Analysis of zz-www.sudokuoftheday.co.uk-20190308-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: .7.259...9...74.3...8.........9..5.4......2....4..3.7.1.......764..1..2.....68.1. initial

Autosolve

position: 37.259...9..874.3.4.8.3.7.....9..5.4....4.2.3..4..3.7.18..92..764..1..28....68.1. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I3: 2,5 => CTR => I3: 9
* PRF # I3: 9 => SOL
* DIS # B6: 2,5 => CTR => B6: 6,9
* PRF # F5: 1,6 => SOL
* DIS # G6: 1,6 => CTR => G6: 8,9
* DIS # I3: 2,5 => CTR => I3: 9
* PRF # I3: 9 => SOL
* DIS # I3: 2 => CTR => I3: 5,9
* DIS # B6: 5,6 => CTR => B6: 2,9
* DIS # H5: 6,8 => CTR => H5: 9
* PRF # H5: 9 => SOL
* PRF # G6: 6,8 => SOL
* DIS # G6: 1,6 => CTR => G6: 8,9
* DIS # C8: 3,5 => CTR => C8: 7,9
* PRF # D7: 3,5 => SOL
* DIS # D9: 5,7 => CTR => D9: 3,4
* DIS # C8: 5,7 => CTR => C8: 3,9
* PRF # F5: 1,6 => SOL
* PRF # G9: 3,9 => SOL
* DIS # C8: 5,7 => CTR => C8: 3,9
* DIS # I3: 2 => CTR => I3: 5,9
* CNT  21 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:

* DIS # I3: 2,5 => CTR => I3: 9
* PRF I3: 9 => SOL
* STA I3: 9
* CNT   2 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

.7.259...9...74.3...8.........9..5.4......2....4..3.7.1.......764..1..2.....68.1. initial
37.259...9..874.3.4.8.3.7.....9..5.4....4.2.3..4..3.7.18..92..764..1..28....68.1. autosolve
371259486956874132428136759213987564867541293594623871185392647649715328732468915 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
C1: 1,6
B3: 2,5
D3: 1,6
F3: 1,6
G1: 4,8
H1: 4,8
I1: 1,6
G2: 1,6
I2: 2,5
H3: 5,9
E4: 2,8
D6: 5,6
E6: 2,8
H4: 6,8
I6: 1,6
C7: 3,5
F8: 5,7
G8: 3,9
I9: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,F3: 1.. / D3 = 1  => 18 pairs (_) / F3 = 1  => 23 pairs (_)
I1,G2: 1.. / I1 = 1  =>  0 pairs (X) / G2 = 1  => 15 pairs (_)
G6,I6: 1.. / G6 = 1  =>  0 pairs (X) / I6 = 1  => 15 pairs (_)
C1,I1: 1.. / C1 = 1  => 15 pairs (_) / I1 = 1  =>  0 pairs (X)
D3,D5: 1.. / D3 = 1  => 18 pairs (_) / D5 = 1  => 23 pairs (_)
G2,G6: 1.. / G2 = 1  => 15 pairs (_) / G6 = 1  =>  0 pairs (X)
I1,I6: 1.. / I1 = 1  =>  0 pairs (X) / I6 = 1  => 15 pairs (_)
I2,I3: 2.. / I2 = 2  => 18 pairs (_) / I3 = 2  =>  0 pairs (X)
E4,E6: 2.. / E4 = 2  => 18 pairs (_) / E6 = 2  => 18 pairs (_)
B3,I3: 2.. / B3 = 2  => 18 pairs (_) / I3 = 2  =>  0 pairs (X)
B4,C4: 3.. / B4 = 3  => 19 pairs (_) / C4 = 3  =>  0 pairs (*)
B4,B9: 3.. / B4 = 3  => 19 pairs (_) / B9 = 3  =>  0 pairs (*)
G1,H1: 4.. / G1 = 4  =>  0 pairs (*) / H1 = 4  =>  0 pairs (X)
D7,D9: 4.. / D7 = 4  => 19 pairs (_) / D9 = 4  =>  0 pairs (*)
D9,G9: 4.. / D9 = 4  =>  0 pairs (*) / G9 = 4  =>  0 pairs (X)
H1,H7: 4.. / H1 = 4  => 18 pairs (_) / H7 = 4  =>  0 pairs (*)
H7,I9: 5.. / H7 = 5  =>  0 pairs (X) / I9 = 5  =>  0 pairs (_)
F5,F8: 5.. / F5 = 5  => 18 pairs (_) / F8 = 5  => 20 pairs (_)
H3,H7: 5.. / H3 = 5  =>  0 pairs (*) / H7 = 5  =>  0 pairs (X)
D3,F3: 6.. / D3 = 6  => 23 pairs (_) / F3 = 6  => 18 pairs (_)
I1,G2: 6.. / I1 = 6  => 15 pairs (_) / G2 = 6  =>  0 pairs (X)
G7,H7: 6.. / G7 = 6  => 17 pairs (_) / H7 = 6  =>  0 pairs (X)
C1,I1: 6.. / C1 = 6  =>  0 pairs (X) / I1 = 6  => 15 pairs (_)
I1,I6: 6.. / I1 = 6  => 15 pairs (_) / I6 = 6  =>  0 pairs (X)
