Analysis of zz-www.sudokuoftheday.co.uk-20060513-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: 1........2....961.6...1...3..5.4.....1..758....9.2..4.57....2...4...67..9...8715. initial

Autosolve

position: 1...6....2...3961.6...1...3..5.4....41..758....9.2..4.57..9.2...4..567..9...8715. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 5,8 => CTR => B1: 3,9
* DIS # B3: 5,8 => CTR => B3: 9
* DIS # D4: 1,6,8 => CTR => D4: 3,9
* DIS # C7: 3,8 => CTR => C7: 1,6
* PRF # C7: 1,6 => SOL
* DIS # H8: 9 => CTR => H8: 3,8
* DIS # H8: 8,9 => CTR => H8: 3
* PRF # H8: 3 => SOL
* DIS # I7: 8 => CTR => I7: 4,6
* CNT   9 HDP CHAINS /  20 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 # B1: 5,8 => CTR => B1: 3,9
* DIS B1: 3,9 # B3: 5,8 => CTR => B3: 9
* PRF B1: 3,9 + B3: 9 => SOL
* STA B1: 3,9 + B3: 9
* CNT   3 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

1........2....961.6...1...3..5.4.....1..758....9.2..4.57....2...4...67..9...8715. initial
1...6....2...3961.6...1...3..5.4....41..758....9.2..4.57..9.2...4..567..9...8715. autosolve
137864925254739618698512473725948361416375892389621547571493286842156739963287154 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
B2: 5,8
G4: 3,9
G6: 3,5
A8: 3,8
C8: 1,2
D8: 1,2
I8: 8,9
I9: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I4,I6: 1.. / I4 = 1  =>  9 pairs (_) / I6 = 1  =>  0 pairs (X)
C7,C8: 1.. / C7 = 1  =>  0 pairs (*) / C8 = 1  =>  0 pairs (X)
C8,D8: 1.. / C8 = 1  =>  7 pairs (_) / D8 = 1  =>  0 pairs (*)
F1,F3: 2.. / F1 = 2  => 10 pairs (_) / F3 = 2  =>  9 pairs (_)
B4,C5: 2.. / B4 = 2  => 10 pairs (_) / C5 = 2  =>  0 pairs (X)
D8,D9: 2.. / D8 = 2  =>  7 pairs (_) / D9 = 2  =>  0 pairs (*)
F3,H3: 2.. / F3 = 2  =>  9 pairs (_) / H3 = 2  => 10 pairs (_)
C8,D8: 2.. / C8 = 2  =>  0 pairs (*) / D8 = 2  =>  0 pairs (X)
B4,B9: 2.. / B4 = 2  => 10 pairs (_) / B9 = 2  =>  0 pairs (X)
B1,C1: 3.. / B1 = 3  =>  0 pairs (*) / C1 = 3  =>  0 pairs (X)
G4,G6: 3.. / G4 = 3  => 10 pairs (_) / G6 = 3  =>  0 pairs (X)
H7,H8: 3.. / H7 = 3  =>  0 pairs (X) / H8 = 3  =>  0 pairs (_)
C5,D5: 3.. / C5 = 3  =>  0 pairs (X) / D5 = 3  =>  0 pairs (_)
A8,H8: 3.. / A8 = 3  =>  0 pairs (X) / H8 = 3  =>  0 pairs (_)
G1,G3: 4.. / G1 = 4  => 10 pairs (_) / G3 = 4  => 11 pairs (_)
I7,I9: 4.. / I7 = 4  =>  0 pairs (X) / I9 = 4  =>  9 pairs (_)
C2,D2: 4.. / C2 = 4  =>  9 pairs (_) / D2 = 4  =>  0 pairs (X)
D9,I9: 4.. / D9 = 4  =>  0 pairs (X) / I9 = 4  =>  9 pairs (_)
G6,I6: 5.. / G6 = 5  => 10 pairs (_) / I6 = 5  =>  0 pairs (X)
A4,A6: 7.. / A4 = 7  => 19 pairs (_) / A6 = 7  =>  9 pairs (_)
A6,I6: 7.. / A6 = 7  =>  9 pairs (_) / I6 = 7  => 19 pairs (_)
C7,A8: 8.. / C7 = 8  =>  0 pairs (X) / A8 = 8  =>  0 pairs (_)
B1,B3: 9.. / B1 = 9  =>  0 pairs (X) / B3 = 9  =>  9 pairs (_)
D4,D5: 9.. / D4 = 9  => 11 pairs (_) / D5 = 9  =>  0 pairs (X)
H8,I8: 9.. / H8 = 9  =>  0 pairs (X) / I8 = 9  =>  9 pairs (_)
* DURATION: 0:00:28.069234  START: 23:07:20.636491  END: 23:07:48.705725 2019-04-30
* CP COUNT: (25)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B2,C8,D8,G4,G6,I8,I9)
* 1...6....2...3961.6...1...3..5.4....41..758....9.2..4.57..9.2...4..567..9...8715.
* PAIR B2: 5,8 BLK 1
B1: 5,8,3,9                              # reduction candidate for 5,8
B1: 5,8 => CTR
* 1.3.6....2...3961.69..1...3.2594.3..41637589238962154757..932..84..56739932487156
B1: 3,9                                  #  9 pairs
B3: 5,8,9                                # reduction candidate for 5,8
B3: 5,8 => CTR
* 193.6....2...3961.6...1...3.2594.3..41637589238962154757..932..84..56739932487156
B3: 9                                    #  9 pairs
* PAIR B2: 5,8 ROW 2
D2: 5,8,4,7                              # reduction candidate for 5,8
D2: 5,8                                  # 11 pairs
I2: 5,8,7                                # reduction candidate for 5,8
I2: 5,8                                  # 11 pairs
* PAIR G4: 3,9 ROW 4
D4: 3,9,1,6,8                            # reduction candidate for 3,9
D4: 1,6,8 => CTR
* 13..6....2...3961.69..1...3.25.4....4139758...69.2..4.57..9.2..34..567..9..387154
D4: 3,9                                  # 11 pairs
* PAIR A8: 3,8 BLK 7
C7: 3,8,1,6                              # reduction candidate for 3,8
C7: 3,8 => CTR
* 1...6....2...3961.6...1...3..5.4....413.758....9.2..4.578.9.2...412567..9..387154
C7: 1,6 => SOLVED
* 137864925254739618698512473725948361416375892389621547571493286842156739963287154
* PAIR A8: 3,8 ROW 8
H8: 3,8,9                                # reduction candidate for 3,8
H8: 9 => CTR
* 1...6....2...3961.6...1...3..5.4....413.758....9.2..4.578.9.2363412567989..387154
H8: 3,8                                  #  9 pairs
* PAIR A8: 3,8 COL A
A4: 3,8,7                                # reduction candidate for 3,8
A4: 3,8                                  #  9 pairs
A6: 3,8,7                                # reduction candidate for 3,8
A6: 3,8                                  # 19 pairs
* PAIR I8: 8,9 BLK 9
H8: 8,9,3                                # reduction candidate for 8,9
H8: 8,9 => CTR
* 1...6....2...3961.6...1...3..5.4....413.758....9.2..4.578.9.2363412567..9..387154
H8: 3 => SOLVED
* 137864925254739618698512473725948361416375892389621547571493286842156739963287154
* PAIR I8: 8,9 COL I
I1: 8,9,2,5,7                            # reduction candidate for 8,9
I1: 8,9                                  # 16 pairs
I1: 2,5,7                                #  8 pairs
* PAIR I9: 4,6 BLK 9
I7: 4,6,8                                # reduction candidate for 4,6
I7: 8 => CTR
* 1...6....25..3961769..1...3..5.4..7.41.37589.7.9.2.34.57..9.26884..567399...87154
I7: 4,6                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060513-absurd-base-pr-000.dot
* REASONING
* DIS # B1: 5,8 => CTR => B1: 3,9
* DIS # B3: 5,8 => CTR => B3: 9
* DIS # D4: 1,6,8 => CTR => D4: 3,9
* DIS # C7: 3,8 => CTR => C7: 1,6
* PRF # C7: 1,6 => SOL
* DIS # H8: 9 => CTR => H8: 3,8
* DIS # H8: 8,9 => CTR => H8: 3
* PRF # H8: 3 => SOL
* DIS # I7: 8 => CTR => I7: 4,6
* CNT   9 HDP CHAINS /  20 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B2,C8,D8,G4,G6,I8,I9)
* 1...6....2...3961.6...1...3..5.4....41..758....9.2..4.57..9.2...4..567..9...8715.
* PAIR B2: 5,8 BLK 1
B1: 5,8,3,9                              # reduction candidate for 5,8
B1: 5,8 => CTR
* 1.3.6....2...3961.69..1...3.2594.3..41637589238962154757..932..84..56739932487156
B3: 5,8,9                                # reduction candidate for 5,8
B3: 5,8 => CTR
* 193.6....2...3961.6...1...3.2594.3..41637589238962154757..932..84..56739932487156
B3: 9 => SOLVED
* 137864925254739618698512473725948361416375892389621547571493286842156739963287154
* DURATION: 0:00:02.383038  START: 23:08:01.826111  END: 23:08:04.209149 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060513-absurd-base-pr-001.dot
* REASONING
* DIS # B1: 5,8 => CTR => B1: 3,9
* DIS B1: 3,9 # B3: 5,8 => CTR => B3: 9
* PRF B1: 3,9 + B3: 9 => SOL
* STA B1: 3,9 + B3: 9
* CNT   3 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060513, absurd

