Analysis of zz-www.sudokuoftheday.co.uk-20190416-absurd-base.sdk

Contents

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

level: medium

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

position: 9.3........8..45....2..9..78...9.6..21.47.8.5....8.2.4...3.546.3.5..7............ initial

Autosolve

position: 9.3...1.6..8.34529..2..93.78...9.6.121.47.8.5....8.2.47..3.546.3.5..791....9..753 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 1,6 => CTR => A3: 4,5
* DIS # D2: 1 => CTR => D2: 6,7
* PRF # F9: 2,8 => SOL
* DIS # F9: 1,6 => CTR => F9: 2,8
* DIS # B6: 6,9 => CTR => B6: 3,5
* PRF # B6: 3,5 => SOL
* DIS # C6: 6,9 => CTR => C6: 7
* DIS # B6: 5,6 => CTR => B6: 3,9
* DIS # D6: 1 => CTR => D6: 5,6
* DIS # A3: 1,4 => CTR => A3: 5,6
* DIS # F6: 3,6 => CTR => F6: 1
* DIS # H6: 3,7 => CTR => H6: 9
* PRF # H6: 9 => SOL
* DIS # H6: 7 => CTR => H6: 3,9
* DIS # B8: 4,6 => CTR => B8: 2,8
* PRF # B8: 2,8 => SOL
* DIS # B9: 4,6 => CTR => B9: 2,8
* PRF # C9: 4,6 => SOL
* DIS # C9: 1 => CTR => C9: 4,6
* DIS # E9: 4,6 => CTR => E9: 1,2
* DIS # A3: 4,6 => CTR => A3: 1,5
* DIS # F9: 1,2 => CTR => F9: 6,8
* DIS # B7: 2,8 => CTR => B7: 9
* PRF # B7: 9 => SOL
* PRF # B8: 2,8 => SOL
* DIS # B8: 4,6 => CTR => B8: 2,8
* DIS # D8: 2,8 => CTR => D8: 6
* PRF # D8: 6 => SOL
* CNT  28 HDP CHAINS /  45 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 # A3: 1,6 => CTR => A3: 4,5
* DIS A3: 4,5 # D1: 7 => CTR => D1: 2,8
* DIS A3: 4,5 + D1: 2,8 # C6: 6,9 => CTR => C6: 7
* DIS A3: 4,5 + D1: 2,8 + C6: 7 # F6: 3,6 => CTR => F6: 1
* PRF A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1 => SOL
* STA A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1
* CNT   5 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

