Analysis of zz-www.sudokuoftheday.co.uk-20060610-absurd-base.sdk

Contents

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

level: medium

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

position: ..24....5..465.8...............2..91..6.....2.13...46..3.1..2..7...45...4.5..3.7. initial

Autosolve

position: ..24...15..465182.15...2.4..4..26.91..6.14..22135..46..3.1..2547.1.45...4.5..317. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 3,9 => CTR => A1: 6,8
* DIS # I2: 7 => CTR => I2: 3,9
* DIS # B1: 7,9 => CTR => B1: 6,8
* DIS # I2: 3 => CTR => I2: 7,9
* DIS # B5: 8 => CTR => B5: 7,9
* DIS # D4: 7,8 => CTR => D4: 3
* PRF # C3: 9 => SOL
* DIS # C3: 7 => CTR => C3: 8,9
* CNT   8 HDP CHAINS /  32 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 # A1: 3,9 => CTR => A1: 6,8
* DIS A1: 6,8 # B1: 7,9 => CTR => B1: 6,8
* DIS A1: 6,8 + B1: 6,8 # B5: 8 => CTR => B5: 7,9
* PRF A1: 6,8 + B1: 6,8 + B5: 7,9 # A5: 5,8 => SOL
* STA A1: 6,8 + B1: 6,8 + B5: 7,9 + A5: 5,8
* CNT   4 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

