Analysis of zz-www.sudokuoftheday.co.uk-20060620-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006

position: ..3...8...1.9...7.8.......6.....4..7765..2.......6.2....489..5.5.......1......792 initial

Autosolve

position: 4.3...8.9.1.9.8.748.......69..584.67765..2948.487692.5..489.6535.....481.8....792 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 5,7 => CTR => B3: 9
* DIS # B3: 5 => CTR => B3: 7,9
* DIS # E3: 3,5 => CTR => E3: 1,2,4,7
* DIS # H3: 1,2 => CTR => H3: 3
* PRF # H3: 3 => SOL
* DIS # G3: 3,5 => CTR => G3: 1
* PRF # G3: 1 => SOL
* PRF # A9: 1,3 => SOL
* DIS # A9: 6 => CTR => A9: 1,3
* DIS # D3: 1,3 => CTR => D3: 2,4
* DIS # E3: 1,3 => CTR => E3: 2,4,5,7
* DIS # E9: 1,3 => CTR => E9: 4,5
* DIS # G3: 5 => CTR => G3: 1,3
* DIS # H3: 2 => CTR => H3: 1,3
* DIS # B8: 7,9 => CTR => B8: 3
* PRF # B8: 3 => SOL
* PRF # A9: 1,6 => SOL
* DIS # A9: 3 => CTR => A9: 1,6
* CNT  18 HDP CHAINS /  36 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 # B3: 5,7 => CTR => B3: 9
* DIS B3: 9 # E3: 3,5 => CTR => E3: 1,2,4
* DIS B3: 9 + E3: 1,2,4 # F3: 1 => CTR => F3: 3,5
* DIS B3: 9 + E3: 1,2,4 + F3: 3,5 # E9: 1,4 => CTR => E9: 3,5
* DIS B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 # H3: 1,2 => CTR => H3: 3
* PRF B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3 => SOL
* STA B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3
* CNT   6 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

..3...8...1.9...7.8.......6.....4..7765..2.......6.2....489..5.5.......1......792 initial
4.3...8.9.1.9.8.748.......69..584.67765..2948.487692.5..489.6535.....481.8....792 autosolve
453176829612938574897245136921584367765312948348769215274891653539627481186453792 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
B1: 5,7
A2: 2,6
C2: 2,6
C3: 7,9
E2: 3,5
H1: 1,2
G2: 3,5
B4: 2,3
C4: 1,2
A6: 1,3
D5: 1,3
E5: 1,3
G4: 1,3
H6: 1,3
A7: 1,2
B7: 2,7
C8: 7,9
C9: 1,6
F7: 1,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C4,A6: 1.. / C4 = 1  =>  0 pairs (*) / A6 = 1  =>  0 pairs (X)
D5,E5: 1.. / D5 = 1  =>  0 pairs (X) / E5 = 1  => 19 pairs (_)
G4,H6: 1.. / G4 = 1  =>  0 pairs (X) / H6 = 1  =>  0 pairs (_)
C4,G4: 1.. / C4 = 1  =>  0 pairs (*) / G4 = 1  =>  0 pairs (X)
A6,H6: 1.. / A6 = 1  =>  0 pairs (X) / H6 = 1  =>  0 pairs (_)
A7,F7: 1.. / A7 = 1  =>  0 pairs (X) / F7 = 1  =>  0 pairs (_)
C4,C9: 1.. / C4 = 1  =>  0 pairs (*) / C9 = 1  =>  0 pairs (X)
G3,G4: 1.. / G3 = 1  =>  0 pairs (*) / G4 = 1  =>  0 pairs (X)
A2,C2: 2.. / A2 = 2  =>  0 pairs (X) / C2 = 2  =>  0 pairs (_)
H1,H3: 2.. / H1 = 2  => 22 pairs (_) / H3 = 2  =>  0 pairs (X)
B4,C4: 2.. / B4 = 2  =>  0 pairs (*) / C4 = 2  =>  0 pairs (X)
A7,B7: 2.. / A7 = 2  =>  0 pairs (*) / B7 = 2  =>  0 pairs (X)
D8,E8: 2.. / D8 = 2  => 20 pairs (_) / E8 = 2  => 20 pairs (_)
A2,A7: 2.. / A2 = 2  =>  0 pairs (X) / A7 = 2  =>  0 pairs (_)
