Analysis of zz-www.sudokuoftheday.co.uk-20060711-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: ..1..2..574..........5..8.33.......6.6..1...4..7..6.2..........5182.......69.354. initial

Autosolve

position: 831..24.5745......6295..8.33.4.2...6962.1...41.74.6.2.493......5182.....276983541 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E1: 6,7 => CTR => E1: 9
* DIS # H1: 9 => CTR => H1: 6,7
* DIS # D7: 6,7 => CTR => D7: 1
* PRF # F3: 4,7 => SOL
* DIS # E8: 4,7 => CTR => E8: 6
* DIS # G2: 2,9 => CTR => G2: 1,6
* DIS # F3: 4 => CTR => F3: 1,7
* DIS # F4: 5,8 => CTR => F4: 7,9
* DIS # F4: 7,8 => CTR => F4: 5,9
* DIS # D5: 7,8 => CTR => D5: 3
* DIS # D5: 8 => CTR => D5: 3,7
* DIS # E6: 3,9 => CTR => E6: 5
* PRF # E6: 5 => SOL
* DIS # G8: 6 => CTR => G8: 3,9
* DIS # E8: 4,7 => CTR => E8: 6
* PRF # F3: 4,7 => SOL
* DIS # G2: 1,9 => CTR => G2: 2,6
* CNT  17 HDP CHAINS /  36 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: 6,7 => CTR => E1: 9
* DIS E1: 9 # D7: 6,7 => CTR => D7: 1
* PRF E1: 9 + D7: 1 => SOL
* STA E1: 9 + D7: 1
* CNT   3 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

..1..2..574..........5..8.33.......6.6..1...4..7..6.2..........5182.......69.354. initial
831..24.5745......6295..8.33.4.2...6962.1...41.74.6.2.493......5182.....276983541 autosolve
831692475745831692629547813354729186962318754187456329493175268518264937276983541 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
D1: 6,7
E3: 4,7
I2: 2,9
H3: 1,7
B4: 5,8
B6: 5,8
D4: 7,8
G5: 3,7
G6: 3,9
I6: 8,9
F8: 4,7
G7: 2,6
H7: 6,8
I8: 7,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,H4: 1.. / G4 = 1  => 15 pairs (_) / H4 = 1  =>  0 pairs (X)
D7,F7: 1.. / D7 = 1  => 17 pairs (_) / F7 = 1  =>  0 pairs (X)
F3,H3: 1.. / F3 = 1  => 17 pairs (_) / H3 = 1  =>  0 pairs (*)
D2,D7: 1.. / D2 = 1  =>  0 pairs (X) / D7 = 1  => 17 pairs (_)
G2,G4: 1.. / G2 = 1  =>  0 pairs (X) / G4 = 1  => 15 pairs (_)
G2,I2: 2.. / G2 = 2  =>  0 pairs (X) / I2 = 2  => 13 pairs (_)
G7,I7: 2.. / G7 = 2  => 13 pairs (_) / I7 = 2  =>  0 pairs (X)
G2,G7: 2.. / G2 = 2  =>  0 pairs (X) / G7 = 2  => 13 pairs (_)
I2,I7: 2.. / I2 = 2  => 13 pairs (_) / I7 = 2  =>  0 pairs (X)
D2,E2: 3.. / D2 = 3  =>  0 pairs (X) / E2 = 3  => 17 pairs (_)
D5,E6: 3.. / D5 = 3  => 17 pairs (_) / E6 = 3  =>  0 pairs (X)
G8,H8: 3.. / G8 = 3  =>  0 pairs (X) / H8 = 3  => 16 pairs (_)
E6,G6: 3.. / E6 = 3  =>  0 pairs (X) / G6 = 3  => 17 pairs (_)
D2,D5: 3.. / D2 = 3  =>  0 pairs (X) / D5 = 3  => 17 pairs (_)
E2,E6: 3.. / E2 = 3  => 17 pairs (_) / E6 = 3  =>  0 pairs (X)
H5,H8: 3.. / H5 = 3  =>  0 pairs (X) / H8 = 3  => 16 pairs (_)
E3,F3: 4.. / E3 = 4  => 14 pairs (_) / F3 = 4  =>  0 pairs (X)
E8,F8: 4.. / E8 = 4  =>  0 pairs (X) / F8 = 4  => 14 pairs (_)
E3,E8: 4.. / E3 = 4  => 14 pairs (_) / E8 = 4  =>  0 pairs (X)
F3,F8: 4.. / F3 = 4  =>  0 pairs (X) / F8 = 4  => 14 pairs (_)
