Analysis of zz-www.sudokuoftheday.co.uk-20190112-absurd-base.sdk

Contents

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

level: medium

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

position: ...1..6....5....8..6....3.7.....3......9......3175...82...1....1.4869.....7.259.. initial

Autosolve

position: ...1..6...15....89.6.59.3175....31.....9.15...3175...829..178..1548697...87.259.1 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 3,7 => CTR => A1: 4,8,9
* DIS # A1: 4,8 => CTR => A1: 3,7,9
* DIS # F3: 2 => CTR => F3: 4,8
* DIS # C1: 2,8 => CTR => C1: 3,9
* DIS # C4: 2,8 => CTR => C4: 6,9
* DIS # A1: 3,7 => CTR => A1: 4,8,9
* DIS # F2: 4 => CTR => F2: 2,6
* DIS # F2: 6 => CTR => F2: 2,4
* DIS # C4: 2,6 => CTR => C4: 8,9
* DIS # H4: 2,6 => CTR => H4: 4,7,9
* DIS # H6: 2,6 => CTR => H6: 4,9
* DIS # F2: 4 => CTR => F2: 2,6
* PRF # H4: 2,4 => SOL
* DIS # H5: 2,4 => CTR => H5: 3,6,7
* DIS # I5: 2,4 => CTR => I5: 3,6
* DIS # H6: 2,4 => CTR => H6: 6,9
* DIS # I5: 4,6 => CTR => I5: 2,3
* PRF # H4: 4,6 => SOL
* DIS # H5: 4,6 => CTR => H5: 2,3,7
* DIS # H6: 4,6 => CTR => H6: 2,9
* CNT  20 HDP CHAINS /  55 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: 3,7 => CTR => A1: 4,8,9
* DIS A1: 4,8,9 # A1: 4,8 => CTR => A1: 9
* DIS A1: 4,8,9 + A1: 9 # F3: 2 => CTR => F3: 4,8
* PRF A1: 4,8,9 + A1: 9 + F3: 4,8 # F2: 2,6 => SOL
* STA A1: 4,8,9 + A1: 9 + F3: 4,8 + F2: 2,6
* CNT   4 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