9.3........8..45....2..9..78...9.6..21.47.8.5....8.2.4...3.546.3.5..7............ initial
9.3...1.6..8.34529..2..93.78...9.6.121.47.8.5....8.2.47..3.546.3.5..791....9..753 autosolve
973852146168734529542169387854293671219476835637581294791325468385647912426918753 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
A2: 1,6
B2: 6,7
E1: 2,5
F1: 2,8
H1: 4,8
H3: 4,8
C4: 4,7
C5: 6,9
A6: 5,6
D4: 2,5
F4: 2,3
F5: 3,6
H4: 3,7
H5: 3,9
C7: 1,9
A9: 4,6
E7: 1,2
I7: 2,8
I8: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,A3: 1.. / A2 = 1  => 19 pairs (_) / A3 = 1  =>  0 pairs (X)
D6,F6: 1.. / D6 = 1  =>  0 pairs (X) / F6 = 1  => 23 pairs (_)
C7,C9: 1.. / C7 = 1  =>  0 pairs (*) / C9 = 1  =>  0 pairs (X)
A2,D2: 1.. / A2 = 1  => 19 pairs (_) / D2 = 1  =>  0 pairs (X)
C7,E7: 1.. / C7 = 1  =>  0 pairs (*) / E7 = 1  =>  0 pairs (X)
F6,F9: 1.. / F6 = 1  => 23 pairs (_) / F9 = 1  =>  0 pairs (X)
D4,F4: 2.. / D4 = 2  =>  0 pairs (*) / F4 = 2  =>  0 pairs (X)
I7,I8: 2.. / I7 = 2  =>  0 pairs (X) / I8 = 2  => 20 pairs (_)
B4,B6: 3.. / B4 = 3  =>  0 pairs (X) / B6 = 3  =>  0 pairs (_)
F5,H5: 3.. / F5 = 3  =>  0 pairs (X) / H5 = 3  =>  0 pairs (_)
H1,H3: 4.. / H1 = 4  => 19 pairs (_) / H3 = 4  =>  0 pairs (X)
B4,C4: 4.. / B4 = 4  =>  0 pairs (X) / C4 = 4  => 20 pairs (_)
E8,E9: 4.. / E8 = 4  => 19 pairs (_) / E9 = 4  =>  0 pairs (X)
B1,H1: 4.. / B1 = 4  =>  0 pairs (X) / H1 = 4  => 19 pairs (_)
B8,E8: 4.. / B8 = 4  =>  0 pairs (X) / E8 = 4  => 19 pairs (_)
A3,A9: 4.. / A3 = 4  =>  0 pairs (X) / A9 = 4  => 19 pairs (_)
C4,C9: 4.. / C4 = 4  => 20 pairs (_) / C9 = 4  =>  0 pairs (X)
E1,E3: 5.. / E1 = 5  => 21 pairs (_) / E3 = 5  =>  0 pairs (X)
D4,D6: 5.. / D4 = 5  =>  0 pairs (X) / D6 = 5  =>  0 pairs (_)
B1,E1: 5.. / B1 = 5  =>  0 pairs (X) / E1 = 5  => 21 pairs (_)
B4,D4: 5.. / B4 = 5  =>  0 pairs (*) / D4 = 5  =>  0 pairs (X)
A3,A6: 5.. / A3 = 5  =>  0 pairs (*) / A6 = 5  =>  0 pairs (X)
C5,F5: 6.. / C5 = 6  =>  0 pairs (X) / F5 = 6  =>  0 pairs (_)
B1,B2: 7.. / B1 = 7  => 22 pairs (_) / B2 = 7  => 20 pairs (_)
D1,D2: 7.. / D1 = 7  => 20 pairs (_) / D2 = 7  => 22 pairs (_)
C4,C6: 7.. / C4 = 7  =>  0 pairs (X) / C6 = 7  => 20 pairs (_)
H4,H6: 7.. / H4 = 7  => 20 pairs (_) / H6 = 7  =>  0 pairs (X)
B1,D1: 7.. / B1 = 7  => 22 pairs (_) / D1 = 7  => 20 pairs (_)
B2,D2: 7.. / B2 = 7  => 20 pairs (_) / D2 = 7  => 22 pairs (_)
C4,H4: 7.. / C4 = 7  =>  0 pairs (X) / H4 = 7  => 20 pairs (_)
C6,H6: 7.. / C6 = 7  => 20 pairs (_) / H6 = 7  =>  0 pairs (X)
H1,H3: 8.. / H1 = 8  =>  0 pairs (X) / H3 = 8  => 19 pairs (_)
D8,F9: 8.. / D8 = 8  =>  0 pairs (X) / F9 = 8  =>  0 pairs (_)
I7,I8: 8.. / I7 = 8  => 20 pairs (_) / I8 = 8  =>  0 pairs (X)
D3,H3: 8.. / D3 = 8  =>  0 pairs (X) / H3 = 8  => 19 pairs (_)
B7,I7: 8.. / B7 = 8  =>  0 pairs (X) / I7 = 8  => 20 pairs (_)
B9,F9: 8.. / B9 = 8  =>  0 pairs (X) / F9 = 8  =>  0 pairs (_)
F1,F9: 8.. / F1 = 8  =>  0 pairs (X) / F9 = 8  =>  0 pairs (_)
H5,H6: 9.. / H5 = 9  =>  0 pairs (X) / H6 = 9  =>  0 pairs (_)
B7,C7: 9.. / B7 = 9  =>  0 pairs (*) / C7 = 9  =>  0 pairs (X)
C5,H5: 9.. / C5 = 9  =>  0 pairs (*) / H5 = 9  =>  0 pairs (X)
B6,B7: 9.. / B6 = 9  =>  0 pairs (X) / B7 = 9  =>  0 pairs (_)
* DURATION: 0:00:49.478077  START: 05:20:20.695686  END: 05:21:10.173763 2019-05-01
* CP COUNT: (42)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A9,B2,C4,C5,C7,D4,E1,E7,F1,F4,F5,H1,H3,H4,H5,I7,I8)
* 9.3...1.6..8.34529..2..93.78...9.6.121.47.8.5....8.2.47..3.546.3.5..791....9..753
* PAIR A2: 1,6 BLK 1
A3: 1,6,4,5                              # reduction candidate for 1,6
A3: 1,6 => CTR
* 9.3..8146..8.34529.42.5938783459267121.47.8.55.7.8.2.47..3.546.3.584791248.9..753
A3: 4,5                                  # 21 pairs
* PAIR A2: 1,6 ROW 2
D2: 1,6,7                                # reduction candidate for 1,6
D2: 7                                    # 22 pairs
D2: 1,6                                  # 20 pairs