Solution

position: 137864925254739618698512473725948361416375892389621547571493286842156739963287154 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 # B1: 5,8 => CTR => B1: 3,9
* INC # B1: 3,9 => UNS
* DIS # B3: 5,8 => CTR => B3: 9
* INC # B3: 9 => UNS
* INC # D2: 5,8 => UNS
* INC # I2: 5,8 => UNS
* INC # D4: 3,9 => UNS
* DIS # D4: 1,6,8 => CTR => D4: 3,9
* DIS # C7: 3,8 => CTR => C7: 1,6
* PRF # C7: 1,6 => SOL
* INC # H8: 3,8 => UNS
* DIS # H8: 9 => CTR => H8: 3,8
* INC # A4: 3,8 => UNS
* INC # A6: 3,8 => UNS
* DIS # H8: 8,9 => CTR => H8: 3
* PRF # H8: 3 => SOL
* INC # I1: 8,9 => UNS
* INC # I1: 2,5,7 => UNS
* INC # I7: 4,6 => UNS
* DIS # I7: 8 => CTR => I7: 4,6
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 5,8 => CTR => B1: 3,9
* DIS B1: 3,9 # B3: 5,8 => CTR => B3: 9
* PRF B1: 3,9 + B3: 9 => SOL
* STA B1: 3,9 + B3: 9
* CNT   3 HDP CHAINS /   2 HYP OPENED