Analysis of zz-www.sudokuoftheday.co.uk-20190426-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: .....92.4...5..3..3..8...6.641....8..7......128.........218.6..5.7.9...2.....5.9. initial

Autosolve

position: .....92.4..95..3.83.48...6.641....8.97...8.2128......649218.6..5.7.9.8.2.....5.9. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 8 => CTR => A1: 1,7
* DIS # H1: 1,7 => CTR => H1: 5
* PRF # E5: 3,5 => SOL
* DIS # E6: 3,5 => CTR => E6: 1,4,7
* DIS # H6: 3,5 => CTR => H6: 4,7
* PRF # H6: 4,7 => SOL
* DIS # H6: 4,5 => CTR => H6: 3,7
* DIS # D9: 3,7 => CTR => D9: 2,4,6
* DIS # E9: 3,7 => CTR => E9: 2,4,6
* DIS # I7: 3,7 => CTR => I7: 5
* PRF # F6: 3,7 => SOL
* DIS # I7: 3,7 => CTR => I7: 5
* DIS # D9: 3,7 => CTR => D9: 2,4,6
* DIS # E9: 3,7 => CTR => E9: 2,4,6
* DIS # I4: 5,9 => CTR => I4: 3,7
* CNT  15 HDP CHAINS /  39 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 # A1: 8 => CTR => A1: 1,7
* DIS A1: 1,7 # H1: 1,7 => CTR => H1: 5
* DIS A1: 1,7 + H1: 5 # G3: 9 => CTR => G3: 1,7
* PRF A1: 1,7 + H1: 5 + G3: 1,7 # E5: 3,5 => SOL
* STA A1: 1,7 + H1: 5 + G3: 1,7 + E5: 3,5
* CNT   4 HDP CHAINS /   9 HYP OPENED

