Analysis of zz-www.sudokuoftheday.co.uk-20060407-absurd-base.sdk

Contents

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

level: medium

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

position: 4.....6.725.6....4....1..5.8..23.5..3.........97..4..27.9.2..3....7..49.68....... initial

Autosolve

position: 4.....6.725.6..9.497641..538..23.5..3.........97..43.2749.2..3....7..49.68..4.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B8: 2 => CTR => B8: 1,3
* DIS # F2: 7,8 => CTR => F2: 3
* DIS # F1: 3,5,9 => CTR => F1: 2,8
* DIS # H1: 2 => CTR => H1: 1,8
* DIS # C2: 3 => CTR => C2: 1,8
* DIS # H1: 1 => CTR => H1: 2,8
* DIS # B5: 1,6 => CTR => B5: 2
* DIS # C5: 1,4 => CTR => C5: 2,5
* PRF # C5: 1,5 => SOL
* PRF # D6: 8 => SOL
* PRF # I5: 8 => SOL
* PRF # F4: 1,9 => SOL
* DIS # H5: 6,8 => CTR => H5: 4,7
* PRF # E6: 5 => SOL
* DIS # C8: 1,5 => CTR => C8: 2,3
* PRF # I8: 1,5 => SOL
* DIS # G5: 7 => CTR => G5: 1,8
* DIS # I7: 1,5 => CTR => I7: 6,8
* PRF # I8: 1,5 => SOL
* DIS # D9: 1,5 => CTR => D9: 3,9
* DIS # F9: 1,5 => CTR => F9: 3,9
* CNT  21 HDP CHAINS /  55 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 # B8: 2 => CTR => B8: 1,3
* DIS B8: 1,3 # F2: 7,8 => CTR => F2: 3
* DIS B8: 1,3 + F2: 3 # F1: 5 => CTR => F1: 2,8
* PRF B8: 1,3 + F2: 3 + F1: 2,8 # D6: 8 => SOL
* STA B8: 1,3 + F2: 3 + F1: 2,8 + D6: 8
* CNT   4 HDP CHAINS /  11 HYP OPENED

