Analysis of zz-www.sudokuoftheday.co.uk-20190311-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019

position: ..........6.7....4...81.7...2..81.4....4.......5.9...2.4.35..2995.....1.......43. initial

Autosolve

position: ...9......6.7....4...81.7...2.581.4....4.....4.569...2.4.35..299532...17...1.9435 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B5: 1,8 => SOL
* PRF # E1: 2,3 => SOL
* DIS # E1: 4,6 => CTR => E1: 2,3
* DIS # F1: 2,3 => CTR => F1: 4,5,6
* DIS # F2: 2,3 => CTR => F2: 5
* DIS # F3: 2,3 => CTR => F3: 4,5,6
* DIS # E5: 2,3 => CTR => E5: 7
* PRF # E5: 7 => SOL
* DIS # B1: 1,8 => CTR => B1: 3,7
* DIS # F5: 3,7 => CTR => F5: 2
* PRF # G5: 3,9 => SOL
* DIS # G2: 3,9 => CTR => G2: 1,2,5
* DIS # A4: 7 => CTR => A4: 3,6
* PRF # B5: 1,8 => SOL
* PRF # G5: 1,3 => SOL
* DIS # B6: 1,3 => CTR => B6: 8
* PRF # B6: 8 => SOL
* DIS # H5: 7,8 => CTR => H5: 5,6,9
* PRF # H5: 5,6,9 => SOL
* DIS # A9: 7,8 => CTR => A9: 2,6
* PRF # C9: 7,8 => SOL
* DIS # B1: 7,8 => CTR => B1: 1,3
* PRF # B1: 1,3 => SOL
* DIS # F8: 4,6 => CTR => F8: 8
* DIS # E1: 4,6 => CTR => E1: 2,3
* PRF # E1: 2,3 => SOL
* DIS # F7: 8 => CTR => F7: 6,7
* DIS # A9: 6,7 => CTR => A9: 2,8
* DIS # C9: 6,7 => CTR => C9: 2,8
* DIS # F7: 6,8 => CTR => F7: 7
* PRF # F7: 7 => SOL
* DIS # F8: 4 => CTR => F8: 6,8
* CNT  32 HDP CHAINS /  61 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 # B5: 1,8 => SOL
* STA B5: 1,8
* CNT   1 HDP CHAINS /   2 HYP OPENED