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

Details

Positions

.....92.4...5..3..3..8...6.641....8..7......128.........218.6..5.7.9...2.....5.9. initial
.....92.4..95..3.83.48...6.641....8.97...8.2128......649218.6..5.7.9.8.2.....5.9. autosolve
168739254729564318354821769641972583973658421285413976492187635517396842836245197 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
C1: 6,8
A2: 1,7
B2: 2,6
H2: 1,7
C5: 3,5
C6: 3,5
G5: 4,5
A9: 1,8
C9: 6,8
F7: 3,7
H8: 1,4
G9: 1,4
I9: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E6,F6: 1.. / E6 = 1  => 19 pairs (_) / F6 = 1  => 16 pairs (_)
H8,G9: 1.. / H8 = 1  =>  0 pairs (X) / G9 = 1  => 18 pairs (_)
A2,H2: 1.. / A2 = 1  => 18 pairs (_) / H2 = 1  => 16 pairs (_)
B8,H8: 1.. / B8 = 1  => 18 pairs (_) / H8 = 1  =>  0 pairs (X)
F3,F6: 1.. / F3 = 1  => 19 pairs (_) / F6 = 1  => 16 pairs (_)
G3,G9: 1.. / G3 = 1  =>  0 pairs (X) / G9 = 1  => 18 pairs (_)
B2,B3: 2.. / B2 = 2  => 16 pairs (_) / B3 = 2  =>  0 pairs (X)
D9,E9: 2.. / D9 = 2  => 13 pairs (_) / E9 = 2  => 19 pairs (_)
D4,D9: 2.. / D4 = 2  => 19 pairs (_) / D9 = 2  => 13 pairs (_)
D1,E1: 3.. / D1 = 3  => 17 pairs (_) / E1 = 3  => 19 pairs (_)
C5,C6: 3.. / C5 = 3  => 12 pairs (_) / C6 = 3  =>  0 pairs (X)
I4,H6: 3.. / I4 = 3  =>  0 pairs (*) / H6 = 3  =>  0 pairs (X)
B8,B9: 3.. / B8 = 3  =>  0 pairs (X) / B9 = 3  => 17 pairs (_)
H6,H7: 3.. / H6 = 3  =>  0 pairs (X) / H7 = 3  =>  0 pairs (_)
E2,F2: 4.. / E2 = 4  => 14 pairs (_) / F2 = 4  => 16 pairs (_)
H8,G9: 4.. / H8 = 4  => 18 pairs (_) / G9 = 4  =>  0 pairs (X)
H6,H8: 4.. / H6 = 4  =>  0 pairs (X) / H8 = 4  => 18 pairs (_)
B1,B3: 5.. / B1 = 5  =>  0 pairs (X) / B3 = 5  => 18 pairs (_)
C5,C6: 5.. / C5 = 5  =>  0 pairs (X) / C6 = 5  => 12 pairs (_)
H7,I7: 5.. / H7 = 5  =>  0 pairs (X) / I7 = 5  => 15 pairs (_)
B1,H1: 5.. / B1 = 5  =>  0 pairs (X) / H1 = 5  => 18 pairs (_)
D5,E5: 6.. / D5 = 6  => 15 pairs (_) / E5 = 6  => 15 pairs (_)
C1,C9: 6.. / C1 = 6  =>  0 pairs (X) / C9 = 6  => 15 pairs (_)
F2,F8: 6.. / F2 = 6  => 15 pairs (_) / F8 = 6  => 16 pairs (_)
A1,A2: 7.. / A1 = 7  => 18 pairs (_) / A2 = 7  => 16 pairs (_)
A2,H2: 7.. / A2 = 7  => 16 pairs (_) / H2 = 7  => 18 pairs (_)
A1,C1: 8.. / A1 = 8  =>  0 pairs (X) / C1 = 8  => 15 pairs (_)
A9,C9: 8.. / A9 = 8  => 15 pairs (_) / C9 = 8  =>  0 pairs (X)
A1,A9: 8.. / A1 = 8  =>  0 pairs (X) / A9 = 8  => 15 pairs (_)
C1,C9: 8.. / C1 = 8  => 15 pairs (_) / C9 = 8  =>  0 pairs (X)
G3,I3: 9.. / G3 = 9  =>  0 pairs (X) / I3 = 9  => 13 pairs (_)
D4,D6: 9.. / D4 = 9  => 14 pairs (_) / D6 = 9  => 13 pairs (_)
D6,G6: 9.. / D6 = 9  => 13 pairs (_) / G6 = 9  => 14 pairs (_)
I3,I4: 9.. / I3 = 9  => 13 pairs (_) / I4 = 9  =>  0 pairs (X)
* DURATION: 0:00:35.730048  START: 05:36:59.113232  END: 05:37:34.843280 2019-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,C1,C5,C6,C9,F7,G5,G9,H2,H8,I9)
* .....92.4..95..3.83.48...6.641....8.97...8.2128......649218.6..5.7.9.8.2.....5.9.
* PAIR A2: 1,7 BLK 1
A1: 1,7,8                                # reduction candidate for 1,7
A1: 8 => CTR
* 8.6..92.47295..3183.48...6.641....8.97...8.2128......649218.6..517.9.8.2.....5.9.
A1: 1,7                                  # 15 pairs
* PAIR B2: 2,6 ROW 2
E2: 2,6,4                                # reduction candidate for 2,6
E2: 2,6                                  # 16 pairs
F2: 2,6,4                                # reduction candidate for 2,6
F2: 2,6                                  # 14 pairs
* PAIR H2: 1,7 BLK 3
H1: 1,7,5                                # reduction candidate for 1,7
H1: 1,7 => CTR
* .586392.4.695..3.8324871.6.641....8.973468521285.13..64921876..517396842836..5197
H1: 5                                    # 18 pairs
G3: 1,7,5,9                              # reduction candidate for 1,7
G3: 1,7                                  # 19 pairs
* PAIR C5: 3,5 ROW 5
E5: 3,5,4,6                              # reduction candidate for 3,5
E5: 3,5 => SOLVED
* 168739254729564318354821769641972583973658421285413976492187635517396842836245197
E5: 4,6                                  # 14 pairs
* PAIR C6: 3,5 ROW 6
E6: 3,5,1,4,7                            # reduction candidate for 3,5
E6: 3,5 => CTR
* .....92.4..95..3.83.48...6.641....8397...8.2128...1..64921836..537.9.812.....5497
E6: 1,4,7                                # 13 pairs
H6: 3,5,4,7                              # reduction candidate for 3,5
H6: 3,5 => CTR
* .586392.4.695..3.8324871.6.641....8.973468521285.13..64921876..517396842836..5197
H6: 4,7 => SOLVED
* 168739254729564318354821769641972583973658421285413976492187635517396842836245197
* PAIR G5: 4,5 BLK 6
G6: 4,5,7,9                              # reduction candidate for 4,5
G6: 4,5                                  # 23 pairs
H6: 4,5,3,7                              # reduction candidate for 4,5
H6: 4,5 => CTR
* ..8..92.4..95.43.83.48.1.69641..2.8397...8.2128..13.56492187635517.9.842836245197
H6: 3,7                                  # 19 pairs
* PAIR G5: 4,5 ROW 5
E5: 4,5,3,6                              # reduction candidate for 4,5
