Analysis of zz-www.sudokuoftheday.co.uk-20060517-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: ....8..4......61.2..5....8...6......49...7.3..2..14....4..759...7.4.961....8..... initial

Autosolve

position: ....8..4..84..61.2..5.4..8...6..8...49...7.3..2..14.6..4..7592..7.4.961....8..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I4: 1,5 => CTR => I4: 4,7,9
* DIS # A8: 2,3 => CTR => A8: 5,8
* DIS # E4: 2,3 => CTR => E4: 5,9
* DIS # I8: 5 => CTR => I8: 3,8
* PRF # A7: 3,8 => SOL
* DIS # G9: 5,7 => CTR => G9: 3,4
* PRF # I9: 5,7 => SOL
* CNT   7 HDP CHAINS /  29 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 # I4: 1,5 => CTR => I4: 4,7,9
* PRF I4: 4,7,9 # E9: 2,3 => SOL
* STA I4: 4,7,9 + E9: 2,3
* CNT   2 HDP CHAINS /  11 HYP OPENED

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

Details

Positions

....8..4......61.2..5....8...6......49...7.3..2..14....4..759...7.4.961....8..... initial
....8..4..84..61.2..5.4..8...6..8...49...7.3..2..14.6..4..7592..7.4.961....8..... autosolve
967182345384756192215943786156398274498267531723514869841675923572439618639821457 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
G3: 3,7
C5: 1,8
I5: 1,5
E8: 2,3
I7: 3,8
H9: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I4,I5: 1.. / I4 = 1  =>  0 pairs (X) / I5 = 1  => 10 pairs (_)
D7,F9: 1.. / D7 = 1  =>  9 pairs (_) / F9 = 1  => 17 pairs (_)
C5,I5: 1.. / C5 = 1  =>  0 pairs (X) / I5 = 1  => 10 pairs (_)
G4,G5: 2.. / G4 = 2  =>  0 pairs (*) / G5 = 2  =>  0 pairs (X)
G4,I4: 4.. / G4 = 4  => 12 pairs (_) / I4 = 4  => 10 pairs (_)
G9,I9: 4.. / G9 = 4  => 10 pairs (_) / I9 = 4  => 12 pairs (_)
G4,G9: 4.. / G4 = 4  => 12 pairs (_) / G9 = 4  => 10 pairs (_)
I4,I9: 4.. / I4 = 4  => 10 pairs (_) / I9 = 4  => 12 pairs (_)
A8,I8: 5.. / A8 = 5  =>  8 pairs (_) / I8 = 5  =>  0 pairs (X)
B4,B9: 5.. / B4 = 5  =>  7 pairs (_) / B9 = 5  =>  0 pairs (X)
I1,I3: 6.. / I1 = 6  =>  7 pairs (_) / I3 = 6  =>  7 pairs (_)
D5,E5: 6.. / D5 = 6  =>  8 pairs (_) / E5 = 6  => 18 pairs (_)
D7,E9: 6.. / D7 = 6  => 18 pairs (_) / E9 = 6  =>  8 pairs (_)
A7,D7: 6.. / A7 = 6  =>  8 pairs (_) / D7 = 6  => 18 pairs (_)
D5,D7: 6.. / D5 = 6  =>  8 pairs (_) / D7 = 6  => 18 pairs (_)
E5,E9: 6.. / E5 = 6  => 18 pairs (_) / E9 = 6  =>  8 pairs (_)
C1,C6: 7.. / C1 = 7  => 20 pairs (_) / C6 = 7  =>  8 pairs (_)
G5,G6: 8.. / G5 = 8  =>  0 pairs (X) / G6 = 8  => 10 pairs (_)
I7,I8: 8.. / I7 = 8  =>  7 pairs (_) / I8 = 8  => 10 pairs (_)
C5,G5: 8.. / C5 = 8  => 10 pairs (_) / G5 = 8  =>  0 pairs (X)
A9,C9: 9.. / A9 = 9  => 10 pairs (_) / C9 = 9  =>  6 pairs (_)
D6,I6: 9.. / D6 = 9  => 14 pairs (_) / I6 = 9  => 12 pairs (_)
C1,C9: 9.. / C1 = 9  => 10 pairs (_) / C9 = 9  =>  6 pairs (_)
E2,E4: 9.. / E2 = 9  => 14 pairs (_) / E4 = 9  => 12 pairs (_)
H2,H4: 9.. / H2 = 9  => 12 pairs (_) / H4 = 9  => 14 pairs (_)
* DURATION: 0:00:21.790840  START: 23:13:02.174155  END: 23:13:23.964995 2019-04-30
* CP COUNT: (25)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,E8,G3,H9,I5,I7)
* ....8..4..84..61.2..5.4..8...6..8...49...7.3..2..14.6..4..7592..7.4.961....8.....
* PAIR G3: 3,7 BLK 3
G1: 3,7,5                                # reduction candidate for 3,7
G1: 3,7                                  # 11 pairs
I1: 3,7,5,6,9                            # reduction candidate for 3,7
I1: 3,7                                  # 16 pairs
I3: 3,7,6,9                              # reduction candidate for 3,7
I3: 3,7                                  # 18 pairs
* PAIR G3: 3,7 ROW 3
A3: 3,7,1,2,6,9                          # reduction candidate for 3,7
A3: 3,7                                  # 11 pairs
D3: 3,7,1,2,9                            # reduction candidate for 3,7
D3: 3,7                                  # 10 pairs
* PAIR G3: 3,7 COL G
G9: 3,7,4,5                              # reduction candidate for 3,7
G9: 3,7                                  # 14 pairs
G9: 4,5                                  #  7 pairs
* PAIR C5: 1,8 COL C
C7: 1,8,3                                # reduction candidate for 1,8
C7: 1,8                                  # 11 pairs
C7: 3                                    # 10 pairs
* PAIR I5: 1,5 BLK 6
I4: 1,5,4,7,9                            # reduction candidate for 1,5
I4: 1,5 => CTR
* ....8..4..84..61.2..5.4..8...6..84.5498..723152..1486..4..7592..7.4.961..5.8...74
I4: 4,7,9                                # 10 pairs
* PAIR E8: 2,3 BLK 8
