. / F7 = 3  => 22 pairs (_) / F8 = 3  => 22 pairs (_)
A1,C1: 4.. / A1 = 4  => 17 pairs (_) / C1 = 4  =>  0 pairs (X)
E8,E9: 4.. / E8 = 4  =>  0 pairs (X) / E9 = 4  =>  0 pairs (_)
I7,I9: 4.. / I7 = 4  => 21 pairs (_) / I9 = 4  =>  0 pairs (X)
C8,E8: 4.. / C8 = 4  =>  0 pairs (*) / E8 = 4  =>  0 pairs (X)
B1,C1: 5.. / B1 = 5  =>  0 pairs (X) / C1 = 5  => 17 pairs (_)
E5,E6: 5.. / E5 = 5  => 19 pairs (_) / E6 = 5  =>  0 pairs (X)
H5,I6: 5.. / H5 = 5  =>  0 pairs (X) / I6 = 5  => 19 pairs (_)
C7,B9: 5.. / C7 = 5  =>  0 pairs (X) / B9 = 5  => 17 pairs (_)
E5,H5: 5.. / E5 = 5  => 19 pairs (_) / H5 = 5  =>  0 pairs (X)
E6,I6: 5.. / E6 = 5  =>  0 pairs (X) / I6 = 5  => 19 pairs (_)
B1,B9: 5.. / B1 = 5  =>  0 pairs (X) / B9 = 5  => 17 pairs (_)
C1,C7: 5.. / C1 = 5  => 17 pairs (_) / C7 = 5  =>  0 pairs (X)
I2,I3: 6.. / I2 = 6  => 18 pairs (_) / I3 = 6  => 19 pairs (_)
H8,H9: 6.. / H8 = 6  =>  0 pairs (X) / H9 = 6  => 18 pairs (_)
A2,C2: 7.. / A2 = 7  => 18 pairs (_) / C2 = 7  =>  0 pairs (X)
G8,H8: 7.. / G8 = 7  =>  0 pairs (X) / H8 = 7  => 20 pairs (_)
A2,A5: 7.. / A2 = 7  => 18 pairs (_) / A5 = 7  =>  0 pairs (X)
A6,B6: 8.. / A6 = 8  =>  0 pairs (X) / B6 = 8  => 20 pairs (_)
E4,F4: 8.. / E4 = 8  =>  0 pairs (X) / F4 = 8  =>  0 pairs (_)
A7,B8: 8.. / A7 = 8  => 20 pairs (_) / B8 = 8  =>  0 pairs (X)
A7,F7: 8.. / A7 = 8  => 20 pairs (_) / F7 = 8  =>  0 pairs (X)
A6,A7: 8.. / A6 = 8  =>  0 pairs (X) / A7 = 8  => 20 pairs (_)
B6,B8: 8.. / B6 = 8  => 20 pairs (_) / B8 = 8  =>  0 pairs (X)
E4,E8: 8.. / E4 = 8  =>  0 pairs (X) / E8 = 8  =>  0 pairs (_)
A1,B1: 9.. / A1 = 9  =>  0 pairs (X) / B1 = 9  => 17 pairs (_)
A5,B5: 9.. / A5 = 9  => 17 pairs (_) / B5 = 9  =>  0 pairs (X)
F4,D6: 9.. / F4 = 9  =>  0 pairs (X) / D6 = 9  =>  0 pairs (_)
I7,G8: 9.. / I7 = 9  =>  0 pairs (X) / G8 = 9  => 20 pairs (_)
F4,I4: 9.. / F4 = 9  =>  0 pairs (X) / I4 = 9  =>  0 pairs (_)
F8,G8: 9.. / F8 = 9  =>  0 pairs (X) / G8 = 9  => 20 pairs (_)
A1,A5: 9.. / A1 = 9  =>  0 pairs (X) / A5 = 9  => 17 pairs (_)
B1,B5: 9.. / B1 = 9  => 17 pairs (_) / B5 = 9  =>  0 pairs (X)
D6,D7: 9.. / D6 = 9  =>  0 pairs (*) / D7 = 9  =>  0 pairs (X)
G6,G8: 9.. / G6 = 9  =>  0 pairs (X) / G8 = 9  => 20 pairs (_)
* DURATION: 0:00:58.434119  START: 00:48:24.774506  END: 00:49:23.208625 2019-05-01
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,C1,C6,D6,D7,E8,E9,F4,G1,G8,H7,I1,I2,I3,I4)
* ...816......49258...873549.54.3..6.....6.43.8.....1.4..7..6.1..1..5....2..91.78..
