Analysis of zz-www.sudokuoftheday.co.uk-20060910-absurd-base.sdk

Contents

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

level: medium

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

position: ........1.......6.....819..25...8.7.8.437.2..3...9.........9..663..4...8..72..3.. initial

Autosolve

position: ........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..3.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E1: 6 => CTR => E1: 2,5
* DIS # D6: 1,6 => CTR => D6: 4,5
* DIS # D6: 1,6 => CTR => D6: 4,5
* DIS # E9: 5 => CTR => E9: 1,6
* DIS # D6: 5,6 => CTR => D6: 1,4
* DIS # G6: 1,5 => CTR => G6: 4,6,8
* DIS # H6: 1,5 => CTR => H6: 4,8
* DIS # H9: 4 => CTR => H9: 1,5
* DIS # G6: 4,5 => CTR => G6: 1,6,8
* DIS # H6: 4,5 => CTR => H6: 1,8
* DIS # D6: 1,6 => CTR => D6: 4,5
* DIS # A7: 5 => CTR => A7: 1,4
* DIS # B2: 1,4 => CTR => B2: 2,9
* DIS # C2: 1,5 => CTR => C2: 3,8
* DIS # E9: 6 => CTR => E9: 1,5
* DIS # E9: 5,6 => CTR => E9: 1
* DIS # H9: 4 => CTR => H9: 1,5
* DIS # G6: 1,5 => CTR => G6: 4,6,8
* DIS # H9: 1 => CTR => H9: 4,5
* CNT  19 HDP CHAINS /  48 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 # E1: 6 => CTR => E1: 2,5
* DIS E1: 2,5 # G6: 4,5,8 => CTR => G6: 1,6
* DIS E1: 2,5 + G6: 1,6 # H9: 4 => CTR => H9: 1,5
* DIS E1: 2,5 + G6: 1,6 + H9: 1,5 # B2: 1,4 => CTR => B2: 2,9
* PRF E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9 => SOL
* STA E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9
* CNT   5 HDP CHAINS /   9 HYP OPENED

