Analysis of zz-www.sudokuoftheday.co.uk-20190220-absurd-base.sdk

Contents

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

level: medium

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

position: 38.....6.5..41.....7...3.......3....6..2...787..6..5......2..5...9.51..7...7.41.6 initial

Autosolve

position: 38..7..6.5.641.7...7..63......1376..6..2.5.787..6..5....7.26.5..69.51..7...7.41.6 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 2,9 => CTR => A3: 1,4
* DIS # F2: 2,9 => CTR => F2: 8
* DIS # B4: 2,9 => CTR => B4: 4,5
* DIS # D3: 8 => CTR => D3: 5,9
* DIS # F2: 2,9 => CTR => F2: 8
* DIS # E6: 4,9 => CTR => E6: 8
* DIS # B5: 4,9 => CTR => B5: 1
* PRF # G5: 4,9 => SOL
* DIS # G5: 3 => CTR => G5: 4,9
* DIS # E6: 4 => CTR => E6: 8,9
* DIS # F2: 2 => CTR => F2: 8,9
* DIS # A4: 2,8 => CTR => A4: 4,9
* DIS # D7: 9 => CTR => D7: 3,8
* DIS # E6: 4 => CTR => E6: 8,9
* CNT  14 HDP CHAINS /  43 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: 2,9 => CTR => A3: 1,4
* PRF A3: 1,4 # D3: 5,9 => SOL
* STA A3: 1,4 + D3: 5,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

