Analysis of zz-www.sudokuoftheday.co.uk-20190228-absurd-base.sdk

Contents

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

level: medium

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

position: 7..923.....8.7.......6.........4....6.1..2...95.....8.8...3.2.7..4......27...4..5 initial

Autosolve

position: 7..923.....847....4..6.8...38..4....641..2...95.....8.8...3.247..42.7...27...4..5 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # C7: 9 => SOL
* DIS # G3: 3,9 => CTR => G3: 1,5,7
* DIS # H3: 3,9 => CTR => H3: 1,2,5,7
* PRF # C9: 6 => SOL
* PRF # E5: 5,9 => SOL
* DIS # F7: 5,9 => CTR => F7: 6
* PRF # F7: 6 => SOL
* CNT   7 HDP CHAINS /  42 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 # C7: 9 => SOL
* STA C7: 9
* CNT   1 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

7..923.....8.7.......6.........4....6.1..2...95.....8.8...3.2.7..4......27...4..5 initial
7..923.....847....4..6.8...38..4....641..2...95.....8.8...3.247..42.7...27...4..5 autosolve
765923814198475326423618579382749651641852793957361482819536247534297168276184935 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
B1: 1,6
C1: 5,6
A2: 1,5
C3: 3,9
F2: 1,5
E3: 1,5
G1: 4,8
H1: 1,5
I1: 4,8
C4: 2,7
C6: 2,7
D4: 5,7
F4: 5,9
D6: 3,7
E6: 1,6
F6: 1,6
I5: 3,9
A8: 1,5
D7: 1,5
D9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,A2: 1.. / B1 = 1  =>  0 pairs (X) / A2 = 1  =>  0 pairs (_)
F2,E3: 1.. / F2 = 1  =>  0 pairs (X) / E3 = 1  =>  0 pairs (_)
E6,F6: 1.. / E6 = 1  =>  0 pairs (X) / F6 = 1  =>  0 pairs (_)
D7,D9: 1.. / D7 = 1  => 21 pairs (_) / D9 = 1  =>  0 pairs (*)
B1,H1: 1.. / B1 = 1  =>  0 pairs (X) / H1 = 1  =>  0 pairs (_)
A2,F2: 1.. / A2 = 1  =>  0 pairs (*) / F2 = 1  =>  0 pairs (X)
B7,D7: 1.. / B7 = 1  =>  0 pairs (*) / D7 = 1  =>  0 pairs (X)
A2,A8: 1.. / A2 = 1  =>  0 pairs (*) / A8 = 1  =>  0 pairs (X)
E3,E6: 1.. / E3 = 1  =>  0 pairs (*) / E6 = 1  =>  0 pairs (X)
F2,F6: 1.. / F2 = 1  =>  0 pairs (X) / F6 = 1  =>  0 pairs (_)
B2,B3: 2.. / B2 = 2  => 22 pairs (_) / B3 = 2  => 21 pairs (_)
C4,C6: 2.. / C4 = 2  => 15 pairs (_) / C6 = 2  => 21 pairs (_)
C6,I6: 2.. / C6 = 2  => 21 pairs (_) / I6 = 2  => 15 pairs (_)
D5,D6: 3.. / D5 = 3  => 22 pairs (_) / D6 = 3  => 21 pairs (_)
B8,C9: 3.. / B8 = 3  => 23 pairs (_) / C9 = 3  => 22 pairs (_)
C3,C9: 3.. / C3 = 3  => 23 pairs (_) / C9 = 3  => 22 pairs (_)
G1,I1: 4.. / G1 = 4  => 19 pairs (_) / I1 = 4  => 19 pairs (_)
G6,I6: 4.. / G6 = 4  => 19 pairs (_) / I6 = 4  => 19 pairs (_)
G1,G6: 4.. / G1 = 4  => 19 pairs (_) / G6 = 4  => 19 pairs (_)
I1,I6: 4.. / I1 = 4  => 19 pairs (_) / I6 = 4  => 19 pairs (_)
C1,A2: 5.. / C1 = 5  =>  0 pairs (*) / A2 = 5  =>  0 pairs (X)
F2,E3: 5.. / F2 = 5  =>  0 pairs (*) / E3 = 5  =>  0 pairs (X)
C7,A8: 5.. / C7 = 5  =>  0 pairs (X) / A8 = 5  =>  0 pairs (_)
C1,H1: 5.. / C1 = 5  =>  0 pairs (*) / H1 = 5  =>  0 pairs (X)
A2,F2: 5.. / A2 = 5  =>  0 pairs (X) / F2 = 5  =>  0 pairs (_)
A8,E8: 5.. / A8 = 5  =>  0 pairs (*) / E8 = 5  =>  0 pairs (X)
A2,A8: 5.. / A2 = 5  =>  0 pairs (X) / A8 = 5  =>  0 pairs (_)
C1,C7: 5.. / C1 = 5  =>  0 pairs (*) / C7 = 5  =>  0 pairs (X)
B1,C1: 6.. / B1 = 6  =>  0 pairs (*) / C1 = 6  =>  0 pairs (X)
E6,F6: 6.. / E6 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
F6,F7: 6.. / F6 = 6  =>  0 pairs (X) / F7 = 6  =>  0 pairs (_)
G3,H3: 7.. / G3 = 7  => 21 pairs (_) / H3 = 7  => 20 pairs (_)
C4,C6: 7.. / C4 = 7  => 21 pairs (_) / C6 = 7  => 15 pairs (_)
