Analysis of zz-www.sudokuoftheday.co.uk-20060801-absurd-base.sdk

Contents

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

level: medium

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

position: .5.....8.2......3...7...6.167...9..4.43...2.85.1....6.8...97.15.....1...1.5.84..6 initial

Autosolve

position: .5.....8.21....53...7...6.167...9154943...2785.1....6.8...97.157....18..1.5.847.6 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C2: 6,9 => SOL
* DIS # C2: 8 => CTR => C2: 6,9
* DIS # D1: 6,9 => CTR => D1: 1,2,7
* DIS # C2: 6 => CTR => C2: 8,9
* DIS # D3: 2,5 => CTR => D3: 8,9
* PRF # D2: 6,8 => SOL
* PRF # C2: 9 => SOL
* DIS # D3: 2,5 => CTR => D3: 8,9
* PRF # F3: 2,5 => SOL
* DIS # H3: 2 => CTR => H3: 4,9
* DIS # I1: 7,9 => CTR => I1: 2
* DIS # D4: 3 => CTR => D4: 2,8
* PRF # D4: 2,3 => SOL
* DIS # D4: 8 => CTR => D4: 2,3
* DIS # E8: 5,6 => CTR => E8: 2,3
* DIS # D5: 5,6 => CTR => D5: 1
* DIS # E2: 6 => CTR => E2: 4,7
* DIS # D4: 3 => CTR => D4: 2,8
* PRF # F3: 2,8 => SOL
* DIS # I8: 2 => CTR => I8: 3,9
* PRF # C8: 2,4 => SOL
* DIS # C8: 9 => CTR => C8: 2,4
* DIS # D7: 2,3 => CTR => D7: 6
* DIS # D8: 2,3 => CTR => D8: 5,6
* PRF # B9: 9 => SOL
* PRF # D4: 2,3 => SOL
* DIS # D4: 8 => CTR => D4: 2,3
* PRF # H8: 2,9 => SOL
* PRF # H3: 4 => SOL
* CNT  29 HDP CHAINS /  61 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* PRF # C2: 6,9 => SOL
* STA C2: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.5.....8.2......3...7...6.167...9..4.43...2.85.1....6.8...97.15.....1...1.5.84..6 initial
.5.....8.21....53...7...6.167...9154943...2785.1....6.8...97.157....18..1.5.847.6 autosolve
456713982219846537387952641678239154943165278521478369832697415764521893195384726 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (21)
A1: 3,4
C1: 6,9
A3: 3,4
B3: 8,9
F2: 6,8
E3: 2,5
G1: 4,9
I2: 7,9
C4: 2,8
B6: 2,8
E4: 2,3
F5: 5,6
D6: 4,7
E6: 4,7
F6: 2,8
G6: 3,9
I6: 3,9
C7: 2,4
D9: 2,3
G7: 3,4
H9: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,E1: 1.. / D1 = 1  =>  0 pairs (X) / E1 = 1  => 23 pairs (_)
D5,E5: 1.. / D5 = 1  => 23 pairs (_) / E5 = 1  =>  0 pairs (X)
D1,D5: 1.. / D1 = 1  =>  0 pairs (X) / D5 = 1  => 23 pairs (_)
E1,E5: 1.. / E1 = 1  => 23 pairs (_) / E5 = 1  =>  0 pairs (X)
I1,H3: 2.. / I1 = 2  => 26 pairs (_) / H3 = 2  =>  0 pairs (X)
C4,B6: 2.. / C4 = 2  =>  0 pairs (X) / B6 = 2  =>  0 pairs (_)
B6,F6: 2.. / B6 = 2  =>  0 pairs (*) / F6 = 2  =>  0 pairs (X)
I1,I8: 2.. / I1 = 2  => 26 pairs (_) / I8 = 2  =>  0 pairs (X)
A1,A3: 3.. / A1 = 3  => 25 pairs (_) / A3 = 3  =>  0 pairs (*)
F1,F3: 3.. / F1 = 3  =>  0 pairs (*) / F3 = 3  =>  0 pairs (X)
D4,E4: 3.. / D4 = 3  =>  0 pairs (X) / E4 = 3  => 21 pairs (_)
G6,I6: 3.. / G6 = 3  =>  0 pairs (*) / I6 = 3  =>  0 pairs (X)
G7,I8: 3.. / G7 = 3  => 25 pairs (_) / I8 = 3  =>  0 pairs (*)
A1,F1: 3.. / A1 = 3  => 25 pairs (_) / F1 = 3  =>  0 pairs (*)
A3,F3: 3.. / A3 = 3  =>  0 pairs (*) / F3 = 3  =>  0 pairs (X)
B9,D9: 3.. / B9 = 3  => 27 pairs (_) / D9 = 3  => 24 pairs (_)
E4,E8: 3.. / E4 = 3  => 21 pairs (_) / E8 = 3  =>  0 pairs (X)
G6,G7: 3.. / G6 = 3  =>  0 pairs (*) / G7 = 3  =>  0 pairs (X)
I6,I8: 3.. / I6 = 3  => 25 pairs (_) / I8 = 3  =>  0 pairs (*)
A1,A3: 4.. / A1 = 4  =>  0 pairs (*) / A3 = 4  =>  0 pairs (X)
D2,E2: 4.. / D2 = 4  => 20 pairs (_) / E2 = 4  => 19 pairs (_)
G1,H3: 4.. / G1 = 4  => 25 pairs (_) / H3 = 4  =>  0 pairs (*)
D6,E6: 4.. / D6 = 4  => 19 pairs (_) / E6 = 4  => 20 pairs (_)
C7,C8: 4.. / C7 = 4  => 25 pairs (_) / C8 = 4  =>  0 pairs (*)