B4,B6: 5.. / B4 = 5  =>  0 pairs (*) / B6 = 5  =>  0 pairs (X)
H4,H5: 5.. / H4 = 5  =>  0 pairs (X) / H5 = 5  => 18 pairs (_)
E7,F7: 5.. / E7 = 5  =>  0 pairs (X) / F7 = 5  =>  0 pairs (_)
F5,H5: 5.. / F5 = 5  =>  0 pairs (X) / H5 = 5  => 18 pairs (_)
B6,E6: 5.. / B6 = 5  =>  0 pairs (X) / E6 = 5  =>  0 pairs (_)
E6,E7: 5.. / E6 = 5  =>  0 pairs (*) / E7 = 5  =>  0 pairs (X)
H1,H3: 7.. / H1 = 7  =>  0 pairs (*) / H3 = 7  =>  0 pairs (X)
G4,G5: 7.. / G4 = 7  =>  0 pairs (X) / G5 = 7  => 16 pairs (_)
I7,I8: 7.. / I7 = 7  =>  0 pairs (X) / I8 = 7  => 21 pairs (_)
D2,F2: 8.. / D2 = 8  => 19 pairs (_) / F2 = 8  => 17 pairs (_)
B4,B6: 8.. / B4 = 8  =>  0 pairs (X) / B6 = 8  =>  0 pairs (_)
H7,I7: 8.. / H7 = 8  =>  0 pairs (X) / I7 = 8  =>  0 pairs (_)
B6,I6: 8.. / B6 = 8  =>  0 pairs (*) / I6 = 8  =>  0 pairs (X)
I6,I7: 8.. / I6 = 8  =>  0 pairs (X) / I7 = 8  =>  0 pairs (_)
F4,E6: 9.. / F4 = 9  => 17 pairs (_) / E6 = 9  =>  0 pairs (X)
E1,H1: 9.. / E1 = 9  => 19 pairs (_) / H1 = 9  =>  0 pairs (X)
F2,F4: 9.. / F2 = 9  =>  0 pairs (X) / F4 = 9  => 17 pairs (_)
* DURATION: 0:00:46.394921  START: 00:36:34.176218  END: 00:37:20.571139 2019-05-01
* CP COUNT: (37)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,D1,D4,E3,F8,G5,G6,G7,H3,H7,I2,I6,I8)
* 831..24.5745......6295..8.33.4.2...6962.1...41.74.6.2.493......5182.....276983541
* PAIR D1: 6,7 BLK 2
E1: 6,7,9                                # reduction candidate for 6,7
E1: 6,7 => CTR
* 831672495745...6126295418733.4.2.1.6962.1.7.4187456.2.4931.72.8518264.37276983541
E1: 9                                    # 19 pairs
* PAIR D1: 6,7 ROW 1
H1: 6,7,9                                # reduction candidate for 6,7
H1: 9 => CTR
* 831672495745...6126295418733.4.2.1.6962.1.7.4187456.2.4931.72.8518264.37276983541
H1: 6,7                                  # 19 pairs
* PAIR D1: 6,7 COL D
D7: 6,7,1                                # reduction candidate for 6,7
D7: 6,7 => CTR
* 831..24.5745138...6295..8133.4.291.696231.784187456.2.493......5182.....276983541
D7: 1                                    # 17 pairs
* PAIR E3: 4,7 BLK 2
F3: 4,7,1                                # reduction candidate for 4,7
F3: 4,7 => SOLVED
* 831692475745831692629547813354729186962318754187456329493175268518264937276983541
F3: 1                                    # 17 pairs
* PAIR E3: 4,7 COL E
E8: 4,7,6                                # reduction candidate for 4,7
E8: 4,7 => CTR
* 831..24.5745.....26295..8.338472...6962.1.7.41574.6.28493.512875182....9276983541
E8: 6                                    # 21 pairs
* PAIR I2: 2,9 BLK 3
G2: 2,9,1,6                              # reduction candidate for 2,9
G2: 2,9 => CTR
* 8316.24.5745....6.6295..81338472.1.6962.1.7.41574.6.28493157682518264...276983541
G2: 1,6                                  # 15 pairs
* PAIR H3: 1,7 ROW 3
F3: 1,7,4                                # reduction candidate for 1,7
