Analysis of zz-www.sudokuoftheday.co.uk-20190224-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: ...4..6..7..3.5..4.2...9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 initial

Autosolve

position: ...4..6..7..3.58.4.24..9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 1,9 => CTR => B1: 3,5,8
* PRF # B8: 1,9 => SOL
* PRF # D8: 7,8 => SOL
* DIS # D8: 9 => CTR => D8: 7,8
* PRF # H1: 7 => SOL
* DIS # G3: 5,7 => CTR => G3: 3
* DIS # H6: 5,7 => CTR => H6: 1,2,4
* DIS # H9: 5,7 => CTR => H9: 1,8
* DIS # C5: 2,3 => CTR => C5: 7,9
* DIS # I6: 2,3 => CTR => I6: 5,7
* DIS # A7: 2,3 => CTR => A7: 6,8,9
* DIS # D4: 2,7 => CTR => D4: 9
* PRF # D4: 9 => SOL
* DIS # H6: 2,7 => CTR => H6: 1,4,5
* DIS # I6: 2,7 => CTR => I6: 3,5
* CNT  15 HDP CHAINS /  33 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: 1,9 => CTR => B1: 3,5,8
* PRF B1: 3,5,8 # B8: 1,9 => SOL
* STA B1: 3,5,8 + B8: 1,9
* CNT   2 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

