Analysis of zz-www.sudokuoftheday.co.uk-20060720-absurd-base.sdk

Contents

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

level: medium

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

position: 57..194...9......82.4.3.....1..8.3...27....8....6..1..............7..543...425..7 initial

Autosolve

position: 57..194...9......82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A2: 1,3 => SOL
* DIS # A2: 6 => CTR => A2: 1,3
* PRF # H2: 2,5 => SOL
* DIS # H2: 3 => CTR => H2: 2,5
* DIS # F2: 4,7 => CTR => F2: 6
* PRF # F2: 6 => SOL
* DIS # F2: 4 => CTR => F2: 6,7
* DIS # H1: 2,6 => CTR => H1: 3
* PRF # H1: 3 => SOL
* DIS # A6: 3,9 => CTR => A6: 8
* DIS # F6: 2,7 => CTR => F6: 3,4
* DIS # H4: 5 => CTR => H4: 2,7
* DIS # H4: 2,5 => CTR => H4: 7
* DIS # G7: 6,9 => CTR => G7: 2,8
* DIS # G9: 6,9 => CTR => G9: 8
* DIS # F7: 1,3 => CTR => F7: 8
* DIS # G7: 6,9 => CTR => G7: 2,8
* PRF # A8: 6,9 => SOL
* DIS # A8: 1,8 => CTR => A8: 6,9
* DIS # F7: 3 => CTR => F7: 1,8
* DIS # A8: 1,8 => CTR => A8: 6,9
* PRF # A8: 6,9 => SOL
* CNT  22 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:

* PRF # A2: 1,3 => SOL
* STA A2: 1,3
* CNT   1 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

