Analysis of zz-www.sudokuoftheday.co.uk-20190406-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: .8......4......6.2.39.658..3....8..6...5..19...7......1..4.2......8.3..7....5.... initial

Autosolve

position: .8....954..19846324392658713..1.87.6...5..19..17......1..4.2......8.3..7....5.... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B7: 6,9 => CTR => B7: 5,7
* DIS # E1: 1 => CTR => E1: 3,7
* DIS # E1: 1,7 => CTR => E1: 3
* DIS # F9: 1,7 => CTR => F9: 6,9
* DIS # F9: 6,7 => CTR => F9: 1,9
* PRF # A6: 2,8 => SOL
* DIS # F9: 1,7 => CTR => F9: 6,9
* DIS # C4: 2,4 => CTR => C4: 5
* DIS # H9: 2,4 => CTR => H9: 1,8
* DIS # I6: 3,8 => CTR => I6: 5
* DIS # I7: 3,8 => CTR => I7: 5,9
* DIS # B7: 7,9 => CTR => B7: 5,6
* DIS # F9: 6,7 => CTR => F9: 1,9
* DIS # F9: 6,7 => CTR => F9: 1,9
* DIS # I7: 3,5 => CTR => I7: 8,9
* CNT  15 HDP CHAINS /  49 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 # B7: 6,9 => CTR => B7: 5,7
* DIS B7: 5,7 # E1: 1 => CTR => E1: 3,7
* DIS B7: 5,7 + E1: 3,7 # F9: 6,7 => CTR => F9: 9
* PRF B7: 5,7 + E1: 3,7 + F9: 9 # E4: 2,4 => SOL
* STA B7: 5,7 + E1: 3,7 + F9: 9 + E4: 2,4
* CNT   4 HDP CHAINS /  12 HYP OPENED

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

Details

Positions

.8......4......6.2.39.658..3....8..6...5..19...7......1..4.2......8.3..7....5.... initial
.8....954..19846324392658713..1.87.6...5..19..17......1..4.2......8.3..7....5.... autosolve
682731954571984632439265871395148726864527193217396485158472369926813547743659218 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A1: 2,6
C1: 2,6
A2: 5,7
B2: 5,7
D1: 3,7
F1: 1,7
F5: 6,7
D6: 3,6
F6: 6,9
H4: 2,4
I5: 3,8
E7: 7,9
E8: 1,9
D9: 6,7
G7: 3,5
H7: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,F1: 1.. / E1 = 1  =>  0 pairs (X) / F1 = 1  => 15 pairs (_)
E8,F9: 1.. / E8 = 1  => 15 pairs (_) / F9 = 1  =>  0 pairs (X)
H8,H9: 1.. / H8 = 1  =>  0 pairs (X) / H9 = 1  => 15 pairs (_)
E8,H8: 1.. / E8 = 1  => 15 pairs (_) / H8 = 1  =>  0 pairs (X)
F9,H9: 1.. / F9 = 1  =>  0 pairs (X) / H9 = 1  => 15 pairs (_)
E1,E8: 1.. / E1 = 1  =>  0 pairs (X) / E8 = 1  => 15 pairs (_)
F1,F9: 1.. / F1 = 1  => 15 pairs (_) / F9 = 1  =>  0 pairs (X)
A1,C1: 2.. / A1 = 2  => 15 pairs (_) / C1 = 2  => 15 pairs (_)
D1,E1: 3.. / D1 = 3  =>  0 pairs (X) / E1 = 3  => 13 pairs (_)
C7,C9: 3.. / C7 = 3  => 18 pairs (_) / C9 = 3  => 18 pairs (_)
E5,I5: 3.. / E5 = 3  =>  0 pairs (X) / I5 = 3  => 17 pairs (_)
D1,D6: 3.. / D1 = 3  =>  0 pairs (X) / D6 = 3  => 13 pairs (_)
A2,B2: 5.. / A2 = 5  =>  9 pairs (_) / B2 = 5  => 15 pairs (_)
B4,C4: 5.. / B4 = 5  =>  0 pairs (X) / C4 = 5  => 16 pairs (_)
