Analysis of zz-www.sudokuoftheday.co.uk-20190119-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: .......2....14958...7.25..98.2..7.4.94.2......56...........3164....9......5...2.. initial

Autosolve

position: 5......2.623149587..7.25..9832..7.4.9412.....756.....22....3164....92.....5...29. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A8: 3 => CTR => A8: 1,4
* DIS # B8: 1,8 => CTR => B8: 6
* DIS # D1: 6,8 => CTR => D1: 3,7
* PRF # E1: 6,8 => SOL
* DIS # I1: 6 => CTR => I1: 1,3
* DIS # B7: 7 => CTR => B7: 8,9
* DIS # C1: 4 => CTR => C1: 8,9
* DIS # D8: 6 => CTR => D8: 4,8
* DIS # A8: 3,4 => CTR => A8: 1
* CNT   9 HDP CHAINS /  35 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 # A8: 3 => CTR => A8: 1,4
* DIS A8: 1,4 # B1: 9 => CTR => B1: 1,8
* PRF A8: 1,4 + B1: 1,8 # E1: 6,8 => SOL
* STA A8: 1,4 + B1: 1,8 + E1: 6,8
* CNT   3 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

.......2....14958...7.25..98.2..7.4.94.2......56...........3164....9......5...2.. initial
5......2.623149587..7.25..9832..7.4.9412.....756.....22....3164....92.....5...29. autosolve
519786423623149587487325619832657941941238756756914832298573164164892375375461298 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (15)
A3: 1,4
B3: 1,8
F1: 6,8
H3: 1,3
F5: 6,8
F6: 1,4
G4: 6,9
H5: 5,7
H6: 1,3
C7: 8,9
C8: 4,8
A9: 3,4
F9: 1,4
H8: 5,7
I9: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I1,H3: 1.. / I1 = 1  => 20 pairs (_) / H3 = 1  => 21 pairs (_)
I4,H6: 1.. / I4 = 1  => 21 pairs (_) / H6 = 1  => 20 pairs (_)
A8,B8: 1.. / A8 = 1  => 18 pairs (_) / B8 = 1  =>  0 pairs (X)
E9,F9: 1.. / E9 = 1  =>  0 pairs (X) / F9 = 1  => 13 pairs (_)
B1,I1: 1.. / B1 = 1  => 21 pairs (_) / I1 = 1  => 20 pairs (_)
E4,I4: 1.. / E4 = 1  => 20 pairs (_) / I4 = 1  => 21 pairs (_)
A3,A8: 1.. / A3 = 1  =>  0 pairs (X) / A8 = 1  => 18 pairs (_)
F6,F9: 1.. / F6 = 1  =>  0 pairs (X) / F9 = 1  => 13 pairs (_)
H3,H6: 1.. / H3 = 1  => 21 pairs (_) / H6 = 1  => 20 pairs (_)
I1,I4: 1.. / I1 = 1  => 20 pairs (_) / I4 = 1  => 21 pairs (_)
A8,A9: 3.. / A8 = 3  =>  0 pairs (X) / A9 = 3  => 18 pairs (_)
A9,I9: 3.. / A9 = 3  => 18 pairs (_) / I9 = 3  =>  0 pairs (X)
H3,H6: 3.. / H3 = 3  => 20 pairs (_) / H6 = 3  => 21 pairs (_)
C1,A3: 4.. / C1 = 4  =>  0 pairs (X) / A3 = 4  => 18 pairs (_)
G1,G3: 4.. / G1 = 4  => 18 pairs (_) / G3 = 4  =>  0 pairs (X)