E5: 4,5                                  # 14 pairs
E5: 3,6                                  # 14 pairs
* PAIR A9: 1,8 COL A
A1: 1,8,7                                # reduction candidate for 1,8
A1: 7                                    # 18 pairs
A1: 1,8                                  # 16 pairs
* PAIR F7: 3,7 BLK 8
D9: 3,7,2,4,6                            # reduction candidate for 3,7
D9: 3,7 => CTR
* ...7.92.4..95..3.83.48..1696412..98.97...85212859.174649218.6355.7.9.812....25497
D9: 2,4,6                                # 13 pairs
E9: 3,7,2,4,6                            # reduction candidate for 3,7
E9: 3,7 => CTR
* ....192541.95..3783548..169641.52.83973..8521285..1.464921876355.7.9.812...2.5497
E9: 2,4,6                                # 13 pairs
* PAIR F7: 3,7 ROW 7
H7: 3,7,5                                # reduction candidate for 3,7
H7: 3,7                                  # 15 pairs
I7: 3,7,5                                # reduction candidate for 3,7
I7: 3,7 => CTR
* .58.392.4.695423.8324871.6.641253.8.973..8.21285.14.36492187653517396842836425197
I7: 5                                    # 15 pairs
* PAIR F7: 3,7 COL F
F4: 3,7,2                                # reduction candidate for 3,7
F4: 3,7                                  # 19 pairs
F6: 3,7,1,4                              # reduction candidate for 3,7
F6: 3,7 => SOLVED
* 168739254729564318354821769641972583973658421285413976492187635517396842836245197
F6: 1,4                                  # 14 pairs
* PAIR I9: 3,7 BLK 9
H7: 3,7,5                                # reduction candidate for 3,7
H7: 3,7                                  # 15 pairs
I7: 3,7,5                                # reduction candidate for 3,7
I7: 3,7 => CTR
* .58.392.4.695423.8324871.6.641253.8.973..8.21285.14.36492187653517396842836425197
I7: 5                                    # 15 pairs
* PAIR I9: 3,7 ROW 9
D9: 3,7,2,4,6                            # reduction candidate for 3,7
D9: 3,7 => CTR
* ...7.92.4..95..3.83.48..1696412..98.97...85212859.174649218.6355.7.9.812....25497
D9: 2,4,6                                # 13 pairs
E9: 3,7,2,4,6                            # reduction candidate for 3,7
E9: 3,7 => CTR
* ....192541.95..3783548..169641.52.83973..8521285..1.464921876355.7.9.812...2.5497
E9: 2,4,6                                # 13 pairs
* PAIR I9: 3,7 COL I
I4: 3,7,5,9                              # reduction candidate for 3,7
I4: 5,9 => CTR
* .58..92.4.695423.8324871.6.6412.3.8.973..8.21285.14.36492187653517.96842836425197
I4: 3,7                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190426-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 8 => CTR => A1: 1,7
* DIS # H1: 1,7 => CTR => H1: 5
* PRF # E5: 3,5 => SOL
* DIS # E6: 3,5 => CTR => E6: 1,4,7
* DIS # H6: 3,5 => CTR => H6: 4,7
* PRF # H6: 4,7 => SOL
* DIS # H6: 4,5 => CTR => H6: 3,7
* DIS # D9: 3,7 => CTR => D9: 2,4,6
* DIS # E9: 3,7 => CTR => E9: 2,4,6
* DIS # I7: 3,7 => CTR => I7: 5
* PRF # F6: 3,7 => SOL
* DIS # I7: 3,7 => CTR => I7: 5
* DIS # D9: 3,7 => CTR => D9: 2,4,6
* DIS # E9: 3,7 => CTR => E9: 2,4,6
* DIS # I4: 5,9 => CTR => I4: 3,7
* CNT  15 HDP CHAINS /  39 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B2,C1,C5,C6,C9,F7,G5,G9,H2,H8,I9)
* .....92.4..95..3.83.48...6.641....8.97...8.2128......649218.6..5.7.9.8.2.....5.9.
* PAIR A2: 1,7 BLK 1
A1: 1,7,8                                # reduction candidate for 1,7
A1: 8 => CTR
* 8.6..92.47295..3183.48...6.641....8.97...8.2128......649218.6..517.9.8.2.....5.9.
* PAIR B2: 2,6 ROW 2
E2: 2,6,4                                # reduction candidate for 2,6
E2: 2,6                                  # 17 pairs
F2: 2,6,4                                # reduction candidate for 2,6
F2: 2,6                                  # 16 pairs
* PAIR H2: 1,7 BLK 3
H1: 1,7,5                                # reduction candidate for 1,7
H1: 1,7 => CTR
* .586392.4.695243.83248...6.641..2.8397346852128......649218.6..517396842836.45197
G3: 1,7,9                                # reduction candidate for 1,7
G3: 1,7                                  # 18 pairs
* RESTART
* PAIR H2: 1,7 BLK 3
G3: 1,7,9                                # reduction candidate for 1,7
G3: 9 => CTR
* .68..9254.295..3183548..967641....8997...8.2128.9...364921836755.7.9.8.28.6..5.9.
* PAIR C5: 3,5 ROW 5
E5: 3,5,4,6                              # reduction candidate for 3,5
E5: 3,5 => SOLVED
* 168739254729564318354821769641972583973658421285413976492187635517396842836245197
* DURATION: 0:00:06.639121  START: 05:37:58.461592  END: 05:38:05.100713 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190426-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 8 => CTR => A1: 1,7
* DIS A1: 1,7 # H1: 1,7 => CTR => H1: 5
* DIS A1: 1,7 + H1: 5 # G3: 9 => CTR => G3: 1,7
* PRF A1: 1,7 + H1: 5 + G3: 1,7 # E5: 3,5 => SOL
* STA A1: 1,7 + H1: 5 + G3: 1,7 + E5: 3,5
* CNT   4 HDP CHAINS /   9 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190426, absurd