G7,H8: 4.. / G7 = 4  =>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
A1,G1: 4.. / A1 = 4  =>  0 pairs (*) / G1 = 4  =>  0 pairs (X)
A3,H3: 4.. / A3 = 4  => 25 pairs (_) / H3 = 4  =>  0 pairs (*)
C7,G7: 4.. / C7 = 4  => 25 pairs (_) / G7 = 4  =>  0 pairs (*)
C8,H8: 4.. / C8 = 4  =>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
D2,D6: 4.. / D2 = 4  => 20 pairs (_) / D6 = 4  => 19 pairs (_)
E2,E6: 4.. / E2 = 4  => 19 pairs (_) / E6 = 4  => 20 pairs (_)
G1,G7: 4.. / G1 = 4  => 25 pairs (_) / G7 = 4  =>  0 pairs (*)
H3,H8: 4.. / H3 = 4  =>  0 pairs (*) / H8 = 4  =>  0 pairs (X)
D8,E8: 5.. / D8 = 5  => 22 pairs (_) / E8 = 5  =>  0 pairs (X)
F3,F5: 5.. / F3 = 5  =>  0 pairs (X) / F5 = 5  => 24 pairs (_)
C1,C2: 6.. / C1 = 6  => 22 pairs (_) / C2 = 6  =>  0 pairs (X)
B7,B8: 6.. / B7 = 6  =>  0 pairs (X) / B8 = 6  => 25 pairs (_)
B7,D7: 6.. / B7 = 6  =>  0 pairs (X) / D7 = 6  => 25 pairs (_)
I1,I2: 7.. / I1 = 7  =>  0 pairs (X) / I2 = 7  => 24 pairs (_)
D6,E6: 7.. / D6 = 7  => 20 pairs (_) / E6 = 7  => 19 pairs (_)
C2,B3: 8.. / C2 = 8  =>  0 pairs (X) / B3 = 8  =>  0 pairs (_)
C4,B6: 8.. / C4 = 8  =>  0 pairs (*) / B6 = 8  =>  0 pairs (X)
D4,F6: 8.. / D4 = 8  =>  0 pairs (X) / F6 = 8  =>  0 pairs (_)
C4,D4: 8.. / C4 = 8  =>  0 pairs (*) / D4 = 8  =>  0 pairs (X)
B6,F6: 8.. / B6 = 8  =>  0 pairs (X) / F6 = 8  =>  0 pairs (_)
B3,B6: 8.. / B3 = 8  =>  0 pairs (*) / B6 = 8  =>  0 pairs (X)
C2,C4: 8.. / C2 = 8  =>  0 pairs (X) / C4 = 8  =>  0 pairs (_)
G6,I6: 9.. / G6 = 9  => 25 pairs (_) / I6 = 9  =>  0 pairs (*)
B9,H9: 9.. / B9 = 9  =>  0 pairs (*) / H9 = 9  =>  0 pairs (X)
G1,G6: 9.. / G1 = 9  =>  0 pairs (*) / G6 = 9  =>  0 pairs (X)
* DURATION: 0:01:05.917351  START: 01:27:58.459991  END: 01:29:04.377342 2019-05-01
* CP COUNT: (50)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B3,B6,C1,C4,C7,D6,D9,E3,E4,E6,F2,F5,F6,G1,G6,G7,H9,I2,I6)
* .5.....8.21....53...7...6.167...9154943...2785.1....6.8...97.157....18..1.5.847.6
* PAIR C1: 6,9 BLK 1
C2: 6,9,8                                # reduction candidate for 6,9
C2: 6,9 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
C2: 8 => CTR
* .56..348.218..653..97...6.1672839154943..5278581..2.6.8.4.973157.9..18421.5.84796
* PAIR C1: 6,9 ROW 1
D1: 6,9,1,2,7                            # reduction candidate for 6,9
D1: 6,9 => CTR
* .5..1248721....5394.7.5362167..29154943165278521..896386..973157....18421.5.84796
D1: 1,2,7                                # 21 pairs
* PAIR B3: 8,9 BLK 1
C2: 8,9,6                                # reduction candidate for 8,9
C2: 6 => CTR
* .5.....8.216..853..87...6.1678..9154943...278521....6.8...97.157....18..1.5.847.6
C2: 8,9                                  # 22 pairs
* PAIR B3: 8,9 ROW 3
D3: 8,9,2,5                              # reduction candidate for 8,9
D3: 2,5 => CTR
* .5.71..82218946537.97..86416728391549431.5278581.72.6.8...97.157....18..1.5.847.6
D3: 8,9                                  # 24 pairs
* PAIR F2: 6,8 BLK 2
D2: 6,8,4,7,9                            # reduction candidate for 6,8
D2: 6,8 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
D2: 4,7,9                                # 21 pairs
* PAIR F2: 6,8 ROW 2
C2: 6,8,9                                # reduction candidate for 6,8
C2: 9 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
C2: 6,8                                  # 23 pairs
* PAIR E3: 2,5 BLK 2
D3: 2,5,8,9                              # reduction candidate for 2,5
D3: 2,5 => CTR
* .5.71..82218946537.97..86416728391549431.5278581.72.6.8...97.157....18..1.5.847.6