G1,H1: 8.. / G1 = 8  => 18 pairs (_) / H1 = 8  =>  0 pairs (*)
E4,E6: 8.. / E4 = 8  => 18 pairs (_) / E6 = 8  => 18 pairs (_)
A5,H5: 8.. / A5 = 8  => 22 pairs (_) / H5 = 8  =>  0 pairs (X)
G1,G6: 8.. / G1 = 8  => 18 pairs (_) / G6 = 8  =>  0 pairs (*)
H3,I3: 9.. / H3 = 9  =>  0 pairs (X) / I3 = 9  =>  0 pairs (_)
H5,G6: 9.. / H5 = 9  =>  0 pairs (*) / G6 = 9  =>  0 pairs (X)
B6,G6: 9.. / B6 = 9  =>  0 pairs (*) / G6 = 9  =>  0 pairs (X)
C8,G8: 9.. / C8 = 9  => 23 pairs (_) / G8 = 9  =>  0 pairs (X)
H3,H5: 9.. / H3 = 9  =>  0 pairs (X) / H5 = 9  =>  0 pairs (_)
I3,I9: 9.. / I3 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
* DURATION: 0:00:53.569473  START: 04:20:19.107046  END: 04:21:12.676519 2019-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,C1,C7,D3,D6,E4,E6,F3,F8,G1,G2,G8,H1,H3,H4,I1,I2,I6,I9)
* 37.259...9..874.3.4.8.3.7.....9..5.4....4.2.3..4..3.7.18..92..764..1..28....68.1.
* PAIR C1: 1,6 BLK 1
B2: 1,6,2,5                              # reduction candidate for 1,6
B2: 1,6                                  # 21 pairs
C2: 1,6,2,5                              # reduction candidate for 1,6
C2: 1,6                                  # 23 pairs
* PAIR C1: 1,6 COL C
C4: 1,6,2,3,7                            # reduction candidate for 1,6
C4: 1,6                                  # 22 pairs
C5: 1,6,5,7,9                            # reduction candidate for 1,6
C5: 1,6                                  # 22 pairs
* PAIR B3: 2,5 BLK 1
B2: 2,5,1,6                              # reduction candidate for 2,5
B2: 2,5                                  # 23 pairs
C2: 2,5,1,6                              # reduction candidate for 2,5
C2: 2,5                                  # 21 pairs
* PAIR B3: 2,5 ROW 3
I3: 2,5,9                                # reduction candidate for 2,5
I3: 2,5 => CTR
* 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..3971183492657649.1.328...368419
I3: 9 => SOLVED
* 371259486956874132428136759213987564867541293594623871185392647649715328732468915
* PAIR B3: 2,5 COL B
B6: 2,5,6,9                              # reduction candidate for 2,5
B6: 2,5 => CTR
* 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..46.397118.492657649.1.328...368419
B6: 6,9                                  # 20 pairs
B9: 2,5,3,9                              # reduction candidate for 2,5
B9: 2,5                                  # 23 pairs
* PAIR D3: 1,6 COL D
D5: 1,6,5,7                              # reduction candidate for 1,6
D5: 1,6                                  # 21 pairs
D5: 5,7                                  # 17 pairs
* PAIR F3: 1,6 COL F
F4: 1,6,7                                # reduction candidate for 1,6
F4: 1,6                                  # 22 pairs
F5: 1,6,5,7                              # reduction candidate for 1,6
F5: 1,6 => SOLVED
* 371259486956874132428136759213987564867541293594623871185392647649715328732468915
F5: 5,7                                  # 22 pairs
* PAIR G2: 1,6 ROW 2
B2: 1,6,2,5                              # reduction candidate for 1,6
B2: 1,6                                  # 21 pairs
