Analysis of zz-www.sudokuoftheday.co.uk-20190424-absurd-base.sdk

Contents

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

level: medium

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

position: .4.1...86.....6571..5.............6....8....7....31.2.8...57...6.1.....54.....9.. initial

Autosolve

position: 74.1.5.86....46571165....9........6....86..57..6.31.2.8..457612621...745457612938 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D2: 2,9 => CTR => D2: 3
* DIS # C1: 2,9 => CTR => C1: 3
* DIS # G3: 2,3 => CTR => G3: 4
* PRF # G3: 4 => SOL
* DIS # C1: 9 => CTR => C1: 2,3
* DIS # G3: 2 => CTR => G3: 3,4
* DIS # A4: 5,9 => CTR => A4: 3
* PRF # A4: 3 => SOL
* DIS # D4: 2,7 => CTR => D4: 5
* PRF # D4: 5 => SOL
* DIS # E3: 8 => CTR => E3: 2,7
* DIS # C4: 4,9 => CTR => C4: 3,8
* DIS # C5: 2,3 => CTR => C5: 4,9
* DIS # D4: 2 => CTR => D4: 5,7
* PRF # A4: 3,9 => SOL
* DIS # A4: 5 => CTR => A4: 3,9
* DIS # B4: 3,9 => CTR => B4: 1,7,8
* DIS # C4: 3,9 => CTR => C4: 4,8
* PRF # G4: 1,3 => SOL
* DIS # G4: 8 => CTR => G4: 1,3
* DIS # B5: 9 => CTR => B5: 1,3
* DIS # B2: 3,9 => CTR => B2: 8
* PRF # B2: 8 => SOL
* DIS # B4: 3,9 => CTR => B4: 1,7,8
* DIS # B5: 3,9 => CTR => B5: 1
* PRF # B5: 1 => SOL
* DIS # C2: 3,9 => CTR => C2: 2,8
* DIS # C4: 3,9 => CTR => C4: 4,8
* DIS # C5: 3,9 => CTR => C5: 2,4
* DIS # D2: 2 => CTR => D2: 3,9
* CNT  30 HDP CHAINS /  47 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: 2,9 => CTR => D2: 3
* DIS D2: 3 # A4: 5,9 => CTR => A4: 3
* PRF D2: 3 + A4: 3 => SOL
* STA D2: 3 + A4: 3
* CNT   3 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