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

Details

Positions

..........6.7....4...81.7...2..81.4....4.......5.9...2.4.35..2995.....1.......43. initial
...9......6.7....4...81.7...2.581.4....4.....4.569...2.4.35..299532...17...1.9435 autosolve
734926581861735294592814763327581946619472358485693172146357829953248617278169435 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
B3: 3,9
E2: 2,3
I1: 1,8
I3: 3,6
F6: 3,7
G4: 3,9
I4: 3,6
I5: 1,8
G6: 1,3
H6: 7,8
B9: 7,8
E8: 4,6
E9: 6,7
G7: 6,8
G8: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A7,C7: 1.. / A7 = 1  => 16 pairs (_) / C7 = 1  => 16 pairs (_)
B6,G6: 1.. / B6 = 1  =>  0 pairs (X) / G6 = 1  =>  0 pairs (_)
I1,I5: 1.. / I1 = 1  =>  0 pairs (*) / I5 = 1  =>  0 pairs (X)
G1,G2: 2.. / G1 = 2  => 15 pairs (_) / G2 = 2  => 17 pairs (_)
E5,F5: 2.. / E5 = 2  =>  0 pairs (X) / F5 = 2  => 17 pairs (_)
A9,C9: 2.. / A9 = 2  => 19 pairs (_) / C9 = 2  => 16 pairs (_)
I3,I4: 3.. / I3 = 3  => 17 pairs (_) / I4 = 3  =>  0 pairs (X)
C1,C3: 4.. / C1 = 4  => 17 pairs (_) / C3 = 4  => 15 pairs (_)
E8,F8: 4.. / E8 = 4  => 15 pairs (_) / F8 = 4  =>  0 pairs (X)
C3,F3: 4.. / C3 = 4  => 15 pairs (_) / F3 = 4  => 17 pairs (_)
E1,E8: 4.. / E1 = 4  =>  0 pairs (X) / E8 = 4  => 15 pairs (_)
G5,H5: 5.. / G5 = 5  => 15 pairs (_) / H5 = 5  =>  0 pairs (*)
I4,H5: 6.. / I4 = 6  => 17 pairs (_) / H5 = 6  =>  0 pairs (X)
G7,G8: 6.. / G7 = 6  =>  0 pairs (X) / G8 = 6  => 13 pairs (_)
I3,I4: 6.. / I3 = 6  =>  0 pairs (X) / I4 = 6  => 17 pairs (_)
A4,C4: 7.. / A4 = 7  =>  0 pairs (X) / C4 = 7  => 16 pairs (_)
H5,H6: 7.. / H5 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
F7,E9: 7.. / F7 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
F6,H6: 7.. / F6 = 7  =>  0 pairs (X) / H6 = 7  =>  0 pairs (_)
B1,B9: 7.. / B1 = 7  =>  0 pairs (X) / B9 = 7  =>  0 pairs (_)
E5,E9: 7.. / E5 = 7  =>  0 pairs (*) / E9 = 7  =>  0 pairs (X)
F7,F8: 8.. / F7 = 8  =>  0 pairs (X) / F8 = 8  => 13 pairs (_)
G7,G8: 8.. / G7 = 8  => 13 pairs (_) / G8 = 8  =>  0 pairs (X)
B6,H6: 8.. / B6 = 8  =>  0 pairs (*) / H6 = 8  =>  0 pairs (X)
F7,G7: 8.. / F7 = 8  =>  0 pairs (X) / G7 = 8  => 13 pairs (_)
F8,G8: 8.. / F8 = 8  => 13 pairs (_) / G8 = 8  =>  0 pairs (X)
I1,I5: 8.. / I1 = 8  =>  0 pairs (X) / I5 = 8  =>  0 pairs (_)
C4,G4: 9.. / C4 = 9  =>  0 pairs (X) / G4 = 9  => 15 pairs (_)
B3,B5: 9.. / B3 = 9  => 16 pairs (_) / B5 = 9  =>  0 pairs (X)
* DURATION: 0:00:43.248509  START: 04:25:33.626905  END: 04:26:16.875414 2019-05-01
* CP COUNT: (29)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B9,E2,E8,E9,F6,G4,G6,G7,G8,H6,I1,I3,I4,I5)
* ...9......6.7....4...81.7...2.581.4....4.....4.569...2.4.35..299532...17...1.9435
* PAIR B3: 3,9 COL B
B5: 3,9,1,8                              # reduction candidate for 3,9
B5: 1,8 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
B5: 3,9                                  # 17 pairs
* PAIR E2: 2,3 BLK 2
E1: 2,3,4,6                              # reduction candidate for 2,3
E1: 2,3 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
E1: 4,6 => CTR
* .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435
F1: 2,3,4,5,6                            # reduction candidate for 2,3
F1: 2,3 => CTR
* .7.9....8.6.7.5.94...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435
F1: 4,5,6                                # 15 pairs
F2: 2,3,5                                # reduction candidate for 2,3
F2: 2,3 => CTR
* 37.9..2...6.7....4.9.81.7.3729581346...4.....4.569.182.4.35..299532...17.8.179435
F2: 5                                    # 16 pairs
F3: 2,3,4,5,6                            # reduction candidate for 2,3
F3: 2,3 => CTR
* .7.9...58.6.7.5.94594812763.2.581.46...42.571415697382.4.35..299532...17.8.179435
F3: 4,5,6                                # 15 pairs
* PAIR E2: 2,3 ROW 2
