Analysis of zz-www.sudokuoftheday.co.uk-20060503-absurd-base.sdk

Contents

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

level: medium

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

position: 4.59....2.32.1.4............9...6..4367..92.8..1.8...397.........38..7...2...3... initial

Autosolve

position: 4.59....2.32.1.4....9.......98..6.74367..92.8.41.8...3974..1...1538.472.826..3.4. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G1: 1,8 => CTR => G1: 3,6
* DIS # H1: 1,8 => CTR => H1: 3,6
* DIS # E3: 5,6 => CTR => E3: 2,3,4
* DIS # H2: 5,6 => CTR => H2: 8,9
* DIS # D7: 5,6 => CTR => D7: 2
* DIS # F3: 5,8 => CTR => F3: 2
* DIS # H2: 6,9 => CTR => H2: 5,8
* DIS # E3: 2,5,6 => CTR => E3: 3,4
* DIS # E4: 3 => CTR => E4: 2,5
* PRF # D6: 2,5 => SOL
* DIS # D6: 7 => CTR => D6: 2,5
* DIS # F6: 2,5 => CTR => F6: 7
* PRF # F6: 7 => SOL
* DIS # G9: 1,5 => CTR => G9: 9
* DIS # H2: 6,9 => CTR => H2: 5,8
* DIS # E9: 9 => CTR => E9: 5,7
* DIS # D6: 2 => CTR => D6: 5,7
* DIS # H1: 3,8 => CTR => H1: 1,6
* DIS # H3: 3,8 => CTR => H3: 1,5,6
* DIS # D7: 5,6 => CTR => D7: 2
* CNT  20 HDP CHAINS /  46 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 # G1: 1,8 => CTR => G1: 3,6
* DIS G1: 3,6 # H1: 1,8 => CTR => H1: 3,6
* PRF G1: 3,6 + H1: 3,6 => SOL
* STA G1: 3,6 + H1: 3,6
* CNT   3 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