B4,B7: 2.. / B4 = 2  =>  0 pairs (*) / B7 = 2  =>  0 pairs (X)
C2,C4: 2.. / C2 = 2  =>  0 pairs (*) / C4 = 2  =>  0 pairs (X)
B4,A6: 3.. / B4 = 3  =>  0 pairs (X) / A6 = 3  =>  0 pairs (_)
D5,E5: 3.. / D5 = 3  => 19 pairs (_) / E5 = 3  =>  0 pairs (X)
G4,H6: 3.. / G4 = 3  =>  0 pairs (*) / H6 = 3  =>  0 pairs (X)
B8,A9: 3.. / B8 = 3  =>  0 pairs (*) / A9 = 3  =>  0 pairs (X)
E2,G2: 3.. / E2 = 3  => 20 pairs (_) / G2 = 3  =>  0 pairs (X)
B4,G4: 3.. / B4 = 3  =>  0 pairs (X) / G4 = 3  =>  0 pairs (_)
A6,H6: 3.. / A6 = 3  =>  0 pairs (*) / H6 = 3  =>  0 pairs (X)
A6,A9: 3.. / A6 = 3  =>  0 pairs (*) / A9 = 3  =>  0 pairs (X)
B4,B8: 3.. / B4 = 3  =>  0 pairs (X) / B8 = 3  =>  0 pairs (_)
H3,H6: 3.. / H3 = 3  =>  0 pairs (*) / H6 = 3  =>  0 pairs (X)
D3,E3: 4.. / D3 = 4  => 22 pairs (_) / E3 = 4  => 21 pairs (_)
D9,E9: 4.. / D9 = 4  => 21 pairs (_) / E9 = 4  => 22 pairs (_)
D3,D9: 4.. / D3 = 4  => 22 pairs (_) / D9 = 4  => 21 pairs (_)
E3,E9: 4.. / E3 = 4  => 21 pairs (_) / E9 = 4  => 22 pairs (_)
B1,B3: 5.. / B1 = 5  => 19 pairs (_) / B3 = 5  =>  0 pairs (X)
G2,G3: 5.. / G2 = 5  => 20 pairs (_) / G3 = 5  =>  0 pairs (X)
E9,F9: 5.. / E9 = 5  => 22 pairs (_) / F9 = 5  => 19 pairs (_)
E2,G2: 5.. / E2 = 5  =>  0 pairs (X) / G2 = 5  => 20 pairs (_)
A2,C2: 6.. / A2 = 6  =>  0 pairs (*) / C2 = 6  =>  0 pairs (X)
D1,F1: 6.. / D1 = 6  => 20 pairs (_) / F1 = 6  => 22 pairs (_)
A9,C9: 6.. / A9 = 6  =>  0 pairs (X) / C9 = 6  =>  0 pairs (_)
D8,F8: 6.. / D8 = 6  => 22 pairs (_) / F8 = 6  => 20 pairs (_)
A2,A9: 6.. / A2 = 6  =>  0 pairs (*) / A9 = 6  =>  0 pairs (X)
C2,C9: 6.. / C2 = 6  =>  0 pairs (X) / C9 = 6  =>  0 pairs (_)
D1,D8: 6.. / D1 = 6  => 20 pairs (_) / D8 = 6  => 22 pairs (_)
F1,F8: 6.. / F1 = 6  => 22 pairs (_) / F8 = 6  => 20 pairs (_)
B7,F7: 7.. / B7 = 7  =>  0 pairs (*) / F7 = 7  =>  0 pairs (X)
C3,C8: 7.. / C3 = 7  => 17 pairs (_) / C8 = 7  =>  0 pairs (X)
B3,C3: 9.. / B3 = 9  => 17 pairs (_) / C3 = 9  =>  0 pairs (X)
B8,C8: 9.. / B8 = 9  =>  0 pairs (X) / C8 = 9  => 17 pairs (_)
B3,B8: 9.. / B3 = 9  => 17 pairs (_) / B8 = 9  =>  0 pairs (X)
C3,C8: 9.. / C3 = 9  =>  0 pairs (X) / C8 = 9  => 17 pairs (_)
* DURATION: 0:00:58.020811  START: 23:58:22.352147  END: 23:59:20.372958 2019-04-30
* CP COUNT: (48)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,B1,B4,B7,C2,C3,C4,C8,C9,D5,E2,E5,F7,G2,G4,H1,H6)
* 4.3...8.9.1.9.8.748.......69..584.67765..2948.487692.5..489.6535.....481.8....792
* PAIR B1: 5,7 BLK 1
B3: 5,7,9                                # reduction candidate for 5,7
B3: 5,7 => CTR
* 4.3...8.96129.8.748.9.....69..584.67765..2948.487692.5..489.653597...481386...792
B3: 9                                    # 17 pairs
* PAIR B1: 5,7 ROW 1
E1: 5,7,1,2                              # reduction candidate for 5,7
E1: 5,7                                  # 21 pairs
F1: 5,7,1,6                              # reduction candidate for 5,7