C2: 1,6,2,5                              # reduction candidate for 1,6
C2: 1,6                                  # 23 pairs
* PAIR G2: 1,6 COL G
G6: 1,6,8,9                              # reduction candidate for 1,6
G6: 1,6 => CTR
* 37.25984.9..874.3.4.8.3.759...9..5848...4.293.94.83.7.18..92.6764..1..28....68.15
G6: 8,9                                  # 17 pairs
* PAIR I2: 2,5 BLK 3
I3: 2,5,9                                # reduction candidate for 2,5
I3: 2,5 => CTR
* 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..3971183492657649.1.328...368419
I3: 9 => SOLVED
* 371259486956874132428136759213987564867541293594623871185392647649715328732468915
* PAIR I2: 2,5 ROW 2
B2: 2,5,1,6                              # reduction candidate for 2,5
B2: 2,5                                  # 23 pairs
C2: 2,5,1,6                              # reduction candidate for 2,5
C2: 2,5                                  # 21 pairs
* PAIR H3: 5,9 BLK 3
I3: 5,9,2                                # reduction candidate for 5,9
I3: 2 => CTR
* 3712598469..874135458.3.792...9..5.4.9..4.2.3..4..3971183492657649.1.328.2..68419
I3: 5,9                                  # 18 pairs
* PAIR E4: 2,8 ROW 4
A4: 2,8,7                                # reduction candidate for 2,8
A4: 7                                    # 23 pairs
A4: 2,8                                  # 21 pairs
* PAIR D6: 5,6 BLK 5
D5: 5,6,1,7                              # reduction candidate for 5,6
D5: 5,6                                  # 21 pairs
F5: 5,6,1,7                              # reduction candidate for 5,6
F5: 5,6                                  # 22 pairs
* PAIR D6: 5,6 ROW 6
B6: 5,6,2,9                              # reduction candidate for 5,6
B6: 5,6 => CTR
* 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..397118.492657649.1.328...368419
B6: 2,9                                  # 20 pairs
* PAIR E6: 2,8 ROW 6
A6: 2,8,5                                # reduction candidate for 2,8
A6: 5                                    # 19 pairs
A6: 2,8                                  # 19 pairs
* PAIR H4: 6,8 BLK 6
H5: 6,8,9                                # reduction candidate for 6,8
H5: 6,8 => CTR
* 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..3971183492657649.1.328...368419
H5: 9 => SOLVED
* 371259486956874132428136759213987564867541293594623871185392647649715328732468915
G6: 6,8,1,9                              # reduction candidate for 6,8
G6: 6,8 => SOLVED
* 371259486956874132428136759213987564867541293594623871185392647649715328732468915
G6: 1,9                                  # 19 pairs
* PAIR I6: 1,6 BLK 6
G6: 1,6,8,9                              # reduction candidate for 1,6
G6: 1,6 => CTR
* 37.25984.9..874.3.4.8.3.759...9..5848...4.293.94.83.7.18..92.6764..1..28....68.15
G6: 8,9                                  # 17 pairs
* PAIR C7: 3,5 BLK 7
C8: 3,5,7,9                              # reduction candidate for 3,5
C8: 3,5 => CTR
* 37.259...9..874.32428.3.759...9..5.4....4.293.94..3.7.18..92..764..1.928.39.68415
C8: 7,9                                  # 21 pairs
B9: 3,5,2,9                              # reduction candidate for 3,5
