Analysis of zz-www.sudokuoftheday.co.uk-20190111-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: ..318....7.5...6......2..51.4.91....5.2...7..........4.69...2.....3...8.........7 initial

Autosolve

position: 6231854797154..628984.2.351.4.91.5.2592...71.......894.69...2.....3...8.........7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D6: 6,7 => CTR => D6: 2,5
* DIS # F6: 6,7 => CTR => F6: 2,3
* DIS # A9: 1,3 => CTR => A9: 2,4,8
* PRF # F6: 3,7 => SOL
* DIS # F5: 3,4 => CTR => F5: 6,8
* DIS # D9: 6,8 => CTR => D9: 2,5
* DIS # F4: 3,6 => CTR => F4: 7
* DIS # E5: 3,6 => CTR => E5: 4
* DIS # F5: 3,6 => CTR => F5: 4,8
* DIS # C6: 1,7 => CTR => C6: 6
* DIS # A7: 1,8 => CTR => A7: 3,4
* PRF # A9: 1,8 => SOL
* DIS # F9: 1,8 => CTR => F9: 2,4,6,9
* DIS # H9: 6 => CTR => H9: 3,4
* DIS # A7: 1,8 => CTR => A7: 3,4
* DIS # F8: 1,9 => CTR => F8: 2,4,6
* DIS # E8: 5,6 => CTR => E8: 4,9
* CNT  17 HDP CHAINS /  43 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 # D6: 6,7 => CTR => D6: 2,5
* DIS D6: 2,5 # F6: 6,7 => CTR => F6: 2,3
* DIS D6: 2,5 + F6: 2,3 # F4: 3 => CTR => F4: 6,7
* PRF D6: 2,5 + F6: 2,3 + F4: 6,7 # A9: 3,8 => SOL
* STA D6: 2,5 + F6: 2,3 + F4: 6,7 + A9: 3,8
* CNT   4 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

..318....7.5...6......2..51.4.91....5.2...7..........4.69...2.....3...8.........7 initial
6231854797154..628984.2.351.4.91.5.2592...71.......894.69...2.....3...8.........7 autosolve
623185479715439628984726351348917562592648713176253894469871235257394186831562947 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
E2: 3,9
F2: 3,9
D3: 6,7
F3: 6,7
A4: 3,8
A6: 1,3
B6: 3,7
D5: 6,8
H4: 3,6
I5: 3,6
B8: 5,7
C8: 1,7
B9: 3,5
C9: 1,8
H7: 3,4
I7: 3,5
G8: 1,9
I8: 5,6
G9: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A6,C6: 1.. / A6 = 1  => 20 pairs (_) / C6 = 1  =>  0 pairs (X)
G8,G9: 1.. / G8 = 1  =>  0 pairs (*) / G9 = 1  =>  0 pairs (X)
A7,F7: 1.. / A7 = 1  =>  0 pairs (X) / F7 = 1  => 19 pairs (_)
D6,F6: 2.. / D6 = 2  =>  0 pairs (*) / F6 = 2  =>  0 pairs (X)
A8,A9: 2.. / A8 = 2  => 20 pairs (_) / A9 = 2  =>  0 pairs (X)
A8,F8: 2.. / A8 = 2  => 20 pairs (_) / F8 = 2  =>  0 pairs (X)
D6,D9: 2.. / D6 = 2  =>  0 pairs (*) / D9 = 2  =>  0 pairs (X)
E2,F2: 3.. / E2 = 3  => 18 pairs (_) / F2 = 3  => 23 pairs (_)
H4,I5: 3.. / H4 = 3  =>  0 pairs (X) / I5 = 3  => 23 pairs (_)
B6,B9: 3.. / B6 = 3  =>  0 pairs (X) / B9 = 3  =>  0 pairs (_)
I5,I7: 3.. / I5 = 3  => 23 pairs (_) / I7 = 3  =>  0 pairs (X)
E5,F5: 4.. / E5 = 4  => 22 pairs (_) / F5 = 4  =>  0 pairs (X)
H7,H9: 4.. / H7 = 4  => 22 pairs (_) / H9 = 4  => 22 pairs (_)
D6,E6: 5.. / D6 = 5  => 21 pairs (_) / E6 = 5  => 20 pairs (_)
B8,B9: 5.. / B8 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
I7,I8: 5.. / I7 = 5  => 23 pairs (_) / I8 = 5  =>  0 pairs (X)
D3,F3: 6.. / D3 = 6  =>  0 pairs (X) / F3 = 6  => 19 pairs (_)
C4,C6: 6.. / C4 = 6  =>  0 pairs (X) / C6 = 6  => 20 pairs (_)
H4,I5: 6.. / H4 = 6  => 23 pairs (_) / I5 = 6  =>  0 pairs (X)
I8,H9: 6.. / I8 = 6  => 23 pairs (_) / H9 = 6  =>  0 pairs (X)
H4,H9: 6.. / H4 = 6  => 23 pairs (_) / H9 = 6  =>  0 pairs (X)
I5,I8: 6.. / I5 = 6  =>  0 pairs (X) / I8 = 6  => 23 pairs (_)
D3,F3: 7.. / D3 = 7  => 19 pairs (_) / F3 = 7  =>  0 pairs (X)
B8,C8: 7.. / B8 = 7  =>  0 pairs (X) / C8 = 7  =>  0 pairs (_)
C4,F4: 7.. / C4 = 7  =>  0 pairs (X) / F4 = 7  => 20 pairs (_)
