Analysis of zz-www.sudokuoftheday.co.uk-20060415-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: 2.38.9...............5...1.89..3.1....76....9.......82.4.1..8.65...869.1...3..7.. initial

Autosolve

position: 2.38.9..........9.9..5...1.89..3.1...276.8..9...9...82.491..8.65.2.869.1...39.7.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D2: 7 => CTR => D2: 2,4
* DIS # H9: 4,5 => CTR => H9: 2
* PRF # D2: 2 => SOL
* DIS # H9: 4,5 => CTR => H9: 2
* DIS # F9: 2 => CTR => F9: 4,5
* CNT   5 HDP CHAINS /  23 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 # D2: 7 => CTR => D2: 2,4
* PRF D2: 2,4 # A6: 1,6 => SOL
* STA D2: 2,4 + A6: 1,6
* CNT   2 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

2.38.9...............5...1.89..3.1....76....9.......82.4.1..8.65...869.1...3..7.. initial
2.38.9..........9.9..5...1.89..3.1...276.8..9...9...82.491..8.65.2.869.1...39.7.. autosolve
213869574458271693976543218895432167327618459164957382749125836532786941681394725 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
H1: 6,7
I2: 3,8
I3: 3,8
D4: 2,4
H4: 6,7
H5: 4,5
A7: 3,7
B8: 3,7
A9: 1,6
D8: 4,7
H8: 3,4
I9: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,E1: 1.. / B1 = 1  => 14 pairs (_) / E1 = 1  => 19 pairs (_)
A5,E5: 1.. / A5 = 1  => 18 pairs (_) / E5 = 1  => 18 pairs (_)
F2,F6: 1.. / F2 = 1  => 16 pairs (_) / F6 = 1  => 17 pairs (_)
G2,G3: 2.. / G2 = 2  => 15 pairs (_) / G3 = 2  => 12 pairs (_)
D4,F4: 2.. / D4 = 2  => 13 pairs (_) / F4 = 2  =>  0 pairs (*)
H7,H9: 2.. / H7 = 2  =>  0 pairs (X) / H9 = 2  => 14 pairs (_)
F9,H9: 2.. / F9 = 2  =>  0 pairs (X) / H9 = 2  => 14 pairs (_)
D2,D4: 2.. / D2 = 2  =>  0 pairs (*) / D4 = 2  =>  0 pairs (X)
F2,F3: 3.. / F2 = 3  => 15 pairs (_) / F3 = 3  => 12 pairs (_)
I2,I3: 3.. / I2 = 3  => 12 pairs (_) / I3 = 3  => 15 pairs (_)
G5,G6: 3.. / G5 = 3  => 13 pairs (_) / G6 = 3  => 17 pairs (_)
A7,B8: 3.. / A7 = 3  =>  0 pairs (X) / B8 = 3  => 16 pairs (_)
H7,H8: 3.. / H7 = 3  => 16 pairs (_) / H8 = 3  =>  0 pairs (X)
F2,I2: 3.. / F2 = 3  => 15 pairs (_) / I2 = 3  => 12 pairs (_)
F3,I3: 3.. / F3 = 3  => 12 pairs (_) / I3 = 3  => 15 pairs (_)
A5,G5: 3.. / A5 = 3  => 17 pairs (_) / G5 = 3  => 13 pairs (_)
A7,H7: 3.. / A7 = 3  =>  0 pairs (X) / H7 = 3  => 16 pairs (_)
B8,H8: 3.. / B8 = 3  => 16 pairs (_) / H8 = 3  =>  0 pairs (X)
B6,B8: 3.. / B6 = 3  =>  0 pairs (X) / B8 = 3  => 16 pairs (_)
D8,F9: 4.. / D8 = 4  =>  0 pairs (X) / F9 = 4  => 16 pairs (_)
D8,H8: 4.. / D8 = 4  =>  0 pairs (X) / H8 = 4  => 16 pairs (_)
H4,G6: 6.. / H4 = 6  => 12 pairs (_) / G6 = 6  => 18 pairs (_)
C4,H4: 6.. / C4 = 6  => 18 pairs (_) / H4 = 6  => 12 pairs (_)
H1,H4: 6.. / H1 = 6  => 18 pairs (_) / H4 = 6  => 12 pairs (_)
H1,I1: 7.. / H1 = 7  => 12 pairs (_) / I1 = 7  => 18 pairs (_)
E6,F6: 7.. / E6 = 7  => 13 pairs (_) / F6 = 7  => 17 pairs (_)
H4,I4: 7.. / H4 = 7  => 18 pairs (_) / I4 = 7  => 12 pairs (_)
A7,B8: 7.. / A7 = 7  => 16 pairs (_) / B8 = 7  =>  0 pairs (X)
B8,D8: 7.. / B8 = 7  =>  0 pairs (X) / D8 = 7  => 16 pairs (_)
A2,A7: 7.. / A2 = 7  =>  0 pairs (X) / A7 = 7  => 16 pairs (_)
D2,D8: 7.. / D2 = 7  =>  0 pairs (X) / D8 = 7  => 16 pairs (_)
H1,H4: 7.. / H1 = 7  => 12 pairs (_) / H4 = 7  => 18 pairs (_)
I1,I4: 7.. / I1 = 7  => 18 pairs (_) / I4 = 7  => 12 pairs (_)
I2,I3: 8.. / I2 = 8  => 15 pairs (_) / I3 = 8  => 12 pairs (_)
B9,C9: 8.. / B9 = 8  => 14 pairs (_) / C9 = 8  => 14 pairs (_)
* DURATION: 0:00:37.506807  START: 22:24:25.759909  END: 22:25:03.266716 2019-04-30
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B8,D4,D8,H1,H4,H5,H8,I2,I3,I9)
* 2.38.9..........9.9..5...1.89..3.1...276.8..9...9...82.491..8.65.2.869.1...39.7..
* PAIR D4: 2,4 BLK 5
F4: 2,4,5                                # reduction candidate for 2,4
F4: 5                                    # 18 pairs
F4: 2,4                                  # 17 pairs
* PAIR D4: 2,4 COL D
D2: 2,4,7                                # reduction candidate for 2,4
D2: 7 => CTR
* 2.38.9......7...9.97.5...1.89.23.1...276.8..9...9...827491..8365324869.1...39.7..
D2: 2,4                                  # 16 pairs