4.59....2.32.1.4............9...6..4367..92.8..1.8...397.........38..7...2...3... initial
4.59....2.32.1.4....9.......98..6.74367..92.8.41.8...3974..1...1538.472.826..3.4. autosolve
415978362732615489689432517598326174367149258241587693974261835153894726826753941 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (23)
B1: 1,8
A2: 6,7
A3: 6,7
B3: 1,8
F1: 7,8
D2: 5,6
F2: 5,8
D3: 3,4
A4: 2,5
A6: 2,5
D4: 1,3
D5: 1,4
E5: 4,5
G4: 1,5
H5: 1,5
G6: 6,9
H6: 6,9
E8: 6,9
D9: 5,7
G7: 3,8
H7: 3,8
I7: 5,6
I8: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,B3: 1.. / B1 = 1  => 22 pairs (_) / B3 = 1  =>  0 pairs (X)
D4,D5: 1.. / D4 = 1  =>  0 pairs (X) / D5 = 1  => 20 pairs (_)
G4,H5: 1.. / G4 = 1  => 20 pairs (_) / H5 = 1  =>  0 pairs (X)
G9,I9: 1.. / G9 = 1  =>  0 pairs (X) / I9 = 1  => 25 pairs (_)
D4,G4: 1.. / D4 = 1  =>  0 pairs (X) / G4 = 1  => 20 pairs (_)
D5,H5: 1.. / D5 = 1  => 20 pairs (_) / H5 = 1  =>  0 pairs (X)
I3,I9: 1.. / I3 = 1  =>  0 pairs (X) / I9 = 1  => 25 pairs (_)
E3,F3: 2.. / E3 = 2  =>  0 pairs (X) / F3 = 2  => 24 pairs (_)
A4,A6: 2.. / A4 = 2  => 27 pairs (_) / A6 = 2  => 20 pairs (_)
D7,E7: 2.. / D7 = 2  => 25 pairs (_) / E7 = 2  =>  0 pairs (X)
A4,E4: 2.. / A4 = 2  => 27 pairs (_) / E4 = 2  => 20 pairs (_)
D6,D7: 2.. / D6 = 2  =>  0 pairs (X) / D7 = 2  => 25 pairs (_)
F3,F6: 2.. / F3 = 2  => 24 pairs (_) / F6 = 2  =>  0 pairs (X)
D4,E4: 3.. / D4 = 3  => 20 pairs (_) / E4 = 3  =>  0 pairs (X)
G7,H7: 3.. / G7 = 3  =>  0 pairs (X) / H7 = 3  => 21 pairs (_)
D3,D4: 3.. / D3 = 3  =>  0 pairs (X) / D4 = 3  => 20 pairs (_)
D3,E3: 4.. / D3 = 4  => 20 pairs (_) / E3 = 4  =>  0 pairs (X)
D5,E5: 4.. / D5 = 4  =>  0 pairs (X) / E5 = 4  => 20 pairs (_)
D3,D5: 4.. / D3 = 4  => 20 pairs (_) / D5 = 4  =>  0 pairs (X)
E3,E5: 4.. / E3 = 4  =>  0 pairs (X) / E5 = 4  => 20 pairs (_)
A4,A6: 5.. / A4 = 5  => 20 pairs (_) / A6 = 5  => 27 pairs (_)
G4,H5: 5.. / G4 = 5  =>  0 pairs (X) / H5 = 5  => 20 pairs (_)
E5,H5: 5.. / E5 = 5  =>  0 pairs (X) / H5 = 5  => 20 pairs (_)
A2,A3: 6.. / A2 = 6  =>  0 pairs (X) / A3 = 6  => 23 pairs (_)
G6,H6: 6.. / G6 = 6  => 19 pairs (_) / H6 = 6  =>  0 pairs (X)
I7,I8: 6.. / I7 = 6  =>  0 pairs (X) / I8 = 6  => 27 pairs (_)
E8,I8: 6.. / E8 = 6  =>  0 pairs (X) / I8 = 6  => 27 pairs (_)
D2,D7: 6.. / D2 = 6  => 24 pairs (_) / D7 = 6  =>  0 pairs (X)
A2,A3: 7.. / A2 = 7  => 23 pairs (_) / A3 = 7  =>  0 pairs (X)
E1,F1: 7.. / E1 = 7  =>  0 pairs (*) / F1 = 7  =>  0 pairs (X)
I2,I3: 7.. / I2 = 7  =>  0 pairs (X) / I3 = 7  => 23 pairs (_)
D6,F6: 7.. / D6 = 7  =>  0 pairs (X) / F6 = 7  =>  0 pairs (_)
D9,E9: 7.. / D9 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
A2,I2: 7.. / A2 = 7  => 23 pairs (_) / I2 = 7  =>  0 pairs (X)
A3,I3: 7.. / A3 = 7  =>  0 pairs (X) / I3 = 7  => 23 pairs (_)
D6,D9: 7.. / D6 = 7  =>  0 pairs (X) / D9 = 7  =>  0 pairs (_)
E1,E9: 7.. / E1 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
F1,F6: 7.. / F1 = 7  =>  0 pairs (X) / F6 = 7  =>  0 pairs (_)
B1,B3: 8.. / B1 = 8  =>  0 pairs (X) / B3 = 8  => 22 pairs (_)
G7,H7: 8.. / G7 = 8  => 21 pairs (_) / H7 = 8  =>  0 pairs (X)
F2,H2: 8.. / F2 = 8  =>  0 pairs (X) / H2 = 8  => 19 pairs (_)
H2,I2: 9.. / H2 = 9  =>  0 pairs (X) / I2 = 9  => 19 pairs (_)
G6,H6: 9.. / G6 = 9  =>  0 pairs (X) / H6 = 9  => 19 pairs (_)
E8,E9: 9.. / E8 = 9  => 27 pairs (_) / E9 = 9  =>  0 pairs (X)
E8,I8: 9.. / E8 = 9  => 27 pairs (_) / I8 = 9  =>  0 pairs (X)
G6,G9: 9.. / G6 = 9  =>  0 pairs (X) / G9 = 9  => 19 pairs (_)
H2,H6: 9.. / H2 = 9  =>  0 pairs (X) / H6 = 9  => 19 pairs (_)
* DURATION: 0:01:18.051834  START: 22:51:08.424203  END: 22:52:26.476037 2019-04-30
* CP COUNT: (47)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A6,B1,B3,D2,D3,D4,D5,D9,E5,E8,F1,F2,G4,G6,G7,H5,H6,H7,I7,I8)