..24....5..465.8...............2..91..6.....2.13...46..3.1..2..7...45...4.5..3.7. initial
..24...15..465182.15...2.4..4..26.91..6.14..22135..46..3.1..2547.1.45...4.5..317. autosolve
682439715374651829159872643847326591596714382213598467938167254761245938425983176 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A2: 3,9
B2: 7,9
A4: 5,8
C4: 7,8
H5: 3,8
I6: 7,8
C7: 8,9
H8: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B8,B9: 2.. / B8 = 2  => 10 pairs (_) / B9 = 2  =>  9 pairs (_)
D8,D9: 2.. / D8 = 2  =>  9 pairs (_) / D9 = 2  => 10 pairs (_)
B8,D8: 2.. / B8 = 2  => 10 pairs (_) / D8 = 2  =>  9 pairs (_)
B9,D9: 2.. / B9 = 2  =>  9 pairs (_) / D9 = 2  => 10 pairs (_)
A1,A2: 3.. / A1 = 3  =>  0 pairs (X) / A2 = 3  =>  8 pairs (_)
E1,E3: 3.. / E1 = 3  => 11 pairs (_) / E3 = 3  =>  8 pairs (_)
D4,D5: 3.. / D4 = 3  => 14 pairs (_) / D5 = 3  =>  0 pairs (X)
A2,I2: 3.. / A2 = 3  =>  8 pairs (_) / I2 = 3  =>  0 pairs (X)
D4,G4: 3.. / D4 = 3  => 14 pairs (_) / G4 = 3  =>  0 pairs (X)
H5,H8: 3.. / H5 = 3  =>  0 pairs (X) / H8 = 3  => 15 pairs (_)
A4,A5: 5.. / A4 = 5  =>  9 pairs (_) / A5 = 5  => 12 pairs (_)
G4,G5: 5.. / G4 = 5  => 12 pairs (_) / G5 = 5  =>  9 pairs (_)
A4,G4: 5.. / A4 = 5  =>  9 pairs (_) / G4 = 5  => 12 pairs (_)
A5,G5: 5.. / A5 = 5  => 12 pairs (_) / G5 = 5  =>  9 pairs (_)
A1,B1: 6.. / A1 = 6  => 14 pairs (_) / B1 = 6  =>  9 pairs (_)
G3,I3: 6.. / G3 = 6  =>  9 pairs (_) / I3 = 6  => 13 pairs (_)
E7,E9: 6.. / E7 = 6  => 14 pairs (_) / E9 = 6  =>  9 pairs (_)
A7,E7: 6.. / A7 = 6  =>  9 pairs (_) / E7 = 6  => 14 pairs (_)
A1,A7: 6.. / A1 = 6  => 14 pairs (_) / A7 = 6  =>  9 pairs (_)
G3,G8: 6.. / G3 = 6  =>  9 pairs (_) / G8 = 6  => 13 pairs (_)
C4,B5: 7.. / C4 = 7  => 11 pairs (_) / B5 = 7  =>  0 pairs (X)
E7,F7: 7.. / E7 = 7  => 11 pairs (_) / F7 = 7  => 10 pairs (_)
B2,I2: 7.. / B2 = 7  => 11 pairs (_) / I2 = 7  =>  0 pairs (X)
C3,C4: 7.. / C3 = 7  =>  0 pairs (X) / C4 = 7  => 11 pairs (_)
H5,I6: 8.. / H5 = 8  => 15 pairs (_) / I6 = 8  =>  0 pairs (X)
H5,H8: 8.. / H5 = 8  => 15 pairs (_) / H8 = 8  =>  0 pairs (X)
A5,B5: 9.. / A5 = 9  => 11 pairs (_) / B5 = 9  => 14 pairs (_)
E6,F6: 9.. / E6 = 9  => 10 pairs (_) / F6 = 9  => 11 pairs (_)
C3,C7: 9.. / C3 = 9  =>  0 pairs (*) / C7 = 9  =>  0 pairs (X)
* DURATION: 0:00:30.588920  START: 23:44:49.044960  END: 23:45:19.633880 2019-04-30
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,C4,C7,H5,H8,I6)
* ..24...15..465182.15...2.4..4..26.91..6.14..22135..46..3.1..2547.1.45...4.5..317.
* PAIR A2: 3,9 BLK 1
A1: 3,9,6,8                              # reduction candidate for 3,9
A1: 3,9 => CTR
* .624...15.7465182.1587.2.4..47.26.91.96.147.22135..46.6391..2547.1.45...4.5.6317.
A1: 6,8                                  #  9 pairs
* PAIR A2: 3,9 ROW 2
I2: 3,9,7                                # reduction candidate for 3,9
I2: 7 => CTR
* ..24...15394651827157982.4.5483267919768145322135.9468.391.82547.1245.8.4.5..317.
I2: 3,9                                  # 11 pairs
* PAIR B2: 7,9 BLK 1
B1: 7,9,6,8                              # reduction candidate for 7,9
B1: 7,9 => CTR
* 6.24...153.465182.158..2.4..47.26.91986.145322135..46..391672547.1.45...4.5..317.
B1: 6,8                                  #  9 pairs
C3: 7,9,8                                # reduction candidate for 7,9
C3: 7,9                                  # 12 pairs
* PAIR B2: 7,9 ROW 2
I2: 7,9,3                                # reduction candidate for 7,9
I2: 3 => CTR
* 3624...15974651823158732.4..47.26.91.96.147.22135..46.6391..2547.1.45...4.5.6317.
I2: 7,9                                  #  8 pairs
* PAIR B2: 7,9 COL B
B5: 7,9,8                                # reduction candidate for 7,9
B5: 8 => CTR
* ..24...15..465182.15...2.4..47.26.91986.145322135..46..3.1..2547.1.45...4.5..317.
B5: 7,9                                  # 11 pairs
* PAIR A4: 5,8 BLK 4
A5: 5,8,9                                # reduction candidate for 5,8
A5: 5,8                                  # 14 pairs
A5: 9                                    # 11 pairs
* PAIR C4: 7,8 BLK 4
B5: 7,8,9                                # reduction candidate for 7,8
B5: 9                                    # 14 pairs
B5: 7,8                                  # 11 pairs
* PAIR C4: 7,8 ROW 4
D4: 7,8,3                                # reduction candidate for 7,8
D4: 7,8 => CTR
* ..24...15.7465182.15...2.4.54..26391..63145822135..467.3.1..2547.1.45.3.4.5..317.
D4: 3                                    # 14 pairs
* PAIR C4: 7,8 COL C
C3: 7,8,9                                # reduction candidate for 7,8
C3: 9 => SOLVED
* 682439715374651829159872643847326591596714382213598467938167254761245938425983176
C3: 7,8                                  # 10 pairs
* PAIR H5: 3,8 ROW 5
D5: 3,8,7                                # reduction candidate for 3,8
D5: 7                                    # 15 pairs
D5: 3,8                                  # 15 pairs
* PAIR I6: 7,8 ROW 6
E6: 7,8,9                                # reduction candidate for 7,8
E6: 7,8                                  # 11 pairs
F6: 7,8,9                                # reduction candidate for 7,8
F6: 7,8                                  # 10 pairs
* PAIR C7: 8,9 BLK 7
A7: 8,9,6                                # reduction candidate for 8,9
A7: 8,9                                  # 14 pairs
B8: 8,9,2,6                              # reduction candidate for 8,9
B8: 8,9                                  # 11 pairs
B9: 8,9,2,6                              # reduction candidate for 8,9
B9: 8,9                                  # 11 pairs
* PAIR C7: 8,9 ROW 7
E7: 8,9,6,7                              # reduction candidate for 8,9
E7: 8,9                                  # 12 pairs
F7: 8,9,7                                # reduction candidate for 8,9
F7: 8,9                                  # 11 pairs
* PAIR C7: 8,9 COL C
C3: 8,9,7                                # reduction candidate for 8,9
C3: 7 => CTR
* ..24...15.94651827157..2.4.5487263919763145822135..46..391..2547.1.45...4.5..317.
C3: 8,9                                  # 11 pairs
* PAIR H8: 3,8 BLK 9
I8: 3,8,6,9                              # reduction candidate for 3,8
I8: 3,8                                  # 12 pairs
I8: 6,9                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060610-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 3,9 => CTR => A1: 6,8
* DIS # I2: 7 => CTR => I2: 3,9
* DIS # B1: 7,9 => CTR => B1: 6,8
* DIS # I2: 3 => CTR => I2: 7,9
* DIS # B5: 8 => CTR => B5: 7,9
* DIS # D4: 7,8 => CTR => D4: 3
* PRF # C3: 9 => SOL
* DIS # C3: 7 => CTR => C3: 8,9
* CNT   8 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B2,C4,C7,H5,H8,I6)
* ..24...15..465182.15...2.4..4..26.91..6.14..22135..46..3.1..2547.1.45...4.5..317.
* PAIR A2: 3,9 BLK 1
A1: 3,9,6,8                              # reduction candidate for 3,9
A1: 3,9 => CTR
* .624...15.7465182.1587.2.4..47.26.91.96.147.22135..46.6391..2547.1.45...4.5.6317.
* PAIR B2: 7,9 BLK 1
B1: 7,9,6,8                              # reduction candidate for 7,9
B1: 7,9 => CTR
* 6.24...153.465182.158..2.4..47.26.91986.145322135..46..391672547.1.45...4.5..317.
* RESTART
* PAIR B2: 7,9 COL B
B5: 7,9,8                                # reduction candidate for 7,9
B5: 8 => CTR
* ..24...15374651829159..2.4..47.26.91986.145322135..46..3.1..2547.1.45...4.5..317.
* PAIR RESTART
* PAIR A4: 5,8 BLK 4
A5: 5,8,9                                # reduction candidate for 5,8
A5: 5,8 => SOLVED
* 682439715374651829159872643847326591596714382213598467938167254761245938425983176
* DURATION: 0:00:04.879988  START: 23:45:38.385949  END: 23:45:43.265937 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060610-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 3,9 => CTR => A1: 6,8
* DIS A1: 6,8 # B1: 7,9 => CTR => B1: 6,8
* DIS A1: 6,8 + B1: 6,8 # B5: 8 => CTR => B5: 7,9
* PRF A1: 6,8 + B1: 6,8 + B5: 7,9 # A5: 5,8 => SOL
* STA A1: 6,8 + B1: 6,8 + B5: 7,9 + A5: 5,8
* CNT   4 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060610, absurd