...1..6....5....8..6....3.7.....3......9......3175...82...1....1.4869.....7.259.. initial
...1..6...15....89.6.59.3175....31.....9.15...3175...829..178..1548697...87.259.1 autosolve
943178625715632489862594317579283146628941573431756298296317854154869732387425961 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
A2: 3,7
A3: 4,8
C3: 2,8
E1: 3,7
D2: 2,6
E2: 3,7
G2: 2,4
D4: 2,6
E4: 4,8
E5: 4,8
F6: 2,6
G6: 2,4
C7: 3,6
A9: 3,6
D7: 3,4
D9: 3,4
H8: 2,3
I8: 2,3
H9: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,F6: 2.. / D4 = 2  => 20 pairs (_) / F6 = 2  =>  0 pairs (X)
H8,I8: 2.. / H8 = 2  => 21 pairs (_) / I8 = 2  => 19 pairs (_)
C3,F3: 2.. / C3 = 2  => 21 pairs (_) / F3 = 2  =>  0 pairs (X)
D2,D4: 2.. / D2 = 2  =>  0 pairs (X) / D4 = 2  => 20 pairs (_)
G2,G6: 2.. / G2 = 2  =>  0 pairs (X) / G6 = 2  => 23 pairs (_)
E1,E2: 3.. / E1 = 3  => 15 pairs (_) / E2 = 3  => 20 pairs (_)
H5,I5: 3.. / H5 = 3  => 21 pairs (_) / I5 = 3  => 19 pairs (_)
C7,A9: 3.. / C7 = 3  => 18 pairs (_) / A9 = 3  => 17 pairs (_)
D7,D9: 3.. / D7 = 3  => 17 pairs (_) / D9 = 3  => 18 pairs (_)
H8,I8: 3.. / H8 = 3  => 19 pairs (_) / I8 = 3  => 21 pairs (_)
A2,E2: 3.. / A2 = 3  => 15 pairs (_) / E2 = 3  => 20 pairs (_)
C7,D7: 3.. / C7 = 3  => 18 pairs (_) / D7 = 3  => 17 pairs (_)
A9,D9: 3.. / A9 = 3  => 17 pairs (_) / D9 = 3  => 18 pairs (_)
C1,C7: 3.. / C1 = 3  => 17 pairs (_) / C7 = 3  => 18 pairs (_)
H5,H8: 3.. / H5 = 3  => 21 pairs (_) / H8 = 3  => 19 pairs (_)
I5,I8: 3.. / I5 = 3  => 19 pairs (_) / I8 = 3  => 21 pairs (_)
E4,E5: 4.. / E4 = 4  =>  0 pairs (X) / E5 = 4  => 18 pairs (_)
D7,D9: 4.. / D7 = 4  => 18 pairs (_) / D9 = 4  => 17 pairs (_)
F2,G2: 4.. / F2 = 4  =>  0 pairs (X) / G2 = 4  => 23 pairs (_)
A3,F3: 4.. / A3 = 4  => 29 pairs (_) / F3 = 4  => 21 pairs (_)
D9,H9: 4.. / D9 = 4  => 17 pairs (_) / H9 = 4  => 18 pairs (_)
G2,G6: 4.. / G2 = 4  => 23 pairs (_) / G6 = 4  =>  0 pairs (X)
H1,I1: 5.. / H1 = 5  => 22 pairs (_) / I1 = 5  => 21 pairs (_)
H7,I7: 5.. / H7 = 5  => 21 pairs (_) / I7 = 5  => 22 pairs (_)
H1,H7: 5.. / H1 = 5  => 22 pairs (_) / H7 = 5  => 21 pairs (_)
I1,I7: 5.. / I1 = 5  => 21 pairs (_) / I7 = 5  => 22 pairs (_)
D2,F2: 6.. / D2 = 6  => 20 pairs (_) / F2 = 6  =>  0 pairs (X)
D4,F6: 6.. / D4 = 6  =>  0 pairs (X) / F6 = 6  => 20 pairs (_)
C7,A9: 6.. / C7 = 6  => 17 pairs (_) / A9 = 6  => 18 pairs (_)
A9,H9: 6.. / A9 = 6  => 18 pairs (_) / H9 = 6  => 17 pairs (_)
D2,D4: 6.. / D2 = 6  => 20 pairs (_) / D4 = 6  =>  0 pairs (X)
F2,F6: 6.. / F2 = 6  =>  0 pairs (X) / F6 = 6  => 20 pairs (_)
E1,E2: 7.. / E1 = 7  => 20 pairs (_) / E2 = 7  => 15 pairs (_)
H4,H5: 7.. / H4 = 7  => 20 pairs (_) / H5 = 7  => 25 pairs (_)
A2,E2: 7.. / A2 = 7  => 20 pairs (_) / E2 = 7  => 15 pairs (_)
B4,H4: 7.. / B4 = 7  => 25 pairs (_) / H4 = 7  => 20 pairs (_)
F1,F3: 8.. / F1 = 8  => 20 pairs (_) / F3 = 8  =>  0 pairs (X)
E4,E5: 8.. / E4 = 8  => 18 pairs (_) / E5 = 8  =>  0 pairs (X)
C4,E4: 8.. / C4 = 8  =>  0 pairs (X) / E4 = 8  => 18 pairs (_)
A1,C1: 9.. / A1 = 9  => 19 pairs (_) / C1 = 9  =>  0 pairs (X)
C4,A6: 9.. / C4 = 9  => 19 pairs (_) / A6 = 9  =>  0 pairs (X)
H4,H6: 9.. / H4 = 9  =>  0 pairs (X) / H6 = 9  => 19 pairs (_)
C4,H4: 9.. / C4 = 9  => 19 pairs (_) / H4 = 9  =>  0 pairs (X)
A6,H6: 9.. / A6 = 9  =>  0 pairs (X) / H6 = 9  => 19 pairs (_)
A1,A6: 9.. / A1 = 9  => 19 pairs (_) / A6 = 9  =>  0 pairs (X)
C1,C4: 9.. / C1 = 9  =>  0 pairs (X) / C4 = 9  => 19 pairs (_)
* DURATION: 0:00:58.243650  START: 02:53:10.763215  END: 02:54:09.006865 2019-05-01
* CP COUNT: (46)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A9,C3,C7,D2,D4,D7,D9,E1,E2,E4,E5,F6,G2,G6,H8,H9,I8)
* ...1..6...15....89.6.59.3175....31.....9.15...3175...829..178..1548697...87.259.1
* PAIR A2: 3,7 BLK 1
A1: 3,7,4,8,9                            # reduction candidate for 3,7
A1: 3,7 => CTR
* .291.8654.15..4289468592317572..319...69.157393175.428293417865154869732687325941
A1: 4,8,9                                # 19 pairs
* PAIR A3: 4,8 BLK 1
A1: 4,8,3,7,9                            # reduction candidate for 4,8
A1: 4,8 => CTR
* ..913.6..315.7..89.6.59.3175....319.7..9.15..93175...82934178..1548697..687325941