G6,I6: 5.. / G6 = 5  =>  0 pairs (X) / I6 = 5  => 16 pairs (_)
A2,A8: 5.. / A2 = 5  =>  9 pairs (_) / A8 = 5  => 15 pairs (_)
I6,I7: 5.. / I6 = 5  => 16 pairs (_) / I7 = 5  =>  0 pairs (X)
A1,C1: 6.. / A1 = 6  => 15 pairs (_) / C1 = 6  => 15 pairs (_)
D9,F9: 6.. / D9 = 6  => 13 pairs (_) / F9 = 6  =>  0 pairs (X)
H7,H8: 6.. / H7 = 6  => 15 pairs (_) / H8 = 6  => 21 pairs (_)
D6,D9: 6.. / D6 = 6  =>  0 pairs (X) / D9 = 6  => 13 pairs (_)
A2,B2: 7.. / A2 = 7  => 15 pairs (_) / B2 = 7  =>  9 pairs (_)
E5,F5: 7.. / E5 = 7  =>  0 pairs (X) / F5 = 7  => 15 pairs (_)
B7,E7: 7.. / B7 = 7  =>  0 pairs (X) / E7 = 7  =>  9 pairs (_)
A2,A9: 7.. / A2 = 7  => 15 pairs (_) / A9 = 7  =>  9 pairs (_)
D1,D9: 7.. / D1 = 7  => 13 pairs (_) / D9 = 7  =>  0 pairs (X)
B4,A6: 9.. / B4 = 9  => 21 pairs (_) / A6 = 9  => 12 pairs (_)
I7,I9: 9.. / I7 = 9  =>  9 pairs (_) / I9 = 9  =>  0 pairs (X)
B4,E4: 9.. / B4 = 9  => 21 pairs (_) / E4 = 9  => 12 pairs (_)
F6,F9: 9.. / F6 = 9  => 20 pairs (_) / F9 = 9  =>  9 pairs (_)
* DURATION: 0:00:31.168476  START: 05:06:26.795725  END: 05:06:57.964201 2019-05-01
* CP COUNT: (30)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B2,C1,D1,D6,D9,E7,E8,F1,F5,F6,G7,H4,H7,I5)
* .8....954..19846324392658713..1.87.6...5..19..17......1..4.2......8.3..7....5....
* PAIR A1: 2,6 COL A
A5: 2,6,8                                # reduction candidate for 2,6
A5: 2,6                                  # 19 pairs
A6: 2,6,8,9                              # reduction candidate for 2,6
A6: 2,6                                  # 24 pairs
A8: 2,6,5,9                              # reduction candidate for 2,6
A8: 2,6                                  # 12 pairs
* PAIR C1: 2,6 COL C
C5: 2,6,4,8                              # reduction candidate for 2,6
C5: 2,6                                  # 21 pairs
C8: 2,6,4,5                              # reduction candidate for 2,6
C8: 2,6                                  # 19 pairs
* PAIR B2: 5,7 COL B
B7: 5,7,6,9                              # reduction candidate for 5,7
B7: 6,9 => CTR
* .8.731954..19846324392658713..1.87.6...5.7193.173.6.851.8472......813..7...659.18
B7: 5,7                                  # 17 pairs
* PAIR D1: 3,7 BLK 2
E1: 3,7,1                                # reduction candidate for 3,7
E1: 1 => CTR
* .8.317954..19846324392658713..1.87.6...57619..17......1..4.2......8.3..7....5....
E1: 3,7                                  # 15 pairs
* PAIR F1: 1,7 BLK 2
E1: 1,7,3                                # reduction candidate for 1,7
E1: 1,7 => CTR
* .8.3.19547519846324392658713951.87.6...5.719..176.9...17.492......8.3..7...756.1.