57..194...9......82.4.3.....1..8.3...27....8....6..1..............7..543...425..7 initial
57..194...9......82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7 autosolve
578219436391546728264837951416982375927153684853674192745368219682791543139425867 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (22)
C1: 3,8
C2: 1,3
B3: 6,8
D1: 2,8
D2: 2,5
E2: 4,7
D3: 5,8
F3: 6,7
I1: 2,6
G2: 2,7
G3: 7,9
A5: 3,9
F4: 2,7
D5: 1,3
E6: 4,7
I4: 2,5
G5: 6,9
B8: 6,8
D7: 1,3
E7: 6,9
E8: 6,9
F8: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A2,C2: 1.. / A2 = 1  =>  0 pairs (X) / C2 = 1  => 23 pairs (_)
H3,I3: 1.. / H3 = 1  => 23 pairs (_) / I3 = 1  => 23 pairs (_)
D5,F5: 1.. / D5 = 1  => 22 pairs (_) / F5 = 1  =>  0 pairs (X)
A8,F8: 1.. / A8 = 1  =>  0 pairs (X) / F8 = 1  => 22 pairs (_)
C2,C9: 1.. / C2 = 1  => 23 pairs (_) / C9 = 1  =>  0 pairs (X)
D5,D7: 1.. / D5 = 1  => 22 pairs (_) / D7 = 1  =>  0 pairs (X)
I3,I7: 1.. / I3 = 1  => 23 pairs (_) / I7 = 1  => 23 pairs (_)
D1,D2: 2.. / D1 = 2  =>  0 pairs (*) / D2 = 2  =>  0 pairs (X)
F4,F6: 2.. / F4 = 2  => 22 pairs (_) / F6 = 2  =>  0 pairs (X)
G2,G7: 2.. / G2 = 2  =>  0 pairs (X) / G7 = 2  =>  0 pairs (_)
H1,H2: 3.. / H1 = 3  =>  0 pairs (*) / H2 = 3  =>  0 pairs (X)
D7,F7: 3.. / D7 = 3  => 22 pairs (_) / F7 = 3  =>  0 pairs (X)
C1,H1: 3.. / C1 = 3  =>  0 pairs (X) / H1 = 3  =>  0 pairs (_)
D5,D7: 3.. / D5 = 3  =>  0 pairs (X) / D7 = 3  => 22 pairs (_)
E2,F2: 4.. / E2 = 4  => 22 pairs (_) / F2 = 4  =>  0 pairs (X)
I5,I6: 4.. / I5 = 4  => 20 pairs (_) / I6 = 4  => 24 pairs (_)
F5,I5: 4.. / F5 = 4  => 24 pairs (_) / I5 = 4  => 20 pairs (_)
E2,E6: 4.. / E2 = 4  => 22 pairs (_) / E6 = 4  =>  0 pairs (X)
D2,D3: 5.. / D2 = 5  =>  0 pairs (*) / D3 = 5  =>  0 pairs (X)
H4,I4: 5.. / H4 = 5  =>  0 pairs (X) / I4 = 5  => 23 pairs (_)
D2,H2: 5.. / D2 = 5  =>  0 pairs (*) / H2 = 5  =>  0 pairs (X)
I3,I4: 5.. / I3 = 5  =>  0 pairs (X) / I4 = 5  => 23 pairs (_)
A2,B3: 6.. / A2 = 6  =>  0 pairs (X) / B3 = 6  =>  0 pairs (_)
F2,F3: 6.. / F2 = 6  =>  0 pairs (*) / F3 = 6  =>  0 pairs (X)
H1,I1: 6.. / H1 = 6  =>  0 pairs (X) / I1 = 6  => 23 pairs (_)
G5,I5: 6.. / G5 = 6  => 23 pairs (_) / I5 = 6  =>  0 pairs (X)
E7,E8: 6.. / E7 = 6  => 22 pairs (_) / E8 = 6  =>  0 pairs (X)
A2,F2: 6.. / A2 = 6  =>  0 pairs (X) / F2 = 6  =>  0 pairs (_)
B3,F3: 6.. / B3 = 6  =>  0 pairs (*) / F3 = 6  =>  0 pairs (X)
B3,B8: 6.. / B3 = 6  =>  0 pairs (*) / B8 = 6  =>  0 pairs (X)
G2,G3: 7.. / G2 = 7  =>  0 pairs (*) / G3 = 7  =>  0 pairs (X)
H4,H6: 7.. / H4 = 7  => 22 pairs (_) / H6 = 7  =>  0 pairs (X)
F3,G3: 7.. / F3 = 7  =>  0 pairs (*) / G3 = 7  =>  0 pairs (X)
F4,H4: 7.. / F4 = 7  =>  0 pairs (X) / H4 = 7  => 22 pairs (_)
E2,E6: 7.. / E2 = 7  =>  0 pairs (X) / E6 = 7  => 22 pairs (_)
C1,B3: 8.. / C1 = 8  =>  0 pairs (*) / B3 = 8  =>  0 pairs (X)
D1,D3: 8.. / D1 = 8  =>  0 pairs (X) / D3 = 8  =>  0 pairs (_)
A6,C6: 8.. / A6 = 8  => 23 pairs (_) / C6 = 8  =>  0 pairs (X)
F7,F8: 8.. / F7 = 8  => 22 pairs (_) / F8 = 8  =>  0 pairs (X)
G7,G9: 8.. / G7 = 8  =>  0 pairs (X) / G9 = 8  => 22 pairs (_)
C1,D1: 8.. / C1 = 8  =>  0 pairs (*) / D1 = 8  =>  0 pairs (X)
B3,D3: 8.. / B3 = 8  =>  0 pairs (X) / D3 = 8  =>  0 pairs (_)
F7,G7: 8.. / F7 = 8  => 22 pairs (_) / G7 = 8  =>  0 pairs (X)
B3,B8: 8.. / B3 = 8  =>  0 pairs (X) / B8 = 8  =>  0 pairs (_)
E7,E8: 9.. / E7 = 9  =>  0 pairs (X) / E8 = 9  => 22 pairs (_)
A8,E8: 9.. / A8 = 9  =>  0 pairs (X) / E8 = 9  => 22 pairs (_)
C6,C9: 9.. / C6 = 9  => 23 pairs (_) / C9 = 9  => 24 pairs (_)
* DURATION: 0:00:58.078274  START: 00:50:03.827069  END: 00:51:01.905343 2019-05-01
* CP COUNT: (47)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B3,B8,C1,C2,D1,D2,D3,D5,D7,E2,E6,E7,E8,F3,F4,F8,G2,G3,G5,I1,I4)