* PAIR B2: 6,7 ROW 2
D2: 6,7,1                                # reduction candidate for 6,7
D2: 1 => CTR
* 9.37.81.6.781345291.2..93.78...9.6.121.47.8.55..6812.47..3.546.3.5..791.4..9.6753
D2: 6,7                                  # 19 pairs
* PAIR F1: 2,8 BLK 2
D1: 2,8,7                                # reduction candidate for 2,8
D1: 2,8                                  # 22 pairs
D1: 7                                    # 20 pairs
* PAIR F1: 2,8 COL F
F9: 2,8,1,6                              # reduction candidate for 2,8
F9: 2,8 => SOLVED
* 973852146168734529542169387854293671219476835637581294791325468385647912426918753
F9: 1,6 => CTR
* 9.3258146..8734529..2..93878..5926.121.47.8.5....8.2.47293154683.5847912.81926753
* PAIR C5: 6,9 BLK 4
B6: 6,9,3,5                              # reduction candidate for 6,9
B6: 6,9 => CTR
* 9.3258146..8734529.52..938783459267121.47.8.55.7.8.2.4729315468345867912.8.92.753
B6: 3,5 => SOLVED
* 973852146168734529542169387854293671219476835637581294791325468385647912426918753
C6: 6,9,7                                # reduction candidate for 6,9
C6: 6,9 => CTR
* 9.3...1.6..8.34529..2..93.78.7.9.63121.473895.39.8.2747913254683.5..7912.249.8753
C6: 7                                    # 20 pairs
* PAIR A6: 5,6 BLK 4
B6: 5,6,3,9                              # reduction candidate for 5,6
B6: 5,6 => CTR
* 9.3...1.6..8.34529..2..93.783459267121.47.8.5..7.8.2947913254683.5..7912.269.8753
B6: 3,9                                  # 20 pairs
* PAIR A6: 5,6 ROW 6
D6: 5,6,1                                # reduction candidate for 5,6
D6: 1 => CTR
* 9.3..81461.8.34529..26193878..5926.121.47.8.5...18.2.47.13254683.58.7912...9.1753
D6: 5,6                                  # 23 pairs
* PAIR A6: 5,6 COL A
A3: 5,6,1,4                              # reduction candidate for 5,6
A3: 1,4 => CTR
* 9.3258146..8734529.52..93878..5926.121.47.8.55...8.2.47293154683.5847912.81926753
A3: 5,6                                  # 20 pairs
* PAIR F5: 3,6 BLK 5
F6: 3,6,1                                # reduction candidate for 3,6
F6: 3,6 => CTR
* 9.3..81461.8.34529..26193878..5926.121.47.8.5...18.2.47.13254683.58.7912...9.1753
F6: 1                                    # 23 pairs
* PAIR H4: 3,7 BLK 6
H6: 3,7,9                                # reduction candidate for 3,7
H6: 3,7 => CTR
* 9.3258146..8734529.52..93878..5926.12164738955...8.2.47293154683.5847912.81926753
H6: 9 => SOLVED
* 973852146168734529542169387854293671219476835637581294791325468385647912426918753
* PAIR H5: 3,9 BLK 6
H6: 3,9,7                                # reduction candidate for 3,9
H6: 7 => CTR
* 9.3...1.6..8.34529..2..93.78.7.9.631216473895539.8.2747913254683.5..7912.249.8753
H6: 3,9                                  # 20 pairs
* PAIR A9: 4,6 BLK 7
B8: 4,6,2,8                              # reduction candidate for 4,6
B8: 4,6 => CTR
* 9.3..8146..8.34529..2.693878345926712164738955976812347.931546.3658479124819.6753
B8: 2,8 => SOLVED
* 973852146168734529542169387854293671219476835637581294791325468385647912426918753
B9: 4,6,2,8                              # reduction candidate for 4,6
B9: 4,6 => CTR
* 9.3..21.6..8.34529..2..93.78..29367121.476835.375812947913.546.3.5..791....9.8753
B9: 2,8                                  # 20 pairs
C9: 4,6,1                                # reduction candidate for 4,6
C9: 4,6 => SOLVED
* 973852146168734529542169387854293671219476835637581294791325468385647912426918753
C9: 1 => CTR
* 9.3..8146..8.34529..2.693878345926712164738955976812347.931546.3658479124819.6753
* PAIR A9: 4,6 ROW 9
E9: 4,6,1,2                              # reduction candidate for 4,6
E9: 4,6 => CTR
* 9.3...1.6..8.34529..2..93.78.429367121.476835.3..8.2.47..3.546.3.5..791....9..753
E9: 1,2                                  # 28 pairs
* PAIR A9: 4,6 COL A
A3: 4,6,1,5                              # reduction candidate for 4,6
A3: 4,6 => CTR