Solution

position: 682439715374651829159872643847326591596714382213598467938167254761245938425983176 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 # A1: 3,9 => CTR => A1: 6,8
* INC # A1: 6,8 => UNS
* INC # I2: 3,9 => UNS
* DIS # I2: 7 => CTR => I2: 3,9
* DIS # B1: 7,9 => CTR => B1: 6,8
* INC # B1: 6,8 => UNS
* INC # C3: 7,9 => UNS
* INC # I2: 7,9 => UNS
* DIS # I2: 3 => CTR => I2: 7,9
* INC # B5: 7,9 => UNS
* DIS # B5: 8 => CTR => B5: 7,9
* INC # A5: 5,8 => UNS
* INC # A5: 9 => UNS
* INC # B5: 7,8 => UNS
* INC # B5: 9 => UNS
* DIS # D4: 7,8 => CTR => D4: 3
* INC # D4: 3 => UNS
* INC # C3: 7,8 => UNS
* PRF # C3: 9 => SOL
* INC # D5: 3,8 => UNS
* INC # D5: 7 => UNS
* INC # E6: 7,8 => UNS
* INC # F6: 7,8 => UNS
* INC # A7: 8,9 => UNS
* INC # B8: 8,9 => UNS
* INC # B9: 8,9 => UNS
* INC # E7: 8,9 => UNS
* INC # F7: 8,9 => UNS
* INC # C3: 8,9 => UNS
* DIS # C3: 7 => CTR => C3: 8,9
* INC # I8: 3,8 => UNS
* INC # I8: 6,9 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 3,9 => CTR => A1: 6,8
* DIS A1: 6,8 # B1: 7,9 => CTR => B1: 6,8
* INC A1: 6,8 + B1: 6,8 # B5: 7,9 => UNS
* DIS A1: 6,8 + B1: 6,8 # B5: 8 => CTR => B5: 7,9
* PRF A1: 6,8 + B1: 6,8 + B5: 7,9 # A5: 5,8 => SOL
* STA A1: 6,8 + B1: 6,8 + B5: 7,9 + A5: 5,8
* CNT   5 HDP CHAINS /   5 HYP OPENED