* PAIR H5: 4,5 BLK 6
I4: 4,5,7                                # reduction candidate for 4,5
I4: 4,5                                  # 18 pairs
G5: 4,5,3                                # reduction candidate for 4,5
G5: 4,5                                  # 17 pairs
G6: 4,5,3,6                              # reduction candidate for 4,5
G6: 4,5                                  # 14 pairs
* PAIR H5: 4,5 ROW 5
E5: 4,5,1                                # reduction candidate for 4,5
E5: 4,5                                  # 18 pairs
E5: 1                                    # 18 pairs
* PAIR H5: 4,5 COL H
H9: 4,5,2                                # reduction candidate for 4,5
H9: 4,5 => CTR
* 2.38.9...7......9.9..5...1.89.23.1...276.8..9.3.9...823491..826572486931...3927..
H9: 2                                    # 14 pairs
* PAIR A9: 1,6 BLK 7
B9: 1,6,8                                # reduction candidate for 1,6
B9: 1,6                                  # 14 pairs
C9: 1,6,8                                # reduction candidate for 1,6
C9: 1,6                                  # 14 pairs
* PAIR A9: 1,6 COL A
A2: 1,6,4,7                              # reduction candidate for 1,6
A2: 1,6                                  # 23 pairs
A6: 1,6,3,4                              # reduction candidate for 1,6
A6: 1,6                                  # 21 pairs
* PAIR D8: 4,7 COL D
D2: 4,7,2                                # reduction candidate for 4,7
D2: 2 => SOLVED
* 213869574458271693976543218895432167327618459164957382749125836532786941681394725
D2: 4,7                                  # 13 pairs
* PAIR I9: 4,5 BLK 9
H9: 4,5,2                                # reduction candidate for 4,5
H9: 4,5 => CTR
* 2.38.9...7......9.9..5...1.89.23.1...276.8..9.3.9...823491..826572486931...3927..
H9: 2                                    # 14 pairs
* PAIR I9: 4,5 ROW 9
F9: 4,5,2                                # reduction candidate for 4,5
F9: 2 => CTR
* 2.38.9......7...9.97.5...1.89..3.1...276.8..9...9...82.491..8.65.2486931...3927..
F9: 4,5                                  # 14 pairs
* PAIR I9: 4,5 COL I
I1: 4,5,7                                # reduction candidate for 4,5
I1: 4,5                                  # 12 pairs
I4: 4,5,7                                # reduction candidate for 4,5
I4: 4,5                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060415-absurd-base-pr-000.dot
* REASONING
* DIS # D2: 7 => CTR => D2: 2,4
* DIS # H9: 4,5 => CTR => H9: 2
* PRF # D2: 2 => SOL
* DIS # H9: 4,5 => CTR => H9: 2
* DIS # F9: 2 => CTR => F9: 4,5
* CNT   5 HDP CHAINS /  23 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,A9,B8,D4,D8,H1,H4,H5,H8,I2,I3,I9)
* 2.38.9..........9.9..5...1.89..3.1...276.8..9...9...82.491..8.65.2.869.1...39.7..
* PAIR D4: 2,4 BLK 5
F4: 2,4,5                                # reduction candidate for 2,4
F4: 5                                    # 18 pairs
F4: 2,4                                  # 17 pairs
* PAIR D4: 2,4 COL D
D2: 2,4,7                                # reduction candidate for 2,4
D2: 7 => CTR
* 2.38.9......7...9.97.5...1.89.23.1...276.8..9...9...827491..8365324869.1...39.7..
* PAIR RESTART
* PAIR A9: 1,6 BLK 7
B9: 1,6,8                                # reduction candidate for 1,6
B9: 1,6                                  # 20 pairs
C9: 1,6,8                                # reduction candidate for 1,6
C9: 1,6                                  # 18 pairs
* PAIR A9: 1,6 COL A
A2: 1,6,4                                # reduction candidate for 1,6
A2: 1,6                                  # 23 pairs
A6: 1,6,3,4                              # reduction candidate for 1,6
A6: 1,6 => SOLVED
* 213869574458271693976543218895432167327618459164957382749125836532786941681394725
* DURATION: 0:00:06.401678  START: 22:25:17.554981  END: 22:25:23.956659 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060415-absurd-base-pr-001.dot
* REASONING
* DIS # D2: 7 => CTR => D2: 2,4
* PRF D2: 2,4 # A6: 1,6 => SOL
* STA D2: 2,4 + A6: 1,6
* CNT   2 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060415, absurd