* 4.59....2.32.1.4....9.......98..6.74367..92.8.41.8...3974..1...1538.472.826..3.4.
* PAIR B1: 1,8 ROW 1
G1: 1,8,3,6                              # reduction candidate for 1,8
G1: 1,8 => CTR
* 4.5937.6273261.4.96.94....7.983.6174367149258.4178.693974261..5153894726826573941
G1: 3,6                                  # 24 pairs
H1: 1,8,3,6                              # reduction candidate for 1,8
H1: 1,8 => CTR
* 4.59.7..2.3261.4..6.9.....7.98..6.74367..92.8.4178..63974261..5153894726826573.41
H1: 3,6                                  # 24 pairs
* PAIR B3: 1,8 ROW 3
G3: 1,8,3,5,6                            # reduction candidate for 1,8
G3: 1,8                                  # 27 pairs
H3: 1,8,3,5,6                            # reduction candidate for 1,8
H3: 1,8                                  # 27 pairs
* PAIR D2: 5,6 BLK 2
E3: 5,6,2,3,4                            # reduction candidate for 5,6
E3: 5,6 => CTR
* 4.5937..2.32.184....94.2....983.6174367149258.41785..39742.1...1538.472.826573941
E3: 2,3,4                                # 23 pairs
* PAIR D2: 5,6 ROW 2
H2: 5,6,8,9                              # reduction candidate for 5,6
H2: 5,6 => CTR
* 4.5937.627326184596.94....7.983.6.74367..92.8.4178.693974261..5153894726826573941
H2: 8,9                                  # 24 pairs
* PAIR D2: 5,6 COL D
D7: 5,6,2                                # reduction candidate for 5,6
D7: 5,6 => CTR
* 4.5978..2.32.15489.89..2..7298..6.74367..92.8541287.939745218..1538.472.8267.3.4.
D7: 2                                    # 25 pairs
* PAIR F2: 5,8 BLK 2
F3: 5,8,2                                # reduction candidate for 5,8
F3: 5,8 => CTR
* 4.5937..27326154896.9428537298356174367149258541782..3974261..5153894726826573941
F3: 2                                    # 24 pairs
* PAIR F2: 5,8 ROW 2
H2: 5,8,6,9                              # reduction candidate for 5,8
H2: 6,9 => CTR
* 4.59.7..2.326184956.9.....7.98..6574367.59218541782963974261...1538.472.826573.4.
H2: 5,8                                  # 19 pairs
* PAIR D3: 3,4 BLK 2
E3: 3,4,2,5,6                            # reduction candidate for 3,4
E3: 2,5,6 => CTR
* 4.5937..2.3261.4.96.94..537.983561743671492585417826939742.1...1538.472.826573941
E3: 3,4                                  # 27 pairs
* PAIR A4: 2,5 ROW 4
E4: 2,5,3                                # reduction candidate for 2,5
E4: 3 => CTR
* 415978..2.326154896.9342...298136574367459218541287..3974.21...1538.472.826793145
E4: 2,5                                  # 20 pairs
* PAIR A6: 2,5 ROW 6
D6: 2,5,7                                # reduction candidate for 2,5
D6: 2,5 => SOLVED
* 415978362732615489689432517598326174367149258241587693974261835153894726826753941
D6: 7 => CTR
* 4.5937.627326154896.94....7.983.6174367149258.4178..93974261..5153894726826573941
F6: 2,5,7                                # reduction candidate for 2,5
F6: 2,5 => CTR
* 4.5937.627326154896.94....7.983.6174367149258.4178..93974261..5153894726826573941
F6: 7 => SOLVED
* 415978362732615489689432517598326174367149258241587693974261835153894726826753941
* PAIR E5: 4,5 COL E
E3: 4,5,2,3,6                            # reduction candidate for 4,5
E3: 4,5                                  # 30 pairs
E3: 2,3,6                                # 20 pairs
* PAIR G4: 1,5 COL G
G3: 1,5,3,6,8                            # reduction candidate for 1,5
G3: 1,5                                  # 21 pairs
G9: 1,5,9                                # reduction candidate for 1,5
G9: 1,5 => CTR
* 4.59.7..2.326184956.9.......98..6.74367..92.8.4178.9639742.1...1538.472.826573149
G9: 9                                    # 19 pairs
* PAIR H5: 1,5 COL H
H3: 1,5,3,6,8                            # reduction candidate for 1,5