* PAIR C1: 4,5 COL C
C7: 4,5,2,3                              # reduction candidate for 4,5
C7: 4,5 => CTR
* ...816......49258..2873549154.3896.7...6.43.8...27194527.9681..18.543762..91278..
C7: 2,3 => SOLVED
* 495816237731492586628735491542378619917654328386921745873269154164583972259147863
* PAIR A3: 2,6 BLK 1
B3: 2,6,1                                # reduction candidate for 2,6
B3: 1                                    # 19 pairs
B3: 2,6                                  # 18 pairs
* PAIR A3: 2,6 COL A
A9: 2,6,3,4                              # reduction candidate for 2,6
A9: 2,6                                  # 21 pairs
A9: 3,4                                  # 18 pairs
* PAIR G1: 2,7 BLK 3
H1: 2,7,3                                # reduction candidate for 2,7
H1: 3 => SOLVED
* 495816237731492586628735491542378619917654328386921745873269154164583972259147863
H1: 2,7                                  # 22 pairs
* PAIR G1: 2,7 COL G
G6: 2,7,9                                # reduction candidate for 2,7
G6: 9 => CTR
* ...8162.....49258...873549.54.3..6.....6.43.8.....194..7.96.1..1..5..7.2..91278..
G6: 2,7                                  # 20 pairs
* PAIR I1: 3,7 BLK 3
H1: 3,7,2                                # reduction candidate for 3,7
H1: 2 => CTR
* .54816723...49258...873549.54.3..61..916.4358...95124747.26.1..1..5..972..9147865
H1: 3,7                                  # 24 pairs
* PAIR I2: 1,6 ROW 2
B2: 1,6,3                                # reduction candidate for 1,6
B2: 1,6                                  # 21 pairs
C2: 1,6,3,7                              # reduction candidate for 1,6
C2: 1,6                                  # 23 pairs
* PAIR I3: 1,6 ROW 3
B3: 1,6,2                                # reduction candidate for 1,6
B3: 1,6                                  # 21 pairs
B3: 2                                    # 18 pairs
* PAIR C6: 3,6 BLK 4
A6: 3,6,8                                # reduction candidate for 3,6
A6: 3,6                                  # 20 pairs
B6: 3,6,8                                # reduction candidate for 3,6
B6: 3,6 => CTR
* ...816......49258...873549.54.3896.7...6.43.88..2.1.4..7..681..18.543972..912786.
B6: 8                                    # 20 pairs
* PAIR C6: 3,6 COL C
C2: 3,6,1,7                              # reduction candidate for 3,6
C2: 3,6 => CTR
* ...816...7..49258...873549.54.3..6.....6.43.8.....1.4..7296.1..1.458...2..91.78..
C2: 1,7                                  # 18 pairs
C8: 3,6,4                                # reduction candidate for 3,6
C8: 3,6 => CTR
* ...816......49258...873549.54.3896.7...6.43.8...271945.7.96.1..1..54.7.2..91278..
C8: 4 => SOLVED
* 495816237731492586628735491542378619917654328386921745873269154164583972259147863
* PAIR F4: 8,9 COL F
F7: 8,9,3                                # reduction candidate for 8,9
F7: 8,9                                  # 22 pairs
F8: 8,9,3                                # reduction candidate for 8,9
F8: 8,9                                  # 22 pairs
* PAIR D6: 2,9 ROW 6
G6: 2,9,7                                # reduction candidate for 2,9
G6: 7 => SOLVED
* 495816237731492586628735491542378619917654328386921745873269154164583972259147863
G6: 2,9                                  # 20 pairs
* PAIR I4: 7,9 BLK 6
G6: 7,9,2                                # reduction candidate for 7,9
G6: 7,9                                  # 24 pairs
I6: 7,9,5                                # reduction candidate for 7,9
I6: 7,9 => CTR
* .54816723...49258...873549.54.3.8619.916.4358.8.951247.7.26913.1..583972..9147865
I6: 5                                    # 19 pairs
* PAIR E9: 2,4 ROW 9
A9: 2,4,3,6                              # reduction candidate for 2,4
A9: 2,4                                  # 23 pairs
A9: 3,6                                  # 18 pairs
* PAIR H7: 3,5 BLK 9
I7: 3,5,4,9                              # reduction candidate for 3,5
I7: 3,5 => CTR
* .95816......49258...873549.54.3896.79.76543.8...2.1.4..7..6.1..1..54.972.59127864
I7: 4,9                                  # 18 pairs
H9: 3,5,6                                # reduction candidate for 3,5
H9: 3,5 => CTR
* ...8162.....49258...873549.54.3..6.....6.43.8.....194..7.96.1..1..5..762..91278..