F3: 4 => CTR
* 831692475745.3...2629574813384729156962.1.7.41.74.6.28493...287518247..9276983541
F3: 1,7                                  # 14 pairs
* PAIR B4: 5,8 ROW 4
F4: 5,8,7,9                              # reduction candidate for 5,8
F4: 5,8 => CTR
* 831..2495745839.626295.18.33.4.2...6962.1...41.7496328493.5.2875182...39276983541
F4: 7,9                                  # 15 pairs
H4: 5,8,1,9                              # reduction candidate for 5,8
H4: 5,8                                  # 22 pairs
* PAIR D4: 7,8 BLK 5
F4: 7,8,5,9                              # reduction candidate for 7,8
F4: 7,8 => CTR
* 831..2495745839.626295.18.33.4.2...6962.1...41.7496328493.5.2875182...39276983541
F4: 5,9                                  # 15 pairs
D5: 7,8,3                                # reduction candidate for 7,8
D5: 7,8 => CTR
* 831..24.57453.8...6295.18733.4.29..6962.1...41.7436928493157.82518264397276983541
D5: 3                                    # 17 pairs
F5: 7,8,5                                # reduction candidate for 7,8
F5: 7,8                                  # 18 pairs
* PAIR G5: 3,7 ROW 5
D5: 3,7,8                                # reduction candidate for 3,7
D5: 8 => CTR
* 831..24.57453.8...6295.18733.4.29..696281...41.7436928493157.82518264397276983541
D5: 3,7                                  # 18 pairs
* PAIR G6: 3,9 ROW 6
E6: 3,9,5                                # reduction candidate for 3,9
E6: 3,9 => CTR
* 8316.24.5745...2696295418.338472...6962.1.7.41574.6.28493157682518264..7276983541
E6: 5 => SOLVED
* 831692475745831692629547813354729186962318754187456329493175268518264937276983541
* PAIR G6: 3,9 COL G
G8: 3,9,6                                # reduction candidate for 3,9
G8: 6 => CTR
* 831..24.5745.....26295..8.338472...6962.1.7541574.6328493.512875182..639276983541
G8: 3,9                                  # 17 pairs
* PAIR I6: 8,9 BLK 6
H4: 8,9,1,5                              # reduction candidate for 8,9
H4: 8,9                                  # 18 pairs
H4: 1,5                                  # 15 pairs
* PAIR F8: 4,7 BLK 8
E8: 4,7,6                                # reduction candidate for 4,7
E8: 4,7 => CTR
* 831..24.5745.....26295..8.338472...6962.1.7.41574.6.28493.512875182....9276983541
E8: 6                                    # 21 pairs
* PAIR F8: 4,7 COL F
F3: 4,7,1                                # reduction candidate for 4,7
F3: 4,7 => SOLVED
* 831692475745831692629547813354729186962318754187456329493175268518264937276983541
F3: 1                                    # 17 pairs
* PAIR G7: 2,6 COL G
G2: 2,6,1,9                              # reduction candidate for 2,6
G2: 1,9 => CTR
* 831..24.5745.....26295..8.338472...6962.1.7541574.6328493.512875182..639276983541
G2: 2,6                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060711-absurd-base-pr-000.dot