H3: 1,5                                  # 24 pairs
H3: 3,6,8                                # 23 pairs
* PAIR H6: 6,9 COL H
H2: 6,9,5,8                              # reduction candidate for 6,9
H2: 6,9 => CTR
* 4.59.7..2.326184956.9.....7.98..6574367.59218541782963974261...1538.472.826573.4.
H2: 5,8                                  # 19 pairs
* PAIR D9: 5,7 BLK 8
E9: 5,7,9                                # reduction candidate for 5,7
E9: 9 => CTR
* 4.5978..2.32.15489.89..2..7.98..6.74367..92.8.41.87.93974..183.15389472.826..3.4.
E9: 5,7                                  # 27 pairs
* PAIR D9: 5,7 COL D
D6: 5,7,2                                # reduction candidate for 5,7
D6: 2 => CTR
* 4.5978..2.32.15489.89..2..7298..6.74367..92.8541287.939745218..1538.472.8267.3.4.
D6: 5,7                                  # 25 pairs
* PAIR G7: 3,8 COL G
G1: 3,8,1,6                              # reduction candidate for 3,8
G1: 3,8                                  # 24 pairs
G3: 3,8,1,5,6                            # reduction candidate for 3,8
G3: 3,8                                  # 25 pairs
* PAIR H7: 3,8 COL H
H1: 3,8,1,6                              # reduction candidate for 3,8
H1: 3,8 => CTR
* 4.59.7..2.326184..6.9.....7.98..6.74367..92.8.4178..63974261..5153894726826573.41
H1: 1,6                                  # 24 pairs
H3: 3,8,1,5,6                            # reduction candidate for 3,8
H3: 3,8 => CTR
* 4.5937..27326184596.94....7.983.6.74367..92.8.4178...3974261..5153894726826573.41
H3: 1,5,6                                # 23 pairs
* PAIR I7: 5,6 ROW 7
D7: 5,6,2                                # reduction candidate for 5,6
D7: 5,6 => CTR
* 4.5978..2.32.15489.89..2..7298..6.74367..92.8541287.939745218..1538.472.8267.3.4.
D7: 2                                    # 25 pairs
E7: 5,6,2                                # reduction candidate for 5,6
E7: 5,6                                  # 25 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060503-absurd-base-pr-000.dot
* REASONING
* DIS # G1: 1,8 => CTR => G1: 3,6
* DIS # H1: 1,8 => CTR => H1: 3,6
* DIS # E3: 5,6 => CTR => E3: 2,3,4
* DIS # H2: 5,6 => CTR => H2: 8,9
* DIS # D7: 5,6 => CTR => D7: 2
* DIS # F3: 5,8 => CTR => F3: 2
* DIS # H2: 6,9 => CTR => H2: 5,8
* DIS # E3: 2,5,6 => CTR => E3: 3,4
* DIS # E4: 3 => CTR => E4: 2,5
* PRF # D6: 2,5 => SOL
* DIS # D6: 7 => CTR => D6: 2,5
* DIS # F6: 2,5 => CTR => F6: 7
* PRF # F6: 7 => SOL
* DIS # G9: 1,5 => CTR => G9: 9
* DIS # H2: 6,9 => CTR => H2: 5,8
* DIS # E9: 9 => CTR => E9: 5,7
* DIS # D6: 2 => CTR => D6: 5,7
* DIS # H1: 3,8 => CTR => H1: 1,6
* DIS # H3: 3,8 => CTR => H3: 1,5,6
* DIS # D7: 5,6 => CTR => D7: 2
* CNT  20 HDP CHAINS /  46 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A4,A6,B1,B3,D2,D3,D4,D5,D9,E5,E8,F1,F2,G4,G6,G7,H5,H6,H7,I7,I8)
* 4.59....2.32.1.4....9.......98..6.74367..92.8.41.8...3974..1...1538.472.826..3.4.
* PAIR B1: 1,8 ROW 1
G1: 1,8,3,6                              # reduction candidate for 1,8
G1: 1,8 => CTR
* 4.5937.6273261.4.96.94....7.983.6174367149258.4178.693974261..5153894726826573941
H1: 1,8,3,6                              # reduction candidate for 1,8
H1: 1,8 => CTR
* 4.59.7..2.3261.4..6.9.....7.98..6.74367..92.8.4178..63974261..5153894726826573.41
H1: 3,6 => SOLVED
* 415978362732615489689432517598326174367149258241587693974261835153894726826753941
* DURATION: 0:00:02.747501  START: 22:53:08.487742  END: 22:53:11.235243 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060503-absurd-base-pr-001.dot
* REASONING
* DIS # G1: 1,8 => CTR => G1: 3,6
* DIS G1: 3,6 # H1: 1,8 => CTR => H1: 3,6
* PRF G1: 3,6 + H1: 3,6 => SOL
* STA G1: 3,6 + H1: 3,6
* CNT   3 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060503, absurd