B9: 3,5                                  # 23 pairs
C9: 3,5,2,7,9                            # reduction candidate for 3,5
C9: 3,5                                  # 24 pairs
* PAIR C7: 3,5 ROW 7
D7: 3,5,4                                # reduction candidate for 3,5
D7: 3,5 => SOLVED
* 371259486956874132428136759213987564867541293594623871185392647649715328732468915
D7: 4                                    # 19 pairs
* PAIR F8: 5,7 BLK 8
D8: 5,7,3                                # reduction candidate for 5,7
D8: 5,7                                  # 23 pairs
D9: 5,7,3,4                              # reduction candidate for 5,7
D9: 5,7 => CTR
* 37.25984.9..874.32428.3.759...9..5.4....4.293.94..3.7.185492367647315928239.68415
D9: 3,4                                  # 20 pairs
* PAIR F8: 5,7 ROW 8
C8: 5,7,3,9                              # reduction candidate for 5,7
C8: 5,7 => CTR
* 37.259...9..874.32428.3.759...9..5.4....4.293.94..3.7.18..92..764.31.928.39.68415
C8: 3,9                                  # 23 pairs
* PAIR F8: 5,7 COL F
F5: 5,7,1,6                              # reduction candidate for 5,7
F5: 1,6 => SOLVED
* 371259486956874132428136759213987564867541293594623871185392647649715328732468915
F5: 5,7                                  # 22 pairs
* PAIR G8: 3,9 BLK 9
G9: 3,9,4                                # reduction candidate for 3,9
G9: 3,9 => SOLVED
* 371259486956874132428136759213987564867541293594623871185392647649715328732468915
G9: 4                                    # 19 pairs
* PAIR G8: 3,9 ROW 8
C8: 3,9,5,7                              # reduction candidate for 3,9
C8: 5,7 => CTR
* 37.259...9..874.32428.3.759...9..5.4....4.293.94..3.7.18..92..764.31.928.39.68415
C8: 3,9                                  # 23 pairs
* PAIR I9: 5,9 ROW 9
B9: 5,9,2,3                              # reduction candidate for 5,9
B9: 5,9                                  # 22 pairs
C9: 5,9,2,3,7                            # reduction candidate for 5,9
C9: 5,9                                  # 23 pairs
* PAIR I9: 5,9 COL I
I3: 5,9,2                                # reduction candidate for 5,9
I3: 2 => CTR
* 3712598469..874135458.3.792...9..5.4.9..4.2.3..4..3971183492657649.1.328.2..68419
I3: 5,9                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190308-absurd-base-pr-000.dot
* REASONING
* DIS # I3: 2,5 => CTR => I3: 9
* PRF # I3: 9 => SOL
* DIS # B6: 2,5 => CTR => B6: 6,9
* PRF # F5: 1,6 => SOL
* DIS # G6: 1,6 => CTR => G6: 8,9
* DIS # I3: 2,5 => CTR => I3: 9
* PRF # I3: 9 => SOL
* DIS # I3: 2 => CTR => I3: 5,9
* DIS # B6: 5,6 => CTR => B6: 2,9
* DIS # H5: 6,8 => CTR => H5: 9
* PRF # H5: 9 => SOL
* PRF # G6: 6,8 => SOL
* DIS # G6: 1,6 => CTR => G6: 8,9
* DIS # C8: 3,5 => CTR => C8: 7,9
* PRF # D7: 3,5 => SOL
* DIS # D9: 5,7 => CTR => D9: 3,4
* DIS # C8: 5,7 => CTR => C8: 3,9
* PRF # F5: 1,6 => SOL
* PRF # G9: 3,9 => SOL
* DIS # C8: 5,7 => CTR => C8: 3,9
* DIS # I3: 2 => CTR => I3: 5,9
* CNT  21 HDP CHAINS /  61 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,C1,C7,D3,D6,E4,E6,F3,F8,G1,G2,G8,H1,H3,H4,I1,I2,I6,I9)
* 37.259...9..874.3.4.8.3.7.....9..5.4....4.2.3..4..3.7.18..92..764..1..28....68.1.