* REASONING
* DIS # E1: 6,7 => CTR => E1: 9
* DIS # H1: 9 => CTR => H1: 6,7
* DIS # D7: 6,7 => CTR => D7: 1
* PRF # F3: 4,7 => SOL
* DIS # E8: 4,7 => CTR => E8: 6
* DIS # G2: 2,9 => CTR => G2: 1,6
* DIS # F3: 4 => CTR => F3: 1,7
* DIS # F4: 5,8 => CTR => F4: 7,9
* DIS # F4: 7,8 => CTR => F4: 5,9
* DIS # D5: 7,8 => CTR => D5: 3
* DIS # D5: 8 => CTR => D5: 3,7
* DIS # E6: 3,9 => CTR => E6: 5
* PRF # E6: 5 => SOL
* DIS # G8: 6 => CTR => G8: 3,9
* DIS # E8: 4,7 => CTR => E8: 6
* PRF # F3: 4,7 => SOL
* DIS # G2: 1,9 => CTR => G2: 2,6
* CNT  17 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B6,D1,D4,E3,F8,G5,G6,G7,H3,H7,I2,I6,I8)
* 831..24.5745......6295..8.33.4.2...6962.1...41.74.6.2.493......5182.....276983541
* PAIR D1: 6,7 BLK 2
E1: 6,7,9                                # reduction candidate for 6,7
E1: 6,7 => CTR
* 831672495745...6126295418733.4.2.1.6962.1.7.4187456.2.4931.72.8518264.37276983541
* PAIR D1: 6,7 COL D
D7: 6,7,1                                # reduction candidate for 6,7
D7: 6,7 => CTR
* 831.924.5745138...6295..8133.4.291.696231.784187456.2.493......5182.....276983541
D7: 1 => SOLVED
* 831692475745831692629547813354729186962318754187456329493175268518264937276983541
* DURATION: 0:00:03.686184  START: 00:37:45.302344  END: 00:37:48.988528 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060711-absurd-base-pr-001.dot
* REASONING
* DIS # E1: 6,7 => CTR => E1: 9
* DIS E1: 9 # D7: 6,7 => CTR => D7: 1
* PRF E1: 9 + D7: 1 => SOL
* STA E1: 9 + D7: 1
* CNT   3 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060711, absurd

Solution

position: 831692475745831692629547813354729186962318754187456329493175268518264937276983541 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 # E1: 6,7 => CTR => E1: 9
* INC # E1: 9 => UNS
* INC # H1: 6,7 => UNS
* DIS # H1: 9 => CTR => H1: 6,7
* DIS # D7: 6,7 => CTR => D7: 1
* INC # D7: 1 => UNS
* PRF # F3: 4,7 => SOL
* INC # F3: 1 => UNS
* DIS # E8: 4,7 => CTR => E8: 6
* INC # E8: 6 => UNS
* DIS # G2: 2,9 => CTR => G2: 1,6
* INC # G2: 1,6 => UNS
* INC # F3: 1,7 => UNS
* DIS # F3: 4 => CTR => F3: 1,7
* DIS # F4: 5,8 => CTR => F4: 7,9
* INC # F4: 7,9 => UNS
* INC # H4: 5,8 => UNS
* DIS # F4: 7,8 => CTR => F4: 5,9
* INC # F4: 5,9 => UNS
* DIS # D5: 7,8 => CTR => D5: 3
* INC # D5: 3 => UNS
* INC # F5: 7,8 => UNS
* INC # D5: 3,7 => UNS
* DIS # D5: 8 => CTR => D5: 3,7
* DIS # E6: 3,9 => CTR => E6: 5
* PRF # E6: 5 => SOL
* INC # G8: 3,9 => UNS
* DIS # G8: 6 => CTR => G8: 3,9
* INC # H4: 8,9 => UNS
* INC # H4: 1,5 => UNS
* DIS # E8: 4,7 => CTR => E8: 6
* INC # E8: 6 => UNS
* PRF # F3: 4,7 => SOL
* INC # F3: 1 => UNS
* INC # G2: 2,6 => UNS
* DIS # G2: 1,9 => CTR => G2: 2,6
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # E1: 6,7 => CTR => E1: 9
* DIS E1: 9 # D7: 6,7 => CTR => D7: 1
* PRF E1: 9 + D7: 1 => SOL
* STA E1: 9 + D7: 1
* CNT   3 HDP CHAINS /   2 HYP OPENED