Analysis of zz-www.sudokuoftheday.co.uk-20060515-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: 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6.24.91...5....9........ initial

Autosolve

position: 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91...59...9.....1.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E2: 7 => CTR => E2: 4,9
* DIS # H4: 3,4 => CTR => H4: 6,9
* DIS # B5: 1,9 => CTR => B5: 2,3,5,8
* DIS # C5: 1,9 => CTR => C5: 2,3,5,8
* DIS # H5: 3,8 => CTR => H5: 4,6,9
* DIS # B6: 3,8 => CTR => B6: 2,9
* DIS # B5: 3,8 => CTR => B5: 1,2,5,9
* DIS # B6: 3,8 => CTR => B6: 2,9
* DIS # C9: 2 => CTR => C9: 4,8
* DIS # G3: 3,8 => CTR => G3: 9
* CNT  10 HDP CHAINS /  42 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 # E2: 7 => CTR => E2: 4,9
* PRF E2: 4,9 # I8: 6 => SOL
* STA E2: 4,9 + I8: 6
* CNT   2 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6.24.91...5....9........ initial
6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91...59...9.....1.. autosolve
615298743729345681843167952371586294458921367296734518587612439132459876964873125 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
E1: 4,9
D3: 1,9
F3: 1,7
A4: 3,4
D5: 1,9
I6: 3,8
B7: 3,8
D8: 4,8
D9: 4,8
E9: 3,7
F9: 3,7
G8: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,F3: 1.. / D3 = 1  => 19 pairs (_) / F3 = 1  =>  0 pairs (X)
I1,I2: 1.. / I1 = 1  => 13 pairs (_) / I2 = 1  => 14 pairs (_)
C4,F4: 1.. / C4 = 1  =>  0 pairs (*) / F4 = 1  =>  0 pairs (X)
D3,D5: 1.. / D3 = 1  => 19 pairs (_) / D5 = 1  =>  0 pairs (X)
E5,E6: 2.. / E5 = 2  => 13 pairs (_) / E6 = 2  =>  0 pairs (X)
H8,H9: 2.. / H8 = 2  => 16 pairs (_) / H9 = 2  => 13 pairs (_)
E9,F9: 3.. / E9 = 3  =>  0 pairs (X) / F9 = 3  => 19 pairs (_)
E1,E2: 4.. / E1 = 4  => 12 pairs (_) / E2 = 4  =>  0 pairs (*)
A4,A5: 4.. / A4 = 4  => 16 pairs (_) / A5 = 4  => 16 pairs (_)
C8,C9: 4.. / C8 = 4  => 16 pairs (_) / C9 = 4  => 12 pairs (_)
D8,D9: 4.. / D8 = 4  => 12 pairs (_) / D9 = 4  => 16 pairs (_)
A5,H5: 4.. / A5 = 4  => 16 pairs (_) / H5 = 4  => 16 pairs (_)
C8,D8: 4.. / C8 = 4  => 16 pairs (_) / D8 = 4  => 12 pairs (_)
C9,D9: 4.. / C9 = 4  => 12 pairs (_) / D9 = 4  => 16 pairs (_)
B5,C5: 5.. / B5 = 5  => 12 pairs (_) / C5 = 5  => 12 pairs (_)
H9,I9: 5.. / H9 = 5  => 20 pairs (_) / I9 = 5  => 12 pairs (_)
C3,H3: 5.. / C3 = 5  => 13 pairs (_) / H3 = 5  => 12 pairs (_)
B1,B5: 5.. / B1 = 5  => 12 pairs (_) / B5 = 5  => 12 pairs (_)
I1,I9: 5.. / I1 = 5  => 20 pairs (_) / I9 = 5  => 12 pairs (_)
F4,F5: 6.. / F4 = 6  =>  0 pairs (*) / F5 = 6  =>  0 pairs (X)
B8,B9: 6.. / B8 = 6  => 16 pairs (_) / B9 = 6  => 13 pairs (_)
F5,H5: 6.. / F5 = 6  => 13 pairs (_) / H5 = 6  =>  0 pairs (*)
