Analysis of zz-www.sudokuoftheday.co.uk-20060426-absurd-base.sdk

Contents

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

level: medium

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

position: ..4.1.2..3....7..5.2..9.8.7.3....1....7..6.5.8............5...869.7.1....7.4.3... initial

Autosolve

position: 7.4.182..389..7.15.2..9.8.7.3..7.18...78.6.5.8..1.........5...869.7.1....7.4.3..1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 5,6 => CTR => C3: 1
* DIS # D1: 3 => CTR => D1: 5,6
* DIS # C3: 6 => CTR => C3: 1,5
* DIS # E2: 4 => CTR => E2: 2,6
* DIS # D7: 9 => CTR => D7: 2,6
* DIS # H3: 3 => CTR => H3: 4,6
* DIS # E2: 2 => CTR => E2: 4,6
* DIS # A5: 1 => CTR => A5: 4,9
* DIS # F4: 4,9 => CTR => F4: 2,5
* DIS # I4: 4,9 => CTR => I4: 2,6
* DIS # A5: 1,4 => CTR => A5: 9
* DIS # A7: 2 => CTR => A7: 1,4
* DIS # C8: 3 => CTR => C8: 5,8
* DIS # D7: 2,9 => CTR => D7: 6
* PRF # D7: 6 => SOL
* PRF # E9: 2,8 => SOL
* DIS # E9: 6 => CTR => E9: 2,8
* CNT  17 HDP CHAINS /  38 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 # C3: 5,6 => CTR => C3: 1
* PRF C3: 1 # D7: 2,6 => SOL
* STA C3: 1 + D7: 2,6
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