Solution

position: 213869574458271693976543218895432167327618459164957382749125836532786941681394725 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 # F4: 2,4 => UNS
* INC # F4: 5 => UNS
* INC # D2: 2,4 => UNS
* DIS # D2: 7 => CTR => D2: 2,4
* INC # I4: 4,5 => UNS
* INC # G5: 4,5 => UNS
* INC # G6: 4,5 => UNS
* INC # E5: 4,5 => UNS
* INC # E5: 1 => UNS
* DIS # H9: 4,5 => CTR => H9: 2
* INC # H9: 2 => UNS
* INC # B9: 1,6 => UNS
* INC # C9: 1,6 => UNS
* INC # A2: 1,6 => UNS
* INC # A6: 1,6 => UNS
* INC # D2: 4,7 => UNS
* PRF # D2: 2 => SOL
* DIS # H9: 4,5 => CTR => H9: 2
* INC # H9: 2 => UNS
* INC # F9: 4,5 => UNS
* DIS # F9: 2 => CTR => F9: 4,5
* INC # I1: 4,5 => UNS
* INC # I4: 4,5 => UNS
* CNT  23 HDP CHAINS /  23 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F4: 2,4 => UNS
* INC # F4: 5 => UNS
* INC # D2: 2,4 => UNS
* DIS # D2: 7 => CTR => D2: 2,4
* INC D2: 2,4 # B9: 1,6 => UNS
* INC D2: 2,4 # C9: 1,6 => UNS
* INC D2: 2,4 # A2: 1,6 => UNS
* PRF D2: 2,4 # A6: 1,6 => SOL
* STA D2: 2,4 + A6: 1,6
* CNT   8 HDP CHAINS /   8 HYP OPENED