G1,I1: 8.. / G1 = 8  => 19 pairs (_) / I1 = 8  => 19 pairs (_)
D5,E5: 8.. / D5 = 8  =>  0 pairs (*) / E5 = 8  =>  0 pairs (X)
D5,D9: 8.. / D5 = 8  =>  0 pairs (*) / D9 = 8  =>  0 pairs (X)
I1,I8: 8.. / I1 = 8  => 19 pairs (_) / I8 = 8  => 19 pairs (_)
F4,E5: 9.. / F4 = 9  => 22 pairs (_) / E5 = 9  =>  0 pairs (X)
F4,F7: 9.. / F4 = 9  => 22 pairs (_) / F7 = 9  =>  0 pairs (X)
* DURATION: 0:01:03.285691  START: 04:06:06.699511  END: 04:07:09.985202 2019-05-01
* CP COUNT: (39)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,C1,C3,C4,C6,D4,D6,D7,D9,E3,E6,F2,F4,F6,G1,H1,I1,I5)
* 7..923.....847....4..6.8...38..4....641..2...95.....8.8...3.247..42.7...27...4..5
* PAIR B1: 1,6 COL B
B7: 1,6,9                                # reduction candidate for 1,6
B7: 1,6                                  # 22 pairs
B8: 1,6,3,9                              # reduction candidate for 1,6
B8: 1,6                                  # 22 pairs
* PAIR C1: 5,6 COL C
C7: 5,6,9                                # reduction candidate for 5,6
C7: 9 => SOLVED
* 765923814198475326423618579382749651641852793957361482819536247534297168276184935
C7: 5,6                                  # 22 pairs
* PAIR C3: 3,9 BLK 1
B2: 3,9,2                                # reduction candidate for 3,9
B2: 3,9                                  # 21 pairs
B3: 3,9,2                                # reduction candidate for 3,9
B3: 3,9                                  # 22 pairs
* PAIR C3: 3,9 ROW 3
G3: 3,9,1,5,7                            # reduction candidate for 3,9
G3: 3,9 => CTR
* 7..923.5.5.8471...4..658.7138..4....641..2...95..16.8.8.51392471.42.7...27.864..5
G3: 1,5,7                                # 20 pairs
H3: 3,9,1,2,5,7                          # reduction candidate for 3,9
H3: 3,9 => CTR
* 7..923.5.5.8471...4..6587.138..4....641..2...95..16.8.8.51392471.42.7...27.864..5
H3: 1,2,5,7                              # 20 pairs
I3: 3,9,1,2                              # reduction candidate for 3,9
I3: 3,9                                  # 24 pairs
* PAIR C3: 3,9 COL C
C9: 3,9,6                                # reduction candidate for 3,9
C9: 6 => SOLVED
* 765923814198475326423618579382749651641852793957361482819536247534297168276184935
C9: 3,9                                  # 22 pairs
* PAIR E3: 1,5 ROW 3
G3: 1,5,3,7,9                            # reduction candidate for 1,5
G3: 1,5                                  # 21 pairs
H3: 1,5,2,3,7,9                          # reduction candidate for 1,5
H3: 1,5                                  # 22 pairs
* PAIR H1: 1,5 BLK 3
G3: 1,5,3,7,9                            # reduction candidate for 1,5
G3: 1,5                                  # 21 pairs
H3: 1,5,2,3,7,9                          # reduction candidate for 1,5
H3: 1,5                                  # 22 pairs
* PAIR H1: 1,5 COL H
H4: 1,5,2,6,7,9                          # reduction candidate for 1,5
H4: 1,5                                  # 21 pairs
H4: 2,6,7,9                              # 20 pairs
* PAIR C4: 2,7 ROW 4
H4: 2,7,1,5,6,9                          # reduction candidate for 2,7
H4: 2,7                                  # 24 pairs
H4: 1,5,6,9                              # 20 pairs
* PAIR D4: 5,7 BLK 5
D5: 5,7,3,8                              # reduction candidate for 5,7
D5: 5,7                                  # 23 pairs
D5: 3,8                                  # 22 pairs
* PAIR D4: 5,7 ROW 4
G4: 5,7,1,6,9                            # reduction candidate for 5,7