E9: 2,3,6                                # reduction candidate for 2,3
E9: 2,3                                  # 18 pairs
F9: 2,3,1                                # reduction candidate for 2,3
F9: 2,3                                  #  9 pairs
* PAIR E8: 2,3 ROW 8
A8: 2,3,5,8                              # reduction candidate for 2,3
A8: 2,3 => CTR
* ....8..4..84..61.2..5.4..8...6..8...49...7.31.2..14.6..4..75928.784.9615...8...7.
A8: 5,8                                  #  7 pairs
C8: 2,3,8                                # reduction candidate for 2,3
C8: 2,3                                  #  9 pairs
* PAIR E8: 2,3 COL E
E4: 2,3,5,9                              # reduction candidate for 2,3
E4: 2,3 => CTR
* ....8..4..84.96152..5.4..8...6..85944986572315239148676413759288724.9615...86..7.
E4: 5,9                                  #  8 pairs
* PAIR I7: 3,8 BLK 9
I8: 3,8,5                                # reduction candidate for 3,8
I8: 5 => CTR
* ....8..4.3847.6192..5.4..8.136.98.5.498..7231527314869643175928872439615.5.8...7.
I8: 3,8                                  #  8 pairs
* PAIR I7: 3,8 ROW 7
A7: 3,8,1,6                              # reduction candidate for 3,8
A7: 3,8 => SOLVED
* 967182345384756192215943786156398274498267531723514869841675923572439618639821457
A7: 1,6                                  #  7 pairs
C7: 3,8,1                                # reduction candidate for 3,8
C7: 3,8                                  #  9 pairs
* PAIR H9: 5,7 BLK 9
G9: 5,7,3,4                              # reduction candidate for 5,7
G9: 5,7 => CTR
* ....8..4..84.961.2..5.4..8.156..84974985.7231.2.91486584167592357.4.9618...8.1..4
G9: 3,4                                  #  7 pairs
I9: 5,7,3,4                              # reduction candidate for 5,7
I9: 5,7 => SOLVED
* 967182345384756192215943786156398274498267531723514869841675923572439618639821457
I9: 3,4                                  #  7 pairs
* PAIR H9: 5,7 COL H
H2: 5,7,9                                # reduction candidate for 5,7
H2: 5,7                                  # 14 pairs
H4: 5,7,9                                # reduction candidate for 5,7
H4: 5,7                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060517-absurd-base-pr-000.dot
* REASONING
* DIS # I4: 1,5 => CTR => I4: 4,7,9
* DIS # A8: 2,3 => CTR => A8: 5,8
* DIS # E4: 2,3 => CTR => E4: 5,9
* DIS # I8: 5 => CTR => I8: 3,8
* PRF # A7: 3,8 => SOL
* DIS # G9: 5,7 => CTR => G9: 3,4
* PRF # I9: 5,7 => SOL
* CNT   7 HDP CHAINS /  29 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,E8,G3,H9,I5,I7)
* ....8..4..84..61.2..5.4..8...6..8...49...7.3..2..14.6..4..7592..7.4.961....8.....
* PAIR G3: 3,7 BLK 3
G1: 3,7,5                                # reduction candidate for 3,7
G1: 3,7                                  # 11 pairs
I1: 3,7,5,6,9                            # reduction candidate for 3,7
I1: 3,7                                  # 16 pairs
I3: 3,7,6,9                              # reduction candidate for 3,7
I3: 3,7                                  # 18 pairs
* PAIR G3: 3,7 ROW 3
A3: 3,7,1,2,6,9                          # reduction candidate for 3,7
A3: 3,7                                  # 11 pairs
D3: 3,7,1,2,9                            # reduction candidate for 3,7
D3: 3,7                                  # 10 pairs
* PAIR G3: 3,7 COL G
G9: 3,7,4,5                              # reduction candidate for 3,7
G9: 3,7                                  # 14 pairs
G9: 4,5                                  #  7 pairs
* PAIR C5: 1,8 COL C
C7: 1,8,3                                # reduction candidate for 1,8
C7: 1,8                                  # 11 pairs
C7: 3                                    # 10 pairs
* PAIR I5: 1,5 BLK 6
I4: 1,5,4,7,9                            # reduction candidate for 1,5
I4: 1,5 => CTR
* ....8..4..84..61.2..5.4..8...6..84.5498..723152..1486..4..7592..7.4.961..5.8...74
* PAIR E8: 2,3 BLK 8
E9: 2,3,6                                # reduction candidate for 2,3
E9: 2,3 => SOLVED
* 967182345384756192215943786156398274498267531723514869841675923572439618639821457
* DURATION: 0:00:07.022467  START: 23:13:38.781692  END: 23:13:45.804159 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060517-absurd-base-pr-001.dot
* REASONING
* DIS # I4: 1,5 => CTR => I4: 4,7,9
* PRF I4: 4,7,9 # E9: 2,3 => SOL
* STA I4: 4,7,9 + E9: 2,3
* CNT   2 HDP CHAINS /  11 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060517, absurd