* 57..194...9......82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7
* PAIR C1: 3,8 COL C
C6: 3,8,9                                # reduction candidate for 3,8
C6: 3,8                                  # 24 pairs
C6: 9                                    # 23 pairs
* PAIR C2: 1,3 BLK 1
A2: 1,3,6                                # reduction candidate for 1,3
A2: 1,3 => SOLVED
* 578219436391546728264837951416982375927153684853674192745368219682791543139425867
A2: 6 => CTR
* 57..194..691....382845367..41698.352.27.5..8..5.6.217.745.......6279.543.3.425..7
* PAIR D2: 2,5 ROW 2
H2: 2,5,3                                # reduction candidate for 2,5
H2: 2,5 => SOLVED
* 578219436391546728264837951416982375927153684853674192745368219682791543139425867
H2: 3 => CTR
* 57..194...9.5..2382.483.7..41698.3...27.5..8..5.6..1..745.......827.1543.3.4258.7
* PAIR E2: 4,7 BLK 2
F2: 4,7,6                                # reduction candidate for 4,7
F2: 4,7 => CTR
* 57..194..691....382845367..41698.352.27.5..8..5.6.217.745.......6279.543.3.425..7
F2: 6 => SOLVED
* 578219436391546728264837951416982375927153684853674192745368219682791543139425867
* PAIR F3: 6,7 BLK 2
F2: 6,7,4                                # reduction candidate for 6,7
F2: 4 => CTR
* 57..194..691..4.382845367..41698.352.27.5..84.5.642179745.......6279.543.39425..7
F2: 6,7                                  # 22 pairs
* PAIR I1: 2,6 BLK 3
H1: 2,6,3                                # reduction candidate for 2,6
H1: 2,6 => CTR
* 5738194...912..7.82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7
H1: 3 => SOLVED
* 578219436391546728264837951416982375927153684853674192745368219682791543139425867
* PAIR I1: 2,6 COL I
I7: 2,6,1,9                              # reduction candidate for 2,6
I7: 2,6                                  # 29 pairs
I7: 1,9                                  # 23 pairs
* PAIR A5: 3,9 BLK 4
A6: 3,9,8                                # reduction candidate for 3,9
A6: 3,9 => CTR
* 5738194...912..7.82.4.3....41698.3...27.5..8..586..1..745........27..543.39425..7
A6: 8                                    # 23 pairs
C6: 3,9,8                                # reduction candidate for 3,9
C6: 3,9                                  # 23 pairs
* PAIR F4: 2,7 BLK 5
F6: 2,7,3,4                              # reduction candidate for 2,7
F6: 2,7 => CTR
* 57.219436.91.742.82.4.367..41698.3..927.5.684.5.64.1..745.689...62791543139425867
F6: 3,4                                  # 22 pairs
* PAIR F4: 2,7 ROW 4
H4: 2,7,5                                # reduction candidate for 2,7
H4: 5 => CTR
* 57..194.6.915742382.4.3....416987352.27.5..8..5.642179745........27..543.39425..7
H4: 2,7                                  # 23 pairs
* PAIR D5: 1,3 BLK 5
F5: 1,3,4                                # reduction candidate for 1,3
F5: 4                                    # 24 pairs
F5: 1,3                                  # 20 pairs
* PAIR E6: 4,7 BLK 5
F6: 4,7,2,3                              # reduction candidate for 4,7
F6: 2,3                                  # 23 pairs
F6: 4,7                                  # 21 pairs
* PAIR I4: 2,5 BLK 6
H4: 2,5,7                                # reduction candidate for 2,5
H4: 2,5 => CTR
* 57.219436.91.742.82.4.367914169873.5927.5.684.5.642179745...9.2.6279.543.39425867
H4: 7                                    # 22 pairs
* PAIR G5: 6,9 BLK 6
I5: 6,9,4                                # reduction candidate for 6,9
I5: 6,9                                  # 24 pairs
I5: 4                                    # 20 pairs
* PAIR G5: 6,9 COL G
G7: 6,9,2,8                              # reduction candidate for 6,9
G7: 6,9 => CTR
* 57.2194.6.9.5..2382.4.3.7..41698.3...27.5..8..5.6..1..745..8.....27.1543.3.4258.7