G4: 5,7                                  # 20 pairs
H4: 5,7,1,2,6,9                          # reduction candidate for 5,7
H4: 5,7                                  # 23 pairs
* PAIR F4: 5,9 BLK 5
E5: 5,9,8                                # reduction candidate for 5,9
E5: 5,9 => SOLVED
* 765923814198475326423618579382749651641852793957361482819536247534297168276184935
E5: 8                                    # 21 pairs
* PAIR F4: 5,9 ROW 4
G4: 5,9,1,6,7                            # reduction candidate for 5,9
G4: 5,9                                  # 18 pairs
H4: 5,9,1,2,6,7                          # reduction candidate for 5,9
H4: 5,9                                  # 20 pairs
* PAIR F4: 5,9 COL F
F7: 5,9,6                                # reduction candidate for 5,9
F7: 5,9 => CTR
* 7..923.....8471...4..658...38..4....641..2...95..16.8.8...3.247..42.7...27...4..5
F7: 6 => SOLVED
* 765923814198475326423618579382749651641852793957361482819536247534297168276184935
* PAIR D6: 3,7 BLK 5
D5: 3,7,5,8                              # reduction candidate for 3,7
D5: 3,7                                  # 21 pairs
D5: 5,8                                  # 15 pairs
* PAIR D6: 3,7 ROW 6
G6: 3,7,4                                # reduction candidate for 3,7
G6: 4                                    # 19 pairs
G6: 3,7                                  # 19 pairs
* PAIR I5: 3,9 BLK 6
G5: 3,9,5,7                              # reduction candidate for 3,9
G5: 3,9                                  # 25 pairs
H5: 3,9,5,7                              # reduction candidate for 3,9
H5: 3,9                                  # 25 pairs
* PAIR I5: 3,9 COL I
I2: 3,9,2,6                              # reduction candidate for 3,9
I2: 3,9                                  # 23 pairs
I3: 3,9,1,2                              # reduction candidate for 3,9
I3: 3,9                                  # 24 pairs
I8: 3,9,1,6,8                            # reduction candidate for 3,9
I8: 3,9                                  # 22 pairs
* PAIR D9: 1,8 ROW 9
G9: 1,8,3,6,9                            # reduction candidate for 1,8
G9: 1,8                                  # 22 pairs
G9: 3,6,9                                # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190228-absurd-base-pr-000.dot
* REASONING
* PRF # C7: 9 => SOL
* DIS # G3: 3,9 => CTR => G3: 1,5,7
* DIS # H3: 3,9 => CTR => H3: 1,2,5,7
* PRF # C9: 6 => SOL
* PRF # E5: 5,9 => SOL
* DIS # F7: 5,9 => CTR => F7: 6
* PRF # F7: 6 => SOL
* CNT   7 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B1,C1,C3,C4,C6,D4,D6,D7,D9,E3,E6,F2,F4,F6,G1,H1,I1,I5)
* 7..923.....847....4..6.8...38..4....641..2...95.....8.8...3.247..42.7...27...4..5
* PAIR B1: 1,6 COL B
B7: 1,6,9                                # reduction candidate for 1,6
B7: 1,6                                  # 22 pairs
B8: 1,6,3,9                              # reduction candidate for 1,6
B8: 1,6                                  # 22 pairs
* PAIR C1: 5,6 COL C
C7: 5,6,9                                # reduction candidate for 5,6
C7: 9 => SOLVED
* 765923814198475326423618579382749651641852793957361482819536247534297168276184935
* DURATION: 0:00:04.535706  START: 04:07:47.171658  END: 04:07:51.707364 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190228-absurd-base-pr-001.dot
* REASONING
* PRF # C7: 9 => SOL
* STA C7: 9
* CNT   1 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190228, absurd