A2: 2,3,1,5,8                            # reduction candidate for 2,3
A2: 2,3                                  # 22 pairs
G2: 2,3,1,5,9                            # reduction candidate for 2,3
G2: 2,3                                  # 18 pairs
* PAIR E2: 2,3 COL E
E5: 2,3,7                                # reduction candidate for 2,3
E5: 2,3 => CTR
* .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435
E5: 7 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
* PAIR I1: 1,8 ROW 1
A1: 1,8,2,3,5,7                          # reduction candidate for 1,8
A1: 1,8                                  # 18 pairs
B1: 1,8,3,7                              # reduction candidate for 1,8
B1: 1,8 => CTR
* ...9....1.6.7.5..4...81.7...2.581.4..1.472..8485693172.4.357829953248617.7.169435
B1: 3,7                                  # 16 pairs
C1: 1,8,2,4,7                            # reduction candidate for 1,8
C1: 1,8                                  # 18 pairs
* PAIR I3: 3,6 ROW 3
F3: 3,6,2,4,5                            # reduction candidate for 3,6
F3: 3,6                                  # 18 pairs
F3: 2,4,5                                # 16 pairs
* PAIR F6: 3,7 BLK 5
E5: 3,7,2                                # reduction candidate for 3,7
E5: 3,7                                  # 17 pairs
F5: 3,7,2                                # reduction candidate for 3,7
F5: 3,7 => CTR
* 37.9....8.6.73...4.9.81.7.3.2.581946.3.42..71415697382.4.35..299532...17.8.179435
F5: 2                                    # 17 pairs
* PAIR G4: 3,9 BLK 6
G5: 3,9,1,5                              # reduction candidate for 3,9
G5: 3,9 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
G5: 1,5                                  # 16 pairs
* PAIR G4: 3,9 COL G
G2: 3,9,1,2,5                            # reduction candidate for 3,9
G2: 3,9 => CTR
* .3.94.2.1.6.7....4...81.7...2.581.4....4..5.848569.172.4.35..299532...17.7.169435
G2: 1,2,5                                # 15 pairs
* PAIR I4: 3,6 ROW 4
A4: 3,6,7                                # reduction candidate for 3,6
A4: 7 => CTR
* .37924561.6.73...4.9481.7.372.581346316472..8485693172641357829953248617.7.169435
A4: 3,6                                  # 16 pairs
* PAIR I5: 1,8 ROW 5
A5: 1,8,3,6                              # reduction candidate for 1,8
A5: 1,8                                  # 19 pairs
B5: 1,8,3,9                              # reduction candidate for 1,8
B5: 1,8 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
B5: 3,9                                  # 17 pairs
C5: 1,8,6,9                              # reduction candidate for 1,8
C5: 1,8                                  # 19 pairs
* PAIR G6: 1,3 BLK 6
G5: 1,3,5,9                              # reduction candidate for 1,3
G5: 1,3 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
G5: 5,9                                  # 16 pairs
* PAIR G6: 1,3 ROW 6
B6: 1,3,8                                # reduction candidate for 1,3
B6: 1,3 => CTR
* .7.9....8.6.7....4...81.7.3327581946...4..57141569738274135..299532...17.8.179435
B6: 8 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
* PAIR G6: 1,3 COL G
G1: 1,3,2,5                              # reduction candidate for 1,3
G1: 1,3                                  # 18 pairs
G2: 1,3,2,5,9                            # reduction candidate for 1,3
G2: 1,3                                  # 16 pairs
* PAIR H6: 7,8 BLK 6
H5: 7,8,5,6,9                            # reduction candidate for 7,8
H5: 7,8 => CTR
* ...9......6.7....4.9.81.7.3327581946..94..5.141569738274135..299532...17.8.1.9435
H5: 5,6,9 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
* PAIR B9: 7,8 BLK 7
A9: 7,8,2,6                              # reduction candidate for 7,8
A9: 7,8 => CTR
* 53792...1.6.7.5..42..81.75..2.581.4..1.4725.8485693172.4.357829953248617872169435