A2,A3: 7.. / A2 = 7  => 19 pairs (_) / A3 = 7  =>  0 pairs (X)
E2,F3: 7.. / E2 = 7  =>  0 pairs (X) / F3 = 7  => 19 pairs (_)
C7,C8: 7.. / C7 = 7  => 18 pairs (_) / C8 = 7  => 14 pairs (_)
E9,F9: 7.. / E9 = 7  => 19 pairs (_) / F9 = 7  =>  0 pairs (X)
H7,H8: 7.. / H7 = 7  => 14 pairs (_) / H8 = 7  => 18 pairs (_)
A2,E2: 7.. / A2 = 7  => 19 pairs (_) / E2 = 7  =>  0 pairs (X)
A3,F3: 7.. / A3 = 7  =>  0 pairs (X) / F3 = 7  => 19 pairs (_)
C7,H7: 7.. / C7 = 7  => 18 pairs (_) / H7 = 7  => 14 pairs (_)
C8,H8: 7.. / C8 = 7  => 14 pairs (_) / H8 = 7  => 18 pairs (_)
E2,E9: 7.. / E2 = 7  =>  0 pairs (X) / E9 = 7  => 19 pairs (_)
F3,F9: 7.. / F3 = 7  => 19 pairs (_) / F9 = 7  =>  0 pairs (X)
D8,D9: 8.. / D8 = 8  => 16 pairs (_) / D9 = 8  => 12 pairs (_)
C4,H4: 9.. / C4 = 9  =>  0 pairs (X) / H4 = 9  => 19 pairs (_)
B6,E6: 9.. / B6 = 9  => 19 pairs (_) / E6 = 9  =>  0 pairs (X)
D3,D5: 9.. / D3 = 9  =>  0 pairs (X) / D5 = 9  => 19 pairs (_)
G3,G5: 9.. / G3 = 9  => 19 pairs (_) / G5 = 9  =>  0 pairs (X)
* DURATION: 0:00:42.806747  START: 23:09:42.958210  END: 23:10:25.764957 2019-04-30
* CP COUNT: (38)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,D3,D5,D8,D9,E1,E9,F3,F9,G8,I6)
* 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91...59...9.....1..
* PAIR E1: 4,9 BLK 2
E2: 4,9,7                                # reduction candidate for 4,9
E2: 7 => CTR
* 6..2487.....3756..74.961..2.7158.29....1....7..67.451.5..6124.91...59...9...371..
E2: 4,9                                  # 19 pairs
* PAIR E1: 4,9 ROW 1
H1: 4,9,3,5                              # reduction candidate for 4,9
H1: 4,9                                  # 13 pairs
H1: 3,5                                  # 13 pairs
* PAIR A4: 3,4 BLK 4
A5: 3,4,2,8                              # reduction candidate for 3,4
A5: 2,8                                  # 17 pairs
A5: 3,4                                  # 16 pairs
* PAIR A4: 3,4 ROW 4
H4: 3,4,6,9                              # reduction candidate for 3,4
H4: 3,4 => CTR
* 6..2.87.....3.56...4..6...2.795812.6...9.6..7..67.451.5..6124.91...59...9....31..
H4: 6,9                                  # 13 pairs
I4: 3,4,6                                # reduction candidate for 3,4
I4: 3,4                                  # 16 pairs
* PAIR D5: 1,9 ROW 5
B5: 1,9,2,3,5,8                          # reduction candidate for 1,9
B5: 1,9 => CTR
* 65.2.873.7..3.568..4.167952473581296.159.6.47.967.451.5386124.91...59...9...731.5
B5: 2,3,5,8                              # 12 pairs
C5: 1,9,2,3,5,8                          # reduction candidate for 1,9
C5: 1,9 => CTR
* 6..2.87..7..3.568.348167952473581296.519.6.47.967.451.5876124391...59...9...731..