E1: 3                                    # 13 pairs
* PAIR F1: 1,7 COL F
F9: 1,7,6,9                              # reduction candidate for 1,7
F9: 1,7 => CTR
* 2867319547519846324392658713951.87.68..5.61936173.9...1..4.2......813..7...657.1.
F9: 6,9                                  # 15 pairs
* PAIR F5: 6,7 COL F
F9: 6,7,1,9                              # reduction candidate for 6,7
F9: 6,7 => CTR
* .8...19545719846324392658713951.87.6...5..19..17..9...1..492...9..813..77.865..19
F9: 1,9                                  #  9 pairs
* PAIR F6: 6,9 ROW 6
A6: 6,9,2,8                              # reduction candidate for 6,9
A6: 2,8 => SOLVED
* 682731954571984632439265871395148726864527193217396485158472369926813547743659218
A6: 6,9                                  # 15 pairs
* PAIR F6: 6,9 COL F
F9: 6,9,1,7                              # reduction candidate for 6,9
F9: 1,7 => CTR
* 2867319547519846324392658713951.87.68..5.61936173.9...1..4.2......813..7...657.1.
F9: 6,9                                  # 15 pairs
* PAIR H4: 2,4 BLK 6
G6: 2,4,3,5                              # reduction candidate for 2,4
G6: 2,4                                  # 17 pairs
H6: 2,4,8                                # reduction candidate for 2,4
H6: 2,4                                  # 23 pairs
* PAIR H4: 2,4 ROW 4
B4: 2,4,5,9                              # reduction candidate for 2,4
B4: 2,4                                  # 12 pairs
C4: 2,4,5                                # reduction candidate for 2,4
C4: 2,4 => CTR
* .8.73195457198463243926587135.1987.6...5.71939173.6...16.472.8..9.813..7...659.1.
C4: 5                                    # 16 pairs
E4: 2,4,9                                # reduction candidate for 2,4
E4: 2,4                                  # 21 pairs
* PAIR H4: 2,4 COL H
H8: 2,4,1,6                              # reduction candidate for 2,4
H8: 2,4                                  # 20 pairs
H9: 2,4,1,8                              # reduction candidate for 2,4
H9: 2,4 => CTR
* .8..17954..19846324392658713..1.87.6...5761936173.....1..4.2......8.3.17....51...
H9: 1,8                                  # 17 pairs
* PAIR I5: 3,8 BLK 6
I6: 3,8,5                                # reduction candidate for 3,8
I6: 3,8 => CTR
* .8...19545719846324392658713951.87.6...5..19..17..95..16.4.23.59..813..7..3.5..19
I6: 5                                    # 16 pairs
* PAIR I5: 3,8 COL I
I7: 3,8,5,9                              # reduction candidate for 3,8
I7: 3,8 => CTR
* .8...19545719846324392658713951.87.6...5..19..17..9..51..4.2...9..813..7....5..19
I7: 5,9                                  # 17 pairs
I9: 3,8,9                                # reduction candidate for 3,8
I9: 3,8                                  #  9 pairs
* PAIR E7: 7,9 BLK 8
F9: 7,9,1,6                              # reduction candidate for 7,9
F9: 1,6                                  # 21 pairs
F9: 7,9                                  # 13 pairs
* PAIR E7: 7,9 ROW 7
B7: 7,9,5,6                              # reduction candidate for 7,9
B7: 7,9 => CTR
* .8...19545719846324392658713..1.87.6...5..19..17..9...1..4.2...9..813..7....5..19
