Analysis of zz-www.sudokuoftheday.co.uk-20190122-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: ...3.4....5.8....3..........3.......9....8..68.4..91...8.....1....92.45.7....19.. initial

Autosolve

position: ...3.45...5.8....3.....5...53.......9....83.6864.391.5289..3617.1.927458745681932 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # A3: 1,6 => SOL
* DIS # E1: 1,6 => CTR => E1: 7,9
* PRF # A3: 1,4 => SOL
* DIS # A3: 3,6 => CTR => A3: 1,4
* PRF # E1: 1,9 => SOL
* PRF # C2: 7 => SOL
* DIS # I3: 1,9 => CTR => I3: 4
* PRF # I3: 4 => SOL
* PRF # E1: 1,9 => SOL
* PRF # H1: 2,7 => SOL
* DIS # H3: 2,7 => CTR => H3: 6,8
* PRF # C2: 2,7 => SOL
* DIS # C2: 6 => CTR => C2: 2,7
* PRF # G4: 2,7 => SOL
* PRF # I3: 4,9 => SOL
* DIS # I3: 1 => CTR => I3: 4,9
* PRF # H4: 2,7,8 => SOL
* PRF # C5: 2,7 => SOL
* DIS # D5: 2,7 => CTR => D5: 1,4,5
* DIS # B3: 2,7 => CTR => B3: 9
* DIS # D4: 2,7 => CTR => D4: 1,4
* DIS # D5: 2,7 => CTR => D5: 1,4,5
* DIS # D3: 1 => CTR => D3: 2,7
* PRF # H4: 2,7,8 => SOL
* PRF # I3: 4,9 => SOL
* DIS # I3: 1 => CTR => I3: 4,9
* PRF # G4: 2,7 => SOL
* DIS # H4: 2,7 => CTR => H4: 4,8,9
* PRF # H1: 2,7 => SOL
* DIS # H3: 2,7 => CTR => H3: 6,8
* DIS # A3: 3,6 => CTR => A3: 1,4
* PRF # A3: 1,4 => SOL
* PRF # C3: 3,6 => SOL
* DIS # C3: 2,7,8 => CTR => C3: 3,6
* PRF # D5: 1,2,7 => SOL
* DIS # E5: 1,7 => CTR => E5: 4,5
* CNT  36 HDP CHAINS /  64 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 # A3: 1,6 => SOL
* STA A3: 1,6
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...3.4....5.8....3..........3.......9....8..68.4..91...8.....1....92.45.7....19.. initial
...3.45...5.8....3.....5...53.......9....83.6864.391.5289..3617.1.927458745681932 autosolve
628394571457816293193275864531462789972158346864739125289543617316927458745681932 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A1: 1,6
A2: 1,4
E2: 1,9
F2: 2,6
I1: 1,9
G2: 2,7
H2: 4,9
B5: 2,7
F4: 2,6
D6: 2,7
I4: 4,9
H6: 2,7
A8: 3,6
C8: 3,6
D7: 4,5
E7: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I1,I3: 1.. / I1 = 1  =>  0 pairs (*) / I3 = 1  =>  0 pairs (X)
C4,C5: 1.. / C4 = 1  =>  0 pairs (*) / C5 = 1  =>  0 pairs (X)
A2,E2: 1.. / A2 = 1  =>  0 pairs (X) / E2 = 1  =>  0 pairs (_)
F2,D3: 2.. / F2 = 2  =>  0 pairs (X) / D3 = 2  =>  0 pairs (_)
D6,H6: 2.. / D6 = 2  =>  0 pairs (X) / H6 = 2  => 19 pairs (_)
F2,F4: 2.. / F2 = 2  =>  0 pairs (X) / F4 = 2  =>  0 pairs (_)
A3,C3: 3.. / A3 = 3  =>  0 pairs (X) / C3 = 3  =>  0 pairs (_)
A8,C8: 3.. / A8 = 3  =>  0 pairs (*) / C8 = 3  =>  0 pairs (X)
A3,A8: 3.. / A3 = 3  =>  0 pairs (X) / A8 = 3  =>  0 pairs (_)
C3,C8: 3.. / C3 = 3  =>  0 pairs (*) / C8 = 3  =>  0 pairs (X)
A2,A3: 4.. / A2 = 4  =>  0 pairs (*) / A3 = 4  =>  0 pairs (X)
H2,I3: 4.. / H2 = 4  =>  0 pairs (X) / I3 = 4  =>  0 pairs (_)
D7,E7: 4.. / D7 = 4  => 14 pairs (_) / E7 = 4  => 14 pairs (_)
A2,H2: 4.. / A2 = 4  =>  0 pairs (*) / H2 = 4  =>  0 pairs (X)
A3,I3: 4.. / A3 = 4  =>  0 pairs (X) / I3 = 4  =>  0 pairs (_)
I3,I4: 4.. / I3 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
D5,E5: 5.. / D5 = 5  => 14 pairs (_) / E5 = 5  => 14 pairs (_)