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

Details

Positions

........1.......6.....819..25...8.7.8.437.2..3...9.........9..663..4...8..72..3.. initial
........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..3.. autosolve
798623541123954867546781932259168473864375219371492685415839726632547198987216354 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
F1: 3,4
E2: 2,5
F2: 3,4
I2: 2,7
I3: 2,7
B5: 1,6
C6: 1,6
E4: 1,6
F5: 5,6
H5: 1,5
I6: 4,5
B7: 1,4
C7: 1,5
D8: 1,5
F9: 5,6
G8: 1,5
I9: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,C6: 1.. / B5 = 1  =>  0 pairs (X) / C6 = 1  => 21 pairs (_)
D8,E9: 1.. / D8 = 1  =>  0 pairs (X) / E9 = 1  => 21 pairs (_)
G8,H9: 1.. / G8 = 1  => 21 pairs (_) / H9 = 1  =>  0 pairs (X)
B5,H5: 1.. / B5 = 1  =>  0 pairs (X) / H5 = 1  => 21 pairs (_)
D8,G8: 1.. / D8 = 1  =>  0 pairs (X) / G8 = 1  => 21 pairs (_)
E9,H9: 1.. / E9 = 1  => 21 pairs (_) / H9 = 1  =>  0 pairs (X)
A2,A7: 1.. / A2 = 1  => 18 pairs (_) / A7 = 1  => 17 pairs (_)
E4,E9: 1.. / E4 = 1  =>  0 pairs (X) / E9 = 1  => 21 pairs (_)
E1,E2: 2.. / E1 = 2  => 21 pairs (_) / E2 = 2  =>  0 pairs (X)
I2,I3: 2.. / I2 = 2  => 21 pairs (_) / I3 = 2  => 23 pairs (_)
B1,E1: 2.. / B1 = 2  =>  0 pairs (X) / E1 = 2  => 21 pairs (_)
B3,I3: 2.. / B3 = 2  => 21 pairs (_) / I3 = 2  => 23 pairs (_)
F1,F2: 3.. / F1 = 3  => 22 pairs (_) / F2 = 3  => 17 pairs (_)
H1,H3: 3.. / H1 = 3  => 18 pairs (_) / H3 = 3  => 25 pairs (_)
C2,F2: 3.. / C2 = 3  => 22 pairs (_) / F2 = 3  => 17 pairs (_)
C3,H3: 3.. / C3 = 3  => 18 pairs (_) / H3 = 3  => 25 pairs (_)
F1,F2: 4.. / F1 = 4  => 17 pairs (_) / F2 = 4  => 22 pairs (_)
D4,D6: 4.. / D4 = 4  => 18 pairs (_) / D6 = 4  => 21 pairs (_)
A7,B7: 4.. / A7 = 4  => 18 pairs (_) / B7 = 4  => 18 pairs (_)
H9,I9: 4.. / H9 = 4  =>  0 pairs (X) / I9 = 4  => 21 pairs (_)
D4,G4: 4.. / D4 = 4  => 18 pairs (_) / G4 = 4  => 21 pairs (_)
I6,I9: 4.. / I6 = 4  =>  0 pairs (X) / I9 = 4  => 21 pairs (_)
F5,D6: 5.. / F5 = 5  => 21 pairs (_) / D6 = 5  =>  0 pairs (X)
A7,C7: 5.. / A7 = 5  =>  0 pairs (X) / C7 = 5  => 18 pairs (_)
F5,H5: 5.. / F5 = 5  => 21 pairs (_) / H5 = 5  =>  0 pairs (X)
D8,G8: 5.. / D8 = 5  => 21 pairs (_) / G8 = 5  =>  0 pairs (X)
F5,F9: 5.. / F5 = 5  => 21 pairs (_) / F9 = 5  =>  0 pairs (X)
I6,I9: 5.. / I6 = 5  => 21 pairs (_) / I9 = 5  =>  0 pairs (X)
B5,C6: 6.. / B5 = 6  => 21 pairs (_) / C6 = 6  =>  0 pairs (X)
G4,G6: 6.. / G4 = 6  =>  0 pairs (X) / G6 = 6  => 21 pairs (_)
E9,F9: 6.. / E9 = 6  =>  0 pairs (X) / F9 = 6  => 21 pairs (_)
B5,F5: 6.. / B5 = 6  => 21 pairs (_) / F5 = 6  =>  0 pairs (X)
F5,F9: 6.. / F5 = 6  =>  0 pairs (X) / F9 = 6  => 21 pairs (_)
I2,I3: 7.. / I2 = 7  => 23 pairs (_) / I3 = 7  => 21 pairs (_)
A1,D1: 7.. / A1 = 7  => 18 pairs (_) / D1 = 7  =>  0 pairs (X)
C1,C2: 8.. / C1 = 8  => 22 pairs (_) / C2 = 8  => 18 pairs (_)
G6,H6: 8.. / G6 = 8  =>  0 pairs (X) / H6 = 8  => 17 pairs (_)
C2,G2: 8.. / C2 = 8  => 18 pairs (_) / G2 = 8  => 22 pairs (_)
H1,H6: 8.. / H1 = 8  =>  0 pairs (X) / H6 = 8  => 17 pairs (_)
B1,B2: 9.. / B1 = 9  => 21 pairs (_) / B2 = 9  => 23 pairs (_)
D1,D2: 9.. / D1 = 9  => 23 pairs (_) / D2 = 9  => 21 pairs (_)
B1,D1: 9.. / B1 = 9  => 21 pairs (_) / D1 = 9  => 23 pairs (_)
B2,D2: 9.. / B2 = 9  => 23 pairs (_) / D2 = 9  => 21 pairs (_)
* DURATION: 0:00:51.596881  START: 02:31:59.835726  END: 02:32:51.432607 2019-05-01
* CP COUNT: (43)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,C6,C7,D8,E2,E4,F1,F2,F5,F9,G8,H5,I2,I3,I6,I9)
* ........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..3..
* PAIR F1: 3,4 ROW 1
H1: 3,4,5,8                              # reduction candidate for 3,4
H1: 5,8                                  # 27 pairs
H1: 3,4                                  # 20 pairs
* PAIR E2: 2,5 BLK 2
E1: 2,5,6                                # reduction candidate for 2,5
E1: 6 => CTR
* .2.96...1.9..2..67...7819.2259.18.738.437.2.937..92......839726632147598987256314