G7: 2,8                                  # 23 pairs
G9: 6,9,8                                # reduction candidate for 6,9
G9: 6,9 => CTR
* 57..194...9....2.828453....41698.3...27.5..8..5.6..1..745...8....27.8543.3.425..7
G9: 8                                    # 22 pairs
* PAIR B8: 6,8 BLK 7
A8: 6,8,1,9                              # reduction candidate for 6,8
A8: 6,8                                  # 22 pairs
A9: 6,8,1,9                              # reduction candidate for 6,8
A9: 6,8                                  # 25 pairs
* PAIR D7: 1,3 BLK 8
F7: 1,3,8                                # reduction candidate for 1,3
F7: 1,3 => CTR
* 57..194...9....2.828453....41698.3...27.5..8..5.6..1..745...8....27.8543.3.425..7
F7: 8                                    # 22 pairs
* PAIR E7: 6,9 ROW 7
G7: 6,9,2,8                              # reduction candidate for 6,9
G7: 6,9 => CTR
* 57.2194.6.9.5..2382.4.3.7..41698.3...27.5..8..5.6..1..745..8.....27.1543.3.4258.7
G7: 2,8                                  # 23 pairs
H7: 6,9,1,2                              # reduction candidate for 6,9
H7: 6,9                                  # 25 pairs
I7: 6,9,1,2                              # reduction candidate for 6,9
I7: 6,9                                  # 26 pairs
* PAIR E8: 6,9 ROW 8
A8: 6,9,1,8                              # reduction candidate for 6,9
A8: 6,9 => SOLVED
* 578219436391546728264837951416982375927153684853674192745368219682791543139425867
A8: 1,8 => CTR
* 57..194..691....382845367..41698.352.27.5..8..5.6.217.745.6.....6279.543.3.425..7
* PAIR F8: 1,8 BLK 8
F7: 1,8,3                                # reduction candidate for 1,8
F7: 3 => CTR
* 57..194...9....2.828453....41698.3...27.5..8..5.6..1..745..38....27.8543.3.425..7
F7: 1,8                                  # 22 pairs
* PAIR F8: 1,8 ROW 8
A8: 1,8,6,9                              # reduction candidate for 1,8
A8: 1,8 => CTR
* 57..194..691....382845367..41698.352.27.5..8..5.6.217.745.6.....6279.543.3.425..7
A8: 6,9 => SOLVED
* 578219436391546728264837951416982375927153684853674192745368219682791543139425867
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060720-absurd-base-pr-000.dot
* REASONING
* PRF # A2: 1,3 => SOL
* DIS # A2: 6 => CTR => A2: 1,3
* PRF # H2: 2,5 => SOL
* DIS # H2: 3 => CTR => H2: 2,5
* DIS # F2: 4,7 => CTR => F2: 6
* PRF # F2: 6 => SOL
* DIS # F2: 4 => CTR => F2: 6,7
* DIS # H1: 2,6 => CTR => H1: 3
* PRF # H1: 3 => SOL
* DIS # A6: 3,9 => CTR => A6: 8
* DIS # F6: 2,7 => CTR => F6: 3,4
* DIS # H4: 5 => CTR => H4: 2,7
* DIS # H4: 2,5 => CTR => H4: 7
* DIS # G7: 6,9 => CTR => G7: 2,8
* DIS # G9: 6,9 => CTR => G9: 8
* DIS # F7: 1,3 => CTR => F7: 8
* DIS # G7: 6,9 => CTR => G7: 2,8
* PRF # A8: 6,9 => SOL
* DIS # A8: 1,8 => CTR => A8: 6,9
* DIS # F7: 3 => CTR => F7: 1,8
* DIS # A8: 1,8 => CTR => A8: 6,9
* PRF # A8: 6,9 => SOL
* CNT  22 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B3,B8,C1,C2,D1,D2,D3,D5,D7,E2,E6,E7,E8,F3,F4,F8,G2,G3,G5,I1,I4)
* 57..194...9......82.4.3....41698.3...27.5..8..5.6..1..745........27..543.3.425..7
* PAIR C1: 3,8 COL C
C6: 3,8,9                                # reduction candidate for 3,8
C6: 3,8                                  # 24 pairs
C6: 9                                    # 23 pairs
* PAIR C2: 1,3 BLK 1
A2: 1,3,6                                # reduction candidate for 1,3
A2: 1,3 => SOLVED
* 578219436391546728264837951416982375927153684853674192745368219682791543139425867
* DURATION: 0:00:03.224190  START: 00:51:35.542598  END: 00:51:38.766788 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060720-absurd-base-pr-001.dot
* REASONING
* PRF # A2: 1,3 => SOL
* STA A2: 1,3
* CNT   1 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060720, absurd