* 9.32581461.8734529.52..93878..5926.121.47.8.55...8.2.47293154683.5847912.81926753
A3: 1,5                                  # 20 pairs
* PAIR E7: 1,2 BLK 8
E9: 1,2,4,6                              # reduction candidate for 1,2
E9: 1,2                                  # 28 pairs
F9: 1,2,6,8                              # reduction candidate for 1,2
F9: 1,2 => CTR
* 9.3.28146..8.34529..2.593878.429367121.47.8.5....8.2.47293154683.58.7912.819.2753
F9: 6,8                                  # 24 pairs
* PAIR I7: 2,8 ROW 7
B7: 2,8,9                                # reduction candidate for 2,8
B7: 2,8 => CTR
* 9.3..8146..8.34529..2.693878345926712164738955976812347.931546.3658479124819.6753
B7: 9 => SOLVED
* 973852146168734529542169387854293671219476835637581294791325468385647912426918753
* PAIR I8: 2,8 ROW 8
B8: 2,8,4,6                              # reduction candidate for 2,8
B8: 2,8 => SOLVED
* 973852146168734529542169387854293671219476835637581294791325468385647912426918753
B8: 4,6 => CTR
* 9.3..8146..8.34529..2.693878345926712164738955976812347.931546.3658479124819.6753
D8: 2,8,6                                # reduction candidate for 2,8
D8: 2,8 => CTR
* 9.3258146..8734529.5216938783459267121647389559768123472931546.3.58.7912.81926753
D8: 6 => SOLVED
* 973852146168734529542169387854293671219476835637581294791325468385647912426918753
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190416-absurd-base-pr-000.dot
* REASONING
* DIS # A3: 1,6 => CTR => A3: 4,5
* DIS # D2: 1 => CTR => D2: 6,7
* PRF # F9: 2,8 => SOL
* DIS # F9: 1,6 => CTR => F9: 2,8
* DIS # B6: 6,9 => CTR => B6: 3,5
* PRF # B6: 3,5 => SOL
* DIS # C6: 6,9 => CTR => C6: 7
* DIS # B6: 5,6 => CTR => B6: 3,9
* DIS # D6: 1 => CTR => D6: 5,6
* DIS # A3: 1,4 => CTR => A3: 5,6
* DIS # F6: 3,6 => CTR => F6: 1
* DIS # H6: 3,7 => CTR => H6: 9
* PRF # H6: 9 => SOL
* DIS # H6: 7 => CTR => H6: 3,9
* DIS # B8: 4,6 => CTR => B8: 2,8
* PRF # B8: 2,8 => SOL
* DIS # B9: 4,6 => CTR => B9: 2,8
* PRF # C9: 4,6 => SOL
* DIS # C9: 1 => CTR => C9: 4,6
* DIS # E9: 4,6 => CTR => E9: 1,2
* DIS # A3: 4,6 => CTR => A3: 1,5
* DIS # F9: 1,2 => CTR => F9: 6,8
* DIS # B7: 2,8 => CTR => B7: 9
* PRF # B7: 9 => SOL
* PRF # B8: 2,8 => SOL
* DIS # B8: 4,6 => CTR => B8: 2,8
* DIS # D8: 2,8 => CTR => D8: 6
* PRF # D8: 6 => SOL
* CNT  28 HDP CHAINS /  45 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A9,B2,C4,C5,C7,D4,E1,E7,F1,F4,F5,H1,H3,H4,H5,I7,I8)
* 9.3...1.6..8.34529..2..93.78...9.6.121.47.8.5....8.2.47..3.546.3.5..791....9..753
* PAIR A2: 1,6 BLK 1
A3: 1,6,4,5                              # reduction candidate for 1,6
A3: 1,6 => CTR
* 9.3..8146..8.34529.42.5938783459267121.47.8.55.7.8.2.47..3.546.3.584791248.9..753
* PAIR F1: 2,8 BLK 2
D1: 2,8,7                                # reduction candidate for 2,8
D1: 7 => CTR
* 9.37..1.6178634529462.593878.4.9.67121.47.8.55.718.2.47..3.546.3.5.6791....94.753
* PAIR C5: 6,9 BLK 4
C6: 6,9,7                                # reduction candidate for 6,9
C6: 6,9 => CTR
* 973.5.146168734529..2..93878.7.9.63121.473895.39.862747913254683.5..79126249..753
* PAIR F5: 3,6 BLK 5
F6: 3,6,1                                # reduction candidate for 3,6
F6: 3,6 => CTR
* 973.58146168734529..26193878.459267121.47.8.5..718.2.47.13254683.5867912...9.1753
F6: 1 => SOLVED
* 973852146168734529542169387854293671219476835637581294791325468385647912426918753
* DURATION: 0:00:06.877145  START: 05:21:41.197584  END: 05:21:48.074729 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190416-absurd-base-pr-001.dot
* REASONING
* DIS # A3: 1,6 => CTR => A3: 4,5
* DIS A3: 4,5 # D1: 7 => CTR => D1: 2,8
* DIS A3: 4,5 + D1: 2,8 # C6: 6,9 => CTR => C6: 7
* DIS A3: 4,5 + D1: 2,8 + C6: 7 # F6: 3,6 => CTR => F6: 1
* PRF A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1 => SOL
* STA A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1
* CNT   5 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190416, absurd