..4.1.2..3....7..5.2..9.8.7.3....1....7..6.5.8............5...869.7.1....7.4.3... initial
7.4.182..389..7.15.2..9.8.7.3..7.18...78.6.5.8..1.........5...869.7.1....7.4.3..1 autosolve
764518239389267415521394867432975186917846352856132974143659728698721543275483691 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B1: 5,6
A3: 1,5
D2: 2,6
F3: 4,5
G2: 4,6
A4: 4,9
B5: 1,4
B6: 5,6
B7: 1,4
C7: 1,3
A9: 2,5
C9: 5,8
F7: 2,9
E8: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A3,C3: 1.. / A3 = 1  =>  0 pairs (X) / C3 = 1  => 26 pairs (_)
A5,B5: 1.. / A5 = 1  =>  0 pairs (X) / B5 = 1  => 14 pairs (_)
B5,B7: 1.. / B5 = 1  => 14 pairs (_) / B7 = 1  =>  0 pairs (X)
C3,C7: 1.. / C3 = 1  => 26 pairs (_) / C7 = 1  =>  0 pairs (X)
D2,E2: 2.. / D2 = 2  => 16 pairs (_) / E2 = 2  =>  0 pairs (X)
C4,C6: 2.. / C4 = 2  => 17 pairs (_) / C6 = 2  => 17 pairs (_)
A7,A9: 2.. / A7 = 2  =>  0 pairs (X) / A9 = 2  => 26 pairs (_)
E5,I5: 2.. / E5 = 2  =>  0 pairs (X) / I5 = 2  => 16 pairs (_)
D1,D3: 3.. / D1 = 3  =>  0 pairs (X) / D3 = 3  => 18 pairs (_)
E5,E6: 3.. / E5 = 3  => 17 pairs (_) / E6 = 3  => 15 pairs (_)
C7,C8: 3.. / C7 = 3  => 26 pairs (_) / C8 = 3  =>  0 pairs (X)
D3,H3: 3.. / D3 = 3  => 18 pairs (_) / H3 = 3  =>  0 pairs (X)
E2,F3: 4.. / E2 = 4  =>  0 pairs (X) / F3 = 4  => 22 pairs (_)
G2,H3: 4.. / G2 = 4  => 22 pairs (_) / H3 = 4  =>  0 pairs (X)
A7,B7: 4.. / A7 = 4  =>  0 pairs (X) / B7 = 4  => 14 pairs (_)
E2,G2: 4.. / E2 = 4  =>  0 pairs (X) / G2 = 4  => 22 pairs (_)
F3,H3: 4.. / F3 = 4  => 22 pairs (_) / H3 = 4  =>  0 pairs (X)
B5,B7: 4.. / B5 = 4  =>  0 pairs (X) / B7 = 4  => 14 pairs (_)
G8,G9: 5.. / G8 = 5  => 16 pairs (_) / G9 = 5  =>  0 pairs (X)
B1,D1: 5.. / B1 = 5  =>  0 pairs (X) / D1 = 5  => 24 pairs (_)
C8,G8: 5.. / C8 = 5  =>  0 pairs (X) / G8 = 5  => 16 pairs (_)
A3,A9: 5.. / A3 = 5  => 26 pairs (_) / A9 = 5  =>  0 pairs (X)
B1,B6: 5.. / B1 = 5  =>  0 pairs (X) / B6 = 5  => 24 pairs (_)
B1,C3: 6.. / B1 = 6  => 24 pairs (_) / C3 = 6  =>  0 pairs (X)
D7,E9: 6.. / D7 = 6  =>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
C4,I4: 6.. / C4 = 6  =>  0 pairs (X) / I4 = 6  => 16 pairs (_)
B1,B6: 6.. / B1 = 6  => 24 pairs (_) / B6 = 6  =>  0 pairs (X)
E2,E9: 6.. / E2 = 6  =>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
G6,H6: 7.. / G6 = 7  => 15 pairs (_) / H6 = 7  => 15 pairs (_)
G7,H7: 7.. / G7 = 7  => 15 pairs (_) / H7 = 7  => 15 pairs (_)
G6,G7: 7.. / G6 = 7  => 15 pairs (_) / G7 = 7  => 15 pairs (_)
H6,H7: 7.. / H6 = 7  => 15 pairs (_) / H7 = 7  => 15 pairs (_)
C8,C9: 8.. / C8 = 8  =>  0 pairs (*) / C9 = 8  =>  0 pairs (X)
E8,E9: 8.. / E8 = 8  => 15 pairs (_) / E9 = 8  =>  0 pairs (*)
C8,E8: 8.. / C8 = 8  =>  0 pairs (*) / E8 = 8  =>  0 pairs (X)
C9,E9: 8.. / C9 = 8  => 15 pairs (_) / E9 = 8  =>  0 pairs (*)
H1,I1: 9.. / H1 = 9  => 18 pairs (_) / I1 = 9  => 16 pairs (_)
A4,A5: 9.. / A4 = 9  =>  0 pairs (X) / A5 = 9  => 13 pairs (_)
D7,F7: 9.. / D7 = 9  =>  0 pairs (X) / F7 = 9  => 25 pairs (_)
G9,H9: 9.. / G9 = 9  => 17 pairs (_) / H9 = 9  => 17 pairs (_)
D4,D7: 9.. / D4 = 9  => 25 pairs (_) / D7 = 9  =>  0 pairs (X)
* DURATION: 0:00:46.415262  START: 22:40:25.584638  END: 22:41:11.999900 2019-04-30
* CP COUNT: (41)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A9,B1,B5,B6,B7,C7,C9,D2,E8,F3,F7,G2)
* 7.4.182..389..7.15.2..9.8.7.3..7.18...78.6.5.8..1.........5...869.7.1....7.4.3..1
* PAIR B1: 5,6 BLK 1
C3: 5,6,1                                # reduction candidate for 5,6
C3: 5,6 => CTR
* 7.4.182..38926741512..948.7.3.97.18.9178.63528..13....241659738693781524578423..1
C3: 1                                    # 26 pairs
* PAIR B1: 5,6 ROW 1
D1: 5,6,3                                # reduction candidate for 5,6
D1: 3 => CTR
* 754318269389..741512659483743..7.1869178.6.5.86.1......41.5.3786937815..5784.3..1
D1: 5,6                                  # 18 pairs
* PAIR A3: 1,5 BLK 1
C3: 1,5,6                                # reduction candidate for 1,5
C3: 6 => CTR
* 754.182..389267415126.9483743.97.1869178.635286.13....2416597.86937815..578423..1
C3: 1,5                                  # 24 pairs
* PAIR D2: 2,6 BLK 2
E2: 2,6,4                                # reduction candidate for 2,6
E2: 4 => CTR
* 7.4.182..389247615.2..95847.3.57.18...78.6.5.8..1........952.6869.781....7.4.3..1
E2: 2,6                                  # 22 pairs
* PAIR D2: 2,6 COL D
D7: 2,6,9                                # reduction candidate for 2,6
D7: 9 => CTR
* 764518239389.2741552139486793.275184..78.6952852149.7...3952..8695781...278463591
D7: 2,6                                  # 25 pairs
* PAIR F3: 4,5 COL F
F4: 4,5,2,9                              # reduction candidate for 4,5
F4: 4,5                                  # 17 pairs
F6: 4,5,2,9                              # reduction candidate for 4,5
