Analysis of zz-www.sudokuoftheday.co.uk-20060726-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: .....8....7...15...2.7...1...8.......15.8472.7....3..4...3...71..9..5....3..198.. initial

Autosolve

position: .51..8..7.7...15...2.756.1...8127....15.8472.7.25.318458.3.29711.9875...237.198.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 4,6 => CTR => A2: 8,9
* PRF # C2: 3,4 => SOL
* DIS # C2: 6 => CTR => C2: 3,4
* DIS # I2: 8,9 => CTR => I2: 2,3,6
* DIS # A4: 3,6 => CTR => A4: 4
* PRF # A4: 4 => SOL
* PRF # I5: 3,6 => SOL
* DIS # I5: 9 => CTR => I5: 3,6
* PRF # B4: 6,9 => SOL
* DIS # B4: 4 => CTR => B4: 6,9
* DIS # I5: 3 => CTR => I5: 6,9
* DIS # H4: 3,6 => CTR => H4: 5,9
* DIS # I4: 3,6 => CTR => I4: 5,9
* PRF # I5: 3,6 => SOL
* DIS # I5: 9 => CTR => I5: 3,6
* DIS # A4: 3,6 => CTR => A4: 4
* PRF # A4: 4 => SOL
* DIS # C2: 3 => CTR => C2: 4,6
* PRF # B4: 4,6 => SOL
* DIS # B4: 9 => CTR => B4: 4,6
* DIS # H9: 5 => CTR => H9: 4,6
* DIS # H9: 5,6 => CTR => H9: 4
* PRF # H9: 4 => SOL
* CNT  23 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: 4,6 => CTR => A2: 8,9
* PRF A2: 8,9 # C2: 3,4 => SOL
* STA A2: 8,9 + C2: 3,4
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

.....8....7...15...2.7...1...8.......15.8472.7....3..4...3...71..9..5....3..198.. initial
.51..8..7.7...15...2.756.1...8127....15.8472.7.25.318458.3.29711.9875...237.198.. autosolve
651438297874291563923756418468127359315984726792563184586342971149875632237619845 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
A3: 8,9
C3: 3,4
G3: 3,4
I3: 8,9
A5: 3,6
B6: 6,9
D5: 6,9
E6: 6,9
G4: 3,6
C7: 4,6
B8: 4,6
E7: 4,6
D9: 4,6
I9: 5,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,D2: 2.. / D1 = 2  => 15 pairs (_) / D2 = 2  => 15 pairs (_)
G1,I2: 2.. / G1 = 2  => 15 pairs (_) / I2 = 2  => 15 pairs (_)
G8,I8: 2.. / G8 = 2  => 15 pairs (_) / I8 = 2  => 15 pairs (_)
D1,G1: 2.. / D1 = 2  => 15 pairs (_) / G1 = 2  => 15 pairs (_)
D2,I2: 2.. / D2 = 2  => 15 pairs (_) / I2 = 2  => 15 pairs (_)
G1,G8: 2.. / G1 = 2  => 15 pairs (_) / G8 = 2  => 15 pairs (_)
I2,I8: 2.. / I2 = 2  => 15 pairs (_) / I8 = 2  => 15 pairs (_)
C2,C3: 3.. / C2 = 3  =>  0 pairs (X) / C3 = 3  => 13 pairs (_)
E1,E2: 3.. / E1 = 3  => 15 pairs (_) / E2 = 3  => 15 pairs (_)
A4,A5: 3.. / A4 = 3  =>  0 pairs (X) / A5 = 3  => 15 pairs (_)
C3,G3: 3.. / C3 = 3  => 13 pairs (_) / G3 = 3  =>  0 pairs (X)
A5,I5: 3.. / A5 = 3  => 15 pairs (_) / I5 = 3  =>  0 pairs (X)
A4,B4: 4.. / A4 = 4  =>  0 pairs (*) / B4 = 4  =>  0 pairs (X)
C7,B8: 4.. / C7 = 4  =>  0 pairs (X) / B8 = 4  =>  0 pairs (_)
E7,D9: 4.. / E7 = 4  =>  0 pairs (*) / D9 = 4  =>  0 pairs (X)
C3,G3: 4.. / C3 = 4  =>  0 pairs (X) / G3 = 4  => 13 pairs (_)
C7,E7: 4.. / C7 = 4  =>  0 pairs (X) / E7 = 4  =>  0 pairs (_)
D9,H9: 4.. / D9 = 4  =>  0 pairs (X) / H9 = 4  =>  0 pairs (_)
B4,B8: 4.. / B4 = 4  =>  0 pairs (X) / B8 = 4  =>  0 pairs (_)
H4,I4: 5.. / H4 = 5  => 13 pairs (_) / I4 = 5  =>  0 pairs (X)
H9,I9: 5.. / H9 = 5  =>  0 pairs (X) / I9 = 5  => 13 pairs (_)
