Analysis of zz-www.sudokuoftheday.co.uk-20190206-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019
Autosolve
Pair Reduction Variants
- Pair Reduction Analysis
- Pair Reduction
Details
Solution
Appendix: Full HDP Chains
- A1. Pair Reduction Analysis
- A2. Pair Reduction

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019

level: medium

position: 4.7...9...............6.27...35....8..14.2.39.....3............1...7.6.52....879. initial

Autosolve

position: 4.7.2.9....27.........6.27.923517468..1482539...693127.....6..213.27.6.52.6..879. autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D3: 3,8 => CTR => D3: 9
* PRF # D3: 9 => SOL
* DIS # B1: 1,5 => CTR => B1: 6,8
* DIS # I2: 3,4 => CTR => I2: 1,6
* DIS # A2: 3,8 => CTR => A2: 5,6
* DIS # A3: 5,8 => CTR => A3: 3
* DIS # A7: 5,8 => CTR => A7: 7
* DIS # B7: 4,5 => CTR => B7: 7,8,9
* DIS # E9: 3 => CTR => E9: 4,5
* DIS # C8: 8 => CTR => C8: 4,9
* PRF # D7: 1,3 => SOL
* DIS # D7: 9 => CTR => D7: 1,3
* DIS # I9: 4 => CTR => I9: 1,3
* PRF # H7: 4,8 => SOL
* PRF # C8: 4,8 => SOL
* DIS # C8: 9 => CTR => C8: 4,8
* CNT  16 HDP CHAINS /  41 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* DIS # D3: 3,8 => CTR => D3: 9
* PRF D3: 9 => SOL
* STA D3: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