A9: 2,6                                  # 16 pairs
C9: 7,8,2,6                              # reduction candidate for 7,8
C9: 7,8 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
C9: 2,6                                  # 16 pairs
* PAIR B9: 7,8 COL B
B1: 7,8,1,3                              # reduction candidate for 7,8
B1: 7,8 => CTR
* .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435
B1: 1,3 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
* PAIR E8: 4,6 BLK 8
F8: 4,6,8                                # reduction candidate for 4,6
F8: 4,6 => CTR
* .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.3586299532..817.8.179435
F8: 8                                    # 13 pairs
* PAIR E8: 4,6 COL E
E1: 4,6,2,3                              # reduction candidate for 4,6
E1: 4,6 => CTR
* .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435
E1: 2,3 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
* PAIR E9: 6,7 BLK 8
F7: 6,7,8                                # reduction candidate for 6,7
F7: 8 => CTR
* .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.3586299532..817.8.179435
F7: 6,7                                  # 13 pairs
* PAIR E9: 6,7 ROW 9
A9: 6,7,2,8                              # reduction candidate for 6,7
A9: 6,7 => CTR
* .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.82179435
A9: 2,8                                  # 16 pairs
C9: 6,7,2,8                              # reduction candidate for 6,7
C9: 6,7 => CTR
* .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...1728.179435
C9: 2,8                                  # 16 pairs
* PAIR G7: 6,8 ROW 7
F7: 6,8,7                                # reduction candidate for 6,8
F7: 6,8 => CTR
* .7.9....8.6.7....4...81.7.3327581946.9.4...71415697382.4.35..299532...17.8.179435
F7: 7 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
* PAIR G8: 6,8 ROW 8
F8: 6,8,4                                # reduction candidate for 6,8
F8: 4 => CTR
* .7.94...8.6.7....4..481.7.3327581946.9.4...71415697382.4.358629953264817.8.179435
F8: 6,8                                  # 15 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190311-absurd-base-pr-000.dot
* REASONING
* PRF # B5: 1,8 => SOL
* PRF # E1: 2,3 => SOL
* DIS # E1: 4,6 => CTR => E1: 2,3
* DIS # F1: 2,3 => CTR => F1: 4,5,6
* DIS # F2: 2,3 => CTR => F2: 5
* DIS # F3: 2,3 => CTR => F3: 4,5,6
* DIS # E5: 2,3 => CTR => E5: 7
* PRF # E5: 7 => SOL
* DIS # B1: 1,8 => CTR => B1: 3,7
* DIS # F5: 3,7 => CTR => F5: 2
* PRF # G5: 3,9 => SOL
* DIS # G2: 3,9 => CTR => G2: 1,2,5
* DIS # A4: 7 => CTR => A4: 3,6
* PRF # B5: 1,8 => SOL
* PRF # G5: 1,3 => SOL
* DIS # B6: 1,3 => CTR => B6: 8
* PRF # B6: 8 => SOL
* DIS # H5: 7,8 => CTR => H5: 5,6,9
* PRF # H5: 5,6,9 => SOL
* DIS # A9: 7,8 => CTR => A9: 2,6
* PRF # C9: 7,8 => SOL
* DIS # B1: 7,8 => CTR => B1: 1,3
* PRF # B1: 1,3 => SOL
* DIS # F8: 4,6 => CTR => F8: 8
* DIS # E1: 4,6 => CTR => E1: 2,3
* PRF # E1: 2,3 => SOL
* DIS # F7: 8 => CTR => F7: 6,7
* DIS # A9: 6,7 => CTR => A9: 2,8
* DIS # C9: 6,7 => CTR => C9: 2,8
* DIS # F7: 6,8 => CTR => F7: 7
* PRF # F7: 7 => SOL
* DIS # F8: 4 => CTR => F8: 6,8
* CNT  32 HDP CHAINS /  61 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B9,E2,E8,E9,F6,G4,G6,G7,G8,H6,I1,I3,I4,I5)
* ...9......6.7....4...81.7...2.581.4....4.....4.569...2.4.35..299532...17...1.9435
* PAIR B3: 3,9 COL B
B5: 3,9,1,8                              # reduction candidate for 3,9
B5: 1,8 => SOLVED
* 734926581861735294592814763327581946619472358485693172146357829953248617278169435
* DURATION: 0:00:02.967441  START: 04:27:09.155998  END: 04:27:12.123439 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190311-absurd-base-pr-001.dot
* REASONING
* PRF # B5: 1,8 => SOL
* STA B5: 1,8
* CNT   1 HDP CHAINS /   2 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190311, absurd