D6,F6: 4.. / D6 = 4  =>  0 pairs (X) / F6 = 4  => 13 pairs (_)
C1,G1: 4.. / C1 = 4  =>  0 pairs (X) / G1 = 4  => 18 pairs (_)
A3,G3: 4.. / A3 = 4  => 18 pairs (_) / G3 = 4  =>  0 pairs (X)
C1,C8: 4.. / C1 = 4  =>  0 pairs (X) / C8 = 4  => 18 pairs (_)
F6,F9: 4.. / F6 = 4  => 13 pairs (_) / F9 = 4  =>  0 pairs (X)
D7,E7: 5.. / D7 = 5  => 19 pairs (_) / E7 = 5  => 16 pairs (_)
H8,I8: 5.. / H8 = 5  => 16 pairs (_) / I8 = 5  => 15 pairs (_)
D4,D7: 5.. / D4 = 5  => 16 pairs (_) / D7 = 5  => 19 pairs (_)
H5,H8: 5.. / H5 = 5  => 15 pairs (_) / H8 = 5  => 16 pairs (_)
B8,B9: 6.. / B8 = 6  => 21 pairs (_) / B9 = 6  =>  0 pairs (X)
D3,G3: 6.. / D3 = 6  =>  0 pairs (X) / G3 = 6  => 19 pairs (_)
B8,D8: 6.. / B8 = 6  => 21 pairs (_) / D8 = 6  =>  0 pairs (X)
F1,F5: 6.. / F1 = 6  => 19 pairs (_) / F5 = 6  => 23 pairs (_)
D1,E1: 7.. / D1 = 7  => 16 pairs (_) / E1 = 7  => 16 pairs (_)
G5,H5: 7.. / G5 = 7  => 15 pairs (_) / H5 = 7  => 16 pairs (_)
B7,B9: 7.. / B7 = 7  =>  0 pairs (X) / B9 = 7  => 21 pairs (_)
G8,H8: 7.. / G8 = 7  => 16 pairs (_) / H8 = 7  => 15 pairs (_)
G5,G8: 7.. / G5 = 7  => 15 pairs (_) / G8 = 7  => 16 pairs (_)
H5,H8: 7.. / H5 = 7  => 16 pairs (_) / H8 = 7  => 15 pairs (_)
B3,D3: 8.. / B3 = 8  => 20 pairs (_) / D3 = 8  =>  0 pairs (X)
F1,F5: 8.. / F1 = 8  => 23 pairs (_) / F5 = 8  => 19 pairs (_)
B1,C1: 9.. / B1 = 9  => 20 pairs (_) / C1 = 9  => 21 pairs (_)
D4,D6: 9.. / D4 = 9  =>  0 pairs (X) / D6 = 9  => 14 pairs (_)
G4,G6: 9.. / G4 = 9  => 14 pairs (_) / G6 = 9  =>  0 pairs (X)
B7,C7: 9.. / B7 = 9  => 21 pairs (_) / C7 = 9  => 20 pairs (_)
D4,G4: 9.. / D4 = 9  =>  0 pairs (X) / G4 = 9  => 14 pairs (_)
D6,G6: 9.. / D6 = 9  => 14 pairs (_) / G6 = 9  =>  0 pairs (X)
B1,B7: 9.. / B1 = 9  => 20 pairs (_) / B7 = 9  => 21 pairs (_)
C1,C7: 9.. / C1 = 9  => 21 pairs (_) / C7 = 9  => 20 pairs (_)
* DURATION: 0:00:49.795396  START: 03:03:57.019272  END: 03:04:46.814668 2019-05-01
* CP COUNT: (44)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B3,C7,C8,F1,F5,F6,F9,G4,H3,H5,H6,H8,I9)
* 5......2.623149587..7.25..9832..7.4.9412.....756.....22....3164....92.....5...29.
* PAIR A3: 1,4 COL A
A8: 1,4,3                                # reduction candidate for 1,4
A8: 3 => CTR
* 5......2.623149587187.25439832..7.4.9412.....756....122....316431.692.....5...29.