`4.7...9...............6.27...35....8..14.2.39.....3............1...7.6.52....879.`	initial
`4.7.2.9....27.........6.27.923517468..1482539...693127.....6..213.27.6.52.6..879.`	autosolve
`467821953592734816318965274923517468671482539845693127789156342134279685256348791`	solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
D1: 3,8
F1: 1,5
E2: 3,4
G2: 3,8
A5: 6,7
B5: 6,7
A6: 5,8
B9: 4,5
F8: 4,9
D9: 1,3
G7: 3,8
H8: 4,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D7,D9: 1.. / D7 = 1  =>  0 pairs (*) / D9 = 1  =>  0 pairs (X)
H7,I9: 1.. / H7 = 1  => 14 pairs (_) / I9 = 1  =>  0 pairs (*)
D7,H7: 1.. / D7 = 1  =>  0 pairs (*) / H7 = 1  =>  0 pairs (X)
D9,I9: 1.. / D9 = 1  => 14 pairs (_) / I9 = 1  =>  0 pairs (*)
A2,A3: 3.. / A2 = 3  =>  0 pairs (X) / A3 = 3  => 14 pairs (_)
G7,I9: 3.. / G7 = 3  => 16 pairs (_) / I9 = 3  =>  0 pairs (X)
D1,I1: 3.. / D1 = 3  =>  0 pairs (X) / I1 = 3  => 14 pairs (_)
G2,G7: 3.. / G2 = 3  =>  0 pairs (X) / G7 = 3  => 16 pairs (_)
B6,C6: 4.. / B6 = 4  => 14 pairs (_) / C6 = 4  => 14 pairs (_)
F3,I3: 4.. / F3 = 4  =>  0 pairs (X) / I3 = 4  => 14 pairs (_)
H1,H2: 5.. / H1 = 5  => 13 pairs (_) / H2 = 5  => 15 pairs (_)
E7,E9: 5.. / E7 = 5  => 14 pairs (_) / E9 = 5  => 15 pairs (_)
B9,E9: 5.. / B9 = 5  => 14 pairs (_) / E9 = 5  => 15 pairs (_)
I1,I2: 6.. / I1 = 6  =>  0 pairs (X) / I2 = 6  => 11 pairs (_)
A5,B5: 6.. / A5 = 6  => 10 pairs (_) / B5 = 6  =>  0 pairs (X)
B1,I1: 6.. / B1 = 6  => 11 pairs (_) / I1 = 6  =>  0 pairs (X)
A2,A5: 6.. / A2 = 6  =>  0 pairs (X) / A5 = 6  => 10 pairs (_)
A5,B5: 7.. / A5 = 7  =>  0 pairs (X) / B5 = 7  => 10 pairs (_)
A7,B7: 7.. / A7 = 7  => 10 pairs (_) / B7 = 7  =>  0 pairs (X)
A5,A7: 7.. / A5 = 7  =>  0 pairs (X) / A7 = 7  => 10 pairs (_)
B5,B7: 7.. / B5 = 7  => 10 pairs (_) / B7 = 7  =>  0 pairs (X)
D1,D3: 8.. / D1 = 8  => 14 pairs (_) / D3 = 8  =>  0 pairs (X)
C8,H8: 8.. / C8 = 8  =>  0 pairs (X) / H8 = 8  => 17 pairs (_)
G2,G7: 8.. / G2 = 8  => 16 pairs (_) / G7 = 8  =>  0 pairs (X)
D7,F8: 9.. / D7 = 9  =>  0 pairs (X) / F8 = 9  =>  0 pairs (_)
B2,F2: 9.. / B2 = 9  => 13 pairs (_) / F2 = 9  =>  0 pairs (X)
C8,F8: 9.. / C8 = 9  =>  0 pairs (X) / F8 = 9  =>  0 pairs (_)
D3,D7: 9.. / D3 = 9  =>  0 pairs (*) / D7 = 9  =>  0 pairs (X)
* DURATION: 0:00:31.421591  START: 03:32:14.347875  END: 03:32:45.769466 2019-05-01
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B5,B9,D1,D9,E2,F1,F8,G2,G7,H8)
* 4.7.2.9....27.........6.27.923517468..1482539...693127.....6..213.27.6.52.6..879.
* PAIR D1: 3,8 BLK 2
D3: 3,8,9                                # reduction candidate for 3,8
D3: 3,8 => CTR
* 4.7.2.9....27.........6.27.923517468..1482539...693127...9.6.121392746852.61.8794
D3: 9 => SOLVED
* 467821953592734816318965274923517468671482539845693127789156342134279685256348791
* PAIR F1: 1,5 BLK 2
F2: 1,5,4,9                              # reduction candidate for 1,5
F2: 1,5                                  # 15 pairs
F3: 1,5,4,9                              # reduction candidate for 1,5
F3: 1,5                                  # 16 pairs
* PAIR F1: 1,5 ROW 1
B1: 1,5,6,8                              # reduction candidate for 1,5
B1: 1,5 => CTR
* 4.732.986..274.3513..86.274923517468..1482539...693127...93681213.27.6.52.6..879.
B1: 6,8                                  # 13 pairs
H1: 1,5,8                                # reduction candidate for 1,5
H1: 1,5                                  # 15 pairs
* PAIR E2: 3,4 ROW 2
I2: 3,4,1,6                              # reduction candidate for 3,4
I2: 3,4 => CTR
* 4.732.9.6..274...33..86.274923517468..1482539...693127...9.631213.27.6.52.6..879.
I2: 1,6                                  # 13 pairs
* PAIR E2: 3,4 COL E
E7: 3,4,5                                # reduction candidate for 3,4
E7: 3,4                                  # 15 pairs
E9: 3,4,5                                # reduction candidate for 3,4
E9: 3,4                                  # 14 pairs
* PAIR G2: 3,8 ROW 2
A2: 3,8,5,6                              # reduction candidate for 3,8
A2: 3,8 => CTR
* 4.7.2.9....274........6.274923517468671482539...6931277....6..213.274685246.5879.
A2: 5,6                                  # 15 pairs
* PAIR A6: 5,8 BLK 4
B6: 5,8,4                                # reduction candidate for 5,8
B6: 5,8                                  # 14 pairs
C6: 5,8,4                                # reduction candidate for 5,8
C6: 5,8                                  # 14 pairs
* PAIR A6: 5,8 COL A