C5: 2,3,5,8                              # 12 pairs
* PAIR I6: 3,8 BLK 6
G5: 3,8,9                                # reduction candidate for 3,8
G5: 3,8                                  # 19 pairs
H5: 3,8,4,6,9                            # reduction candidate for 3,8
H5: 3,8 => CTR
* 6..2.87.....3.56...4..6...237.5812..4..9.6..7.967.451.5..6124.91...59...9.....1..
H5: 4,6,9                                # 12 pairs
* PAIR I6: 3,8 ROW 6
A6: 3,8,2                                # reduction candidate for 3,8
A6: 3,8                                  # 15 pairs
B6: 3,8,2,9                              # reduction candidate for 3,8
B6: 3,8 => CTR
* 6..2487.....3756..74.961..2.7158.29....12...72.679451.5..6124.91...59...9...371..
B6: 2,9                                  # 13 pairs
* PAIR I6: 3,8 COL I
I8: 3,8,6                                # reduction candidate for 3,8
I8: 3,8                                  # 18 pairs
I8: 6                                    # 17 pairs
* PAIR B7: 3,8 BLK 7
C7: 3,8,7                                # reduction candidate for 3,8
C7: 3,8                                  # 14 pairs
B8: 3,8,2,6                              # reduction candidate for 3,8
B8: 3,8                                  # 17 pairs
C8: 3,8,2,4,7                            # reduction candidate for 3,8
C8: 3,8                                  # 16 pairs
* PAIR B7: 3,8 ROW 7
H7: 3,8,7                                # reduction candidate for 3,8
H7: 3,8                                  # 18 pairs
H7: 7                                    # 14 pairs
* PAIR B7: 3,8 COL B
B5: 3,8,1,2,5,9                          # reduction candidate for 3,8
B5: 3,8 => CTR
* 65.2.8731.1.3.5648.4.167952.715862944.5921867.967.451.5..6124.91...59..696....1.5
B5: 1,2,5,9                              # 12 pairs
B6: 3,8,2,9                              # reduction candidate for 3,8
B6: 3,8 => CTR
* 6..2487.....3756..74.961..2.7158.29....12...72.679451.5..6124.91...59...9...371..
B6: 2,9                                  # 13 pairs
* PAIR D8: 4,8 ROW 8
C8: 4,8,2,3,7                            # reduction candidate for 4,8
C8: 4,8                                  # 20 pairs
C8: 2,3,7                                # 12 pairs
* PAIR D9: 4,8 ROW 9
C9: 4,8,2                                # reduction candidate for 4,8
C9: 2 => CTR
* 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91.4859376962...1..
C9: 4,8                                  # 15 pairs
* PAIR G8: 3,8 BLK 9
H7: 3,8,7                                # reduction candidate for 3,8
H7: 3,8                                  # 18 pairs
H8: 3,8,2,6,7                            # reduction candidate for 3,8
H8: 3,8                                  # 16 pairs
I8: 3,8,6                                # reduction candidate for 3,8
I8: 3,8                                  # 18 pairs
* PAIR G8: 3,8 ROW 8
B8: 3,8,2,6                              # reduction candidate for 3,8
B8: 3,8                                  # 17 pairs
C8: 3,8,2,4,7                            # reduction candidate for 3,8
C8: 3,8                                  # 16 pairs
* PAIR G8: 3,8 COL G
G3: 3,8,9                                # reduction candidate for 3,8
G3: 3,8 => CTR
* 6..2487.....3756..74.961..2.7.58.2........9.7..679451.5..6124.91...59...9.....1..