A8: 1,4                                  # 18 pairs
* PAIR B3: 1,8 BLK 1
B1: 1,8,9                                # reduction candidate for 1,8
B1: 1,8                                  # 21 pairs
B1: 9                                    # 20 pairs
* PAIR B3: 1,8 COL B
B8: 1,8,6                                # reduction candidate for 1,8
B8: 1,8 => CTR
* 59.7..421623149587417.256.9832..794.9412.....7569.4..2279..3164...692....65471298
B8: 6                                    # 21 pairs
* PAIR F1: 6,8 BLK 2
D1: 6,8,3,7                              # reduction candidate for 6,8
D1: 6,8 => CTR
* 519.76423623149587487325619832..7941941238756756914832298753164164892..53.54.1298
D1: 3,7                                  # 16 pairs
E1: 6,8,3,7                              # reduction candidate for 6,8
E1: 6,8 => SOLVED
* 519786423623149587487325619832657941941238756756914832298573164164892375375461298
E1: 3,7                                  # 16 pairs
D3: 6,8,3                                # reduction candidate for 6,8
D3: 6,8                                  # 20 pairs
* PAIR H3: 1,3 BLK 3
I1: 1,3,6                                # reduction candidate for 1,3
I1: 6 => CTR
* 519378426623149587487625319832.57.419412.6...756....32298..3164164892753375461298
I1: 1,3                                  # 17 pairs
* PAIR F5: 6,8 BLK 5
E5: 6,8,3,5                              # reduction candidate for 6,8
E5: 6,8                                  # 20 pairs
E5: 3,5                                  # 16 pairs
* PAIR F5: 6,8 ROW 5
G5: 6,8,3,7                              # reduction candidate for 6,8
G5: 6,8                                  # 18 pairs
I5: 6,8,3,5                              # reduction candidate for 6,8
I5: 6,8                                  # 18 pairs
* PAIR G4: 6,9 ROW 4
D4: 6,9,5                                # reduction candidate for 6,9
D4: 6,9                                  # 19 pairs
D4: 5                                    # 16 pairs
* PAIR H6: 1,3 ROW 6
E6: 1,3,8                                # reduction candidate for 1,3
E6: 8                                    # 29 pairs
E6: 1,3                                  # 16 pairs
* PAIR C7: 8,9 BLK 7
B7: 8,9,7                                # reduction candidate for 8,9
B7: 7 => CTR
* 59.37..21623149587..7.25.39832.1794.9412.....7569.4.12279..3164.6.492...48576129.
B7: 8,9                                  # 21 pairs
* PAIR C7: 8,9 COL C
C1: 8,9,4                                # reduction candidate for 8,9
C1: 4 => CTR
* 594....21623149587187.25439832.17.4.9412.....756..4.12279..3164.18692.....5...29.
C1: 8,9                                  # 18 pairs
* PAIR C8: 4,8 ROW 8
D8: 4,8,6                                # reduction candidate for 4,8
D8: 6 => CTR
* 59.7..421623149587417.256.9832..794.9412.....7569.4..2279..3164...692....65471298
D8: 4,8                                  # 21 pairs
* PAIR C8: 4,8 COL C
C1: 4,8,9                                # reduction candidate for 4,8
C1: 9                                    # 21 pairs
C1: 4,8                                  # 20 pairs
* PAIR A9: 3,4 BLK 7
A8: 3,4,1                                # reduction candidate for 3,4
A8: 3,4 => CTR
* 5......2.623149587187.25439832..7.4.9412.....756....122....3164.1.692.....5...29.
A8: 1                                    # 18 pairs
* PAIR I9: 3,8 BLK 9
G8: 3,8,7                                # reduction candidate for 3,8
G8: 3,8                                  # 15 pairs
I8: 3,8,5                                # reduction candidate for 3,8
I8: 3,8                                  # 16 pairs
* PAIR I9: 3,8 COL I
I5: 3,8,5,6                              # reduction candidate for 3,8
I5: 3,8                                  # 19 pairs
I5: 5,6                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190119-absurd-base-pr-000.dot
* REASONING
* DIS # A8: 3 => CTR => A8: 1,4
* DIS # B8: 1,8 => CTR => B8: 6
* DIS # D1: 6,8 => CTR => D1: 3,7
* PRF # E1: 6,8 => SOL
* DIS # I1: 6 => CTR => I1: 1,3
* DIS # B7: 7 => CTR => B7: 8,9
* DIS # C1: 4 => CTR => C1: 8,9
* DIS # D8: 6 => CTR => D8: 4,8
* DIS # A8: 3,4 => CTR => A8: 1
* CNT   9 HDP CHAINS /  35 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A9,B3,C7,C8,F1,F5,F6,F9,G4,H3,H5,H6,H8,I9)
* 5......2.623149587..7.25..9832..7.4.9412.....756.....22....3164....92.....5...29.