D3: 8,9                                  # 24 pairs
F3: 2,5,3,8                              # reduction candidate for 2,5
F3: 2,5 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
F3: 3,8                                  # 25 pairs
* PAIR E3: 2,5 COL E
E8: 2,5,3,6                              # reduction candidate for 2,5
E8: 3,6                                  # 27 pairs
E8: 2,5                                  # 24 pairs
* PAIR G1: 4,9 BLK 3
H3: 4,9,2                                # reduction candidate for 4,9
H3: 2 => CTR
* 35....48.21....53.4.7.53621672839154943..5278581..29638.4.973157.95618421.5384796
H3: 4,9                                  # 26 pairs
* PAIR I2: 7,9 BLK 3
I1: 7,9,2                                # reduction candidate for 7,9
I1: 7,9 => CTR
* 356..248.218..653.497.5362167...9154943..52785.1...9638.4.973157.95.18421.5.84796
I1: 2                                    # 26 pairs
* PAIR I2: 7,9 ROW 2
D2: 7,9,4,6,8                            # reduction candidate for 7,9
D2: 7,9                                  # 21 pairs
D2: 4,6,8                                # 21 pairs
* PAIR C4: 2,8 ROW 4
D4: 2,8,3                                # reduction candidate for 2,8
D4: 3 => CTR
* .5.....8.21....53...7...6.1678329154943...278521..8.6.8...97.157...318..135284796
D4: 2,8                                  # 21 pairs
* PAIR E4: 2,3 BLK 5
D4: 2,3,8                                # reduction candidate for 2,3
D4: 2,3 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
D4: 8 => CTR
* .5.....8.218..653..97..86.1672839154943..5278581..2.6.8.4.973157.9..18421.5.84796
* PAIR E4: 2,3 COL E
E8: 2,3,5,6                              # reduction candidate for 2,3
E8: 5,6 => CTR
* .56.2348.21....53...7...6.1672839154943...278581..2.6.8.4.973157.9..18421.5.84796
E8: 2,3                                  # 24 pairs
* PAIR F5: 5,6 BLK 5
D5: 5,6,1                                # reduction candidate for 5,6
D5: 5,6 => CTR
* .5.1...8.21....53...79..6.167.839154943.1.278581....6.8...97.157....18..1.5.847.6
D5: 1                                    # 23 pairs
E5: 5,6,1                                # reduction candidate for 5,6
E5: 5,6                                  # 23 pairs
* PAIR D6: 4,7 COL D
D2: 4,7,6,8,9                            # reduction candidate for 4,7
D2: 4,7                                  # 22 pairs
D2: 6,8,9                                # 20 pairs
* PAIR E6: 4,7 COL E
E2: 4,7,6                                # reduction candidate for 4,7
E2: 6 => CTR
* .5.....8.21.468537.87...6.1678..9154943..6278521....6.8...97.157....18..1.5.847.6
E2: 4,7                                  # 22 pairs
* PAIR F6: 2,8 BLK 5
D4: 2,8,3                                # reduction candidate for 2,8
D4: 3 => CTR
* .5.....8.21....53...7...6.1678329154943...278521..8.6.8...97.157...318..135284796
D4: 2,8                                  # 21 pairs
* PAIR F6: 2,8 COL F
F3: 2,8,3,5                              # reduction candidate for 2,8
F3: 2,8 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
F3: 3,5                                  # 22 pairs
* PAIR I6: 3,9 COL I
I8: 3,9,2                                # reduction candidate for 3,9
I8: 2 => CTR
* 356..248.218..653.497..362167...9154943..52785.1...9638.4.973157.9..18421.5.84796
I8: 3,9                                  # 26 pairs
* PAIR C7: 2,4 BLK 7
C8: 2,4,9                                # reduction candidate for 2,4
C8: 2,4 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