D7,E7: 5.. / D7 = 5  => 14 pairs (_) / E7 = 5  => 14 pairs (_)
D5,D7: 5.. / D5 = 5  => 14 pairs (_) / D7 = 5  => 14 pairs (_)
E5,E7: 5.. / E5 = 5  => 14 pairs (_) / E7 = 5  => 14 pairs (_)
H1,H3: 6.. / H1 = 6  =>  0 pairs (X) / H3 = 6  => 16 pairs (_)
E4,F4: 6.. / E4 = 6  =>  0 pairs (*) / F4 = 6  =>  0 pairs (X)
A8,C8: 6.. / A8 = 6  =>  0 pairs (X) / C8 = 6  =>  0 pairs (_)
C2,F2: 6.. / C2 = 6  =>  0 pairs (X) / F2 = 6  =>  0 pairs (_)
F2,F4: 6.. / F2 = 6  =>  0 pairs (*) / F4 = 6  =>  0 pairs (X)
C2,G2: 7.. / C2 = 7  =>  0 pairs (*) / G2 = 7  =>  0 pairs (X)
D6,H6: 7.. / D6 = 7  => 19 pairs (_) / H6 = 7  =>  0 pairs (X)
C1,C3: 8.. / C1 = 8  => 16 pairs (_) / C3 = 8  =>  0 pairs (X)
G4,H4: 8.. / G4 = 8  => 21 pairs (_) / H4 = 8  =>  0 pairs (*)
C1,H1: 8.. / C1 = 8  => 16 pairs (_) / H1 = 8  =>  0 pairs (X)
G3,G4: 8.. / G3 = 8  =>  0 pairs (*) / G4 = 8  =>  0 pairs (X)
B1,B3: 9.. / B1 = 9  =>  0 pairs (X) / B3 = 9  => 18 pairs (_)
H4,I4: 9.. / H4 = 9  =>  0 pairs (X) / I4 = 9  =>  0 pairs (_)
E2,H2: 9.. / E2 = 9  =>  0 pairs (X) / H2 = 9  =>  0 pairs (_)
H2,H4: 9.. / H2 = 9  =>  0 pairs (*) / H4 = 9  =>  0 pairs (X)
* DURATION: 0:00:42.011158  START: 03:07:30.786005  END: 03:08:12.797163 2019-05-01
* CP COUNT: (35)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A8,B5,C8,D6,D7,E2,E7,F2,F4,G2,H2,H6,I1,I4)
* ...3.45...5.8....3.....5...53.......9....83.6864.391.5289..3617.1.927458745681932
* PAIR A1: 1,6 BLK 1
A3: 1,6,3,4                              # reduction candidate for 1,6
A3: 1,6 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
A3: 3,4                                  # 17 pairs
* PAIR A1: 1,6 ROW 1
E1: 1,6,7,9                              # reduction candidate for 1,6
E1: 1,6 => CTR
* 6.83145.915.896.4349327586153..627949....8326864.391.5289..3617316927458745681932
E1: 7,9                                  # 17 pairs
* PAIR A2: 1,4 BLK 1
A3: 1,4,3,6                              # reduction candidate for 1,4
A3: 1,4 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
A3: 3,6 => CTR
* ...3.45..45.81..93.....5...53.......9....83.6864.391.5289..3617.1.927458745681932
* PAIR E2: 1,9 BLK 2
E1: 1,9,6,7                              # reduction candidate for 1,9
E1: 1,9 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
E1: 6,7                                  # 17 pairs
E3: 1,9,6,7                              # reduction candidate for 1,9
E3: 1,9                                  # 20 pairs
* PAIR F2: 2,6 ROW 2
C2: 2,6,7                                # reduction candidate for 2,6
C2: 7 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
C2: 2,6                                  # 18 pairs
* PAIR I1: 1,9 BLK 3
I3: 1,9,4                                # reduction candidate for 1,9
I3: 1,9 => CTR
* 6.83.45..15.896.434.32.5...53.....949....83.6864.391.5289..3617316927458745681932
I3: 4 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
* PAIR I1: 1,9 ROW 1
E1: 1,9,6,7                              # reduction candidate for 1,9
E1: 1,9 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
E1: 6,7                                  # 17 pairs
* PAIR G2: 2,7 BLK 3