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

Details

Positions

4.....6.725.6....4....1..5.8..23.5..3.........97..4..27.9.2..3....7..49.68....... initial
4.....6.725.6..9.497641..538..23.5..3.........97..43.2749.2..3....7..49.68..4.... autosolve
413592687258673914976418253864231579325967148197854362749125836532786491681349725 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B1: 1,3
E2: 7,8
F3: 2,8
H2: 1,8
G3: 2,8
B4: 1,6
C4: 1,4
A6: 1,5
I4: 1,9
H6: 6,8
A8: 1,5
G7: 1,8
G9: 2,7
H9: 2,7
I9: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H2: 1.. / H1 = 1  =>  0 pairs (X) / H2 = 1  => 16 pairs (_)
C2,H2: 1.. / C2 = 1  =>  0 pairs (X) / H2 = 1  => 16 pairs (_)
A6,D6: 1.. / A6 = 1  =>  0 pairs (*) / D6 = 1  =>  0 pairs (X)
A6,A8: 1.. / A6 = 1  =>  0 pairs (*) / A8 = 1  =>  0 pairs (X)
G5,G7: 1.. / G5 = 1  =>  0 pairs (*) / G7 = 1  =>  0 pairs (X)
F1,F3: 2.. / F1 = 2  => 26 pairs (_) / F3 = 2  =>  0 pairs (X)
H1,G3: 2.. / H1 = 2  =>  0 pairs (X) / G3 = 2  => 26 pairs (_)
B5,C5: 2.. / B5 = 2  => 16 pairs (_) / C5 = 2  =>  0 pairs (X)
B8,C8: 2.. / B8 = 2  =>  0 pairs (X) / C8 = 2  => 16 pairs (_)
G9,H9: 2.. / G9 = 2  =>  0 pairs (X) / H9 = 2  => 26 pairs (_)
F1,H1: 2.. / F1 = 2  => 26 pairs (_) / H1 = 2  =>  0 pairs (X)
F3,G3: 2.. / F3 = 2  =>  0 pairs (X) / G3 = 2  => 26 pairs (_)
B5,B8: 2.. / B5 = 2  => 16 pairs (_) / B8 = 2  =>  0 pairs (X)
C5,C8: 2.. / C5 = 2  =>  0 pairs (X) / C8 = 2  => 16 pairs (_)
G3,G9: 2.. / G3 = 2  => 26 pairs (_) / G9 = 2  =>  0 pairs (X)
H1,H9: 2.. / H1 = 2  =>  0 pairs (X) / H9 = 2  => 26 pairs (_)
C2,F2: 3.. / C2 = 3  =>  0 pairs (X) / F2 = 3  => 19 pairs (_)
B1,B8: 3.. / B1 = 3  =>  0 pairs (X) / B8 = 3  => 19 pairs (_)
D1,D9: 3.. / D1 = 3  =>  0 pairs (X) / D9 = 3  => 19 pairs (_)
C4,C5: 4.. / C4 = 4  => 15 pairs (_) / C5 = 4  =>  0 pairs (X)
H4,H5: 4.. / H4 = 4  =>  0 pairs (X) / H5 = 4  => 15 pairs (_)
C4,H4: 4.. / C4 = 4  => 15 pairs (_) / H4 = 4  =>  0 pairs (X)
C5,H5: 4.. / C5 = 4  =>  0 pairs (X) / H5 = 4  => 15 pairs (_)
C5,A6: 5.. / C5 = 5  =>  0 pairs (*) / A6 = 5  =>  0 pairs (X)
A6,A8: 5.. / A6 = 5  => 17 pairs (_) / A8 = 5  =>  0 pairs (*)
B4,B5: 6.. / B4 = 6  => 16 pairs (_) / B5 = 6  =>  0 pairs (X)
I7,I8: 6.. / I7 = 6  => 16 pairs (_) / I8 = 6  => 17 pairs (_)
E6,H6: 6.. / E6 = 6  =>  0 pairs (X) / H6 = 6  => 16 pairs (_)
F7,I7: 6.. / F7 = 6  => 17 pairs (_) / I7 = 6  => 16 pairs (_)
E2,F2: 7.. / E2 = 7  => 15 pairs (_) / F2 = 7  =>  0 pairs (X)
G9,H9: 7.. / G9 = 7  => 26 pairs (_) / H9 = 7  =>  0 pairs (X)
F4,H4: 7.. / F4 = 7  => 20 pairs (_) / H4 = 7  => 26 pairs (_)
E2,E5: 7.. / E2 = 7  => 15 pairs (_) / E5 = 7  =>  0 pairs (X)
G5,G9: 7.. / G5 = 7  =>  0 pairs (X) / G9 = 7  => 26 pairs (_)
C1,C2: 8.. / C1 = 8  => 18 pairs (_) / C2 = 8  => 19 pairs (_)
F3,G3: 8.. / F3 = 8  => 26 pairs (_) / G3 = 8  =>  0 pairs (X)
I4,I5: 9.. / I4 = 9  => 16 pairs (_) / I5 = 9  =>  0 pairs (X)
D9,F9: 9.. / D9 = 9  =>  0 pairs (X) / F9 = 9  => 16 pairs (_)
F4,I4: 9.. / F4 = 9  =>  0 pairs (X) / I4 = 9  => 16 pairs (_)
E1,E5: 9.. / E1 = 9  => 15 pairs (_) / E5 = 9  => 20 pairs (_)
* DURATION: 0:00:46.039146  START: 22:12:49.551754  END: 22:13:35.590900 2019-04-30
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B1,B4,C4,E2,F3,G3,G7,G9,H2,H6,H9,I4,I9)
* 4.....6.725.6..9.497641..538..23.5..3.........97..43.2749.2..3....7..49.68..4....
* PAIR B1: 1,3 BLK 1
C1: 1,3,8                                # reduction candidate for 1,3
C1: 1,3                                  # 19 pairs
C2: 1,3,8                                # reduction candidate for 1,3
C2: 1,3                                  # 18 pairs
* PAIR B1: 1,3 COL B
B8: 1,3,2                                # reduction candidate for 1,3
B8: 2 => CTR
* 43....6.725.6739.497641..538.423.5.93.2...148597184362749.218361237.8495685349721
B8: 1,3                                  # 16 pairs
* PAIR E2: 7,8 BLK 2
F2: 7,8,3                                # reduction candidate for 7,8
F2: 7,8 => CTR
* 418...6272536..91497641285386.23754932........97..43.2749.2.13..327..49.68..4.275
F2: 3                                    # 19 pairs
* PAIR E2: 7,8 COL E
E5: 7,8,5,6,9                            # reduction candidate for 7,8
E5: 7,8                                  # 18 pairs