C8: 9 => CTR
* .56...48.218..653.497..36216728.9154943...2785.1....6.8.4.973157.9..18421.5.84796
* PAIR D9: 2,3 BLK 8
D7: 2,3,6                                # reduction candidate for 2,3
D7: 2,3 => CTR
* .5.....8.218..653..97528641672839154943...278581..2.6.86..97.157....18..1.5.847.6
D7: 6                                    # 25 pairs
D8: 2,3,5,6                              # reduction candidate for 2,3
D8: 2,3 => CTR
* .5.....8221....537..7.2.6.1672839154943...278581..2.6.824697315769.518..1.5.847.6
D8: 5,6                                  # 22 pairs
E8: 2,3,5,6                              # reduction candidate for 2,3
E8: 2,3                                  # 24 pairs
* PAIR D9: 2,3 ROW 9
B9: 2,3,9                                # reduction candidate for 2,3
B9: 9 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
B9: 2,3                                  # 26 pairs
* PAIR D9: 2,3 COL D
D4: 2,3,8                                # reduction candidate for 2,3
D4: 2,3 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
D4: 8 => CTR
* .5.....8.218..653..97..86.1672839154943..5278581..2.6.8.4.973157.9..18421.5.84796
* PAIR H9: 2,9 BLK 9
H8: 2,9,4                                # reduction candidate for 2,9
H8: 2,9 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
H8: 4                                    # 25 pairs
I8: 2,9,3                                # reduction candidate for 2,9
I8: 2,9                                  # 25 pairs
* PAIR H9: 2,9 ROW 9
B9: 2,9,3                                # reduction candidate for 2,9
B9: 3                                    # 27 pairs
B9: 2,9                                  # 24 pairs
* PAIR H9: 2,9 COL H
H3: 2,9,4                                # reduction candidate for 2,9
H3: 4 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
H3: 2,9                                  # 25 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060801-absurd-base-pr-000.dot
* REASONING
* PRF # C2: 6,9 => SOL
* DIS # C2: 8 => CTR => C2: 6,9
* DIS # D1: 6,9 => CTR => D1: 1,2,7
* DIS # C2: 6 => CTR => C2: 8,9
* DIS # D3: 2,5 => CTR => D3: 8,9
* PRF # D2: 6,8 => SOL
* PRF # C2: 9 => SOL
* DIS # D3: 2,5 => CTR => D3: 8,9
* PRF # F3: 2,5 => SOL
* DIS # H3: 2 => CTR => H3: 4,9
* DIS # I1: 7,9 => CTR => I1: 2
* DIS # D4: 3 => CTR => D4: 2,8
* PRF # D4: 2,3 => SOL
* DIS # D4: 8 => CTR => D4: 2,3
* DIS # E8: 5,6 => CTR => E8: 2,3
* DIS # D5: 5,6 => CTR => D5: 1
* DIS # E2: 6 => CTR => E2: 4,7
* DIS # D4: 3 => CTR => D4: 2,8
* PRF # F3: 2,8 => SOL
* DIS # I8: 2 => CTR => I8: 3,9
* PRF # C8: 2,4 => SOL
* DIS # C8: 9 => CTR => C8: 2,4
* DIS # D7: 2,3 => CTR => D7: 6
* DIS # D8: 2,3 => CTR => D8: 5,6
* PRF # B9: 9 => SOL
* PRF # D4: 2,3 => SOL
* DIS # D4: 8 => CTR => D4: 2,3
* PRF # H8: 2,9 => SOL
* PRF # H3: 4 => SOL
* CNT  29 HDP CHAINS /  61 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B3,B6,C1,C4,C7,D6,D9,E3,E4,E6,F2,F5,F6,G1,G6,G7,H9,I2,I6)
* .5.....8.21....53...7...6.167...9154943...2785.1....6.8...97.157....18..1.5.847.6
* PAIR C1: 6,9 BLK 1
C2: 6,9,8                                # reduction candidate for 6,9
C2: 6,9 => SOLVED
* 456713982219846537387952641678239154943165278521478369832697415764521893195384726
* DURATION: 0:00:01.794071  START: 01:29:52.723580  END: 01:29:54.517651 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060801-absurd-base-pr-001.dot
* REASONING
* PRF # C2: 6,9 => SOL
* STA C2: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060801, absurd