* PAIR A3: 1,4 COL A
A8: 1,4,3                                # reduction candidate for 1,4
A8: 3 => CTR
* 5......2.623149587187.25439832..7.4.9412.....756....122....316431.692.....5...29.
* PAIR RESTART
* PAIR B3: 1,8 BLK 1
B1: 1,8,9                                # reduction candidate for 1,8
B1: 9 => CTR
* 598376.21623149587..7.25.39832.1794.9412.....7569.4.122.9753164...892...375461298
* PAIR F1: 6,8 BLK 2
E1: 6,8,7                                # reduction candidate for 6,8
E1: 6,8 => SOLVED
* 519786423623149587487325619832657941941238756756914832298573164164892375375461298
* DURATION: 0:00:04.320465  START: 03:05:08.791513  END: 03:05:13.111978 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190119-absurd-base-pr-001.dot
* REASONING
* DIS # A8: 3 => CTR => A8: 1,4
* DIS A8: 1,4 # B1: 9 => CTR => B1: 1,8
* PRF A8: 1,4 + B1: 1,8 # E1: 6,8 => SOL
* STA A8: 1,4 + B1: 1,8 + E1: 6,8
* CNT   3 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190119, absurd

Solution

position: 519786423623149587487325619832657941941238756756914832298573164164892375375461298 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 # A8: 1,4 => UNS
* DIS # A8: 3 => CTR => A8: 1,4
* INC # B1: 1,8 => UNS
* INC # B1: 9 => UNS
* DIS # B8: 1,8 => CTR => B8: 6
* INC # B8: 6 => UNS
* DIS # D1: 6,8 => CTR => D1: 3,7
* INC # D1: 3,7 => UNS
* PRF # E1: 6,8 => SOL
* INC # E1: 3,7 => UNS
* INC # D3: 6,8 => UNS
* INC # I1: 1,3 => UNS
* DIS # I1: 6 => CTR => I1: 1,3
* INC # E5: 6,8 => UNS
* INC # E5: 3,5 => UNS
* INC # G5: 6,8 => UNS
* INC # I5: 6,8 => UNS
* INC # D4: 6,9 => UNS
* INC # D4: 5 => UNS
* INC # E6: 1,3 => UNS
* INC # E6: 8 => UNS
* INC # B7: 8,9 => UNS
* DIS # B7: 7 => CTR => B7: 8,9
* INC # C1: 8,9 => UNS
* DIS # C1: 4 => CTR => C1: 8,9
* INC # D8: 4,8 => UNS
* DIS # D8: 6 => CTR => D8: 4,8
* INC # C1: 4,8 => UNS
* INC # C1: 9 => UNS
* DIS # A8: 3,4 => CTR => A8: 1
* INC # A8: 1 => UNS
* INC # G8: 3,8 => UNS
* INC # I8: 3,8 => UNS
* INC # I5: 3,8 => UNS
* INC # I5: 5,6 => UNS
* CNT  35 HDP CHAINS /  35 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A8: 1,4 => UNS
* DIS # A8: 3 => CTR => A8: 1,4
* INC A8: 1,4 # B1: 1,8 => UNS
* DIS A8: 1,4 # B1: 9 => CTR => B1: 1,8
* PRF A8: 1,4 + B1: 1,8 # E1: 6,8 => SOL
* STA A8: 1,4 + B1: 1,8 + E1: 6,8
* CNT   5 HDP CHAINS /   5 HYP OPENED