F1: 5,7                                  # 22 pairs
* PAIR C3: 7,9 BLK 1
B3: 7,9,5                                # reduction candidate for 7,9
B3: 5 => CTR
* 473...8.96129.8574859.7...69..584.67765..2948.487692.5..489.653597...481386...792
B3: 7,9                                  # 19 pairs
* PAIR E2: 3,5 BLK 2
E3: 3,5,1,2,4,7                          # reduction candidate for 3,5
E3: 3,5 => CTR
* 4.3...8196129.8.748..4.1.269..584.67765..2948.48769235..489.6535.....481386145792
E3: 1,2,4,7                              # 19 pairs
F3: 3,5,1,7                              # reduction candidate for 3,5
F3: 3,5                                  # 20 pairs
* PAIR E2: 3,5 COL E
E9: 3,5,1,4                              # reduction candidate for 3,5
E9: 3,5                                  # 22 pairs
E9: 1,4                                  # 20 pairs
* PAIR H1: 1,2 BLK 3
H3: 1,2,3                                # reduction candidate for 1,2
H3: 1,2 => CTR
* 4.3...8.96129.8.748.......69..584.67765..2948.48769235..489.6535.....481386...792
H3: 3 => SOLVED
* 453176829612938574897245136921584367765312948348769215274891653539627481186453792
* PAIR H1: 1,2 ROW 1
D1: 1,2,6                                # reduction candidate for 1,2
D1: 1,2                                  # 22 pairs
E1: 1,2,5,7                              # reduction candidate for 1,2
E1: 1,2                                  # 22 pairs
* PAIR G2: 3,5 BLK 3
G3: 3,5,1                                # reduction candidate for 3,5
G3: 3,5 => CTR
* 4.3...8.9.1.9.8.748.......69..584167765..294814876923527489.6535.....481.8....792
G3: 1 => SOLVED
* 453176829612938574897245136921584367765312948348769215274891653539627481186453792
* PAIR A6: 1,3 COL A
A9: 1,3,6                                # reduction candidate for 1,3
A9: 1,3 => SOLVED
* 453176829612938574897245136921584367765312948348769215274891653539627481186453792
A9: 6 => CTR
* 4.3...8.9.1.9.8.748.......69..584.67765..294834876921512489.6535.....481.8....792
* PAIR D5: 1,3 COL D
D3: 1,3,2,4                              # reduction candidate for 1,3
D3: 1,3 => CTR
* 4.3...8196129.8.748...4..269..584.67765..2948.48769235..489.6535.....4813864..792
D3: 2,4                                  # 20 pairs
D9: 1,3,4                                # reduction candidate for 1,3
D9: 1,3                                  # 22 pairs
* PAIR E5: 1,3 COL E
E3: 1,3,2,4,5,7                          # reduction candidate for 1,3
E3: 1,3 => CTR
* 4.3...8196129.8.748..4.1.269..584.67765..2948.48769235..489.6535.....481386145792
E3: 2,4,5,7                              # 19 pairs
E9: 1,3,4,5                              # reduction candidate for 1,3
E9: 1,3 => CTR
* 453...8.9.1.9583748...4.5.6932584167765..294814876923527489165359....481.8.4.5792
E9: 4,5                                  # 20 pairs
* PAIR G4: 1,3 COL G