B6,B8: 7.. / B6 = 7  =>  0 pairs (*) / B8 = 7  =>  0 pairs (X)
E6,E7: 7.. / E6 = 7  =>  0 pairs (X) / E7 = 7  => 20 pairs (_)
A4,C4: 8.. / A4 = 8  => 18 pairs (_) / C4 = 8  =>  0 pairs (*)
D5,F5: 8.. / D5 = 8  =>  0 pairs (X) / F5 = 8  => 21 pairs (_)
C4,C9: 8.. / C4 = 8  =>  0 pairs (*) / C9 = 8  =>  0 pairs (X)
E2,F2: 9.. / E2 = 9  => 23 pairs (_) / F2 = 9  => 18 pairs (_)
G8,G9: 9.. / G8 = 9  => 16 pairs (_) / G9 = 9  =>  0 pairs (*)
* DURATION: 0:00:34.148890  START: 02:51:55.446579  END: 02:52:29.595469 2019-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,B8,B9,C8,C9,D3,D5,E2,F2,F3,G8,G9,H4,H7,I5,I7,I8)
* 6231854797154..628984.2.351.4.91.5.2592...71.......894.69...2.....3...8.........7
* PAIR D3: 6,7 COL D
D6: 6,7,2,5                              # reduction candidate for 6,7
D6: 6,7 => CTR
* 6231854797154..628984.2.351.4.91.5325928..716.3..52894.6957.24327.3...85.5.2...67
D6: 2,5                                  # 20 pairs
* PAIR F3: 6,7 COL F
F4: 6,7,3                                # reduction candidate for 6,7
F4: 6,7                                  # 21 pairs
F6: 6,7,2,3                              # reduction candidate for 6,7
F6: 6,7 => CTR
* 6231854797154..628984726351.4.91.5.2592...71...6257894.69.7.2...713..985.586..1.7
F6: 2,3                                  # 20 pairs
* PAIR A4: 3,8 COL A
A7: 3,8,1,4                              # reduction candidate for 3,8
A7: 3,8                                  # 22 pairs
A9: 3,8,1,2,4                            # reduction candidate for 3,8
A9: 3,8                                  # 18 pairs
* PAIR A6: 1,3 COL A
A7: 1,3,4,8                              # reduction candidate for 1,3
A7: 1,3                                  # 21 pairs
A9: 1,3,2,4,8                            # reduction candidate for 1,3
A9: 1,3 => CTR
* 6231854797154..628984.2.35184.913562592..8713..6...8944698712352.13.4986358...147
A9: 2,4,8                                # 19 pairs
* PAIR B6: 3,7 ROW 6
E6: 3,7,5,6                              # reduction candidate for 3,7
E6: 3,7                                  # 22 pairs
F6: 3,7,2,6                              # reduction candidate for 3,7
F6: 3,7 => SOLVED
* 623185479715439628984726351348917562592648713176253894469871235257394186831562947
F6: 2,6                                  # 20 pairs
* PAIR D5: 6,8 BLK 5
F5: 6,8,3,4                              # reduction candidate for 6,8
F5: 3,4 => CTR
* 6231854797154..628984.2.351.4.91.5.25928..71..7....894.69.7.243.573...86.3......7
F5: 6,8                                  # 21 pairs
* PAIR D5: 6,8 COL D
D9: 6,8,2,5                              # reduction candidate for 6,8
D9: 6,8 => CTR
* 6231854797154..628984726351.469175325926..71....25.894.6957.2.3...3...85.5.....67
D9: 2,5                                  # 20 pairs
* PAIR H4: 3,6 ROW 4
F4: 3,6,7                                # reduction candidate for 3,6
F4: 3,6 => CTR
* 6231854797154..628984.2.35184791.5.2592..871.136...894.698712.5.7135.98..58...1.7
F4: 7                                    # 20 pairs
* PAIR H4: 3,6 COL H
H9: 3,6,4                                # reduction candidate for 3,6
H9: 4                                    # 22 pairs
H9: 3,6                                  # 22 pairs
* PAIR I5: 3,6 ROW 5
E5: 3,6,4                                # reduction candidate for 3,6