...4..6..7..3.5..4.2...9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 initial
...4..6..7..3.58.4.24..9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9 autosolve
935418672716325894824769351571986423249531768368247915683192547197854236452673189 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
B2: 1,9
C2: 6,9
D3: 7,8
E3: 6,7
H2: 2,9
H3: 5,7
A6: 2,3
D6: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A8,B8: 1.. / A8 = 1  =>  8 pairs (_) / B8 = 1  =>  0 pairs (X)
G9,H9: 1.. / G9 = 1  =>  9 pairs (_) / H9 = 1  => 10 pairs (_)
B2,E2: 1.. / B2 = 1  =>  8 pairs (_) / E2 = 1  =>  0 pairs (X)
A1,A8: 1.. / A1 = 1  =>  0 pairs (X) / A8 = 1  =>  8 pairs (_)
G5,G9: 1.. / G5 = 1  => 10 pairs (_) / G9 = 1  =>  9 pairs (_)
D4,D6: 2.. / D4 = 2  =>  0 pairs (X) / D6 = 2  =>  0 pairs (_)
E2,H2: 2.. / E2 = 2  =>  8 pairs (_) / H2 = 2  => 10 pairs (_)
C9,E9: 2.. / C9 = 2  =>  9 pairs (_) / E9 = 2  => 17 pairs (_)
F1,F7: 2.. / F1 = 2  => 16 pairs (_) / F7 = 2  =>  9 pairs (_)
I1,G3: 3.. / I1 = 3  =>  0 pairs (X) / G3 = 3  => 12 pairs (_)
E5,E6: 3.. / E5 = 3  =>  0 pairs (*) / E6 = 3  =>  0 pairs (X)
A3,G3: 3.. / A3 = 3  =>  0 pairs (X) / G3 = 3  => 12 pairs (_)
E8,F8: 4.. / E8 = 4  =>  9 pairs (_) / F8 = 4  =>  0 pairs (*)
G7,H7: 4.. / G7 = 4  =>  9 pairs (_) / H7 = 4  => 10 pairs (_)
E6,E8: 4.. / E6 = 4  =>  0 pairs (*) / E8 = 4  =>  0 pairs (X)
G4,G7: 4.. / G4 = 4  => 10 pairs (_) / G7 = 4  =>  9 pairs (_)
B1,C1: 5.. / B1 = 5  => 10 pairs (_) / C1 = 5  =>  9 pairs (_)
G3,H3: 5.. / G3 = 5  =>  0 pairs (X) / H3 = 5  =>  8 pairs (_)
H6,I6: 5.. / H6 = 5  =>  0 pairs (X) / I6 = 5  =>  8 pairs (_)
C2,A3: 6.. / C2 = 6  =>  8 pairs (_) / A3 = 6  =>  0 pairs (X)
E2,E3: 6.. / E2 = 6  =>  0 pairs (X) / E3 = 6  =>  8 pairs (_)
F4,F5: 6.. / F4 = 6  =>  0 pairs (*) / F5 = 6  =>  0 pairs (X)
C2,E2: 6.. / C2 = 6  =>  8 pairs (_) / E2 = 6  =>  0 pairs (X)
A3,E3: 6.. / A3 = 6  =>  0 pairs (X) / E3 = 6  =>  8 pairs (_)
B4,C5: 7.. / B4 = 7  =>  0 pairs (*) / C5 = 7  =>  0 pairs (X)
F1,D3: 8.. / F1 = 8  =>  0 pairs (*) / D3 = 8  =>  0 pairs (X)
H5,I5: 8.. / H5 = 8  =>  8 pairs (_) / I5 = 8  =>  8 pairs (_)
A3,D3: 8.. / A3 = 8  =>  0 pairs (*) / D3 = 8  =>  0 pairs (X)
B9,H9: 8.. / B9 = 8  =>  8 pairs (_) / H9 = 8  => 10 pairs (_)
D3,D8: 8.. / D3 = 8  =>  9 pairs (_) / D8 = 8  =>  0 pairs (*)
H1,H2: 9.. / H1 = 9  => 10 pairs (_) / H2 = 9  =>  8 pairs (_)
D4,E5: 9.. / D4 = 9  =>  0 pairs (*) / E5 = 9  =>  0 pairs (X)
B4,D4: 9.. / B4 = 9  =>  0 pairs (X) / D4 = 9  =>  0 pairs (_)
D4,D8: 9.. / D4 = 9  =>  0 pairs (*) / D8 = 9  =>  0 pairs (X)
* DURATION: 0:00:41.016753  START: 03:58:48.886262  END: 03:59:29.903015 2019-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,C2,D3,D6,E3,H2,H3)
* ...4..6..7..3.58.4.24..9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9
* PAIR B2: 1,9 BLK 1
A1: 1,9,3,8                              # reduction candidate for 1,9
A1: 1,9                                  # 10 pairs
B1: 1,9,3,5,8                            # reduction candidate for 1,9
B1: 1,9 => CTR
* ..54..6..7..3.58.4.248.9..15.128....94.5.....2687..9..6..1.....1..9..2364..6.3..9
B1: 3,5,8                                #  8 pairs
* PAIR B2: 1,9 COL B
B8: 1,9,5,7,8                            # reduction candidate for 1,9
B8: 1,9 => SOLVED
* 935418672716325894824769351571986423249531768368247915683192547197854236452673189
B8: 5,7,8                                #  8 pairs
* PAIR C2: 6,9 COL C
C7: 6,9,2,3,5,7                          # reduction candidate for 6,9
C7: 6,9                                  # 11 pairs
C8: 6,9,5,7                              # reduction candidate for 6,9
C8: 6,9                                  # 10 pairs
* PAIR D3: 7,8 BLK 2
F1: 7,8,1,2                              # reduction candidate for 7,8
F1: 7,8                                  # 11 pairs
F1: 1,2                                  # 11 pairs
* PAIR D3: 7,8 COL D
D8: 7,8,9                                # reduction candidate for 7,8
D8: 7,8 => SOLVED
* 935418672716325894824769351571986423249531768368247915683192547197854236452673189
D8: 9 => CTR
* ...41.6..71.3.58.46248793515912847633475961..268731945...1..4..1..94.23.4..6.3.19
* PAIR H2: 2,9 BLK 3
H1: 2,9,7                                # reduction candidate for 2,9
H1: 7 => SOLVED
* 935418672716325894824769351571986423249531768368247915683192547197854236452673189
H1: 2,9                                  # 10 pairs
* PAIR H3: 5,7 BLK 3
G3: 5,7,3                                # reduction candidate for 5,7
G3: 5,7 => CTR
* ...4..6.37.63.58.4324869..1591.8.....4.5.....26873.9.5...1........94.23.4..6.3..9
G3: 3                                    # 12 pairs
* PAIR H3: 5,7 COL H
H6: 5,7,1,2,4                            # reduction candidate for 5,7
H6: 5,7 => CTR
* ...4..6.37..3.58.4.24..9..1571986342.4.5371..3682..9...3.1..4........23.4..6.3.19
H6: 1,2,4                                # 11 pairs
H7: 5,7,4,6,8                            # reduction candidate for 5,7
H7: 5,7                                  # 18 pairs
H9: 5,7,1,8                              # reduction candidate for 5,7
H9: 5,7 => CTR
* 8..4..6.37.63.58.4324869571591.8.....4.5.....26873.9.5...1..4.....94.23.48.6.3159
H9: 1,8                                  #  9 pairs
* PAIR A6: 2,3 BLK 4
A5: 2,3,9                                # reduction candidate for 2,3
A5: 2,3                                  # 18 pairs
C5: 2,3,7,9                              # reduction candidate for 2,3
C5: 2,3 => CTR
* ...4.269.7..3.582462487935157198.4629425.....3682..9..2..1........7..23.4..623..9
C5: 7,9                                  #  9 pairs
* PAIR A6: 2,3 ROW 6
I6: 2,3,5,7                              # reduction candidate for 2,3
I6: 2,3 => CTR
* ...4..6.37..3.58.43248695715.1.8.....4.5.....268...95....1...........23.4..6.3..9
I6: 5,7                                  #  9 pairs
* PAIR A6: 2,3 COL A
A7: 2,3,6,8,9                            # reduction candidate for 2,3
A7: 2,3 => CTR
* ...4.26.77..3.5824.248793515.198...29425....33682..9.52..1...........23.4..623..9
A7: 6,8,9                                #  8 pairs
* PAIR D6: 2,7 BLK 5
D4: 2,7,9                                # reduction candidate for 2,7
D4: 2,7 => CTR
* ...41.6..71.3.58.46248793515912847633475961..268731945...1..4..1..94.23.4..6.3.19
D4: 9 => SOLVED
* 935418672716325894824769351571986423249531768368247915683192547197854236452673189
* PAIR D6: 2,7 ROW 6
H6: 2,7,1,4,5                            # reduction candidate for 2,7
H6: 2,7 => CTR
* ...4..6.37..3.58.4.24..9751571986342.4.5371..3682..975.3.1..4.....7..23.4.7623519
H6: 1,4,5                                #  8 pairs
I6: 2,7,3,5                              # reduction candidate for 2,7
I6: 2,7 => CTR
* ...4..6.37..3.58.43248695715.1.8.....4.5.....2687..95....1...........23.4..6.3..9
I6: 3,5                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190224-absurd-base-pr-000.dot
* REASONING
* DIS # B1: 1,9 => CTR => B1: 3,5,8
* PRF # B8: 1,9 => SOL
* PRF # D8: 7,8 => SOL
* DIS # D8: 9 => CTR => D8: 7,8
* PRF # H1: 7 => SOL
* DIS # G3: 5,7 => CTR => G3: 3
* DIS # H6: 5,7 => CTR => H6: 1,2,4
* DIS # H9: 5,7 => CTR => H9: 1,8
* DIS # C5: 2,3 => CTR => C5: 7,9
* DIS # I6: 2,3 => CTR => I6: 5,7
* DIS # A7: 2,3 => CTR => A7: 6,8,9
* DIS # D4: 2,7 => CTR => D4: 9
* PRF # D4: 9 => SOL
* DIS # H6: 2,7 => CTR => H6: 1,4,5
* DIS # I6: 2,7 => CTR => I6: 3,5
* CNT  15 HDP CHAINS /  33 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,B2,C2,D3,D6,E3,H2,H3)
* ...4..6..7..3.58.4.24..9..15.1.8.....4.5......68...9.....1...........23.4..6.3..9
* PAIR B2: 1,9 BLK 1
A1: 1,9,3,8                              # reduction candidate for 1,9
A1: 1,9                                  # 10 pairs
B1: 1,9,3,5,8                            # reduction candidate for 1,9
B1: 1,9 => CTR
* ..54..6..7..3.58.4.248.9..15.128....94.5.....2687..9..6..1.....1..9..2364..6.3..9
* RESTART
* PAIR B2: 1,9 BLK 1
A1: 1,9,3,8                              # reduction candidate for 1,9
A1: 1,9                                  # 10 pairs
A1: 3,8                                  #  9 pairs
* PAIR B2: 1,9 COL B
B8: 1,9,5,7,8                            # reduction candidate for 1,9
B8: 1,9 => SOLVED
* 935418672716325894824769351571986423249531768368247915683192547197854236452673189
* DURATION: 0:00:04.644161  START: 03:59:52.446942  END: 03:59:57.091103 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190224-absurd-base-pr-001.dot
* REASONING
* DIS # B1: 1,9 => CTR => B1: 3,5,8
* PRF B1: 3,5,8 # B8: 1,9 => SOL
* STA B1: 3,5,8 + B8: 1,9
* CNT   2 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190224, absurd