Solution

position: 415978362732615489689432517598326174367149258241587693974261835153894726826753941 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 # G1: 1,8 => CTR => G1: 3,6
* INC # G1: 3,6 => UNS
* DIS # H1: 1,8 => CTR => H1: 3,6
* INC # H1: 3,6 => UNS
* INC # G3: 1,8 => UNS
* INC # H3: 1,8 => UNS
* DIS # E3: 5,6 => CTR => E3: 2,3,4
* INC # E3: 2,3,4 => UNS
* DIS # H2: 5,6 => CTR => H2: 8,9
* INC # H2: 8,9 => UNS
* DIS # D7: 5,6 => CTR => D7: 2
* INC # D7: 2 => UNS
* DIS # F3: 5,8 => CTR => F3: 2
* INC # F3: 2 => UNS
* INC # H2: 5,8 => UNS
* DIS # H2: 6,9 => CTR => H2: 5,8
* INC # E3: 3,4 => UNS
* DIS # E3: 2,5,6 => CTR => E3: 3,4
* INC # E4: 2,5 => UNS
* DIS # E4: 3 => CTR => E4: 2,5
* PRF # D6: 2,5 => SOL
* DIS # D6: 7 => CTR => D6: 2,5
* DIS # F6: 2,5 => CTR => F6: 7
* PRF # F6: 7 => SOL
* INC # E3: 4,5 => UNS
* INC # E3: 2,3,6 => UNS
* INC # G3: 1,5 => UNS
* DIS # G9: 1,5 => CTR => G9: 9
* INC # G9: 9 => UNS
* INC # H3: 1,5 => UNS
* INC # H3: 3,6,8 => UNS
* DIS # H2: 6,9 => CTR => H2: 5,8
* INC # H2: 5,8 => UNS
* INC # E9: 5,7 => UNS
* DIS # E9: 9 => CTR => E9: 5,7
* INC # D6: 5,7 => UNS
* DIS # D6: 2 => CTR => D6: 5,7
* INC # G1: 3,8 => UNS
* INC # G3: 3,8 => UNS
* DIS # H1: 3,8 => CTR => H1: 1,6
* INC # H1: 1,6 => UNS
* DIS # H3: 3,8 => CTR => H3: 1,5,6
* INC # H3: 1,5,6 => UNS
* DIS # D7: 5,6 => CTR => D7: 2
* INC # D7: 2 => UNS
* INC # E7: 5,6 => UNS
* CNT  46 HDP CHAINS /  46 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # G1: 1,8 => CTR => G1: 3,6
* DIS G1: 3,6 # H1: 1,8 => CTR => H1: 3,6
* PRF G1: 3,6 + H1: 3,6 => SOL
* STA G1: 3,6 + H1: 3,6
* CNT   3 HDP CHAINS /   2 HYP OPENED