H4,H9: 5.. / H4 = 5  => 13 pairs (_) / H9 = 5  =>  0 pairs (X)
I4,I9: 5.. / I4 = 5  =>  0 pairs (X) / I9 = 5  => 13 pairs (_)
D5,E6: 6.. / D5 = 6  =>  0 pairs (X) / E6 = 6  =>  0 pairs (_)
C7,B8: 6.. / C7 = 6  =>  0 pairs (*) / B8 = 6  =>  0 pairs (X)
E7,D9: 6.. / E7 = 6  =>  0 pairs (X) / D9 = 6  =>  0 pairs (_)
B6,E6: 6.. / B6 = 6  =>  0 pairs (X) / E6 = 6  =>  0 pairs (_)
C7,E7: 6.. / C7 = 6  =>  0 pairs (*) / E7 = 6  =>  0 pairs (X)
C2,C7: 6.. / C2 = 6  =>  0 pairs (X) / C7 = 6  =>  0 pairs (_)
D5,D9: 6.. / D5 = 6  =>  0 pairs (X) / D9 = 6  =>  0 pairs (_)
E6,E7: 6.. / E6 = 6  =>  0 pairs (*) / E7 = 6  =>  0 pairs (X)
A2,A3: 8.. / A2 = 8  => 13 pairs (_) / A3 = 8  =>  0 pairs (X)
I2,I3: 8.. / I2 = 8  =>  0 pairs (X) / I3 = 8  => 13 pairs (_)
A2,I2: 8.. / A2 = 8  => 13 pairs (_) / I2 = 8  =>  0 pairs (X)
A3,I3: 8.. / A3 = 8  =>  0 pairs (X) / I3 = 8  => 13 pairs (_)
B4,B6: 9.. / B4 = 9  =>  0 pairs (X) / B6 = 9  =>  0 pairs (_)
D5,E6: 9.. / D5 = 9  =>  0 pairs (*) / E6 = 9  =>  0 pairs (X)
A3,I3: 9.. / A3 = 9  => 13 pairs (_) / I3 = 9  =>  0 pairs (X)
D5,I5: 9.. / D5 = 9  =>  0 pairs (*) / I5 = 9  =>  0 pairs (X)
B6,E6: 9.. / B6 = 9  =>  0 pairs (*) / E6 = 9  =>  0 pairs (X)
* DURATION: 0:00:49.434727  START: 01:18:13.515773  END: 01:19:02.950500 2019-05-01
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B8,C3,C7,D5,D9,E6,E7,G3,G4,I3,I9)
* .51..8..7.7...15...2.756.1...8127....15.8472.7.25.318458.3.29711.9875...237.198..
* PAIR A3: 8,9 BLK 1
A2: 8,9,4,6                              # reduction candidate for 8,9
A2: 4,6 => CTR
* .51..8..7.7...15.882.756.19..8127.95.1598472.792563184586342971149875..2237.198..
A2: 8,9                                  # 16 pairs
* PAIR C3: 3,4 BLK 1
C2: 3,4,6                                # reduction candidate for 3,4
C2: 3,4 => SOLVED
* 651438297874291563923756418468127359315984726792563184586342971149875632237619845
C2: 6 => CTR
* .51..8..7.76..15...2375641...8127....15.8472.7.25.3184584362971169875.4.2374198..
* PAIR G3: 3,4 BLK 3
G1: 3,4,2,6                              # reduction candidate for 3,4
G1: 3,4                                  # 23 pairs
H1: 3,4,6,9                              # reduction candidate for 3,4
H1: 3,4                                  # 17 pairs
H2: 3,4,6,9                              # reduction candidate for 3,4
H2: 3,4                                  # 18 pairs
* PAIR G3: 3,4 COL G
G8: 3,4,2,6                              # reduction candidate for 3,4
G8: 3,4                                  # 18 pairs
G8: 2,6                                  # 15 pairs
* PAIR I3: 8,9 BLK 3
I2: 8,9,2,3,6                            # reduction candidate for 8,9
I2: 8,9 => CTR
* .51..82.7.762.15...2375641..481276.56159847237925631845843.2971169875..2237.198.6
I2: 2,3,6                                # 13 pairs
* PAIR A5: 3,6 BLK 4
A4: 3,6,4                                # reduction candidate for 3,6
A4: 3,6 => CTR
* .51..8..7.7...15...2.756.1..48127....15.8472.79256318458.3.29711.9875...237.198..