Solution

position: 456713982219846537387952641678239154943165278521478369832697415764521893195384726 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:

* PRF # C2: 6,9 => SOL
* DIS # C2: 8 => CTR => C2: 6,9
* DIS # D1: 6,9 => CTR => D1: 1,2,7
* INC # D1: 1,2,7 => UNS
* INC # C2: 8,9 => UNS
* DIS # C2: 6 => CTR => C2: 8,9
* INC # D3: 8,9 => UNS
* DIS # D3: 2,5 => CTR => D3: 8,9
* PRF # D2: 6,8 => SOL
* INC # D2: 4,7,9 => UNS
* INC # C2: 6,8 => UNS
* PRF # C2: 9 => SOL
* DIS # D3: 2,5 => CTR => D3: 8,9
* INC # D3: 8,9 => UNS
* PRF # F3: 2,5 => SOL
* INC # F3: 3,8 => UNS
* INC # E8: 2,5 => UNS
* INC # E8: 3,6 => UNS
* INC # H3: 4,9 => UNS
* DIS # H3: 2 => CTR => H3: 4,9
* DIS # I1: 7,9 => CTR => I1: 2
* INC # I1: 2 => UNS
* INC # D2: 7,9 => UNS
* INC # D2: 4,6,8 => UNS
* INC # D4: 2,8 => UNS
* DIS # D4: 3 => CTR => D4: 2,8
* PRF # D4: 2,3 => SOL
* DIS # D4: 8 => CTR => D4: 2,3
* INC # E8: 2,3 => UNS
* DIS # E8: 5,6 => CTR => E8: 2,3
* DIS # D5: 5,6 => CTR => D5: 1
* INC # D5: 1 => UNS
* INC # E5: 5,6 => UNS
* INC # D2: 4,7 => UNS
* INC # D2: 6,8,9 => UNS
* INC # E2: 4,7 => UNS
* DIS # E2: 6 => CTR => E2: 4,7
* INC # D4: 2,8 => UNS
* DIS # D4: 3 => CTR => D4: 2,8
* PRF # F3: 2,8 => SOL
* INC # F3: 3,5 => UNS
* INC # I8: 3,9 => UNS
* DIS # I8: 2 => CTR => I8: 3,9
* PRF # C8: 2,4 => SOL
* DIS # C8: 9 => CTR => C8: 2,4
* DIS # D7: 2,3 => CTR => D7: 6
* INC # D7: 6 => UNS
* DIS # D8: 2,3 => CTR => D8: 5,6
* INC # D8: 5,6 => UNS
* INC # E8: 2,3 => UNS
* INC # B9: 2,3 => UNS
* PRF # B9: 9 => SOL
* PRF # D4: 2,3 => SOL
* DIS # D4: 8 => CTR => D4: 2,3
* PRF # H8: 2,9 => SOL
* INC # H8: 4 => UNS
* INC # I8: 2,9 => UNS
* INC # B9: 2,9 => UNS
* INC # B9: 3 => UNS
* INC # H3: 2,9 => UNS
* PRF # H3: 4 => SOL
* CNT  61 HDP CHAINS /  61 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # C2: 6,9 => SOL
* STA C2: 6,9
* CNT   1 HDP CHAINS /   1 HYP OPENED