Solution

position: 578219436391546728264837951416982375927153684853674192745368219682791543139425867 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 # C6: 3,8 => UNS
* INC # C6: 9 => UNS
* PRF # A2: 1,3 => SOL
* DIS # A2: 6 => CTR => A2: 1,3
* PRF # H2: 2,5 => SOL
* DIS # H2: 3 => CTR => H2: 2,5
* DIS # F2: 4,7 => CTR => F2: 6
* PRF # F2: 6 => SOL
* INC # F2: 6,7 => UNS
* DIS # F2: 4 => CTR => F2: 6,7
* DIS # H1: 2,6 => CTR => H1: 3
* PRF # H1: 3 => SOL
* INC # I7: 2,6 => UNS
* INC # I7: 1,9 => UNS
* DIS # A6: 3,9 => CTR => A6: 8
* INC # A6: 8 => UNS
* INC # C6: 3,9 => UNS
* DIS # F6: 2,7 => CTR => F6: 3,4
* INC # F6: 3,4 => UNS
* INC # H4: 2,7 => UNS
* DIS # H4: 5 => CTR => H4: 2,7
* INC # F5: 1,3 => UNS
* INC # F5: 4 => UNS
* INC # F6: 4,7 => UNS
* INC # F6: 2,3 => UNS
* DIS # H4: 2,5 => CTR => H4: 7
* INC # H4: 7 => UNS
* INC # I5: 6,9 => UNS
* INC # I5: 4 => UNS
* DIS # G7: 6,9 => CTR => G7: 2,8
* INC # G7: 2,8 => UNS
* DIS # G9: 6,9 => CTR => G9: 8
* INC # G9: 8 => UNS
* INC # A8: 6,8 => UNS
* INC # A9: 6,8 => UNS
* DIS # F7: 1,3 => CTR => F7: 8
* INC # F7: 8 => UNS
* DIS # G7: 6,9 => CTR => G7: 2,8
* INC # G7: 2,8 => UNS
* INC # H7: 6,9 => UNS
* INC # I7: 6,9 => UNS
* PRF # A8: 6,9 => SOL
* DIS # A8: 1,8 => CTR => A8: 6,9
* INC # F7: 1,8 => UNS
* DIS # F7: 3 => CTR => F7: 1,8
* DIS # A8: 1,8 => CTR => A8: 6,9
* PRF # A8: 6,9 => SOL
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C6: 3,8 => UNS
* INC # C6: 9 => UNS
* PRF # A2: 1,3 => SOL
* STA A2: 1,3
* CNT   3 HDP CHAINS /   3 HYP OPENED