B7: 5,6                                  #  9 pairs
* PAIR E8: 1,9 BLK 8
F9: 1,9,6,7                              # reduction candidate for 1,9
F9: 6,7 => CTR
* .8...19545719846324392658713951.87.6...5..19..17..9...1..492...9..813..77.865..19
F9: 1,9                                  #  9 pairs
* PAIR D9: 6,7 BLK 8
F9: 6,7,1,9                              # reduction candidate for 6,7
F9: 6,7 => CTR
* .8...19545719846324392658713951.87.6...5..19..17..9...1..492...9..813..77.865..19
F9: 1,9                                  #  9 pairs
* PAIR G7: 3,5 BLK 9
I7: 3,5,8,9                              # reduction candidate for 3,5
I7: 3,5 => CTR
* .8...19545719846324392658713951.87.6...5..19..17..9...1..4.2...9..813..7....5..19
I7: 8,9                                  # 17 pairs
* PAIR G7: 3,5 ROW 7
C7: 3,5,6,8                              # reduction candidate for 3,5
C7: 6,8                                  # 19 pairs
C7: 3,5                                  # 19 pairs
* PAIR G7: 3,5 COL G
G6: 3,5,2,4                              # reduction candidate for 3,5
G6: 3,5                                  # 23 pairs
G6: 2,4                                  # 17 pairs
* PAIR H7: 6,8 ROW 7
C7: 6,8,3,5                              # reduction candidate for 6,8
C7: 6,8                                  # 19 pairs
C7: 3,5                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190406-absurd-base-pr-000.dot
* REASONING
* DIS # B7: 6,9 => CTR => B7: 5,7
* DIS # E1: 1 => CTR => E1: 3,7
* DIS # E1: 1,7 => CTR => E1: 3
* DIS # F9: 1,7 => CTR => F9: 6,9
* DIS # F9: 6,7 => CTR => F9: 1,9
* PRF # A6: 2,8 => SOL
* DIS # F9: 1,7 => CTR => F9: 6,9
* DIS # C4: 2,4 => CTR => C4: 5
* DIS # H9: 2,4 => CTR => H9: 1,8
* DIS # I6: 3,8 => CTR => I6: 5
* DIS # I7: 3,8 => CTR => I7: 5,9
* DIS # B7: 7,9 => CTR => B7: 5,6
* DIS # F9: 6,7 => CTR => F9: 1,9
* DIS # F9: 6,7 => CTR => F9: 1,9
* DIS # I7: 3,5 => CTR => I7: 8,9
* CNT  15 HDP CHAINS /  49 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B2,C1,D1,D6,D9,E7,E8,F1,F5,F6,G7,H4,H7,I5)
* .8....954..19846324392658713..1.87.6...5..19..17......1..4.2......8.3..7....5....
* PAIR A1: 2,6 COL A
A5: 2,6,8                                # reduction candidate for 2,6
A5: 2,6                                  # 19 pairs
A6: 2,6,8,9                              # reduction candidate for 2,6
A6: 2,6                                  # 24 pairs
A8: 2,6,5,9                              # reduction candidate for 2,6
A8: 2,6                                  # 12 pairs
* PAIR C1: 2,6 COL C
C5: 2,6,4,8                              # reduction candidate for 2,6
C5: 2,6                                  # 21 pairs
C8: 2,6,4,5                              # reduction candidate for 2,6
C8: 2,6                                  # 19 pairs
* PAIR B2: 5,7 COL B
B7: 5,7,6,9                              # reduction candidate for 5,7
B7: 6,9 => CTR
* .8.731954..19846324392658713..1.87.6...5.7193.173.6.851.8472......813..7...659.18
* PAIR RESTART
* PAIR D1: 3,7 BLK 2
E1: 3,7,1                                # reduction candidate for 3,7
E1: 1 => CTR
* .8.317954..19846324392658713.51.87.6...57619..17......1..4.2......8.3..7....5....