G3: 1,3,5                                # reduction candidate for 1,3
G3: 5 => CTR
* 4.3...8.9.1.9.8.748.....5.69..584167765..294814876923527489.6535.....481.8....792
G3: 1,3                                  # 20 pairs
* PAIR H6: 1,3 COL H
H3: 1,3,2                                # reduction candidate for 1,3
H3: 2 => CTR
* 4.3...8196129.8.748......269..584.67765..2948.48769235..489.6535.....481386...792
H3: 1,3                                  # 22 pairs
* PAIR C8: 7,9 BLK 7
B8: 7,9,3                                # reduction candidate for 7,9
B8: 7,9 => CTR
* 4.3...8.9.1.9.8.748.......6932584167765..294814876923527489165359....481.8....792
B8: 3 => SOLVED
* 453176829612938574897245136921584367765312948348769215274891653539627481186453792
* PAIR C9: 1,6 BLK 7
A9: 1,6,3                                # reduction candidate for 1,6
A9: 1,6 => SOLVED
* 453176829612938574897245136921584367765312948348769215274891653539627481186453792
A9: 3 => CTR
* 4.3...8.96129.8.748.......6921584367765..29483487692.5..489.6535.....481.8....792
* PAIR F7: 1,7 COL F
F1: 1,7,5,6                              # reduction candidate for 1,7
F1: 1,7                                  # 23 pairs
F3: 1,7,3,5                              # reduction candidate for 1,7
F3: 1,7                                  # 26 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060620-absurd-base-pr-000.dot
* REASONING
* DIS # B3: 5,7 => CTR => B3: 9
* DIS # B3: 5 => CTR => B3: 7,9
* DIS # E3: 3,5 => CTR => E3: 1,2,4,7
* DIS # H3: 1,2 => CTR => H3: 3
* PRF # H3: 3 => SOL
* DIS # G3: 3,5 => CTR => G3: 1
* PRF # G3: 1 => SOL
* PRF # A9: 1,3 => SOL
* DIS # A9: 6 => CTR => A9: 1,3
* DIS # D3: 1,3 => CTR => D3: 2,4
* DIS # E3: 1,3 => CTR => E3: 2,4,5,7
* DIS # E9: 1,3 => CTR => E9: 4,5
* DIS # G3: 5 => CTR => G3: 1,3
* DIS # H3: 2 => CTR => H3: 1,3
* DIS # B8: 7,9 => CTR => B8: 3
* PRF # B8: 3 => SOL
* PRF # A9: 1,6 => SOL
* DIS # A9: 3 => CTR => A9: 1,6
* CNT  18 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A7,B1,B4,B7,C2,C3,C4,C8,C9,D5,E2,E5,F7,G2,G4,H1,H6)
* 4.3...8.9.1.9.8.748.......69..584.67765..2948.487692.5..489.6535.....481.8....792
* PAIR B1: 5,7 BLK 1
B3: 5,7,9                                # reduction candidate for 5,7
B3: 5,7 => CTR
* 4.3...8.96129.8.748.9.....69..584.67765..2948.487692.5..489.653597...481386...792
* PAIR E2: 3,5 BLK 2
E3: 3,5,1,2,4                            # reduction candidate for 3,5
E3: 3,5 => CTR
* 453...8196129.8.748974.1.269..584.67765..2948.48769235..489.6535.9...481386145792
F3: 3,5,1                                # reduction candidate for 3,5
F3: 3,5                                  # 18 pairs
* RESTART
* PAIR E2: 3,5 BLK 2
F3: 3,5,1                                # reduction candidate for 3,5
F3: 1 => CTR
* 453...8.9.1.95837489734152693258416776513294814876923527489.6535.9...481.8....792
* PAIR E2: 3,5 COL E