H9: 6                                    # 18 pairs
I9: 3,5,4                                # reduction candidate for 3,5
I9: 3,5                                  # 21 pairs
* PAIR H7: 3,5 ROW 7
C7: 3,5,2,4                              # reduction candidate for 3,5
C7: 3,5                                  # 28 pairs
C7: 2,4                                  # 18 pairs
* PAIR G8: 7,9 COL G
G6: 7,9,2                                # reduction candidate for 7,9
G6: 2 => CTR
* ...816723...49258...873549.54.3..61....6.4358...951247.7.2691341.4583972..9147865
G6: 7,9                                  # 24 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060719-absurd-base-pr-000.dot
* REASONING
* DIS # C7: 4,5 => CTR => C7: 2,3
* PRF # C7: 2,3 => SOL
* PRF # H1: 3 => SOL
* DIS # G6: 9 => CTR => G6: 2,7
* DIS # H1: 2 => CTR => H1: 3,7
* DIS # B6: 3,6 => CTR => B6: 8
* DIS # C2: 3,6 => CTR => C2: 1,7
* DIS # C8: 3,6 => CTR => C8: 4
* PRF # C8: 4 => SOL
* PRF # G6: 7 => SOL
* DIS # I6: 7,9 => CTR => I6: 5
* DIS # I7: 3,5 => CTR => I7: 4,9
* DIS # H9: 3,5 => CTR => H9: 6
* DIS # G6: 2 => CTR => G6: 7,9
* CNT  14 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B1,C1,C6,D6,D7,E8,E9,F4,G1,G8,H7,I1,I2,I3,I4)
* ...816......49258...873549.54.3..6.....6.43.8.....1.4..7..6.1..1..5....2..91.78..
* PAIR C1: 4,5 COL C
C7: 4,5,2,3                              # reduction candidate for 4,5
C7: 4,5 => CTR
* ...816......49258..2873549154.3896.7...6.43.8...27194527.9681..18.543762..91278..
C7: 2,3 => SOLVED
* 495816237731492586628735491542378619917654328386921745873269154164583972259147863
* DURATION: 0:00:02.574734  START: 00:49:52.098626  END: 00:49:54.673360 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060719-absurd-base-pr-001.dot
* REASONING
* DIS # C7: 4,5 => CTR => C7: 2,3
* PRF C7: 2,3 => SOL
* STA C7: 2,3
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060719, absurd

Solution

position: 495816237731492586628735491542378619917654328386921745873269154164583972259147863 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 # C7: 4,5 => CTR => C7: 2,3
* PRF # C7: 2,3 => SOL
* INC # B3: 2,6 => UNS
* INC # B3: 1 => UNS
* INC # A9: 2,6 => UNS
* INC # A9: 3,4 => UNS
* INC # H1: 2,7 => UNS
* PRF # H1: 3 => SOL
* INC # G6: 2,7 => UNS
* DIS # G6: 9 => CTR => G6: 2,7
* INC # H1: 3,7 => UNS
* DIS # H1: 2 => CTR => H1: 3,7
* INC # B2: 1,6 => UNS
* INC # C2: 1,6 => UNS
* INC # B3: 1,6 => UNS
* INC # B3: 2 => UNS
* INC # A6: 3,6 => UNS
* DIS # B6: 3,6 => CTR => B6: 8
* INC # B6: 8 => UNS
* DIS # C2: 3,6 => CTR => C2: 1,7
* INC # C2: 1,7 => UNS
* DIS # C8: 3,6 => CTR => C8: 4
* PRF # C8: 4 => SOL
* INC # F7: 8,9 => UNS
* INC # F8: 8,9 => UNS
* INC # G6: 2,9 => UNS
* PRF # G6: 7 => SOL
* INC # G6: 7,9 => UNS
* DIS # I6: 7,9 => CTR => I6: 5
* INC # I6: 5 => UNS
* INC # A9: 2,4 => UNS
* INC # A9: 3,6 => UNS
* DIS # I7: 3,5 => CTR => I7: 4,9
* INC # I7: 4,9 => UNS
* DIS # H9: 3,5 => CTR => H9: 6
* INC # H9: 6 => UNS
* INC # I9: 3,5 => UNS
* INC # C7: 3,5 => UNS
* INC # C7: 2,4 => UNS
* INC # G6: 7,9 => UNS
* DIS # G6: 2 => CTR => G6: 7,9
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C7: 4,5 => CTR => C7: 2,3
* PRF C7: 2,3 => SOL
* STA C7: 2,3
* CNT   2 HDP CHAINS /   1 HYP OPENED