.4.1...86.....6571..5.............6....8....7....31.2.8...57...6.1.....54.....9.. initial
74.1.5.86....46571165....9........6....86..57..6.31.2.8..457612621...745457612938 autosolve
743195286982346571165278493378524169214869357596731824839457612621983745457612938 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
E1: 2,9
F3: 3,8
G1: 2,3
I3: 3,4
A6: 5,9
E4: 2,7
F4: 4,9
F5: 4,9
D6: 5,7
I4: 3,9
G5: 1,3
G6: 4,8
I6: 4,9
B7: 3,9
C7: 3,9
D8: 3,9
E8: 8,9
F8: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B4,B5: 1.. / B4 = 1  =>  0 pairs (X) / B5 = 1  =>  0 pairs (_)
G4,G5: 1.. / G4 = 1  =>  0 pairs (*) / G5 = 1  =>  0 pairs (X)
B4,G4: 1.. / B4 = 1  =>  0 pairs (X) / G4 = 1  =>  0 pairs (_)
B5,G5: 1.. / B5 = 1  =>  0 pairs (*) / G5 = 1  =>  0 pairs (X)
G1,G3: 2.. / G1 = 2  => 19 pairs (_) / G3 = 2  =>  0 pairs (X)
A5,C5: 2.. / A5 = 2  => 19 pairs (_) / C5 = 2  =>  0 pairs (X)
D4,E4: 2.. / D4 = 2  =>  0 pairs (X) / E4 = 2  => 16 pairs (_)
A2,A5: 2.. / A2 = 2  =>  0 pairs (X) / A5 = 2  => 19 pairs (_)
B7,C7: 3.. / B7 = 3  => 16 pairs (_) / C7 = 3  =>  0 pairs (X)
D8,F8: 3.. / D8 = 3  =>  0 pairs (X) / F8 = 3  => 16 pairs (_)
C1,G1: 3.. / C1 = 3  => 19 pairs (_) / G1 = 3  =>  0 pairs (X)
F3,F8: 3.. / F3 = 3  =>  0 pairs (X) / F8 = 3  => 16 pairs (_)
I3,I4: 3.. / I3 = 3  =>  0 pairs (*) / I4 = 3  =>  0 pairs (X)
G3,I3: 4.. / G3 = 4  =>  0 pairs (*) / I3 = 4  =>  0 pairs (X)
C4,C5: 4.. / C4 = 4  =>  0 pairs (X) / C5 = 4  => 18 pairs (_)
F4,F5: 4.. / F4 = 4  => 18 pairs (_) / F5 = 4  =>  0 pairs (X)
G6,I6: 4.. / G6 = 4  =>  0 pairs (X) / I6 = 4  =>  0 pairs (_)
C4,F4: 4.. / C4 = 4  =>  0 pairs (X) / F4 = 4  => 18 pairs (_)
C5,F5: 4.. / C5 = 4  => 18 pairs (_) / F5 = 4  =>  0 pairs (X)
G3,G6: 4.. / G3 = 4  =>  0 pairs (*) / G6 = 4  =>  0 pairs (X)
I3,I6: 4.. / I3 = 4  =>  0 pairs (X) / I6 = 4  =>  0 pairs (_)
A4,A6: 5.. / A4 = 5  =>  0 pairs (X) / A6 = 5  =>  0 pairs (_)
D4,D6: 5.. / D4 = 5  =>  0 pairs (*) / D6 = 5  =>  0 pairs (X)
A4,D4: 5.. / A4 = 5  =>  0 pairs (X) / D4 = 5  =>  0 pairs (_)
A6,D6: 5.. / A6 = 5  =>  0 pairs (*) / D6 = 5  =>  0 pairs (X)
D3,E3: 7.. / D3 = 7  =>  0 pairs (X) / E3 = 7  => 16 pairs (_)
B4,B6: 7.. / B4 = 7  =>  0 pairs (*) / B6 = 7  =>  0 pairs (X)
B6,D6: 7.. / B6 = 7  =>  0 pairs (X) / D6 = 7  =>  0 pairs (_)
E3,E4: 7.. / E3 = 7  => 16 pairs (_) / E4 = 7  =>  0 pairs (X)
B2,C2: 8.. / B2 = 8  =>  0 pairs (*) / C2 = 8  =>  0 pairs (X)
E3,F3: 8.. / E3 = 8  =>  0 pairs (X) / F3 = 8  => 16 pairs (_)
G4,G6: 8.. / G4 = 8  =>  0 pairs (X) / G6 = 8  =>  0 pairs (_)
E8,F8: 8.. / E8 = 8  => 16 pairs (_) / F8 = 8  =>  0 pairs (X)
B6,G6: 8.. / B6 = 8  =>  0 pairs (X) / G6 = 8  =>  0 pairs (_)
C2,C4: 8.. / C2 = 8  =>  0 pairs (X) / C4 = 8  =>  0 pairs (_)
E3,E8: 8.. / E3 = 8  =>  0 pairs (X) / E8 = 8  => 16 pairs (_)
F3,F8: 8.. / F3 = 8  => 16 pairs (_) / F8 = 8  =>  0 pairs (X)
E1,D2: 9.. / E1 = 9  => 16 pairs (_) / D2 = 9  =>  0 pairs (X)
F4,F5: 9.. / F4 = 9  =>  0 pairs (X) / F5 = 9  => 18 pairs (_)
I4,I6: 9.. / I4 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
B7,C7: 9.. / B7 = 9  =>  0 pairs (X) / C7 = 9  => 16 pairs (_)
D8,E8: 9.. / D8 = 9  => 16 pairs (_) / E8 = 9  =>  0 pairs (X)
C1,E1: 9.. / C1 = 9  =>  0 pairs (X) / E1 = 9  => 16 pairs (_)
D2,D8: 9.. / D2 = 9  =>  0 pairs (X) / D8 = 9  => 16 pairs (_)
E1,E8: 9.. / E1 = 9  => 16 pairs (_) / E8 = 9  =>  0 pairs (X)
* DURATION: 0:00:54.562225  START: 05:33:45.789242  END: 05:34:40.351467 2019-05-01
* CP COUNT: (45)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C7,D6,D8,E1,E4,E8,F3,F4,F5,F8,G1,G5,G6,I3,I4,I6)
* 74.1.5.86....46571165....9........6....86..57..6.31.2.8..457612621...745457612938
* PAIR E1: 2,9 BLK 2
D2: 2,9,3                                # reduction candidate for 2,9
D2: 2,9 => CTR
* 74.1.5386....46571165...294.1....863...86.1575.6.314298..457612621...745457612938
D2: 3                                    # 19 pairs