A2: 5,8,3,6                              # reduction candidate for 5,8
A2: 5,8                                  # 13 pairs
A3: 5,8,3                                # reduction candidate for 5,8
A3: 5,8 => CTR
* 4.7.2.9..3.274.8......6.274923517468671482539...6931277....63.213.274685246..879.
A3: 3                                    # 14 pairs
A7: 5,8,7                                # reduction candidate for 5,8
A7: 5,8 => CTR
* 4.732.9.66.274....3..86.274923517468761482539...693127.7.9.6.121392746.52.6..879.
A7: 7                                    # 10 pairs
* PAIR B9: 4,5 BLK 7
B7: 4,5,7,8,9                            # reduction candidate for 4,5
B7: 4,5 => CTR
* 4.7.2.9....274......5.6.2749235174686714825395846931277....6..213.274685246.5879.
B7: 7,8,9                                # 12 pairs
C7: 4,5,8,9                              # reduction candidate for 4,5
C7: 4,5                                  # 15 pairs
* PAIR B9: 4,5 ROW 9
E9: 4,5,3                                # reduction candidate for 4,5
E9: 3 => CTR
* 4.7.2.9....27.........6.27.923517468..1482539...693127....56..213.274685256.38794
E9: 4,5                                  # 14 pairs
* PAIR B9: 4,5 COL B
B6: 4,5,8                                # reduction candidate for 4,5
B6: 8                                    # 14 pairs
B6: 4,5                                  # 13 pairs
* PAIR F8: 4,9 ROW 8
C8: 4,9,8                                # reduction candidate for 4,9
C8: 8 => CTR
* 4.782.9.3.9273.8.6..596.27.923517468..1482539..4693127..9..6..21382796452.6..879.
C8: 4,9                                  # 17 pairs
* PAIR F8: 4,9 COL F
F2: 4,9,1,5                              # reduction candidate for 4,9
F2: 4,9                                  # 16 pairs
F3: 4,9,1,5                              # reduction candidate for 4,9
F3: 4,9                                  # 15 pairs
* PAIR D9: 1,3 BLK 8
D7: 1,3,9                                # reduction candidate for 1,3
D7: 1,3 => SOLVED
* 467821953592734816318965274923517468671482539845693127789156342134279685256348791
D7: 9 => CTR
* 4.7.2.9....27.........6.27.923517468..1482539...693127...9.6.121392746852.61.8794
* PAIR D9: 1,3 ROW 9
I9: 1,3,4                                # reduction candidate for 1,3
I9: 4 => CTR
* 4.7.2.95...274........6.27.923517468..1482539...693127.....631213.27.6852.6138794
I9: 1,3                                  # 14 pairs
* PAIR H8: 4,8 BLK 9
H7: 4,8,1                                # reduction candidate for 4,8
H7: 4,8 => SOLVED
* 467821953592734816318965274923517468671482539845693127789156342134279685256348791
H7: 1                                    # 14 pairs
* PAIR H8: 4,8 ROW 8
C8: 4,8,9                                # reduction candidate for 4,8
C8: 4,8 => SOLVED
* 467821953592734816318965274923517468671482539845693127789156342134279685256348791
C8: 9 => CTR
* 4.7.2.9....274.8......6.274923517468..1482539...693127...9.63.21392746852.6..879.
* PAIR H8: 4,8 COL H
H2: 4,8,1,5                              # reduction candidate for 4,8
H2: 4,8                                  # 15 pairs
H2: 1,5                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190206-absurd-base-pr-000.dot
* REASONING
* DIS # D3: 3,8 => CTR => D3: 9
* PRF # D3: 9 => SOL
* DIS # B1: 1,5 => CTR => B1: 6,8
* DIS # I2: 3,4 => CTR => I2: 1,6
* DIS # A2: 3,8 => CTR => A2: 5,6
* DIS # A3: 5,8 => CTR => A3: 3
* DIS # A7: 5,8 => CTR => A7: 7
* DIS # B7: 4,5 => CTR => B7: 7,8,9
* DIS # E9: 3 => CTR => E9: 4,5
* DIS # C8: 8 => CTR => C8: 4,9
* PRF # D7: 1,3 => SOL
* DIS # D7: 9 => CTR => D7: 1,3
* DIS # I9: 4 => CTR => I9: 1,3
* PRF # H7: 4,8 => SOL
* PRF # C8: 4,8 => SOL
* DIS # C8: 9 => CTR => C8: 4,8
* CNT  16 HDP CHAINS /  41 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B5,B9,D1,D9,E2,F1,F8,G2,G7,H8)
* 4.7.2.9....27.........6.27.923517468..1482539...693127.....6..213.27.6.52.6..879.
* PAIR D1: 3,8 BLK 2
D3: 3,8,9                                # reduction candidate for 3,8
D3: 3,8 => CTR
* 4.7.2.9....27.........6.27.923517468..1482539...693127...9.6.121392746852.61.8794
D3: 9 => SOLVED
* 467821953592734816318965274923517468671482539845693127789156342134279685256348791
* DURATION: 0:00:02.045837  START: 03:33:11.251078  END: 03:33:13.296915 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190206-absurd-base-pr-001.dot
* REASONING
* DIS # D3: 3,8 => CTR => D3: 9
* PRF D3: 9 => SOL
* STA D3: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190206, absurd