E1: 2,5                                  # 22 pairs
* PAIR C6: 1,6 ROW 6
D6: 1,6,4,5                              # reduction candidate for 1,6
D6: 1,6 => CTR
* ........1.......6.....819..2594.8.738.4375219371692.....583972663214759898725634.
D6: 4,5                                  # 20 pairs
G6: 1,6,4,5,8                            # reduction candidate for 1,6
G6: 1,6                                  # 20 pairs
* PAIR E4: 1,6 BLK 5
D4: 1,6,4                                # reduction candidate for 1,6
D4: 1,6                                  # 21 pairs
D6: 1,6,4,5                              # reduction candidate for 1,6
D6: 1,6 => CTR
* ........1.......6.....819..2594.8.738.4375219371692.....583972663214759898725634.
D6: 4,5                                  # 20 pairs
* PAIR E4: 1,6 ROW 4
G4: 1,6,4                                # reduction candidate for 1,6
G4: 4                                    # 21 pairs
G4: 1,6                                  # 18 pairs
* PAIR E4: 1,6 COL E
E9: 1,6,5                                # reduction candidate for 1,6
E9: 5 => CTR
* ........1.......6.....819..259.18.738.437.2.937..92......839726632147598987256314
E9: 1,6                                  # 22 pairs
* PAIR F5: 5,6 BLK 5
D6: 5,6,1,4                              # reduction candidate for 5,6
D6: 5,6 => CTR
* ........1.......6.....819..2594186738.437.2.937..92......8397266321475989872..314
D6: 1,4                                  # 21 pairs
* PAIR H5: 1,5 BLK 6
G6: 1,5,4,6,8                            # reduction candidate for 1,5
G6: 1,5 => CTR
* ........1.......6.....819..2594186738.4375219371692.84...839726632.47.989872..345
G6: 4,6,8                                # 17 pairs
H6: 1,5,4,8                              # reduction candidate for 1,5
H6: 1,5 => CTR
* ..3..4581..8.5346.....8193.2594.86738.43752193716928.....839726632.47.989872..345
H6: 4,8                                  # 18 pairs
* PAIR H5: 1,5 COL H
H9: 1,5,4                                # reduction candidate for 1,5
H9: 4 => CTR
* ........1.......6.....819..2591684738.437.2.937..92......839726632.47198987216345
H9: 1,5                                  # 21 pairs
* PAIR I6: 4,5 BLK 6
G6: 4,5,1,6,8                            # reduction candidate for 4,5
G6: 4,5 => CTR
* ........1.......6.....819..259..86738.437.2.937..92.8....839726632.4719898721.3..
G6: 1,6,8                                # 17 pairs
H6: 4,5,1,8                              # reduction candidate for 4,5
H6: 4,5 => CTR
* ..3..4581..8..346.....8193.2594.86738.437.2193716928.....839726632.47.989872..3..
H6: 1,8                                  # 18 pairs
* PAIR I6: 4,5 ROW 6
D6: 4,5,1,6                              # reduction candidate for 4,5
D6: 1,6 => CTR
* ........1.......6.....819..2594.8.738.4375219371692.....583972663214759898725634.
D6: 4,5                                  # 20 pairs
* PAIR B7: 1,4 BLK 7
A7: 1,4,5                                # reduction candidate for 1,4
A7: 5 => CTR
* ........11......6.....819..259..8.73814376259376592..45418397266321475989872..3..
A7: 1,4                                  # 18 pairs
* PAIR B7: 1,4 COL B
B2: 1,4,2,9                              # reduction candidate for 1,4
B2: 1,4 => CTR
* .9672...171.95..62.2.6819.7259168473864375219371492685145839726632547198987216354
B2: 2,9                                  # 22 pairs
* PAIR C7: 1,5 BLK 7
A7: 1,5,4                                # reduction candidate for 1,5
A7: 4                                    # 18 pairs
A7: 1,5                                  # 18 pairs
* PAIR C7: 1,5 COL C
C2: 1,5,3,8                              # reduction candidate for 1,5
C2: 1,5 => CTR
* ..8..4531.....386...3.8194.259..8673814376259376.92.8....839726632.47.989872..3..
C2: 3,8                                  # 18 pairs
* PAIR D8: 1,5 BLK 8
E9: 1,5,6                                # reduction candidate for 1,5