Solution

position: 967182345384756192215943786156398274498267531723514869841675923572439618639821457 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 # G1: 3,7 => UNS
* INC # I1: 3,7 => UNS
* INC # I3: 3,7 => UNS
* INC # A3: 3,7 => UNS
* INC # D3: 3,7 => UNS
* INC # G9: 3,7 => UNS
* INC # G9: 4,5 => UNS
* INC # C7: 1,8 => UNS
* INC # C7: 3 => UNS
* DIS # I4: 1,5 => CTR => I4: 4,7,9
* INC # I4: 4,7,9 => UNS
* INC # E9: 2,3 => UNS
* INC # F9: 2,3 => UNS
* DIS # A8: 2,3 => CTR => A8: 5,8
* INC # A8: 5,8 => UNS
* INC # C8: 2,3 => UNS
* DIS # E4: 2,3 => CTR => E4: 5,9
* INC # E4: 5,9 => UNS
* INC # I8: 3,8 => UNS
* DIS # I8: 5 => CTR => I8: 3,8
* PRF # A7: 3,8 => SOL
* INC # A7: 1,6 => UNS
* INC # C7: 3,8 => UNS
* DIS # G9: 5,7 => CTR => G9: 3,4
* INC # G9: 3,4 => UNS
* PRF # I9: 5,7 => SOL
* INC # I9: 3,4 => UNS
* INC # H2: 5,7 => UNS
* INC # H4: 5,7 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 3,7 => UNS
* INC # I1: 3,7 => UNS
* INC # I3: 3,7 => UNS
* INC # A3: 3,7 => UNS
* INC # D3: 3,7 => UNS
* INC # G9: 3,7 => UNS
* INC # G9: 4,5 => UNS
* INC # C7: 1,8 => UNS
* INC # C7: 3 => UNS
* DIS # I4: 1,5 => CTR => I4: 4,7,9
* PRF I4: 4,7,9 # E9: 2,3 => SOL
* STA I4: 4,7,9 + E9: 2,3
* CNT  11 HDP CHAINS /  11 HYP OPENED