* PAIR E1: 2,9 ROW 1
C1: 2,9,3                                # reduction candidate for 2,9
C1: 2,9 => CTR
* 74.1.5386....46571165...294.1....863...86.1575.6.314298..457612621...745457612938
C1: 3                                    # 19 pairs
* PAIR G1: 2,3 BLK 3
G3: 2,3,4                                # reduction candidate for 2,3
G3: 2,3 => CTR
* 74.1.5.86....46571165....94.1....863...86.1575.6.314298..457612621...745457612938
G3: 4 => SOLVED
* 743195286982346571165278493378524169214869357596731824839457612621983745457612938
* PAIR G1: 2,3 ROW 1
C1: 2,3,9                                # reduction candidate for 2,3
C1: 9 => CTR
* 749125386...946571165...294...27..63...86.157.76531.2.8..457612621...745457612938
C1: 2,3                                  # 16 pairs
* PAIR I3: 3,4 BLK 3
G3: 3,4,2                                # reduction candidate for 3,4
G3: 2 => CTR
* 74.1.5386....46571165...294.1....863...86.1575.6.314298..457612621...745457612938
G3: 3,4                                  # 19 pairs
* PAIR A6: 5,9 BLK 4
A4: 5,9,3                                # reduction candidate for 5,9
A4: 5,9 => CTR
* 74.1.53863...46571165...294.....4.63234869157..6.31429893457612621...745457612938
A4: 3 => SOLVED
* 743195286982346571165278493378524169214869357596731824839457612621983745457612938
* PAIR E4: 2,7 BLK 5
D4: 2,7,5                                # reduction candidate for 2,7
D4: 2,7 => CTR
* 7431952862..346571165..84935....4.693..869.579765318248..457612621..3745457612938
D4: 5 => SOLVED
* 743195286982346571165278493378524169214869357596731824839457612621983745457612938
* PAIR E4: 2,7 COL E
E3: 2,7,8                                # reduction candidate for 2,7
E3: 8 => CTR
* 74.1.5.86....46571165783294....7..63...86.157.76531.2.8..457612621...745457612938
E3: 2,7                                  # 16 pairs
* PAIR F4: 4,9 ROW 4
C4: 4,9,3,8                              # reduction candidate for 4,9
C4: 4,9 => CTR
* 74.1.5.86..8.46571165....9.......163...86..57..6.31.2.8..457612621...745457612938
C4: 3,8                                  # 19 pairs
* PAIR F5: 4,9 ROW 5
C5: 4,9,2,3                              # reduction candidate for 4,9
C5: 2,3 => CTR
* 74.1.5.86....46571165....9...4..9.63...864157..6.31.298..457612621...745457612938
C5: 4,9                                  # 21 pairs
* PAIR D6: 5,7 BLK 5
D4: 5,7,2                                # reduction candidate for 5,7
D4: 2 => CTR
* 7431952862..3465711657284935..274.693..869.579765318248..457612621..3745457612938
D4: 5,7                                  # 16 pairs
* PAIR I4: 3,9 ROW 4
A4: 3,9,5                                # reduction candidate for 3,9
A4: 3,9 => SOLVED
* 743195286982346571165278493378524169214869357596731824839457612621983745457612938
A4: 5 => CTR
* 7431952862..346571165..84935....4.693..869.579765318248..457612621..3745457612938
B4: 3,9,1,7,8                            # reduction candidate for 3,9
B4: 3,9 => CTR
* 743195286.8.346571165..8493......16..1.86.357.765318248..457612621...745457612938
B4: 1,7,8                                # 18 pairs
C4: 3,9,4,8                              # reduction candidate for 3,9
C4: 3,9 => CTR
* 742195386..8246571165...294....24.63234869157..6.3142989.457612621...745457612938
C4: 4,8                                  # 19 pairs
* PAIR G5: 1,3 BLK 6
G4: 1,3,8                                # reduction candidate for 1,3
G4: 1,3 => SOLVED
* 743195286982346571165278493378524169214869357596731824839457612621983745457612938
G4: 8 => CTR
* 74.1.5.86....46571165....9..1....86....86.157..6.31.2.8..457612621...745457612938
* PAIR G5: 1,3 ROW 5
B5: 1,3,9                                # reduction candidate for 1,3
B5: 9 => CTR
* 74.1.5.86....46571165....9..1.....6..9.864157576.31.2.8..457612621...745457612938
B5: 1,3                                  # 20 pairs
* PAIR B7: 3,9 COL B