Solution

position: 734926581861735294592814763327581946619472358485693172146357829953248617278169435 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 # B5: 3,9 => UNS
* PRF # B5: 1,8 => SOL
* PRF # E1: 2,3 => SOL
* DIS # E1: 4,6 => CTR => E1: 2,3
* DIS # F1: 2,3 => CTR => F1: 4,5,6
* INC # F1: 4,5,6 => UNS
* DIS # F2: 2,3 => CTR => F2: 5
* INC # F2: 5 => UNS
* DIS # F3: 2,3 => CTR => F3: 4,5,6
* INC # F3: 4,5,6 => UNS
* INC # A2: 2,3 => UNS
* INC # G2: 2,3 => UNS
* DIS # E5: 2,3 => CTR => E5: 7
* PRF # E5: 7 => SOL
* INC # A1: 1,8 => UNS
* DIS # B1: 1,8 => CTR => B1: 3,7
* INC # B1: 3,7 => UNS
* INC # C1: 1,8 => UNS
* INC # F3: 3,6 => UNS
* INC # F3: 2,4,5 => UNS
* INC # E5: 3,7 => UNS
* DIS # F5: 3,7 => CTR => F5: 2
* INC # F5: 2 => UNS
* PRF # G5: 3,9 => SOL
* INC # G5: 1,5 => UNS
* DIS # G2: 3,9 => CTR => G2: 1,2,5
* INC # G2: 1,2,5 => UNS
* INC # A4: 3,6 => UNS
* DIS # A4: 7 => CTR => A4: 3,6
* INC # A5: 1,8 => UNS
* PRF # B5: 1,8 => SOL
* INC # B5: 3,9 => UNS
* INC # C5: 1,8 => UNS
* PRF # G5: 1,3 => SOL
* INC # G5: 5,9 => UNS
* DIS # B6: 1,3 => CTR => B6: 8
* PRF # B6: 8 => SOL
* INC # G1: 1,3 => UNS
* INC # G2: 1,3 => UNS
* DIS # H5: 7,8 => CTR => H5: 5,6,9
* PRF # H5: 5,6,9 => SOL
* DIS # A9: 7,8 => CTR => A9: 2,6
* INC # A9: 2,6 => UNS
* PRF # C9: 7,8 => SOL
* INC # C9: 2,6 => UNS
* DIS # B1: 7,8 => CTR => B1: 1,3
* PRF # B1: 1,3 => SOL
* DIS # F8: 4,6 => CTR => F8: 8
* INC # F8: 8 => UNS
* DIS # E1: 4,6 => CTR => E1: 2,3
* PRF # E1: 2,3 => SOL
* INC # F7: 6,7 => UNS
* DIS # F7: 8 => CTR => F7: 6,7
* DIS # A9: 6,7 => CTR => A9: 2,8
* INC # A9: 2,8 => UNS
* DIS # C9: 6,7 => CTR => C9: 2,8
* INC # C9: 2,8 => UNS
* DIS # F7: 6,8 => CTR => F7: 7
* PRF # F7: 7 => SOL
* INC # F8: 6,8 => UNS
* DIS # F8: 4 => CTR => F8: 6,8
* CNT  61 HDP CHAINS /  61 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B5: 3,9 => UNS
* PRF # B5: 1,8 => SOL
* STA B5: 1,8
* CNT   2 HDP CHAINS /   2 HYP OPENED