* PAIR C1: 1,6 BLK 1
B2: 1,6,2,5                              # reduction candidate for 1,6
B2: 1,6                                  # 21 pairs
C2: 1,6,2,5                              # reduction candidate for 1,6
C2: 1,6                                  # 23 pairs
* PAIR C1: 1,6 COL C
C4: 1,6,2,3,7                            # reduction candidate for 1,6
C4: 1,6                                  # 22 pairs
C5: 1,6,5,7,9                            # reduction candidate for 1,6
C5: 1,6                                  # 22 pairs
* PAIR B3: 2,5 BLK 1
B2: 2,5,1,6                              # reduction candidate for 2,5
B2: 2,5                                  # 23 pairs
C2: 2,5,1,6                              # reduction candidate for 2,5
C2: 2,5                                  # 21 pairs
* PAIR B3: 2,5 ROW 3
I3: 2,5,9                                # reduction candidate for 2,5
I3: 2,5 => CTR
* 3712598469..87413.4.8.3.79....9..5.4.9..4.2.3..4..3971183492657649.1.328...368419
I3: 9 => SOLVED
* 371259486956874132428136759213987564867541293594623871185392647649715328732468915
* DURATION: 0:00:07.443123  START: 04:22:02.484899  END: 04:22:09.928022 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190308-absurd-base-pr-001.dot
* REASONING
* DIS # I3: 2,5 => CTR => I3: 9
* PRF I3: 9 => SOL
* STA I3: 9
* CNT   2 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190308, absurd

Solution

position: 371259486956874132428136759213987564867541293594623871185392647649715328732468915 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 # B2: 1,6 => UNS
* INC # C2: 1,6 => UNS
* INC # C4: 1,6 => UNS
* INC # C5: 1,6 => UNS
* INC # B2: 2,5 => UNS
* INC # C2: 2,5 => UNS
* DIS # I3: 2,5 => CTR => I3: 9
* PRF # I3: 9 => SOL
* DIS # B6: 2,5 => CTR => B6: 6,9
* INC # B6: 6,9 => UNS
* INC # B9: 2,5 => UNS
* INC # D5: 1,6 => UNS
* INC # D5: 5,7 => UNS
* INC # F4: 1,6 => UNS
* PRF # F5: 1,6 => SOL
* INC # F5: 5,7 => UNS
* INC # B2: 1,6 => UNS
* INC # C2: 1,6 => UNS
* DIS # G6: 1,6 => CTR => G6: 8,9
* INC # G6: 8,9 => UNS
* DIS # I3: 2,5 => CTR => I3: 9
* PRF # I3: 9 => SOL
* INC # B2: 2,5 => UNS
* INC # C2: 2,5 => UNS
* INC # I3: 5,9 => UNS
* DIS # I3: 2 => CTR => I3: 5,9
* INC # A4: 2,8 => UNS
* INC # A4: 7 => UNS
* INC # D5: 5,6 => UNS
* INC # F5: 5,6 => UNS
* DIS # B6: 5,6 => CTR => B6: 2,9
* INC # B6: 2,9 => UNS
* INC # A6: 2,8 => UNS
* INC # A6: 5 => UNS
* DIS # H5: 6,8 => CTR => H5: 9
* PRF # H5: 9 => SOL
* PRF # G6: 6,8 => SOL
* INC # G6: 1,9 => UNS
* DIS # G6: 1,6 => CTR => G6: 8,9
* INC # G6: 8,9 => UNS
* DIS # C8: 3,5 => CTR => C8: 7,9
* INC # C8: 7,9 => UNS
* INC # B9: 3,5 => UNS
* INC # C9: 3,5 => UNS
* PRF # D7: 3,5 => SOL
* INC # D7: 4 => UNS
* INC # D8: 5,7 => UNS
* DIS # D9: 5,7 => CTR => D9: 3,4
* INC # D9: 3,4 => UNS
* DIS # C8: 5,7 => CTR => C8: 3,9
* INC # C8: 3,9 => UNS
* INC # F5: 5,7 => UNS
* PRF # F5: 1,6 => SOL
* PRF # G9: 3,9 => SOL
* INC # G9: 4 => UNS
* INC # C8: 3,9 => UNS
* DIS # C8: 5,7 => CTR => C8: 3,9
* INC # B9: 5,9 => UNS
* INC # C9: 5,9 => UNS
* INC # I3: 5,9 => UNS
* DIS # I3: 2 => CTR => I3: 5,9
* CNT  61 HDP CHAINS /  61 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 1,6 => UNS
* INC # C2: 1,6 => UNS
* INC # C4: 1,6 => UNS
* INC # C5: 1,6 => UNS
* INC # B2: 2,5 => UNS
* INC # C2: 2,5 => UNS
* DIS # I3: 2,5 => CTR => I3: 9
* PRF I3: 9 => SOL
* STA I3: 9
* CNT   8 HDP CHAINS /   7 HYP OPENED