B2: 3,9,8                                # reduction candidate for 3,9
B2: 3,9 => CTR
* 743195286298346571165..849338....16..1.86.357..6.318248..457612621...745457612938
B2: 8 => SOLVED
* 743195286982346571165278493378524169214869357596731824839457612621983745457612938
B4: 3,9,1,7,8                            # reduction candidate for 3,9
B4: 3,9 => CTR
* 743195286.8.346571165..8493......16..1.86.357.765318248..457612621...745457612938
B4: 1,7,8                                # 18 pairs
B5: 3,9,1                                # reduction candidate for 3,9
B5: 3,9 => CTR
* 74.1.5.86.8..46571165...493518..4369..4869157976531824893457612621..3745457612938
B5: 1 => SOLVED
* 743195286982346571165278493378524169214869357596731824839457612621983745457612938
* PAIR C7: 3,9 COL C
C1: 3,9,2                                # reduction candidate for 3,9
C1: 3,9                                  # 24 pairs
C2: 3,9,2,8                              # reduction candidate for 3,9
C2: 3,9 => CTR
* 742195386.8..46571165....9...8..4.6...4869.57..6.318248..457612621...745457612938
C2: 2,8                                  # 19 pairs
C4: 3,9,4,8                              # reduction candidate for 3,9
C4: 3,9 => CTR
* 742195386..8246571165...294....24.63234869157..6.3142989.457612621...745457612938
C4: 4,8                                  # 19 pairs
C5: 3,9,2,4                              # reduction candidate for 3,9
C5: 3,9 => CTR
* 74.1.5.86....46571165....9...4..9.632..864157..6.31.298..457612621...745457612938
C5: 2,4                                  # 19 pairs
* PAIR D8: 3,9 COL D
D2: 3,9,2                                # reduction candidate for 3,9
D2: 2 => CTR
* 7421953863..24657116537829491..2..632..86.157..6.314298..457612621983745457612938
D2: 3,9                                  # 24 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190424-absurd-base-pr-000.dot
* REASONING
* DIS # D2: 2,9 => CTR => D2: 3
* DIS # C1: 2,9 => CTR => C1: 3
* DIS # G3: 2,3 => CTR => G3: 4
* PRF # G3: 4 => SOL
* DIS # C1: 9 => CTR => C1: 2,3
* DIS # G3: 2 => CTR => G3: 3,4
* DIS # A4: 5,9 => CTR => A4: 3
* PRF # A4: 3 => SOL
* DIS # D4: 2,7 => CTR => D4: 5
* PRF # D4: 5 => SOL
* DIS # E3: 8 => CTR => E3: 2,7
* DIS # C4: 4,9 => CTR => C4: 3,8
* DIS # C5: 2,3 => CTR => C5: 4,9
* DIS # D4: 2 => CTR => D4: 5,7
* PRF # A4: 3,9 => SOL
* DIS # A4: 5 => CTR => A4: 3,9
* DIS # B4: 3,9 => CTR => B4: 1,7,8
* DIS # C4: 3,9 => CTR => C4: 4,8
* PRF # G4: 1,3 => SOL
* DIS # G4: 8 => CTR => G4: 1,3
* DIS # B5: 9 => CTR => B5: 1,3
* DIS # B2: 3,9 => CTR => B2: 8
* PRF # B2: 8 => SOL
* DIS # B4: 3,9 => CTR => B4: 1,7,8
* DIS # B5: 3,9 => CTR => B5: 1
* PRF # B5: 1 => SOL
* DIS # C2: 3,9 => CTR => C2: 2,8
* DIS # C4: 3,9 => CTR => C4: 4,8
* DIS # C5: 3,9 => CTR => C5: 2,4
* DIS # D2: 2 => CTR => D2: 3,9
* CNT  30 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B7,C7,D6,D8,E1,E4,E8,F3,F4,F5,F8,G1,G5,G6,I3,I4,I6)
* 74.1.5.86....46571165....9........6....86..57..6.31.2.8..457612621...745457612938
* PAIR E1: 2,9 BLK 2
D2: 2,9,3                                # reduction candidate for 2,9
D2: 2,9 => CTR
* 74.1.5386....46571165...294.1....863...86.1575.6.314298..457612621...745457612938
* PAIR A6: 5,9 BLK 4
A4: 5,9,3                                # reduction candidate for 5,9
A4: 5,9 => CTR
* 74319528629.346571165..8.9........6.3.2864157..6.31.2.839457612621983745457612938
A4: 3 => SOLVED
* 743195286982346571165278493378524169214869357596731824839457612621983745457612938
* DURATION: 0:00:03.785499  START: 05:35:12.984202  END: 05:35:16.769701 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190424-absurd-base-pr-001.dot
* REASONING
* DIS # D2: 2,9 => CTR => D2: 3
* DIS D2: 3 # A4: 5,9 => CTR => A4: 3
* PRF D2: 3 + A4: 3 => SOL
* STA D2: 3 + A4: 3
* CNT   3 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190424, absurd