A1: 3,7,9                                # 19 pairs
* PAIR A3: 4,8 ROW 3
F3: 4,8,2                                # reduction candidate for 4,8
F3: 2 => CTR
* ...1.8654.156.428946859231754.2831..8..9415...3175642829..178..154869732687325941
F3: 4,8                                  # 21 pairs
* PAIR A3: 4,8 COL A
A5: 4,8,6,7                              # reduction candidate for 4,8
A5: 4,8                                  # 34 pairs
A5: 6,7                                  # 23 pairs
* PAIR C3: 2,8 BLK 1
C1: 2,8,3,9                              # reduction candidate for 2,8
C1: 2,8 => CTR
* 9..13.6..315.7..89.6.59.3175.9.831..7.89415..63175...829..178..1548697...87.259.1
C1: 3,9                                  # 20 pairs
* PAIR C3: 2,8 ROW 3
F3: 2,8,4                                # reduction candidate for 2,8
F3: 2,8                                  # 29 pairs
F3: 4                                    # 21 pairs
* PAIR C3: 2,8 COL C
C4: 2,8,6,9                              # reduction candidate for 2,8
C4: 2,8 => CTR
* ..91..654.15..428946.59.31757.2431968.69.157393175.428293417865154869732687325941
C4: 6,9                                  # 19 pairs
C5: 2,8,6                                # reduction candidate for 2,8
C5: 2,8                                  # 21 pairs
* PAIR E1: 3,7 ROW 1
A1: 3,7,4,8,9                            # reduction candidate for 3,7
A1: 3,7 => CTR
* .291.8654.15..4289468592317572..319...69.157393175.428293417865154869732687325941
A1: 4,8,9                                # 19 pairs
* PAIR D2: 2,6 BLK 2
F2: 2,6,4                                # reduction candidate for 2,6
F2: 4 => CTR
* ..91..6...156.428946.59.3175782431966429.157393175642829..178..154869732.87.259.1
F2: 2,6                                  # 23 pairs
* PAIR G2: 2,4 BLK 3
H1: 2,4,5                                # reduction candidate for 2,4
H1: 2,4                                  # 21 pairs
I1: 2,4,5                                # reduction candidate for 2,4
I1: 2,4                                  # 22 pairs
* PAIR G2: 2,4 ROW 2
F2: 2,4,6                                # reduction candidate for 2,4
F2: 6 => CTR
* ...1..6...15..6489.6.59.3175..6.31.....9.15...31752..829..178..1548697...87.259.1
F2: 2,4                                  # 20 pairs
* PAIR D4: 2,6 ROW 4
C4: 2,6,8,9                              # reduction candidate for 2,6
C4: 2,6 => CTR
* ..91..6...15....89.6.59.3175...8319....94157393175...82934178..154869732687325941
C4: 8,9                                  # 20 pairs
H4: 2,6,4,7,9                            # reduction candidate for 2,6
H4: 2,6 => CTR
* ...1..6...15....89.6.59.317579.831.4...94157343175.29829..178.6154869732687325941
H4: 4,7,9                                # 19 pairs
I4: 2,6,4                                # reduction candidate for 2,6
I4: 2,6                                  # 22 pairs
* PAIR E5: 4,8 ROW 5
A5: 4,8,6,7                              # reduction candidate for 4,8
A5: 4,8                                  # 34 pairs
A5: 6,7                                  # 23 pairs
* PAIR F6: 2,6 ROW 6
H6: 2,6,4,9                              # reduction candidate for 2,6
H6: 2,6 => CTR
* ..91..6...15..428946.59.31757.243196.4298157393175642829..178..154869732.87.259.1
H6: 4,9                                  # 20 pairs
* PAIR F6: 2,6 COL F
F2: 2,6,4                                # reduction candidate for 2,6
F2: 4 => CTR
* ..91..6...156.428946.59.3175782431966429.157393175642829..178..154869732.87.259.1
F2: 2,6                                  # 23 pairs
* PAIR G6: 2,4 BLK 6
H4: 2,4,6,7,9                            # reduction candidate for 2,4
H4: 2,4 => SOLVED
* 943178625715632489862594317579283146628941573431756298296317854154869732387425961
H4: 6,7,9                                # 19 pairs
I4: 2,4,6                                # reduction candidate for 2,4
I4: 2,4                                  # 23 pairs
H5: 2,4,3,6,7                            # reduction candidate for 2,4
H5: 2,4 => CTR
* 9..1..6...15....89.6.59.3175.9.83176...941523.3175..9829..178..154869732.87.259.1