F6: 4,5                                  # 16 pairs
* PAIR G2: 4,6 BLK 3
H3: 4,6,3                                # reduction candidate for 4,6
H3: 3 => CTR
* 75431826938926741512659483743.97.1869178.6.5.86.1.....241.593786937815..578423691
H3: 4,6                                  # 18 pairs
* PAIR G2: 4,6 ROW 2
E2: 4,6,2                                # reduction candidate for 4,6
E2: 2 => CTR
* 7.4.182.938962741552139486743..7.1869178463528..1.........5...869.781.24278463591
E2: 4,6                                  # 16 pairs
* PAIR G2: 4,6 COL G
G6: 4,6,3,7,9                            # reduction candidate for 4,6
G6: 4,6                                  # 21 pairs
G6: 3,7,9                                # 14 pairs
* PAIR A4: 4,9 BLK 4
A5: 4,9,1                                # reduction candidate for 4,9
A5: 1 => CTR
* 7.4.182.9389..7.15521.948.793..751841478.695.85.149..6413952..8695781.42278463591
A5: 4,9                                  # 14 pairs
* PAIR A4: 4,9 ROW 4
F4: 4,9,2,5                              # reduction candidate for 4,9
F4: 4,9 => CTR
* 7.4.182.9389..7.15521.948.743..7918.9178.6.5.85.1........952..869.781...278463591
F4: 2,5                                  # 15 pairs
I4: 4,9,2,6                              # reduction candidate for 4,9
I4: 4,9 => CTR
* 764518239389627415521394867936275184..78.6.528521.9..6...95267869.781.2.278463591
I4: 2,6                                  # 15 pairs
* PAIR B5: 1,4 BLK 4
A5: 1,4,9                                # reduction candidate for 1,4
A5: 1,4 => CTR
* 7.4.182.9389..7.15521.948.793..75184..78.695.85.149..6..3952..8695781.42278463591
A5: 9                                    # 13 pairs
* PAIR B6: 5,6 BLK 4
C4: 5,6,2                                # reduction candidate for 5,6
C4: 5,6                                  # 17 pairs
C6: 5,6,2                                # reduction candidate for 5,6
C6: 5,6                                  # 17 pairs
* PAIR B7: 1,4 BLK 7
A7: 1,4,2                                # reduction candidate for 1,4
A7: 2 => CTR
* 7.4.182..38926741512..948.7.3.97.18.9178.63528..13....241659738693781524578423..1
A7: 1,4                                  # 26 pairs
* PAIR C9: 5,8 BLK 7
C8: 5,8,3                                # reduction candidate for 5,8
C8: 3 => CTR
* 7.4.182..38926741512..948.7.3.97.18.9178.63528..13....241659738693781524578423..1
C8: 5,8                                  # 26 pairs
* PAIR F7: 2,9 BLK 8
D7: 2,9,6                                # reduction candidate for 2,9
D7: 2,9 => CTR
* 76451823938962741552139486743.97518...78.6.5285.1.......3.5.678695781324278463591
D7: 6 => SOLVED
* 764518239389267415521394867432975186917846352856132974143659728698721543275483691
* PAIR F7: 2,9 COL F
F4: 2,9,4,5                              # reduction candidate for 2,9
F4: 2,9                                  # 16 pairs
F6: 2,9,4,5                              # reduction candidate for 2,9
F6: 2,9                                  # 17 pairs
* PAIR E8: 2,8 BLK 8
E9: 2,8,6                                # reduction candidate for 2,8
E9: 2,8 => SOLVED
* 764518239389267415521394867432975186917846352856132974143659728698721543275483691
E9: 6 => CTR
* 76451823938962741552139486743.97518...78.6.5285.1.......3.5.678695781324278463591
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060426-absurd-base-pr-000.dot
* REASONING
* DIS # C3: 5,6 => CTR => C3: 1
* DIS # D1: 3 => CTR => D1: 5,6
* DIS # C3: 6 => CTR => C3: 1,5
* DIS # E2: 4 => CTR => E2: 2,6
* DIS # D7: 9 => CTR => D7: 2,6
* DIS # H3: 3 => CTR => H3: 4,6
* DIS # E2: 2 => CTR => E2: 4,6
* DIS # A5: 1 => CTR => A5: 4,9
* DIS # F4: 4,9 => CTR => F4: 2,5
* DIS # I4: 4,9 => CTR => I4: 2,6
* DIS # A5: 1,4 => CTR => A5: 9
* DIS # A7: 2 => CTR => A7: 1,4
* DIS # C8: 3 => CTR => C8: 5,8
* DIS # D7: 2,9 => CTR => D7: 6
* PRF # D7: 6 => SOL
* PRF # E9: 2,8 => SOL
* DIS # E9: 6 => CTR => E9: 2,8
* CNT  17 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,A9,B1,B5,B6,B7,C7,C9,D2,E8,F3,F7,G2)
* 7.4.182..389..7.15.2..9.8.7.3..7.18...78.6.5.8..1.........5...869.7.1....7.4.3..1
* PAIR B1: 5,6 BLK 1
C3: 5,6,1                                # reduction candidate for 5,6
C3: 5,6 => CTR
* 7.4.182..38926741512..948.7.3.97.18.9178.63528..13....241659738693781524578423..1
* PAIR D2: 2,6 COL D
D7: 2,6,9                                # reduction candidate for 2,6
D7: 2,6 => SOLVED
* 764518239389267415521394867432975186917846352856132974143659728698721543275483691
* DURATION: 0:00:03.260808  START: 22:41:37.082805  END: 22:41:40.343613 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060426-absurd-base-pr-001.dot
* REASONING
* DIS # C3: 5,6 => CTR => C3: 1
* PRF C3: 1 # D7: 2,6 => SOL
* STA C3: 1 + D7: 2,6
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060426, absurd