E9: 6 => CTR
* ........1.......6.....819..259.18.738.437.2.937..92......839726632147598987265314
E9: 1,5                                  # 21 pairs
* PAIR D8: 1,5 COL D
D6: 1,5,4,6                              # reduction candidate for 1,5
D6: 1,5                                  # 23 pairs
D6: 4,6                                  # 21 pairs
* PAIR F9: 5,6 BLK 8
E9: 5,6,1                                # reduction candidate for 5,6
E9: 5,6 => CTR
* ........1.......6.....819..259.18.738.437.2.937..92......8397266321475989872..314
E9: 1                                    # 21 pairs
* PAIR G8: 1,5 BLK 9
H9: 1,5,4                                # reduction candidate for 1,5
H9: 4 => CTR
* ........1.......6.....819..2591684738.437.2.937..92......839726632.47198987216345
H9: 1,5                                  # 21 pairs
* PAIR G8: 1,5 COL G
G6: 1,5,4,6,8                            # reduction candidate for 1,5
G6: 1,5 => CTR
* ........1.......6.....819..2594186738.4375219371692.84...839726632.47.989872..345
G6: 4,6,8                                # 17 pairs
* PAIR I9: 4,5 BLK 9
H9: 4,5,1                                # reduction candidate for 4,5
H9: 1 => CTR
* ........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..314
H9: 4,5                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060910-absurd-base-pr-000.dot
* REASONING
* DIS # E1: 6 => CTR => E1: 2,5
* DIS # D6: 1,6 => CTR => D6: 4,5
* DIS # D6: 1,6 => CTR => D6: 4,5
* DIS # E9: 5 => CTR => E9: 1,6
* DIS # D6: 5,6 => CTR => D6: 1,4
* DIS # G6: 1,5 => CTR => G6: 4,6,8
* DIS # H6: 1,5 => CTR => H6: 4,8
* DIS # H9: 4 => CTR => H9: 1,5
* DIS # G6: 4,5 => CTR => G6: 1,6,8
* DIS # H6: 4,5 => CTR => H6: 1,8
* DIS # D6: 1,6 => CTR => D6: 4,5
* DIS # A7: 5 => CTR => A7: 1,4
* DIS # B2: 1,4 => CTR => B2: 2,9
* DIS # C2: 1,5 => CTR => C2: 3,8
* DIS # E9: 6 => CTR => E9: 1,5
* DIS # E9: 5,6 => CTR => E9: 1
* DIS # H9: 4 => CTR => H9: 1,5
* DIS # G6: 1,5 => CTR => G6: 4,6,8
* DIS # H9: 1 => CTR => H9: 4,5
* CNT  19 HDP CHAINS /  48 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,B7,C6,C7,D8,E2,E4,F1,F2,F5,F9,G8,H5,I2,I3,I6,I9)
* ........1.......6.....819..259..8.738.437.2.937..92......839726632.47.989872..3..
* PAIR F1: 3,4 ROW 1
H1: 3,4,5,8                              # reduction candidate for 3,4
H1: 5,8                                  # 27 pairs
H1: 3,4                                  # 20 pairs
* PAIR E2: 2,5 BLK 2
E1: 2,5,6                                # reduction candidate for 2,5
E1: 6 => CTR
* .2.96...1.9..2..67...7819.2259.18.738.437.2.937..92......839726632147598987256314
* PAIR C6: 1,6 ROW 6
G6: 1,6,4,5,8                            # reduction candidate for 1,6
G6: 4,5,8 => CTR
* ........1.......6.....819..259..86738.4376259376592.14...839726632147.989872..3..
* PAIR RESTART
* PAIR H5: 1,5 COL H
H9: 1,5,4                                # reduction candidate for 1,5
H9: 4 => CTR
* ........1.......6.....819..259..8.738.437.219371.92685..5839726632547.989872..3..
* PAIR RESTART
* PAIR B7: 1,4 COL B
B2: 1,4,2,9                              # reduction candidate for 1,4
B2: 1,4 => CTR
* 79.62.5.1...95..6.5...819..259168473864375219371492685..5839726632547198987216354
B2: 2,9 => SOLVED
* 798623541123954867546781932259168473864375219371492685415839726632547198987216354
* DURATION: 0:00:08.546588  START: 02:33:21.835232  END: 02:33:30.381820 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060910-absurd-base-pr-001.dot
* REASONING
* DIS # E1: 6 => CTR => E1: 2,5
* DIS E1: 2,5 # G6: 4,5,8 => CTR => G6: 1,6
* DIS E1: 2,5 + G6: 1,6 # H9: 4 => CTR => H9: 1,5
* DIS E1: 2,5 + G6: 1,6 + H9: 1,5 # B2: 1,4 => CTR => B2: 2,9
* PRF E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9 => SOL
* STA E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9
* CNT   5 HDP CHAINS /   9 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Sep&YEAR=2006, 20060910, absurd