Solution

position: 935418672716325894824769351571986423249531768368247915683192547197854236452673189 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 # A1: 1,9 => UNS
* DIS # B1: 1,9 => CTR => B1: 3,5,8
* INC # B1: 3,5,8 => UNS
* PRF # B8: 1,9 => SOL
* INC # B8: 5,7,8 => UNS
* INC # C7: 6,9 => UNS
* INC # C8: 6,9 => UNS
* INC # F1: 7,8 => UNS
* INC # F1: 1,2 => UNS
* PRF # D8: 7,8 => SOL
* DIS # D8: 9 => CTR => D8: 7,8
* INC # H1: 2,9 => UNS
* PRF # H1: 7 => SOL
* DIS # G3: 5,7 => CTR => G3: 3
* INC # G3: 3 => UNS
* DIS # H6: 5,7 => CTR => H6: 1,2,4
* INC # H6: 1,2,4 => UNS
* INC # H7: 5,7 => UNS
* DIS # H9: 5,7 => CTR => H9: 1,8
* INC # H9: 1,8 => UNS
* INC # A5: 2,3 => UNS
* DIS # C5: 2,3 => CTR => C5: 7,9
* INC # C5: 7,9 => UNS
* DIS # I6: 2,3 => CTR => I6: 5,7
* INC # I6: 5,7 => UNS
* DIS # A7: 2,3 => CTR => A7: 6,8,9
* INC # A7: 6,8,9 => UNS
* DIS # D4: 2,7 => CTR => D4: 9
* PRF # D4: 9 => SOL
* DIS # H6: 2,7 => CTR => H6: 1,4,5
* INC # H6: 1,4,5 => UNS
* DIS # I6: 2,7 => CTR => I6: 3,5
* INC # I6: 3,5 => UNS
* CNT  33 HDP CHAINS /  33 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 1,9 => UNS
* DIS # B1: 1,9 => CTR => B1: 3,5,8
* INC B1: 3,5,8 # A1: 1,9 => UNS
* INC B1: 3,5,8 # A1: 3,8 => UNS
* PRF B1: 3,5,8 # B8: 1,9 => SOL
* STA B1: 3,5,8 + B8: 1,9
* CNT   5 HDP CHAINS /   5 HYP OPENED