A4: 4 => SOLVED
* 651438297874291563923756418468127359315984726792563184586342971149875632237619845
* PAIR A5: 3,6 ROW 5
I5: 3,6,9                                # reduction candidate for 3,6
I5: 3,6 => SOLVED
* 651438297874291563923756418468127359315984726792563184586342971149875632237619845
I5: 9 => CTR
* .51..8..7.7...15...2.756.1...8127...3156847297625931845863429711.9875...237.198..
* PAIR B6: 6,9 BLK 4
B4: 6,9,4                                # reduction candidate for 6,9
B4: 6,9 => SOLVED
* 651438297874291563923756418468127359315984726792563184586342971149875632237619845
B4: 4 => CTR
* .51..8..7.7...15...2.756.1..48127....15.8472.79256318458.3.29711.9875...237.198..
* PAIR D5: 6,9 ROW 5
I5: 6,9,3                                # reduction candidate for 6,9
I5: 3 => CTR
* .51..8..7.7...15...2.756.1...8127....15984723792563184586342971149875...237619845
I5: 6,9                                  # 15 pairs
* PAIR G4: 3,6 BLK 6
H4: 3,6,5,9                              # reduction candidate for 3,6
H4: 3,6 => CTR
* .51..8..7.7...15...2.756.1...8127..5.15.847297.259318458.362971169875...237.198..
H4: 5,9                                  # 15 pairs
I4: 3,6,5,9                              # reduction candidate for 3,6
I4: 3,6 => CTR
* .51..8..7.7...15...2.756.1...8127.5..15.847297.259318458.362971169875...237.198..
I4: 5,9                                  # 15 pairs
I5: 3,6,9                                # reduction candidate for 3,6
I5: 3,6 => SOLVED
* 651438297874291563923756418468127359315984726792563184586342971149875632237619845
I5: 9 => CTR
* .51..8..7.7...15...2.756.1...8127...3156847297625931845863429711.9875...237.198..
* PAIR G4: 3,6 ROW 4
A4: 3,6,4                                # reduction candidate for 3,6
A4: 3,6 => CTR
* .51..8..7.7...15...2.756.1..48127....15.8472.79256318458.3.29711.9875...237.198..
A4: 4 => SOLVED
* 651438297874291563923756418468127359315984726792563184586342971149875632237619845
* PAIR G4: 3,6 COL G
G1: 3,6,2,4                              # reduction candidate for 3,6
G1: 3,6                                  # 15 pairs
G8: 3,6,2,4                              # reduction candidate for 3,6
G8: 3,6                                  # 15 pairs
* PAIR C7: 4,6 COL C
C2: 4,6,3                                # reduction candidate for 4,6
C2: 3 => CTR
* .51..8..7.73..15...2475631.4.81276..31568472976259318458.3.29711.9875...237.198..
C2: 4,6                                  # 13 pairs
* PAIR B8: 4,6 ROW 8
G8: 4,6,2,3                              # reduction candidate for 4,6
G8: 4,6                                  # 17 pairs
H8: 4,6,3                                # reduction candidate for 4,6
H8: 4,6                                  # 17 pairs
* PAIR B8: 4,6 COL B
B4: 4,6,9                                # reduction candidate for 4,6
B4: 4,6 => SOLVED
* 651438297874291563923756418468127359315984726792563184586342971149875632237619845
B4: 9 => CTR
* .51..8..7.7...15...2.756.1.498127...315.84729762593184586342971149875...2376198..
* PAIR D9: 4,6 ROW 9
H9: 4,6,5                                # reduction candidate for 4,6
H9: 5 => CTR
* .51..8..7.7...15...2.756.1...8127..5.1568472976259318458.3.29711.9875...237419856
H9: 4,6                                  # 13 pairs
* PAIR I9: 5,6 BLK 9
H9: 5,6,4                                # reduction candidate for 5,6
H9: 5,6 => CTR
* .51..8..7.7...15...2.756.1...8127....1568472976259318458.3.29711.9875...2374198..