38.....6.5..41.....7...3.......3....6..2...787..6..5......2..5...9.51..7...7.41.6 initial
38..7..6.5.641.7...7..63......1376..6..2.5.787..6..5....7.26.5..69.51..7...7.41.6 autosolve
381972465596418732472563891958137624613245978724689513147826359869351247235794186 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
B2: 2,9
D1: 5,9
F1: 2,9
C4: 5,8
E5: 4,9
F6: 8,9
A9: 2,8
C9: 5,8
D8: 3,8
E9: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,C5: 1.. / B5 = 1  => 12 pairs (_) / C5 = 1  =>  0 pairs (X)
H6,I6: 1.. / H6 = 1  => 12 pairs (_) / I6 = 1  => 13 pairs (_)
A7,B7: 1.. / A7 = 1  => 12 pairs (_) / B7 = 1  =>  0 pairs (X)
C1,I1: 1.. / C1 = 1  => 13 pairs (_) / I1 = 1  => 11 pairs (_)
A3,A7: 1.. / A3 = 1  =>  0 pairs (X) / A7 = 1  => 12 pairs (_)
B5,B7: 1.. / B5 = 1  => 12 pairs (_) / B7 = 1  =>  0 pairs (X)
H3,H6: 1.. / H3 = 1  => 13 pairs (_) / H6 = 1  => 12 pairs (_)
F1,F2: 2.. / F1 = 2  => 12 pairs (_) / F2 = 2  =>  0 pairs (X)
H2,I2: 3.. / H2 = 3  => 17 pairs (_) / I2 = 3  => 11 pairs (_)
C5,C6: 3.. / C5 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
B7,B9: 3.. / B7 = 3  =>  0 pairs (X) / B9 = 3  => 10 pairs (_)
D7,D8: 3.. / D7 = 3  => 15 pairs (_) / D8 = 3  => 10 pairs (_)
C5,G5: 3.. / C5 = 3  =>  0 pairs (*) / G5 = 3  =>  0 pairs (X)
B9,H9: 3.. / B9 = 3  => 10 pairs (_) / H9 = 3  =>  0 pairs (X)
E5,E6: 4.. / E5 = 4  => 14 pairs (_) / E6 = 4  =>  0 pairs (X)
D1,D3: 5.. / D1 = 5  => 10 pairs (_) / D3 = 5  =>  0 pairs (*)
I1,I3: 5.. / I1 = 5  =>  0 pairs (*) / I3 = 5  =>  0 pairs (X)
B4,C4: 5.. / B4 = 5  =>  9 pairs (_) / C4 = 5  =>  0 pairs (X)
B9,C9: 5.. / B9 = 5  =>  0 pairs (X) / C9 = 5  =>  9 pairs (_)
D1,I1: 5.. / D1 = 5  => 10 pairs (_) / I1 = 5  =>  0 pairs (*)
D3,I3: 5.. / D3 = 5  =>  0 pairs (*) / I3 = 5  =>  0 pairs (X)
B4,B9: 5.. / B4 = 5  =>  9 pairs (_) / B9 = 5  =>  0 pairs (X)
C4,C9: 5.. / C4 = 5  =>  0 pairs (X) / C9 = 5  =>  9 pairs (_)
F2,D3: 8.. / F2 = 8  => 14 pairs (_) / D3 = 8  =>  0 pairs (X)
A4,C4: 8.. / A4 = 8  =>  0 pairs (X) / C4 = 8  =>  9 pairs (_)
E6,F6: 8.. / E6 = 8  => 14 pairs (_) / F6 = 8  =>  0 pairs (X)
F2,H2: 8.. / F2 = 8  => 14 pairs (_) / H2 = 8  =>  0 pairs (X)
C4,C9: 8.. / C4 = 8  =>  9 pairs (_) / C9 = 8  =>  0 pairs (X)
E6,E9: 8.. / E6 = 8  => 14 pairs (_) / E9 = 8  =>  0 pairs (X)
F2,F6: 8.. / F2 = 8  => 14 pairs (_) / F6 = 8  =>  0 pairs (X)
B2,A3: 9.. / B2 = 9  => 15 pairs (_) / A3 = 9  =>  0 pairs (X)
D7,E9: 9.. / D7 = 9  =>  0 pairs (X) / E9 = 9  => 14 pairs (_)
E9,H9: 9.. / E9 = 9  => 14 pairs (_) / H9 = 9  =>  0 pairs (X)
A3,A4: 9.. / A3 = 9  =>  0 pairs (X) / A4 = 9  => 15 pairs (_)
* DURATION: 0:00:45.118837  START: 03:52:12.645800  END: 03:52:57.764637 2019-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B2,C4,C9,D1,D8,E5,E9,F1,F6)
* 38..7..6.5.641.7...7..63......1376..6..2.5.787..6..5....7.26.5..69.51..7...7.41.6
* PAIR B2: 2,9 BLK 1
A3: 2,9,1,4                              # reduction candidate for 2,9
A3: 2,9 => CTR
* 38..7..6.52641.7..97..63....581376..6132.5.787926.85..147.26.59.69.51..7.357.41.6
A3: 1,4                                  # 16 pairs
* PAIR B2: 2,9 ROW 2
F2: 2,9,8                                # reduction candidate for 2,9
F2: 2,9 => CTR
* 38157.46.5.641.78397.863..5..81376..6..2.5.787..6.8531..7926354469351827235784196
F2: 8                                    # 14 pairs
H2: 2,9,3,8                              # reduction candidate for 2,9
H2: 2,9                                  # 16 pairs
I2: 2,9,3                                # reduction candidate for 2,9
I2: 2,9                                  # 17 pairs
* PAIR B2: 2,9 COL B
B4: 2,9,4,5                              # reduction candidate for 2,9
B4: 2,9 => CTR
* 38..7..6.5.641.7.3.7..63...8.51376..6..2453787.36895...37826.5..69351..7258794136
B4: 4,5                                  # 11 pairs
B6: 2,9,4                                # reduction candidate for 2,9
B6: 2,9                                  # 14 pairs
* PAIR D1: 5,9 BLK 2
D3: 5,9,8                                # reduction candidate for 5,9
D3: 8 => CTR
* 38157.46.5.641.78397.863..5..81376..6..2.5.787..6.8531..7926354469351827235784196
D3: 5,9                                  # 14 pairs
* PAIR D1: 5,9 ROW 1
I1: 5,9,1,2,4                            # reduction candidate for 5,9
I1: 5,9                                  # 15 pairs
I1: 1,2,4                                # 10 pairs
* PAIR F1: 2,9 BLK 2
F2: 2,9,8                                # reduction candidate for 2,9
F2: 2,9 => CTR
* 38157.46.5.641.78397.863..5..81376..6..2.5.787..6.8531..7926354469351827235784196
F2: 8                                    # 14 pairs
* PAIR F1: 2,9 ROW 1