Solution

position: 765923814198475326423618579382749651641852793957361482819536247534297168276184935 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 # B7: 1,6 => UNS
* INC # B8: 1,6 => UNS
* INC # C7: 5,6 => UNS
* PRF # C7: 9 => SOL
* INC # B2: 3,9 => UNS
* INC # B3: 3,9 => UNS
* DIS # G3: 3,9 => CTR => G3: 1,5,7
* INC # G3: 1,5,7 => UNS
* DIS # H3: 3,9 => CTR => H3: 1,2,5,7
* INC # H3: 1,2,5,7 => UNS
* INC # I3: 3,9 => UNS
* INC # C9: 3,9 => UNS
* PRF # C9: 6 => SOL
* INC # G3: 1,5 => UNS
* INC # H3: 1,5 => UNS
* INC # G3: 1,5 => UNS
* INC # H3: 1,5 => UNS
* INC # H4: 1,5 => UNS
* INC # H4: 2,6,7,9 => UNS
* INC # H4: 2,7 => UNS
* INC # H4: 1,5,6,9 => UNS
* INC # D5: 5,7 => UNS
* INC # D5: 3,8 => UNS
* INC # G4: 5,7 => UNS
* INC # H4: 5,7 => UNS
* PRF # E5: 5,9 => SOL
* INC # E5: 8 => UNS
* INC # G4: 5,9 => UNS
* INC # H4: 5,9 => UNS
* DIS # F7: 5,9 => CTR => F7: 6
* PRF # F7: 6 => SOL
* INC # D5: 3,7 => UNS
* INC # D5: 5,8 => UNS
* INC # G6: 3,7 => UNS
* INC # G6: 4 => UNS
* INC # G5: 3,9 => UNS
* INC # H5: 3,9 => UNS
* INC # I2: 3,9 => UNS
* INC # I3: 3,9 => UNS
* INC # I8: 3,9 => UNS
* INC # G9: 1,8 => UNS
* INC # G9: 3,6,9 => UNS
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B7: 1,6 => UNS
* INC # B8: 1,6 => UNS
* INC # C7: 5,6 => UNS
* PRF # C7: 9 => SOL
* STA C7: 9
* CNT   4 HDP CHAINS /   4 HYP OPENED