H9: 4 => SOLVED
* 651438297874291563923756418468127359315984726792563184586342971149875632237619845
* PAIR I9: 5,6 COL I
I4: 5,6,3,9                              # reduction candidate for 5,6
I4: 5,6                                  # 19 pairs
I4: 3,9                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060726-absurd-base-pr-000.dot
* REASONING
* DIS # A2: 4,6 => CTR => A2: 8,9
* PRF # C2: 3,4 => SOL
* DIS # C2: 6 => CTR => C2: 3,4
* DIS # I2: 8,9 => CTR => I2: 2,3,6
* DIS # A4: 3,6 => CTR => A4: 4
* PRF # A4: 4 => SOL
* PRF # I5: 3,6 => SOL
* DIS # I5: 9 => CTR => I5: 3,6
* PRF # B4: 6,9 => SOL
* DIS # B4: 4 => CTR => B4: 6,9
* DIS # I5: 3 => CTR => I5: 6,9
* DIS # H4: 3,6 => CTR => H4: 5,9
* DIS # I4: 3,6 => CTR => I4: 5,9
* PRF # I5: 3,6 => SOL
* DIS # I5: 9 => CTR => I5: 3,6
* DIS # A4: 3,6 => CTR => A4: 4
* PRF # A4: 4 => SOL
* DIS # C2: 3 => CTR => C2: 4,6
* PRF # B4: 4,6 => SOL
* DIS # B4: 9 => CTR => B4: 4,6
* DIS # H9: 5 => CTR => H9: 4,6
* DIS # H9: 5,6 => CTR => H9: 4
* PRF # H9: 4 => SOL
* CNT  23 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,B6,B8,C3,C7,D5,D9,E6,E7,G3,G4,I3,I9)
* .51..8..7.7...15...2.756.1...8127....15.8472.7.25.318458.3.29711.9875...237.198..
* PAIR A3: 8,9 BLK 1
A2: 8,9,4,6                              # reduction candidate for 8,9
A2: 4,6 => CTR
* .51..8..7.7...15.882.756.19..8127.95.1598472.792563184586342971149875..2237.198..
* PAIR C3: 3,4 BLK 1
C2: 3,4,6                                # reduction candidate for 3,4
C2: 3,4 => SOLVED
* 651438297874291563923756418468127359315984726792563184586342971149875632237619845
* DURATION: 0:00:02.908419  START: 01:19:31.749721  END: 01:19:34.658140 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060726-absurd-base-pr-001.dot
* REASONING
* DIS # A2: 4,6 => CTR => A2: 8,9
* PRF A2: 8,9 # C2: 3,4 => SOL
* STA A2: 8,9 + C2: 3,4
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060726, absurd

Solution

position: 651438297874291563923756418468127359315984726792563184586342971149875632237619845 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 # A2: 8,9 => UNS
* DIS # A2: 4,6 => CTR => A2: 8,9
* PRF # C2: 3,4 => SOL
* DIS # C2: 6 => CTR => C2: 3,4
* INC # G1: 3,4 => UNS
* INC # H1: 3,4 => UNS
* INC # H2: 3,4 => UNS
* INC # G8: 3,4 => UNS
* INC # G8: 2,6 => UNS
* DIS # I2: 8,9 => CTR => I2: 2,3,6
* INC # I2: 2,3,6 => UNS
* DIS # A4: 3,6 => CTR => A4: 4
* PRF # A4: 4 => SOL
* PRF # I5: 3,6 => SOL
* DIS # I5: 9 => CTR => I5: 3,6
* PRF # B4: 6,9 => SOL
* DIS # B4: 4 => CTR => B4: 6,9
* INC # I5: 6,9 => UNS
* DIS # I5: 3 => CTR => I5: 6,9
* DIS # H4: 3,6 => CTR => H4: 5,9
* INC # H4: 5,9 => UNS
* DIS # I4: 3,6 => CTR => I4: 5,9
* INC # I4: 5,9 => UNS
* PRF # I5: 3,6 => SOL
* DIS # I5: 9 => CTR => I5: 3,6
* DIS # A4: 3,6 => CTR => A4: 4
* PRF # A4: 4 => SOL
* INC # G1: 3,6 => UNS
* INC # G8: 3,6 => UNS
* INC # C2: 4,6 => UNS
* DIS # C2: 3 => CTR => C2: 4,6
* INC # G8: 4,6 => UNS
* INC # H8: 4,6 => UNS
* PRF # B4: 4,6 => SOL
* DIS # B4: 9 => CTR => B4: 4,6
* INC # H9: 4,6 => UNS
* DIS # H9: 5 => CTR => H9: 4,6
* DIS # H9: 5,6 => CTR => H9: 4
* PRF # H9: 4 => SOL
* INC # I4: 5,6 => UNS
* INC # I4: 3,9 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 8,9 => UNS
* DIS # A2: 4,6 => CTR => A2: 8,9
* PRF A2: 8,9 # C2: 3,4 => SOL
* STA A2: 8,9 + C2: 3,4
* CNT   3 HDP CHAINS /   3 HYP OPENED