E5: 3,6 => CTR
* 6231854797154..628984.2.351.4.91.5.25928.471..7....894.69.7.243.573...86.3......7
E5: 4                                    # 22 pairs
F5: 3,6,4,8                              # reduction candidate for 3,6
F5: 3,6 => CTR
* 6231854797154..628984.2.351.4.91.5.259284.71.......894.69...2.....3...8.........7
F5: 4,8                                  # 20 pairs
* PAIR C8: 1,7 COL C
C6: 1,7,6                                # reduction candidate for 1,7
C6: 1,7 => CTR
* 6231854797154..6289847263518469175325928..716.37652894169.7.243...3...85.58....67
C6: 6                                    # 20 pairs
* PAIR C9: 1,8 BLK 7
A7: 1,8,3,4                              # reduction candidate for 1,8
A7: 1,8 => CTR
* 6231854797154..628984726351.4.917562592...713.76...894.69.74235457392186231..8.47
A7: 3,4                                  # 21 pairs
A9: 1,8,2,3,4                            # reduction candidate for 1,8
A9: 1,8 => SOLVED
* 623185479715439628984726351348917562592648713176253894469871235257394186831562947
A9: 2,3,4                                # 19 pairs
* PAIR C9: 1,8 ROW 9
F9: 1,8,2,4,6,9                          # reduction candidate for 1,8
F9: 1,8 => CTR
* 6231854797154..628984726351.4.917562592...713.76...894.69.7.235.573..186231..8947
F9: 2,4,6,9                              # 19 pairs
* PAIR H7: 3,4 BLK 9
H9: 3,4,6                                # reduction candidate for 3,4
H9: 6 => CTR
* 6231854797154..628984.2.351.4.91.532592...716.3....894.69...243.713..985358....67
H9: 3,4                                  # 23 pairs
* PAIR H7: 3,4 ROW 7
A7: 3,4,1,8                              # reduction candidate for 3,4
A7: 1,8 => CTR
* 6231854797154..628984726351.4.917562592...713.76...894.69.74235457392186231..8.47
A7: 3,4                                  # 21 pairs
* PAIR G8: 1,9 ROW 8
F8: 1,9,2,4,6                            # reduction candidate for 1,9
F8: 1,9 => CTR
* 623185479715493628984.2.351348917562592864713176.328944697..2.525734..86.31...947
F8: 2,4,6                                # 19 pairs
* PAIR I8: 5,6 ROW 8
E8: 5,6,4,9                              # reduction candidate for 5,6
E8: 5,6 => CTR
* 6231854797154..628984.2.35184.91.5.2592..871.13....894.698712.5.7135.986.58...1.7
E8: 4,9                                  # 20 pairs
* PAIR G9: 1,9 ROW 9
F9: 1,9,2,4,6,8                          # reduction candidate for 1,9
F9: 2,4,6,8                              # 19 pairs
F9: 1,9                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190111-absurd-base-pr-000.dot
* REASONING
* DIS # D6: 6,7 => CTR => D6: 2,5
* DIS # F6: 6,7 => CTR => F6: 2,3
* DIS # A9: 1,3 => CTR => A9: 2,4,8
* PRF # F6: 3,7 => SOL
* DIS # F5: 3,4 => CTR => F5: 6,8
* DIS # D9: 6,8 => CTR => D9: 2,5
* DIS # F4: 3,6 => CTR => F4: 7
* DIS # E5: 3,6 => CTR => E5: 4
* DIS # F5: 3,6 => CTR => F5: 4,8
* DIS # C6: 1,7 => CTR => C6: 6
* DIS # A7: 1,8 => CTR => A7: 3,4
* PRF # A9: 1,8 => SOL
* DIS # F9: 1,8 => CTR => F9: 2,4,6,9
* DIS # H9: 6 => CTR => H9: 3,4
* DIS # A7: 1,8 => CTR => A7: 3,4
* DIS # F8: 1,9 => CTR => F8: 2,4,6
* DIS # E8: 5,6 => CTR => E8: 4,9
* CNT  17 HDP CHAINS /  43 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B6,B8,B9,C8,C9,D3,D5,E2,F2,F3,G8,G9,H4,H7,I5,I7,I8)
* 6231854797154..628984.2.351.4.91.5.2592...71.......894.69...2.....3...8.........7