G3: 9                                    # 19 pairs
G5: 3,8,9                                # reduction candidate for 3,8
G5: 3,8                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060515-absurd-base-pr-000.dot
* REASONING
* DIS # E2: 7 => CTR => E2: 4,9
* DIS # H4: 3,4 => CTR => H4: 6,9
* DIS # B5: 1,9 => CTR => B5: 2,3,5,8
* DIS # C5: 1,9 => CTR => C5: 2,3,5,8
* DIS # H5: 3,8 => CTR => H5: 4,6,9
* DIS # B6: 3,8 => CTR => B6: 2,9
* DIS # B5: 3,8 => CTR => B5: 1,2,5,9
* DIS # B6: 3,8 => CTR => B6: 2,9
* DIS # C9: 2 => CTR => C9: 4,8
* DIS # G3: 3,8 => CTR => G3: 9
* CNT  10 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B7,D3,D5,D8,D9,E1,E9,F3,F9,G8,I6)
* 6..2.87.....3.56...4..6...2.7.58.2..........7..67.451.5..6124.91...59...9.....1..
* PAIR E1: 4,9 BLK 2
E2: 4,9,7                                # reduction candidate for 4,9
E2: 7 => CTR
* 6..2487.....3756..74.961..2.7158.29....1....7..67.451.5..6124.91...59...9...371..
* PAIR I6: 3,8 COL I
I8: 3,8,6                                # reduction candidate for 3,8
I8: 6 => SOLVED
* 615298743729345681843167952371586294458921367296734518587612439132459876964873125
* DURATION: 0:00:04.181131  START: 23:10:50.049009  END: 23:10:54.230140 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060515-absurd-base-pr-001.dot
* REASONING
* DIS # E2: 7 => CTR => E2: 4,9
* PRF E2: 4,9 # I8: 6 => SOL
* STA E2: 4,9 + I8: 6
* CNT   2 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060515, absurd

Solution

position: 615298743729345681843167952371586294458921367296734518587612439132459876964873125 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 # E2: 4,9 => UNS
* DIS # E2: 7 => CTR => E2: 4,9
* INC # H1: 4,9 => UNS
* INC # H1: 3,5 => UNS
* INC # A5: 3,4 => UNS
* INC # A5: 2,8 => UNS
* DIS # H4: 3,4 => CTR => H4: 6,9
* INC # H4: 6,9 => UNS
* INC # I4: 3,4 => UNS
* DIS # B5: 1,9 => CTR => B5: 2,3,5,8
* INC # B5: 2,3,5,8 => UNS
* DIS # C5: 1,9 => CTR => C5: 2,3,5,8
* INC # C5: 2,3,5,8 => UNS
* INC # G5: 3,8 => UNS
* DIS # H5: 3,8 => CTR => H5: 4,6,9
* INC # H5: 4,6,9 => UNS
* INC # A6: 3,8 => UNS
* DIS # B6: 3,8 => CTR => B6: 2,9
* INC # B6: 2,9 => UNS
* INC # I8: 3,8 => UNS
* INC # I8: 6 => UNS
* INC # C7: 3,8 => UNS
* INC # B8: 3,8 => UNS
* INC # C8: 3,8 => UNS
* INC # H7: 3,8 => UNS
* INC # H7: 7 => UNS
* DIS # B5: 3,8 => CTR => B5: 1,2,5,9
* INC # B5: 1,2,5,9 => UNS
* DIS # B6: 3,8 => CTR => B6: 2,9
* INC # B6: 2,9 => UNS
* INC # C8: 4,8 => UNS
* INC # C8: 2,3,7 => UNS
* INC # C9: 4,8 => UNS
* DIS # C9: 2 => CTR => C9: 4,8
* INC # H7: 3,8 => UNS
* INC # H8: 3,8 => UNS
* INC # I8: 3,8 => UNS
* INC # B8: 3,8 => UNS
* INC # C8: 3,8 => UNS
* DIS # G3: 3,8 => CTR => G3: 9
* INC # G3: 9 => UNS
* INC # G5: 3,8 => UNS
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E2: 4,9 => UNS
* DIS # E2: 7 => CTR => E2: 4,9
* INC E2: 4,9 # I8: 3,8 => UNS
* PRF E2: 4,9 # I8: 6 => SOL
* STA E2: 4,9 + I8: 6
* CNT   4 HDP CHAINS /   4 HYP OPENED