Solution

position: 168739254729564318354821769641972583973658421285413976492187635517396842836245197 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: 1,7 => UNS
* DIS # A1: 8 => CTR => A1: 1,7
* INC # E2: 2,6 => UNS
* INC # F2: 2,6 => UNS
* DIS # H1: 1,7 => CTR => H1: 5
* INC # H1: 5 => UNS
* INC # G3: 1,7 => UNS
* PRF # E5: 3,5 => SOL
* INC # E5: 4,6 => UNS
* DIS # E6: 3,5 => CTR => E6: 1,4,7
* INC # E6: 1,4,7 => UNS
* DIS # H6: 3,5 => CTR => H6: 4,7
* PRF # H6: 4,7 => SOL
* INC # G6: 4,5 => UNS
* DIS # H6: 4,5 => CTR => H6: 3,7
* INC # H6: 3,7 => UNS
* INC # E5: 4,5 => UNS
* INC # E5: 3,6 => UNS
* INC # A1: 1,8 => UNS
* INC # A1: 7 => UNS
* DIS # D9: 3,7 => CTR => D9: 2,4,6
* INC # D9: 2,4,6 => UNS
* DIS # E9: 3,7 => CTR => E9: 2,4,6
* INC # E9: 2,4,6 => UNS
* INC # H7: 3,7 => UNS
* DIS # I7: 3,7 => CTR => I7: 5
* INC # I7: 5 => UNS
* INC # F4: 3,7 => UNS
* PRF # F6: 3,7 => SOL
* INC # F6: 1,4 => UNS
* INC # H7: 3,7 => UNS
* DIS # I7: 3,7 => CTR => I7: 5
* INC # I7: 5 => UNS
* DIS # D9: 3,7 => CTR => D9: 2,4,6
* INC # D9: 2,4,6 => UNS
* DIS # E9: 3,7 => CTR => E9: 2,4,6
* INC # E9: 2,4,6 => UNS
* INC # I4: 3,7 => UNS
* DIS # I4: 5,9 => CTR => I4: 3,7
* CNT  39 HDP CHAINS /  39 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 1,7 => UNS
* DIS # A1: 8 => CTR => A1: 1,7
* INC A1: 1,7 # E2: 2,6 => UNS
* INC A1: 1,7 # F2: 2,6 => UNS
* DIS A1: 1,7 # H1: 1,7 => CTR => H1: 5
* INC A1: 1,7 + H1: 5 # G3: 1,7 => UNS
* INC A1: 1,7 + H1: 5 # G3: 1,7 => UNS
* DIS A1: 1,7 + H1: 5 # G3: 9 => CTR => G3: 1,7
* PRF A1: 1,7 + H1: 5 + G3: 1,7 # E5: 3,5 => SOL
* STA A1: 1,7 + H1: 5 + G3: 1,7 + E5: 3,5
* CNT   9 HDP CHAINS /   9 HYP OPENED