Solution

position: 973852146168734529542169387854293671219476835637581294791325468385647912426918753 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 # A3: 1,6 => CTR => A3: 4,5
* INC # A3: 4,5 => UNS
* INC # D2: 1,6 => UNS
* INC # D2: 7 => UNS
* INC # D2: 6,7 => UNS
* DIS # D2: 1 => CTR => D2: 6,7
* INC # D1: 2,8 => UNS
* INC # D1: 7 => UNS
* PRF # F9: 2,8 => SOL
* DIS # F9: 1,6 => CTR => F9: 2,8
* DIS # B6: 6,9 => CTR => B6: 3,5
* PRF # B6: 3,5 => SOL
* DIS # C6: 6,9 => CTR => C6: 7
* INC # C6: 7 => UNS
* DIS # B6: 5,6 => CTR => B6: 3,9
* INC # B6: 3,9 => UNS
* INC # D6: 5,6 => UNS
* DIS # D6: 1 => CTR => D6: 5,6
* INC # A3: 5,6 => UNS
* DIS # A3: 1,4 => CTR => A3: 5,6
* DIS # F6: 3,6 => CTR => F6: 1
* INC # F6: 1 => UNS
* DIS # H6: 3,7 => CTR => H6: 9
* PRF # H6: 9 => SOL
* INC # H6: 3,9 => UNS
* DIS # H6: 7 => CTR => H6: 3,9
* DIS # B8: 4,6 => CTR => B8: 2,8
* PRF # B8: 2,8 => SOL
* DIS # B9: 4,6 => CTR => B9: 2,8
* INC # B9: 2,8 => UNS
* PRF # C9: 4,6 => SOL
* DIS # C9: 1 => CTR => C9: 4,6
* DIS # E9: 4,6 => CTR => E9: 1,2
* INC # E9: 1,2 => UNS
* DIS # A3: 4,6 => CTR => A3: 1,5
* INC # A3: 1,5 => UNS
* INC # E9: 1,2 => UNS
* DIS # F9: 1,2 => CTR => F9: 6,8
* INC # F9: 6,8 => UNS
* DIS # B7: 2,8 => CTR => B7: 9
* PRF # B7: 9 => SOL
* PRF # B8: 2,8 => SOL
* DIS # B8: 4,6 => CTR => B8: 2,8
* DIS # D8: 2,8 => CTR => D8: 6
* PRF # D8: 6 => SOL
* CNT  45 HDP CHAINS /  45 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 1,6 => CTR => A3: 4,5
* INC A3: 4,5 # D1: 2,8 => UNS
* DIS A3: 4,5 # D1: 7 => CTR => D1: 2,8
* DIS A3: 4,5 + D1: 2,8 # C6: 6,9 => CTR => C6: 7
* DIS A3: 4,5 + D1: 2,8 + C6: 7 # F6: 3,6 => CTR => F6: 1
* PRF A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1 => SOL
* STA A3: 4,5 + D1: 2,8 + C6: 7 + F6: 1
* CNT   6 HDP CHAINS /   5 HYP OPENED