H1: 2,7,6,8                              # reduction candidate for 2,7
H1: 2,7 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
H1: 6,8                                  # 19 pairs
G3: 2,7,8                                # reduction candidate for 2,7
G3: 2,7                                  # 21 pairs
H3: 2,7,6,8                              # reduction candidate for 2,7
H3: 2,7 => CTR
* ...3.456..5.8....3.....58..53.....899....8346864.391.5289..3617.1.927458745681932
H3: 6,8                                  # 17 pairs
* PAIR G2: 2,7 ROW 2
C2: 2,7,6                                # reduction candidate for 2,7
C2: 2,7 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
C2: 6 => CTR
* 1..3.45.94568.27.3.....5...53...6...9....83.6864.391.5289..3617613927458745681932
* PAIR G2: 2,7 COL G
G4: 2,7,8                                # reduction candidate for 2,7
G4: 2,7 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
G4: 8                                    # 21 pairs
* PAIR H2: 4,9 BLK 3
I3: 4,9,1                                # reduction candidate for 4,9
I3: 4,9 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
I3: 1 => CTR
* 6.83145.9.5.8...434.3..5..153.....949....83.6864.391.5289..3617316927458745681932
* PAIR H2: 4,9 COL H
H4: 4,9,2,7,8                            # reduction candidate for 4,9
H4: 2,7,8 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
H4: 4,9                                  # 26 pairs
* PAIR B5: 2,7 BLK 4
C4: 2,7,1                                # reduction candidate for 2,7
C4: 2,7                                  # 17 pairs
C5: 2,7,1                                # reduction candidate for 2,7
C5: 2,7 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
C5: 1                                    # 17 pairs
* PAIR B5: 2,7 ROW 5
D5: 2,7,1,4,5                            # reduction candidate for 2,7
D5: 2,7 => CTR
* ...3.45..45.81..93.....5..453.......9...58346864.391.5289543617.1.927458745681932
D5: 1,4,5                                # 16 pairs
H5: 2,7,4                                # reduction candidate for 2,7
H5: 2,7                                  # 26 pairs
* PAIR B5: 2,7 COL B
B1: 2,7,9                                # reduction candidate for 2,7
B1: 2,7                                  # 18 pairs
B3: 2,7,9                                # reduction candidate for 2,7
B3: 2,7 => CTR
* 692374581.578.6..3...2.5.6.53..62...92...83.6864739125289..3617316927458745681932
B3: 9                                    # 18 pairs
* PAIR D6: 2,7 BLK 5
D4: 2,7,1,4                              # reduction candidate for 2,7
D4: 2,7 => CTR
* ...3.45..15.8927434.31.5..953...6.949....83.6864.391.5289..3617316927458745681932
D4: 1,4                                  # 17 pairs
D5: 2,7,1,4,5                            # reduction candidate for 2,7
D5: 2,7 => CTR
* ...3.45..45.81..93.....5..453.......9...58346864.391.5289543617.1.927458745681932
D5: 1,4,5                                # 16 pairs
* PAIR D6: 2,7 COL D
D3: 2,7,1                                # reduction candidate for 2,7
D3: 1 => CTR
* ...3.45.11568.27.3...1.5...53...6...9....83.6864.391.5289..3617.1.927458745681932