Solution

position: 764518239389267415521394867432975186917846352856132974143659728698721543275483691 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 # C3: 5,6 => CTR => C3: 1
* INC # C3: 1 => UNS
* INC # D1: 5,6 => UNS
* DIS # D1: 3 => CTR => D1: 5,6
* INC # C3: 1,5 => UNS
* DIS # C3: 6 => CTR => C3: 1,5
* INC # E2: 2,6 => UNS
* DIS # E2: 4 => CTR => E2: 2,6
* INC # D7: 2,6 => UNS
* DIS # D7: 9 => CTR => D7: 2,6
* INC # F4: 4,5 => UNS
* INC # F6: 4,5 => UNS
* INC # H3: 4,6 => UNS
* DIS # H3: 3 => CTR => H3: 4,6
* INC # E2: 4,6 => UNS
* DIS # E2: 2 => CTR => E2: 4,6
* INC # G6: 4,6 => UNS
* INC # G6: 3,7,9 => UNS
* INC # A5: 4,9 => UNS
* DIS # A5: 1 => CTR => A5: 4,9
* DIS # F4: 4,9 => CTR => F4: 2,5
* INC # F4: 2,5 => UNS
* DIS # I4: 4,9 => CTR => I4: 2,6
* INC # I4: 2,6 => UNS
* DIS # A5: 1,4 => CTR => A5: 9
* INC # A5: 9 => UNS
* INC # C4: 5,6 => UNS
* INC # C6: 5,6 => UNS
* INC # A7: 1,4 => UNS
* DIS # A7: 2 => CTR => A7: 1,4
* INC # C8: 5,8 => UNS
* DIS # C8: 3 => CTR => C8: 5,8
* DIS # D7: 2,9 => CTR => D7: 6
* PRF # D7: 6 => SOL
* INC # F4: 2,9 => UNS
* INC # F6: 2,9 => UNS
* PRF # E9: 2,8 => SOL
* DIS # E9: 6 => CTR => E9: 2,8
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C3: 5,6 => CTR => C3: 1
* PRF C3: 1 # D7: 2,6 => SOL
* STA C3: 1 + D7: 2,6
* CNT   2 HDP CHAINS /   2 HYP OPENED