G1: 2,9,4                                # reduction candidate for 2,9
G1: 2,9                                  # 13 pairs
I1: 2,9,1,4,5                            # reduction candidate for 2,9
I1: 2,9                                  # 15 pairs
* PAIR E5: 4,9 BLK 5
E6: 4,9,8                                # reduction candidate for 4,9
E6: 4,9 => CTR
* 38.57..6.5.641.783.7.863..59581376426..2.5.787..6.8531817926354469351827235784196
E6: 8                                    # 14 pairs
* PAIR E5: 4,9 ROW 5
B5: 4,9,1                                # reduction candidate for 4,9
B5: 4,9 => CTR
* 38..7..615.641.7..17..63..59581376..641295378723648519.17926.53.69351..7.35784196
B5: 1                                    # 12 pairs
G5: 4,9,3                                # reduction candidate for 4,9
G5: 4,9 => SOLVED
* 381972465596418732472563891958137624613245978724689513147826359869351247235794186
G5: 3 => CTR
* 38..7..6.59641.7...7..63...9.81376..6..2953787.36485....7926.5..69351..7..5784196
* PAIR F6: 8,9 BLK 5
E6: 8,9,4                                # reduction candidate for 8,9
E6: 4 => CTR
* 38.57..6.5.641.783.7.863..59581376426412953787..6485....7926.54469351827235784196
E6: 8,9                                  # 14 pairs
* PAIR F6: 8,9 COL F
F2: 8,9,2                                # reduction candidate for 8,9
F2: 2 => CTR
* 38.579.6.596412783.7.8639.59.81376..6..295.787..64853...7.26.5..69351..7...784196
F2: 8,9                                  # 12 pairs
* PAIR A9: 2,8 BLK 7
A8: 2,8,4                                # reduction candidate for 2,8
A8: 4                                    # 14 pairs
A8: 2,8                                  # 13 pairs
* PAIR A9: 2,8 ROW 9
H9: 2,8,3,9                              # reduction candidate for 2,8
H9: 2,8                                  # 15 pairs
H9: 3,9                                  # 12 pairs
* PAIR A9: 2,8 COL A
A4: 2,8,4,9                              # reduction candidate for 2,8
A4: 2,8 => CTR
* 38..7..6.52641.7..97..63......1376..61.2.5.787.26..5..137.26.5.469351..7258794136
A4: 4,9                                  # 10 pairs
* PAIR D8: 3,8 BLK 8
D7: 3,8,9                                # reduction candidate for 3,8
D7: 9 => CTR
* 38157.46.5.641.78397.863..5.581376..6..2.5.787..6.8531..7926354469351827235784196
D7: 3,8                                  # 14 pairs
* PAIR D8: 3,8 ROW 8
G8: 3,8,2,4                              # reduction candidate for 3,8
G8: 3,8                                  # 15 pairs
H8: 3,8,2,4                              # reduction candidate for 3,8
H8: 3,8                                  # 13 pairs
* PAIR E9: 8,9 BLK 8
D7: 8,9,3                                # reduction candidate for 8,9
D7: 3                                    # 15 pairs
D7: 8,9                                  # 10 pairs
* PAIR E9: 8,9 ROW 9
H9: 8,9,2,3                              # reduction candidate for 8,9
H9: 2,3                                  # 17 pairs
H9: 8,9                                  # 11 pairs
* PAIR E9: 8,9 COL E
E6: 8,9,4                                # reduction candidate for 8,9
E6: 4 => CTR
* 38.57..6.5.641.783.7.863..59581376426412953787..6485....7926.54469351827235784196
E6: 8,9                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190220-absurd-base-pr-000.dot
* REASONING
* DIS # A3: 2,9 => CTR => A3: 1,4
* DIS # F2: 2,9 => CTR => F2: 8
* DIS # B4: 2,9 => CTR => B4: 4,5
* DIS # D3: 8 => CTR => D3: 5,9
* DIS # F2: 2,9 => CTR => F2: 8
* DIS # E6: 4,9 => CTR => E6: 8
* DIS # B5: 4,9 => CTR => B5: 1
* PRF # G5: 4,9 => SOL
* DIS # G5: 3 => CTR => G5: 4,9
* DIS # E6: 4 => CTR => E6: 8,9
* DIS # F2: 2 => CTR => F2: 8,9
* DIS # A4: 2,8 => CTR => A4: 4,9
* DIS # D7: 9 => CTR => D7: 3,8
* DIS # E6: 4 => CTR => E6: 8,9
* CNT  14 HDP CHAINS /  43 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B2,C4,C9,D1,D8,E5,E9,F1,F6)
* 38..7..6.5.641.7...7..63......1376..6..2.5.787..6..5....7.26.5..69.51..7...7.41.6
* PAIR B2: 2,9 BLK 1
A3: 2,9,1,4                              # reduction candidate for 2,9
A3: 2,9 => CTR
* 38..7..6.52641.7..97..63....581376..6132.5.787926.85..147.26.59.69.51..7.357.41.6
* PAIR D1: 5,9 BLK 2
D3: 5,9,8                                # reduction candidate for 5,9
D3: 5,9 => SOLVED
* 381972465596418732472563891958137624613245978724689513147826359869351247235794186
* DURATION: 0:00:03.410558  START: 03:53:29.441004  END: 03:53:32.851562 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190220-absurd-base-pr-001.dot
* REASONING
* DIS # A3: 2,9 => CTR => A3: 1,4
* PRF A3: 1,4 # D3: 5,9 => SOL
* STA A3: 1,4 + D3: 5,9
* CNT   2 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190220, absurd