D3: 2,7                                  # 18 pairs
* PAIR I4: 4,9 BLK 6
H4: 4,9,2,7,8                            # reduction candidate for 4,9
H4: 2,7,8 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
H4: 4,9                                  # 26 pairs
* PAIR I4: 4,9 COL I
I3: 4,9,1                                # reduction candidate for 4,9
I3: 4,9 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
I3: 1 => CTR
* 6.83145.9.5.8...434.3..5..153.....949....83.6864.391.5289..3617316927458745681932
* PAIR H6: 2,7 BLK 6
G4: 2,7,8                                # reduction candidate for 2,7
G4: 2,7 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
G4: 8                                    # 21 pairs
H4: 2,7,4,8,9                            # reduction candidate for 2,7
H4: 2,7 => CTR
* 6.83.45.145.816.931.32.578453..628799....8346864739125289..3617316927458745681932
H4: 4,8,9                                # 16 pairs
H5: 2,7,4                                # reduction candidate for 2,7
H5: 2,7                                  # 26 pairs
* PAIR H6: 2,7 COL H
H1: 2,7,6,8                              # reduction candidate for 2,7
H1: 2,7 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
H1: 6,8                                  # 19 pairs
H3: 2,7,6,8                              # reduction candidate for 2,7
H3: 2,7 => CTR
* ...3.456..5.8....3.....58..53.....899....8346864.391.5289..3617.1.927458745681932
H3: 6,8                                  # 17 pairs
* PAIR A8: 3,6 COL A
A3: 3,6,1,4                              # reduction candidate for 3,6
A3: 3,6 => CTR
* ...3.45..45.81..93.....5...53.......9....83.6864.391.5289..3617.1.927458745681932
A3: 1,4 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
* PAIR C8: 3,6 COL C
C3: 3,6,2,7,8                            # reduction candidate for 3,6
C3: 3,6 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
C3: 2,7,8 => CTR
* ...3.45...5.8....33....5..453......99....83.6864.391.5289..3617613927458745681932
* PAIR D7: 4,5 COL D
D5: 4,5,1,2,7                            # reduction candidate for 4,5
D5: 1,2,7 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
D5: 4,5                                  # 17 pairs
* PAIR E7: 4,5 COL E
E5: 4,5,1,7                              # reduction candidate for 4,5
E5: 1,7 => CTR
* ...3.45.145681..93.....5..453.146..99.1578346864239175289453617.1.927458745681932
E5: 4,5                                  # 17 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190122-absurd-base-pr-000.dot
* REASONING
* PRF # A3: 1,6 => SOL
* DIS # E1: 1,6 => CTR => E1: 7,9
* PRF # A3: 1,4 => SOL
* DIS # A3: 3,6 => CTR => A3: 1,4
* PRF # E1: 1,9 => SOL
* PRF # C2: 7 => SOL
* DIS # I3: 1,9 => CTR => I3: 4
* PRF # I3: 4 => SOL
* PRF # E1: 1,9 => SOL
* PRF # H1: 2,7 => SOL
* DIS # H3: 2,7 => CTR => H3: 6,8
* PRF # C2: 2,7 => SOL
* DIS # C2: 6 => CTR => C2: 2,7
* PRF # G4: 2,7 => SOL
* PRF # I3: 4,9 => SOL
* DIS # I3: 1 => CTR => I3: 4,9
* PRF # H4: 2,7,8 => SOL
* PRF # C5: 2,7 => SOL
* DIS # D5: 2,7 => CTR => D5: 1,4,5
* DIS # B3: 2,7 => CTR => B3: 9