Solution

position: 743195286982346571165278493378524169214869357596731824839457612621983745457612938 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 # D2: 2,9 => CTR => D2: 3
* INC # D2: 3 => UNS
* DIS # C1: 2,9 => CTR => C1: 3
* INC # C1: 3 => UNS
* DIS # G3: 2,3 => CTR => G3: 4
* PRF # G3: 4 => SOL
* INC # C1: 2,3 => UNS
* DIS # C1: 9 => CTR => C1: 2,3
* INC # G3: 3,4 => UNS
* DIS # G3: 2 => CTR => G3: 3,4
* DIS # A4: 5,9 => CTR => A4: 3
* PRF # A4: 3 => SOL
* DIS # D4: 2,7 => CTR => D4: 5
* PRF # D4: 5 => SOL
* INC # E3: 2,7 => UNS
* DIS # E3: 8 => CTR => E3: 2,7
* DIS # C4: 4,9 => CTR => C4: 3,8
* INC # C4: 3,8 => UNS
* INC # C5: 4,9 => UNS
* DIS # C5: 2,3 => CTR => C5: 4,9
* INC # D4: 5,7 => UNS
* DIS # D4: 2 => CTR => D4: 5,7
* PRF # A4: 3,9 => SOL
* DIS # A4: 5 => CTR => A4: 3,9
* DIS # B4: 3,9 => CTR => B4: 1,7,8
* INC # B4: 1,7,8 => UNS
* DIS # C4: 3,9 => CTR => C4: 4,8
* INC # C4: 4,8 => UNS
* PRF # G4: 1,3 => SOL
* DIS # G4: 8 => CTR => G4: 1,3
* INC # B5: 1,3 => UNS
* DIS # B5: 9 => CTR => B5: 1,3
* DIS # B2: 3,9 => CTR => B2: 8
* PRF # B2: 8 => SOL
* DIS # B4: 3,9 => CTR => B4: 1,7,8
* INC # B4: 1,7,8 => UNS
* DIS # B5: 3,9 => CTR => B5: 1
* PRF # B5: 1 => SOL
* INC # C1: 3,9 => UNS
* DIS # C2: 3,9 => CTR => C2: 2,8
* INC # C2: 2,8 => UNS
* DIS # C4: 3,9 => CTR => C4: 4,8
* INC # C4: 4,8 => UNS
* DIS # C5: 3,9 => CTR => C5: 2,4
* INC # C5: 2,4 => UNS
* INC # D2: 3,9 => UNS
* DIS # D2: 2 => CTR => D2: 3,9
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D2: 2,9 => CTR => D2: 3
* DIS D2: 3 # A4: 5,9 => CTR => A4: 3
* PRF D2: 3 + A4: 3 => SOL
* STA D2: 3 + A4: 3
* CNT   3 HDP CHAINS /   2 HYP OPENED