* PAIR F5: 6,7 COL F
F9: 6,7,9                                # reduction candidate for 6,7
F9: 6,7 => CTR
* .8...1954..19846324392658713.51.87.6...5..19..17..9...1..492...9..8135.7....5..19
* PAIR RESTART
* PAIR H4: 2,4 ROW 4
B4: 2,4,9                                # reduction candidate for 2,4
B4: 2,4                                  # 12 pairs
E4: 2,4,9                                # reduction candidate for 2,4
E4: 2,4 => SOLVED
* 682731954571984632439265871395148726864527193217396485158472369926813547743659218
* DURATION: 0:00:09.391068  START: 05:07:26.972125  END: 05:07:36.363193 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190406-absurd-base-pr-001.dot
* REASONING
* DIS # B7: 6,9 => CTR => B7: 5,7
* DIS B7: 5,7 # E1: 1 => CTR => E1: 3,7
* DIS B7: 5,7 + E1: 3,7 # F9: 6,7 => CTR => F9: 9
* PRF B7: 5,7 + E1: 3,7 + F9: 9 # E4: 2,4 => SOL
* STA B7: 5,7 + E1: 3,7 + F9: 9 + E4: 2,4
* CNT   4 HDP CHAINS /  12 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190406, absurd

Solution

position: 682731954571984632439265871395148726864527193217396485158472369926813547743659218 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 # A5: 2,6 => UNS
* INC # A6: 2,6 => UNS
* INC # A8: 2,6 => UNS
* INC # C5: 2,6 => UNS
* INC # C8: 2,6 => UNS
* INC # B7: 5,7 => UNS
* DIS # B7: 6,9 => CTR => B7: 5,7
* INC # E1: 3,7 => UNS
* DIS # E1: 1 => CTR => E1: 3,7
* DIS # E1: 1,7 => CTR => E1: 3
* INC # E1: 3 => UNS
* DIS # F9: 1,7 => CTR => F9: 6,9
* INC # F9: 6,9 => UNS
* DIS # F9: 6,7 => CTR => F9: 1,9
* INC # F9: 1,9 => UNS
* INC # A6: 6,9 => UNS
* PRF # A6: 2,8 => SOL
* INC # F9: 6,9 => UNS
* DIS # F9: 1,7 => CTR => F9: 6,9
* INC # G6: 2,4 => UNS
* INC # H6: 2,4 => UNS
* INC # B4: 2,4 => UNS
* DIS # C4: 2,4 => CTR => C4: 5
* INC # C4: 5 => UNS
* INC # E4: 2,4 => UNS
* INC # H8: 2,4 => UNS
* DIS # H9: 2,4 => CTR => H9: 1,8
* INC # H9: 1,8 => UNS
* DIS # I6: 3,8 => CTR => I6: 5
* INC # I6: 5 => UNS
* DIS # I7: 3,8 => CTR => I7: 5,9
* INC # I7: 5,9 => UNS
* INC # I9: 3,8 => UNS
* INC # F9: 7,9 => UNS
* INC # F9: 1,6 => UNS
* DIS # B7: 7,9 => CTR => B7: 5,6
* INC # B7: 5,6 => UNS
* INC # F9: 1,9 => UNS
* DIS # F9: 6,7 => CTR => F9: 1,9
* DIS # F9: 6,7 => CTR => F9: 1,9
* INC # F9: 1,9 => UNS
* DIS # I7: 3,5 => CTR => I7: 8,9
* INC # I7: 8,9 => UNS
* INC # C7: 3,5 => UNS
* INC # C7: 6,8 => UNS
* INC # G6: 3,5 => UNS
* INC # G6: 2,4 => UNS
* INC # C7: 6,8 => UNS
* INC # C7: 3,5 => UNS
* CNT  49 HDP CHAINS /  49 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 2,6 => UNS
* INC # A6: 2,6 => UNS
* INC # A8: 2,6 => UNS
* INC # C5: 2,6 => UNS
* INC # C8: 2,6 => UNS
* INC # B7: 5,7 => UNS
* DIS # B7: 6,9 => CTR => B7: 5,7
* INC B7: 5,7 # E1: 3,7 => UNS
* DIS B7: 5,7 # E1: 1 => CTR => E1: 3,7
* DIS B7: 5,7 + E1: 3,7 # F9: 6,7 => CTR => F9: 9
* INC B7: 5,7 + E1: 3,7 + F9: 9 # B4: 2,4 => UNS
* PRF B7: 5,7 + E1: 3,7 + F9: 9 # E4: 2,4 => SOL
* STA B7: 5,7 + E1: 3,7 + F9: 9 + E4: 2,4
* CNT  12 HDP CHAINS /  12 HYP OPENED