Solution

position: 467821953592734816318965274923517468671482539845693127789156342134279685256348791 solved

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 # D3: 3,8 => CTR => D3: 9
* PRF # D3: 9 => SOL
* INC # F2: 1,5 => UNS
* INC # F3: 1,5 => UNS
* DIS # B1: 1,5 => CTR => B1: 6,8
* INC # B1: 6,8 => UNS
* INC # H1: 1,5 => UNS
* DIS # I2: 3,4 => CTR => I2: 1,6
* INC # I2: 1,6 => UNS
* INC # E7: 3,4 => UNS
* INC # E9: 3,4 => UNS
* DIS # A2: 3,8 => CTR => A2: 5,6
* INC # A2: 5,6 => UNS
* INC # B6: 5,8 => UNS
* INC # C6: 5,8 => UNS
* INC # A2: 5,8 => UNS
* DIS # A3: 5,8 => CTR => A3: 3
* INC # A3: 3 => UNS
* DIS # A7: 5,8 => CTR => A7: 7
* INC # A7: 7 => UNS
* DIS # B7: 4,5 => CTR => B7: 7,8,9
* INC # B7: 7,8,9 => UNS
* INC # C7: 4,5 => UNS
* INC # E9: 4,5 => UNS
* DIS # E9: 3 => CTR => E9: 4,5
* INC # B6: 4,5 => UNS
* INC # B6: 8 => UNS
* INC # C8: 4,9 => UNS
* DIS # C8: 8 => CTR => C8: 4,9
* INC # F2: 4,9 => UNS
* INC # F3: 4,9 => UNS
* PRF # D7: 1,3 => SOL
* DIS # D7: 9 => CTR => D7: 1,3
* INC # I9: 1,3 => UNS
* DIS # I9: 4 => CTR => I9: 1,3
* PRF # H7: 4,8 => SOL
* INC # H7: 1 => UNS
* PRF # C8: 4,8 => SOL
* DIS # C8: 9 => CTR => C8: 4,8
* INC # H2: 4,8 => UNS
* INC # H2: 1,5 => UNS
* CNT  41 HDP CHAINS /  41 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D3: 3,8 => CTR => D3: 9
* PRF D3: 9 => SOL
* STA D3: 9
* CNT   2 HDP CHAINS /   1 HYP OPENED