* DIS # D4: 2,7 => CTR => D4: 1,4
* DIS # D5: 2,7 => CTR => D5: 1,4,5
* DIS # D3: 1 => CTR => D3: 2,7
* PRF # H4: 2,7,8 => SOL
* PRF # I3: 4,9 => SOL
* DIS # I3: 1 => CTR => I3: 4,9
* PRF # G4: 2,7 => SOL
* DIS # H4: 2,7 => CTR => H4: 4,8,9
* PRF # H1: 2,7 => SOL
* DIS # H3: 2,7 => CTR => H3: 6,8
* DIS # A3: 3,6 => CTR => A3: 1,4
* PRF # A3: 1,4 => SOL
* PRF # C3: 3,6 => SOL
* DIS # C3: 2,7,8 => CTR => C3: 3,6
* PRF # D5: 1,2,7 => SOL
* DIS # E5: 1,7 => CTR => E5: 4,5
* CNT  36 HDP CHAINS /  64 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,A8,B5,C8,D6,D7,E2,E7,F2,F4,G2,H2,H6,I1,I4)
* ...3.45...5.8....3.....5...53.......9....83.6864.391.5289..3617.1.927458745681932
* PAIR A1: 1,6 BLK 1
A3: 1,6,3,4                              # reduction candidate for 1,6
A3: 1,6 => SOLVED
* 628394571457816293193275864531462789972158346864739125289543617316927458745681932
* DURATION: 0:00:01.573272  START: 03:08:59.248514  END: 03:09:00.821786 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190122-absurd-base-pr-001.dot
* REASONING
* PRF # A3: 1,6 => SOL
* STA A3: 1,6
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190122, absurd

Solution

position: 628394571457816293193275864531462789972158346864739125289543617316927458745681932 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:

* PRF # A3: 1,6 => SOL
* INC # A3: 3,4 => UNS
* DIS # E1: 1,6 => CTR => E1: 7,9
* INC # E1: 7,9 => UNS
* PRF # A3: 1,4 => SOL
* DIS # A3: 3,6 => CTR => A3: 1,4
* PRF # E1: 1,9 => SOL
* INC # E1: 6,7 => UNS
* INC # E3: 1,9 => UNS
* INC # C2: 2,6 => UNS
* PRF # C2: 7 => SOL
* DIS # I3: 1,9 => CTR => I3: 4
* PRF # I3: 4 => SOL
* PRF # E1: 1,9 => SOL
* INC # E1: 6,7 => UNS
* PRF # H1: 2,7 => SOL
* INC # H1: 6,8 => UNS
* INC # G3: 2,7 => UNS
* DIS # H3: 2,7 => CTR => H3: 6,8
* INC # H3: 6,8 => UNS
* PRF # C2: 2,7 => SOL
* DIS # C2: 6 => CTR => C2: 2,7
* PRF # G4: 2,7 => SOL
* INC # G4: 8 => UNS
* PRF # I3: 4,9 => SOL
* DIS # I3: 1 => CTR => I3: 4,9
* INC # H4: 4,9 => UNS
* PRF # H4: 2,7,8 => SOL
* INC # C4: 2,7 => UNS
* PRF # C5: 2,7 => SOL
* INC # C5: 1 => UNS
* DIS # D5: 2,7 => CTR => D5: 1,4,5
* INC # D5: 1,4,5 => UNS
* INC # H5: 2,7 => UNS
* INC # B1: 2,7 => UNS
* DIS # B3: 2,7 => CTR => B3: 9
* INC # B3: 9 => UNS
* DIS # D4: 2,7 => CTR => D4: 1,4
* INC # D4: 1,4 => UNS
* DIS # D5: 2,7 => CTR => D5: 1,4,5
* INC # D5: 1,4,5 => UNS
* INC # D3: 2,7 => UNS
* DIS # D3: 1 => CTR => D3: 2,7
* INC # H4: 4,9 => UNS
* PRF # H4: 2,7,8 => SOL
* PRF # I3: 4,9 => SOL
* DIS # I3: 1 => CTR => I3: 4,9
* PRF # G4: 2,7 => SOL
* INC # G4: 8 => UNS
* DIS # H4: 2,7 => CTR => H4: 4,8,9
* INC # H4: 4,8,9 => UNS
* INC # H5: 2,7 => UNS
* PRF # H1: 2,7 => SOL
* INC # H1: 6,8 => UNS
* DIS # H3: 2,7 => CTR => H3: 6,8
* INC # H3: 6,8 => UNS
* DIS # A3: 3,6 => CTR => A3: 1,4
* PRF # A3: 1,4 => SOL
* PRF # C3: 3,6 => SOL
* DIS # C3: 2,7,8 => CTR => C3: 3,6
* INC # D5: 4,5 => UNS
* PRF # D5: 1,2,7 => SOL
* INC # E5: 4,5 => UNS
* DIS # E5: 1,7 => CTR => E5: 4,5
* CNT  64 HDP CHAINS /  64 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # A3: 1,6 => SOL
* STA A3: 1,6
* CNT   1 HDP CHAINS /   1 HYP OPENED