Solution

position: 798623541123954867546781932259168473864375219371492685415839726632547198987216354 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:

* INC # H1: 3,4 => UNS
* INC # H1: 5,8 => UNS
* INC # E1: 2,5 => UNS
* DIS # E1: 6 => CTR => E1: 2,5
* DIS # D6: 1,6 => CTR => D6: 4,5
* INC # D6: 4,5 => UNS
* INC # G6: 1,6 => UNS
* INC # D4: 1,6 => UNS
* DIS # D6: 1,6 => CTR => D6: 4,5
* INC # D6: 4,5 => UNS
* INC # G4: 1,6 => UNS
* INC # G4: 4 => UNS
* INC # E9: 1,6 => UNS
* DIS # E9: 5 => CTR => E9: 1,6
* DIS # D6: 5,6 => CTR => D6: 1,4
* INC # D6: 1,4 => UNS
* DIS # G6: 1,5 => CTR => G6: 4,6,8
* INC # G6: 4,6,8 => UNS
* DIS # H6: 1,5 => CTR => H6: 4,8
* INC # H6: 4,8 => UNS
* INC # H9: 1,5 => UNS
* DIS # H9: 4 => CTR => H9: 1,5
* DIS # G6: 4,5 => CTR => G6: 1,6,8
* INC # G6: 1,6,8 => UNS
* DIS # H6: 4,5 => CTR => H6: 1,8
* INC # H6: 1,8 => UNS
* INC # D6: 4,5 => UNS
* DIS # D6: 1,6 => CTR => D6: 4,5
* INC # A7: 1,4 => UNS
* DIS # A7: 5 => CTR => A7: 1,4
* DIS # B2: 1,4 => CTR => B2: 2,9
* INC # B2: 2,9 => UNS
* INC # A7: 1,5 => UNS
* INC # A7: 4 => UNS
* DIS # C2: 1,5 => CTR => C2: 3,8
* INC # C2: 3,8 => UNS
* INC # E9: 1,5 => UNS
* DIS # E9: 6 => CTR => E9: 1,5
* INC # D6: 1,5 => UNS
* INC # D6: 4,6 => UNS
* DIS # E9: 5,6 => CTR => E9: 1
* INC # E9: 1 => UNS
* INC # H9: 1,5 => UNS
* DIS # H9: 4 => CTR => H9: 1,5
* DIS # G6: 1,5 => CTR => G6: 4,6,8
* INC # G6: 4,6,8 => UNS
* INC # H9: 4,5 => UNS
* DIS # H9: 1 => CTR => H9: 4,5
* CNT  48 HDP CHAINS /  48 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 3,4 => UNS
* INC # H1: 5,8 => UNS
* INC # E1: 2,5 => UNS
* DIS # E1: 6 => CTR => E1: 2,5
* INC E1: 2,5 # G6: 1,6 => UNS
* DIS E1: 2,5 # G6: 4,5,8 => CTR => G6: 1,6
* INC E1: 2,5 + G6: 1,6 # H9: 1,5 => UNS
* DIS E1: 2,5 + G6: 1,6 # H9: 4 => CTR => H9: 1,5
* DIS E1: 2,5 + G6: 1,6 + H9: 1,5 # B2: 1,4 => CTR => B2: 2,9
* PRF E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9 => SOL
* STA E1: 2,5 + G6: 1,6 + H9: 1,5 + B2: 2,9
* CNT  10 HDP CHAINS /   9 HYP OPENED