H5: 3,6,7                                # 19 pairs
I5: 2,4,3,6                              # reduction candidate for 2,4
I5: 2,4 => CTR
* 9..1..6...15....89.6.59.3175.9.83176...941532.3175..9829..178..154869723.87.259.1
I5: 3,6                                  # 20 pairs
H6: 2,4,6,9                              # reduction candidate for 2,4
H6: 2,4 => CTR
* ..91..654.156.428946.59.3175782.3196...9.1573931756..8293417865154869732687325941
H6: 6,9                                  # 20 pairs
* PAIR H8: 2,3 COL H
H5: 2,3,4,6,7                            # reduction candidate for 2,3
H5: 2,3                                  # 23 pairs
H5: 4,6,7                                # 20 pairs
* PAIR I8: 2,3 COL I
I5: 2,3,4,6                              # reduction candidate for 2,3
I5: 4,6 => CTR
* 9..1..6...15....89.6.59.3175.9.8317....9415366317524982963178..154869723387425961
I5: 2,3                                  # 22 pairs
* PAIR H9: 4,6 BLK 9
H7: 4,6,5                                # reduction candidate for 4,6
H7: 4,6                                  # 22 pairs
I7: 4,6,5                                # reduction candidate for 4,6
I7: 4,6                                  # 21 pairs
* PAIR H9: 4,6 COL H
H4: 4,6,2,7,9                            # reduction candidate for 4,6
H4: 4,6 => SOLVED
* 943178625715632489862594317579283146628941573431756298296317854154869732387425961
H4: 2,7,9                                # 19 pairs
H5: 4,6,2,3,7                            # reduction candidate for 4,6
H5: 4,6 => CTR
* 9..1..625.15...489.6259.3175.9.8317..2.941563.3175..9829..178..154869732.87.259.1
H5: 2,3,7                                # 19 pairs
H6: 4,6,2,9                              # reduction candidate for 4,6
H6: 4,6 => CTR
* ..91..625.15...489.6259.31757.2.319..2.9.15739317562482934178..154869732.87.259.1
H6: 2,9                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190112-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 3,7 => CTR => A1: 4,8,9
* DIS # A1: 4,8 => CTR => A1: 3,7,9
* DIS # F3: 2 => CTR => F3: 4,8
* DIS # C1: 2,8 => CTR => C1: 3,9
* DIS # C4: 2,8 => CTR => C4: 6,9
* DIS # A1: 3,7 => CTR => A1: 4,8,9
* DIS # F2: 4 => CTR => F2: 2,6
* DIS # F2: 6 => CTR => F2: 2,4
* DIS # C4: 2,6 => CTR => C4: 8,9
* DIS # H4: 2,6 => CTR => H4: 4,7,9
* DIS # H6: 2,6 => CTR => H6: 4,9
* DIS # F2: 4 => CTR => F2: 2,6
* PRF # H4: 2,4 => SOL
* DIS # H5: 2,4 => CTR => H5: 3,6,7
* DIS # I5: 2,4 => CTR => I5: 3,6
* DIS # H6: 2,4 => CTR => H6: 6,9
* DIS # I5: 4,6 => CTR => I5: 2,3
* PRF # H4: 4,6 => SOL
* DIS # H5: 4,6 => CTR => H5: 2,3,7
* DIS # H6: 4,6 => CTR => H6: 2,9
* CNT  20 HDP CHAINS /  55 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A3,A9,C3,C7,D2,D4,D7,D9,E1,E2,E4,E5,F6,G2,G6,H8,H9,I8)
* ...1..6...15....89.6.59.3175....31.....9.15...3175...829..178..1548697...87.259.1
* PAIR A2: 3,7 BLK 1
A1: 3,7,4,8,9                            # reduction candidate for 3,7
A1: 3,7 => CTR
* .291.8654.15..4289468592317572..319...69.157393175.428293417865154869732687325941
* PAIR A3: 4,8 BLK 1
A1: 4,8,9                                # reduction candidate for 4,8
A1: 4,8 => CTR
* ..913.6..315.7..89.6.59.3175....319.7..9.15..93175...82934178..1548697..687325941
* PAIR A3: 4,8 ROW 3
F3: 4,8,2                                # reduction candidate for 4,8
F3: 2 => CTR
* 9..1.86...15..42894685923175.9.831.....9415...3175..9829..178..1548697...87.259.1
* PAIR RESTART
* PAIR D2: 2,6 BLK 2
F2: 2,6,4                                # reduction candidate for 2,6
F2: 2,6 => SOLVED
* 943178625715632489862594317579283146628941573431756298296317854154869732387425961
* DURATION: 0:00:06.114050  START: 02:54:46.607526  END: 02:54:52.721576 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190112-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 3,7 => CTR => A1: 4,8,9
* DIS A1: 4,8,9 # A1: 4,8 => CTR => A1: 9
* DIS A1: 4,8,9 + A1: 9 # F3: 2 => CTR => F3: 4,8
* PRF A1: 4,8,9 + A1: 9 + F3: 4,8 # F2: 2,6 => SOL
* STA A1: 4,8,9 + A1: 9 + F3: 4,8 + F2: 2,6
* CNT   4 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190112, absurd