E5: 5,6,9                                # 15 pairs
* PAIR F3: 2,8 BLK 2
F1: 2,8,3,5,9                            # reduction candidate for 2,8
F1: 3,5,9 => CTR
* 431...627258673914976412853814237569362...741597164382749.2.13.12578649.683941275
F1: 2,8                                  # 22 pairs
* PAIR H2: 1,8 BLK 3
H1: 1,8,2                                # reduction candidate for 1,8
H1: 2 => CTR
* 431...627258673914976412853814237569362...741597164382749.2.13.12578649.683941275
H1: 1,8                                  # 26 pairs
* PAIR H2: 1,8 ROW 2
C2: 1,8,3                                # reduction candidate for 1,8
C2: 3 => CTR
* 418...6272536..91497641285386.23754932........97..43.2749.2.13..327..49.68..4.275
C2: 1,8                                  # 19 pairs
* PAIR G3: 2,8 BLK 3
H1: 2,8,1                                # reduction candidate for 2,8
H1: 1 => CTR
* 438..26172516739849764182538.423.5793.2.67148.97..4362749.2.83...378.49.685349721
H1: 2,8                                  # 16 pairs
* PAIR B4: 1,6 BLK 4
B5: 1,6,2                                # reduction candidate for 1,6
B5: 1,6 => CTR
* 43....6.725.6739.497641..5381423.5.9362...148597184362749.21836123768495685349721
B5: 2                                    # 16 pairs
* PAIR B4: 1,6 ROW 4
F4: 1,6,7,9                              # reduction candidate for 1,6
F4: 1,6                                  # 26 pairs
F4: 7,9                                  # 16 pairs
* PAIR C4: 1,4 BLK 4
C5: 1,4,2,5                              # reduction candidate for 1,4
C5: 1,4 => CTR
* 41....6.725.6..91497641..5386123.549324...178597184362749.218361327.8495685.4.721
C5: 2,5                                  # 16 pairs
* PAIR A6: 1,5 BLK 4
C5: 1,5,2,4                              # reduction candidate for 1,5
C5: 1,5 => SOLVED
* 413592687258673914976418253864231579325967148197854362749125836532786491681349725
C5: 2,4                                  # 18 pairs
* PAIR A6: 1,5 ROW 6
D6: 1,5,8                                # reduction candidate for 1,5
D6: 8 => SOLVED
* 413592687258673914976418253864231579325967148197854362749125836532786491681349725
D6: 1,5                                  # 17 pairs
* PAIR I4: 1,9 BLK 6
I5: 1,9,8                                # reduction candidate for 1,9
I5: 8 => SOLVED
* 413592687258673914976418253864231579325967148197854362749125836532786491681349725
I5: 1,9                                  # 23 pairs
* PAIR I4: 1,9 ROW 4
F4: 1,9,6,7                              # reduction candidate for 1,9
F4: 1,9 => SOLVED
* 413592687258673914976418253864231579325967148197854362749125836532786491681349725
F4: 6,7                                  # 20 pairs
* PAIR H6: 6,8 BLK 6
H5: 6,8,4,7                              # reduction candidate for 6,8
H5: 6,8 => CTR
* 4.....6.725.6..9.497641..538..23.54.3.4...7..5971.43.2749.2.13.1.27..49.685.4....
H5: 4,7                                  # 16 pairs
* PAIR H6: 6,8 ROW 6
E6: 6,8,5                                # reduction candidate for 6,8
E6: 5 => SOLVED
* 413592687258673914976418253864231579325967148197854362749125836532786491681349725
E6: 6,8                                  # 17 pairs
* PAIR A8: 1,5 BLK 7
C8: 1,5,2,3                              # reduction candidate for 1,5
C8: 1,5 => CTR
* 4.....6.725.6..9.497641..538..23.5..3.2....4.5971.43.2749.2..3.1257.349.683.4....
C8: 2,3                                  # 16 pairs
C9: 1,5,3                                # reduction candidate for 1,5
C9: 1,5                                  # 20 pairs
* PAIR A8: 1,5 ROW 8
F8: 1,5,3,6,8                            # reduction candidate for 1,5
F8: 1,5                                  # 23 pairs
I8: 1,5,6,8                              # reduction candidate for 1,5
I8: 1,5 => SOLVED
* 413592687258673914976418253864231579325967148197854362749125836532786491681349725
I8: 6,8                                  # 16 pairs
* PAIR G7: 1,8 BLK 9
I7: 1,8,5,6                              # reduction candidate for 1,8
I7: 1,8                                  # 22 pairs
I8: 1,8,5,6                              # reduction candidate for 1,8
I8: 1,8                                  # 19 pairs
* PAIR G7: 1,8 ROW 7