* PAIR D3: 6,7 COL D
D6: 6,7,2,5                              # reduction candidate for 6,7
D6: 6,7 => CTR
* 6231854797154..628984.2.351.4.91.5325928..716.3..52894.6957.24327.3...85.5.2...67
* PAIR RESTART
* PAIR F3: 6,7 COL F
F4: 6,7,3                                # reduction candidate for 6,7
F4: 6,7                                  # 22 pairs
F6: 6,7,2,3                              # reduction candidate for 6,7
F6: 6,7 => CTR
* 6231854797154..628984726351.4.91.5.2592...71...6257894.69.7.2...713..985.586..1.7
* RESTART
* PAIR F3: 6,7 COL F
F4: 6,7,3                                # reduction candidate for 6,7
F4: 3 => CTR
* 6231854797154..628984.2.351.47913562592...713.36.72894.69...2.5271354.8.........7
* PAIR RESTART
* PAIR A4: 3,8 COL A
A7: 3,8,1,4                              # reduction candidate for 3,8
A7: 3,8                                  # 25 pairs
A9: 3,8,1,2,4                            # reduction candidate for 3,8
A9: 3,8 => SOLVED
* 623185479715439628984726351348917562592648713176253894469871235257394186831562947
* DURATION: 0:00:06.006351  START: 02:52:55.807244  END: 02:53:01.813595 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190111-absurd-base-pr-001.dot
* REASONING
* DIS # D6: 6,7 => CTR => D6: 2,5
* DIS D6: 2,5 # F6: 6,7 => CTR => F6: 2,3
* DIS D6: 2,5 + F6: 2,3 # F4: 3 => CTR => F4: 6,7
* PRF D6: 2,5 + F6: 2,3 + F4: 6,7 # A9: 3,8 => SOL
* STA D6: 2,5 + F6: 2,3 + F4: 6,7 + A9: 3,8
* CNT   4 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jan&YEAR=2019, 20190111, absurd

Solution

position: 623185479715439628984726351348917562592648713176253894469871235257394186831562947 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 # D6: 6,7 => CTR => D6: 2,5
* INC # D6: 2,5 => UNS
* INC # F4: 6,7 => UNS
* DIS # F6: 6,7 => CTR => F6: 2,3
* INC # F6: 2,3 => UNS
* INC # A7: 3,8 => UNS
* INC # A9: 3,8 => UNS
* INC # A7: 1,3 => UNS
* DIS # A9: 1,3 => CTR => A9: 2,4,8
* INC # A9: 2,4,8 => UNS
* INC # E6: 3,7 => UNS
* PRF # F6: 3,7 => SOL
* INC # F6: 2,6 => UNS
* INC # F5: 6,8 => UNS
* DIS # F5: 3,4 => CTR => F5: 6,8
* DIS # D9: 6,8 => CTR => D9: 2,5
* INC # D9: 2,5 => UNS
* DIS # F4: 3,6 => CTR => F4: 7
* INC # F4: 7 => UNS
* INC # H9: 3,6 => UNS
* INC # H9: 4 => UNS
* DIS # E5: 3,6 => CTR => E5: 4
* INC # E5: 4 => UNS
* DIS # F5: 3,6 => CTR => F5: 4,8
* INC # F5: 4,8 => UNS
* DIS # C6: 1,7 => CTR => C6: 6
* INC # C6: 6 => UNS
* DIS # A7: 1,8 => CTR => A7: 3,4
* INC # A7: 3,4 => UNS
* PRF # A9: 1,8 => SOL
* INC # A9: 2,3,4 => UNS
* DIS # F9: 1,8 => CTR => F9: 2,4,6,9
* INC # F9: 2,4,6,9 => UNS
* INC # H9: 3,4 => UNS
* DIS # H9: 6 => CTR => H9: 3,4
* INC # A7: 3,4 => UNS
* DIS # A7: 1,8 => CTR => A7: 3,4
* DIS # F8: 1,9 => CTR => F8: 2,4,6
* INC # F8: 2,4,6 => UNS
* DIS # E8: 5,6 => CTR => E8: 4,9
* INC # E8: 4,9 => UNS
* INC # F9: 1,9 => UNS
* INC # F9: 2,4,6,8 => UNS
* CNT  43 HDP CHAINS /  43 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D6: 6,7 => CTR => D6: 2,5
* INC D6: 2,5 # F4: 6,7 => UNS
* DIS D6: 2,5 # F6: 6,7 => CTR => F6: 2,3
* INC D6: 2,5 + F6: 2,3 # F4: 6,7 => UNS
* DIS D6: 2,5 + F6: 2,3 # F4: 3 => CTR => F4: 6,7
* INC D6: 2,5 + F6: 2,3 + F4: 6,7 # A7: 3,8 => UNS
* PRF D6: 2,5 + F6: 2,3 + F4: 6,7 # A9: 3,8 => SOL
* STA D6: 2,5 + F6: 2,3 + F4: 6,7 + A9: 3,8
* CNT   7 HDP CHAINS /   7 HYP OPENED