Solution

position: 943178625715632489862594317579283146628941573431756298296317854154869732387425961 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 # A1: 3,7 => CTR => A1: 4,8,9
* INC # A1: 4,8,9 => UNS
* DIS # A1: 4,8 => CTR => A1: 3,7,9
* INC # A1: 3,7,9 => UNS
* INC # F3: 4,8 => UNS
* DIS # F3: 2 => CTR => F3: 4,8
* INC # A5: 4,8 => UNS
* INC # A5: 6,7 => UNS
* DIS # C1: 2,8 => CTR => C1: 3,9
* INC # C1: 3,9 => UNS
* INC # F3: 2,8 => UNS
* INC # F3: 4 => UNS
* DIS # C4: 2,8 => CTR => C4: 6,9
* INC # C4: 6,9 => UNS
* INC # C5: 2,8 => UNS
* DIS # A1: 3,7 => CTR => A1: 4,8,9
* INC # A1: 4,8,9 => UNS
* INC # F2: 2,6 => UNS
* DIS # F2: 4 => CTR => F2: 2,6
* INC # H1: 2,4 => UNS
* INC # I1: 2,4 => UNS
* INC # F2: 2,4 => UNS
* DIS # F2: 6 => CTR => F2: 2,4
* DIS # C4: 2,6 => CTR => C4: 8,9
* INC # C4: 8,9 => UNS
* DIS # H4: 2,6 => CTR => H4: 4,7,9
* INC # H4: 4,7,9 => UNS
* INC # I4: 2,6 => UNS
* INC # A5: 4,8 => UNS
* INC # A5: 6,7 => UNS
* DIS # H6: 2,6 => CTR => H6: 4,9
* INC # H6: 4,9 => UNS
* INC # F2: 2,6 => UNS
* DIS # F2: 4 => CTR => F2: 2,6
* PRF # H4: 2,4 => SOL
* INC # H4: 6,7,9 => UNS
* INC # I4: 2,4 => UNS
* DIS # H5: 2,4 => CTR => H5: 3,6,7
* INC # H5: 3,6,7 => UNS
* DIS # I5: 2,4 => CTR => I5: 3,6
* INC # I5: 3,6 => UNS
* DIS # H6: 2,4 => CTR => H6: 6,9
* INC # H6: 6,9 => UNS
* INC # H5: 2,3 => UNS
* INC # H5: 4,6,7 => UNS
* INC # I5: 2,3 => UNS
* DIS # I5: 4,6 => CTR => I5: 2,3
* INC # H7: 4,6 => UNS
* INC # I7: 4,6 => UNS
* PRF # H4: 4,6 => SOL
* INC # H4: 2,7,9 => UNS
* DIS # H5: 4,6 => CTR => H5: 2,3,7
* INC # H5: 2,3,7 => UNS
* DIS # H6: 4,6 => CTR => H6: 2,9
* INC # H6: 2,9 => UNS
* CNT  55 HDP CHAINS /  55 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 3,7 => CTR => A1: 4,8,9
* DIS A1: 4,8,9 # A1: 4,8 => CTR => A1: 9
* INC A1: 4,8,9 + A1: 9 # F3: 4,8 => UNS
* DIS A1: 4,8,9 + A1: 9 # F3: 2 => CTR => F3: 4,8
* PRF A1: 4,8,9 + A1: 9 + F3: 4,8 # F2: 2,6 => SOL
* STA A1: 4,8,9 + A1: 9 + F3: 4,8 + F2: 2,6
* CNT   5 HDP CHAINS /   5 HYP OPENED