D7: 1,8,5                                # reduction candidate for 1,8
D7: 1,8                                  # 18 pairs
F7: 1,8,5,6                              # reduction candidate for 1,8
F7: 1,8                                  # 18 pairs
* PAIR G7: 1,8 COL G
G5: 1,8,7                                # reduction candidate for 1,8
G5: 7 => CTR
* 431...627258673914976412853814237569362...741597164382749.2.13.12578649.683941275
G5: 1,8                                  # 26 pairs
* PAIR I9: 1,5 BLK 9
I7: 1,5,6,8                              # reduction candidate for 1,5
I7: 1,5 => CTR
* 4...926.725.6739.497641825386.2315.93...6.1.8.97854362749.2683.5..78.49668..4.72.
I7: 6,8                                  # 17 pairs
I8: 1,5,6,8                              # reduction candidate for 1,5
I8: 1,5 => SOLVED
* 413592687258673914976418253864231579325967148197854362749125836532786491681349725
I8: 6,8                                  # 16 pairs
* PAIR I9: 1,5 ROW 9
C9: 1,5,3                                # reduction candidate for 1,5
C9: 1,5                                  # 20 pairs
D9: 1,5,3,9                              # reduction candidate for 1,5
D9: 1,5 => CTR
* 4..3..6.72536..91497641..538..23.5..3..9......97..43.2749.2..3..327..49.68..4....
D9: 3,9                                  # 16 pairs
F9: 1,5,3,9                              # reduction candidate for 1,5
F9: 1,5 => CTR
* 4..3..6.72536..91497641..538..23.5..3.........97..43.2749.2..3..327..49.68.94....
F9: 3,9                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060407-absurd-base-pr-000.dot
* REASONING
* DIS # B8: 2 => CTR => B8: 1,3
* DIS # F2: 7,8 => CTR => F2: 3
* DIS # F1: 3,5,9 => CTR => F1: 2,8
* DIS # H1: 2 => CTR => H1: 1,8
* DIS # C2: 3 => CTR => C2: 1,8
* DIS # H1: 1 => CTR => H1: 2,8
* DIS # B5: 1,6 => CTR => B5: 2
* DIS # C5: 1,4 => CTR => C5: 2,5
* PRF # C5: 1,5 => SOL
* PRF # D6: 8 => SOL
* PRF # I5: 8 => SOL
* PRF # F4: 1,9 => SOL
* DIS # H5: 6,8 => CTR => H5: 4,7
* PRF # E6: 5 => SOL
* DIS # C8: 1,5 => CTR => C8: 2,3
* PRF # I8: 1,5 => SOL
* DIS # G5: 7 => CTR => G5: 1,8
* DIS # I7: 1,5 => CTR => I7: 6,8
* PRF # I8: 1,5 => SOL
* DIS # D9: 1,5 => CTR => D9: 3,9
* DIS # F9: 1,5 => CTR => F9: 3,9
* CNT  21 HDP CHAINS /  55 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B1,B4,C4,E2,F3,G3,G7,G9,H2,H6,H9,I4,I9)
* 4.....6.725.6..9.497641..538..23.5..3.........97..43.2749.2..3....7..49.68..4....
* PAIR B1: 1,3 BLK 1
C1: 1,3,8                                # reduction candidate for 1,3
C1: 1,3                                  # 19 pairs
C2: 1,3,8                                # reduction candidate for 1,3
C2: 1,3                                  # 18 pairs
* PAIR B1: 1,3 COL B
B8: 1,3,2                                # reduction candidate for 1,3
B8: 2 => CTR
* 43....6.725.6739.497641..538.423.5.93.2...148597184362749.218361237.8495685349721
* PAIR RESTART
* PAIR B1: 1,3 BLK 1
C1: 1,3,8                                # reduction candidate for 1,3
C1: 1,3                                  # 16 pairs
C2: 1,3,8                                # reduction candidate for 1,3
C2: 1,3                                  # 19 pairs
* PAIR E2: 7,8 BLK 2
F2: 7,8,3                                # reduction candidate for 7,8
F2: 7,8 => CTR
* 418...6272536..91497641285386.23754932........97..43.2749.2.13..327..49.68..4.275
* PAIR F3: 2,8 BLK 2
F1: 2,8,5                                # reduction candidate for 2,8
F1: 5 => CTR
* 413..562725867391497641285386.23.5.932........97..43.2749.2.13..327.149.681349275
* PAIR A6: 1,5 ROW 6
D6: 1,5,8                                # reduction candidate for 1,5
D6: 8 => SOLVED
* 413592687258673914976418253864231579325967148197854362749125836532786491681349725
* DURATION: 0:00:08.930144  START: 22:14:09.904751  END: 22:14:18.834895 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060407-absurd-base-pr-001.dot
* REASONING
* DIS # B8: 2 => CTR => B8: 1,3
* DIS B8: 1,3 # F2: 7,8 => CTR => F2: 3
* DIS B8: 1,3 + F2: 3 # F1: 5 => CTR => F1: 2,8
* PRF B8: 1,3 + F2: 3 + F1: 2,8 # D6: 8 => SOL
* STA B8: 1,3 + F2: 3 + F1: 2,8 + D6: 8
* CNT   4 HDP CHAINS /  11 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060407, absurd