Solution

position: 381972465596418732472563891958137624613245978724689513147826359869351247235794186 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: 2,9 => CTR => A3: 1,4
* INC # A3: 1,4 => UNS
* DIS # F2: 2,9 => CTR => F2: 8
* INC # F2: 8 => UNS
* INC # H2: 2,9 => UNS
* INC # I2: 2,9 => UNS
* DIS # B4: 2,9 => CTR => B4: 4,5
* INC # B4: 4,5 => UNS
* INC # B6: 2,9 => UNS
* INC # D3: 5,9 => UNS
* DIS # D3: 8 => CTR => D3: 5,9
* INC # I1: 5,9 => UNS
* INC # I1: 1,2,4 => UNS
* DIS # F2: 2,9 => CTR => F2: 8
* INC # F2: 8 => UNS
* INC # G1: 2,9 => UNS
* INC # I1: 2,9 => UNS
* DIS # E6: 4,9 => CTR => E6: 8
* INC # E6: 8 => UNS
* DIS # B5: 4,9 => CTR => B5: 1
* INC # B5: 1 => UNS
* PRF # G5: 4,9 => SOL
* DIS # G5: 3 => CTR => G5: 4,9
* INC # E6: 8,9 => UNS
* DIS # E6: 4 => CTR => E6: 8,9
* INC # F2: 8,9 => UNS
* DIS # F2: 2 => CTR => F2: 8,9
* INC # A8: 2,8 => UNS
* INC # A8: 4 => UNS
* INC # H9: 2,8 => UNS
* INC # H9: 3,9 => UNS
* DIS # A4: 2,8 => CTR => A4: 4,9
* INC # A4: 4,9 => UNS
* INC # D7: 3,8 => UNS
* DIS # D7: 9 => CTR => D7: 3,8
* INC # G8: 3,8 => UNS
* INC # H8: 3,8 => UNS
* INC # D7: 8,9 => UNS
* INC # D7: 3 => UNS
* INC # H9: 8,9 => UNS
* INC # H9: 2,3 => UNS
* INC # E6: 8,9 => UNS
* DIS # E6: 4 => CTR => E6: 8,9
* CNT  43 HDP CHAINS /  43 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 2,9 => CTR => A3: 1,4
* PRF A3: 1,4 # D3: 5,9 => SOL
* STA A3: 1,4 + D3: 5,9
* CNT   2 HDP CHAINS /   2 HYP OPENED