E9: 3,5,1,4                              # reduction candidate for 3,5
E9: 1,4 => CTR
* 453...8.9.1.958374897..35.6932584167765..294814876923527489.6535.9...481.8....792
* PAIR RESTART
* PAIR H1: 1,2 BLK 3
H3: 1,2,3                                # reduction candidate for 1,2
H3: 1,2 => CTR
* 453...8.9612938574897.453.69..584.67765312948.48769235..489.6535.9...481386451792
H3: 3 => SOLVED
* 453176829612938574897245136921584367765312948348769215274891653539627481186453792
* DURATION: 0:00:08.687359  START: 23:59:46.087632  END: 23:59:54.774991 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060620-absurd-base-pr-001.dot
* REASONING
* DIS # B3: 5,7 => CTR => B3: 9
* DIS B3: 9 # E3: 3,5 => CTR => E3: 1,2,4
* DIS B3: 9 + E3: 1,2,4 # F3: 1 => CTR => F3: 3,5
* DIS B3: 9 + E3: 1,2,4 + F3: 3,5 # E9: 1,4 => CTR => E9: 3,5
* DIS B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 # H3: 1,2 => CTR => H3: 3
* PRF B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3 => SOL
* STA B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3
* CNT   6 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060620, absurd

Solution

position: 453176829612938574897245136921584367765312948348769215274891653539627481186453792 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 # B3: 5,7 => CTR => B3: 9
* INC # B3: 9 => UNS
* INC # E1: 5,7 => UNS
* INC # F1: 5,7 => UNS
* INC # B3: 7,9 => UNS
* DIS # B3: 5 => CTR => B3: 7,9
* DIS # E3: 3,5 => CTR => E3: 1,2,4,7
* INC # E3: 1,2,4,7 => UNS
* INC # F3: 3,5 => UNS
* INC # E9: 3,5 => UNS
* INC # E9: 1,4 => UNS
* DIS # H3: 1,2 => CTR => H3: 3
* PRF # H3: 3 => SOL
* INC # D1: 1,2 => UNS
* INC # E1: 1,2 => UNS
* DIS # G3: 3,5 => CTR => G3: 1
* PRF # G3: 1 => SOL
* PRF # A9: 1,3 => SOL
* DIS # A9: 6 => CTR => A9: 1,3
* DIS # D3: 1,3 => CTR => D3: 2,4
* INC # D3: 2,4 => UNS
* INC # D9: 1,3 => UNS
* DIS # E3: 1,3 => CTR => E3: 2,4,5,7
* INC # E3: 2,4,5,7 => UNS
* DIS # E9: 1,3 => CTR => E9: 4,5
* INC # E9: 4,5 => UNS
* INC # G3: 1,3 => UNS
* DIS # G3: 5 => CTR => G3: 1,3
* INC # H3: 1,3 => UNS
* DIS # H3: 2 => CTR => H3: 1,3
* DIS # B8: 7,9 => CTR => B8: 3
* PRF # B8: 3 => SOL
* PRF # A9: 1,6 => SOL
* DIS # A9: 3 => CTR => A9: 1,6
* INC # F1: 1,7 => UNS
* INC # F3: 1,7 => UNS
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B3: 5,7 => CTR => B3: 9
* DIS B3: 9 # E3: 3,5 => CTR => E3: 1,2,4
* INC B3: 9 + E3: 1,2,4 # F3: 3,5 => UNS
* INC B3: 9 + E3: 1,2,4 # F3: 3,5 => UNS
* DIS B3: 9 + E3: 1,2,4 # F3: 1 => CTR => F3: 3,5
* INC B3: 9 + E3: 1,2,4 + F3: 3,5 # E9: 3,5 => UNS
* DIS B3: 9 + E3: 1,2,4 + F3: 3,5 # E9: 1,4 => CTR => E9: 3,5
* DIS B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 # H3: 1,2 => CTR => H3: 3
* PRF B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3 => SOL
* STA B3: 9 + E3: 1,2,4 + F3: 3,5 + E9: 3,5 + H3: 3
* CNT   9 HDP CHAINS /   8 HYP OPENED