Solution

position: 413592687258673914976418253864231579325967148197854362749125836532786491681349725 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 # C1: 1,3 => UNS
* INC # C2: 1,3 => UNS
* INC # B8: 1,3 => UNS
* DIS # B8: 2 => CTR => B8: 1,3
* DIS # F2: 7,8 => CTR => F2: 3
* INC # F2: 3 => UNS
* INC # E5: 7,8 => UNS
* INC # E5: 5,6,9 => UNS
* INC # F1: 2,8 => UNS
* DIS # F1: 3,5,9 => CTR => F1: 2,8
* INC # H1: 1,8 => UNS
* DIS # H1: 2 => CTR => H1: 1,8
* INC # C2: 1,8 => UNS
* DIS # C2: 3 => CTR => C2: 1,8
* INC # H1: 2,8 => UNS
* DIS # H1: 1 => CTR => H1: 2,8
* DIS # B5: 1,6 => CTR => B5: 2
* INC # B5: 2 => UNS
* INC # F4: 1,6 => UNS
* INC # F4: 7,9 => UNS
* DIS # C5: 1,4 => CTR => C5: 2,5
* INC # C5: 2,5 => UNS
* PRF # C5: 1,5 => SOL
* INC # C5: 2,4 => UNS
* INC # D6: 1,5 => UNS
* PRF # D6: 8 => SOL
* INC # I5: 1,9 => UNS
* PRF # I5: 8 => SOL
* PRF # F4: 1,9 => SOL
* INC # F4: 6,7 => UNS
* DIS # H5: 6,8 => CTR => H5: 4,7
* INC # H5: 4,7 => UNS
* INC # E6: 6,8 => UNS
* PRF # E6: 5 => SOL
* DIS # C8: 1,5 => CTR => C8: 2,3
* INC # C8: 2,3 => UNS
* INC # C9: 1,5 => UNS
* INC # F8: 1,5 => UNS
* PRF # I8: 1,5 => SOL
* INC # I8: 6,8 => UNS
* INC # I7: 1,8 => UNS
* INC # I8: 1,8 => UNS
* INC # D7: 1,8 => UNS
* INC # F7: 1,8 => UNS
* INC # G5: 1,8 => UNS
* DIS # G5: 7 => CTR => G5: 1,8
* DIS # I7: 1,5 => CTR => I7: 6,8
* INC # I7: 6,8 => UNS
* PRF # I8: 1,5 => SOL
* INC # I8: 6,8 => UNS
* INC # C9: 1,5 => UNS
* DIS # D9: 1,5 => CTR => D9: 3,9
* INC # D9: 3,9 => UNS
* DIS # F9: 1,5 => CTR => F9: 3,9
* INC # F9: 3,9 => UNS
* CNT  55 HDP CHAINS /  55 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,3 => UNS
* INC # C2: 1,3 => UNS
* INC # B8: 1,3 => UNS
* DIS # B8: 2 => CTR => B8: 1,3
* INC B8: 1,3 # C1: 1,3 => UNS
* INC B8: 1,3 # C2: 1,3 => UNS
* DIS B8: 1,3 # F2: 7,8 => CTR => F2: 3
* INC B8: 1,3 + F2: 3 # F1: 2,8 => UNS
* DIS B8: 1,3 + F2: 3 # F1: 5 => CTR => F1: 2,8
* INC B8: 1,3 + F2: 3 + F1: 2,8 # D6: 1,5 => UNS
* PRF B8: 1,3 + F2: 3 + F1: 2,8 # D6: 8 => SOL
* STA B8: 1,3 + F2: 3 + F1: 2,8 + D6: 8
* CNT  11 HDP CHAINS /  11 HYP OPENED