Analysis of zz-www.sudokuoftheday.co.uk-20190207-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: 15............3....861......6.4...5...5..294..91...6....78...2.......4.5.3.62...7 initial

Autosolve

position: 15...6........3....861......6.4..758875362941491..8632..78...2.....3.4.5.3.62...7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C1: 2,4 => CTR => C1: 3,9
* DIS # H2: 7,9 => CTR => H2: 1,6,8
* PRF # A3: 7,9 => SOL
* DIS # E3: 7,9 => CTR => E3: 4,5
* PRF # A3: 7,9 => SOL
* DIS # C1: 4,9 => CTR => C1: 2,3
* PRF # F7: 1,9 => SOL
* DIS # F8: 1,9 => CTR => F8: 7
* DIS # F9: 1,9 => CTR => F9: 4,5
* PRF # D2: 5,7 => SOL
* DIS # E2: 5,7 => CTR => E2: 4,8,9
* DIS # A7: 5,9 => CTR => A7: 6
* DIS # F9: 5,9 => CTR => F9: 1,4
* DIS # F8: 1 => CTR => F8: 7,9
* DIS # D1: 7,9 => CTR => D1: 2
* DIS # H8: 1,8 => CTR => H8: 6,9
* DIS # G2: 1,8 => CTR => G2: 2,5
* CNT  17 HDP CHAINS /  44 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 # C1: 2,4 => CTR => C1: 3,9
* DIS C1: 3,9 # C2: 9 => CTR => C2: 2,4
* DIS C1: 3,9 + C2: 2,4 # F8: 1,9 => CTR => F8: 7
* PRF C1: 3,9 + C2: 2,4 + F8: 7 => SOL
* STA C1: 3,9 + C2: 2,4 + F8: 7
* CNT   4 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

15............3....861......6.4...5...5..294..91...6....78...2.......4.5.3.62...7 initial
15...6........3....861......6.4..758875362941491..8632..78...2.....3.4.5.3.62...7 autosolve
153296874924783516786145293362419758875362941491578632647851329218937465539624187 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
B2: 2,4
H3: 7,9
A4: 2,3
C4: 2,3
E4: 1,9
F4: 1,9
D6: 5,7
E6: 5,7
B7: 1,4
B8: 1,2
A9: 5,9
D8: 7,9
G7: 1,3
G9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,H2: 1.. / G2 = 1  =>  0 pairs (X) / H2 = 1  => 17 pairs (_)
E4,F4: 1.. / E4 = 1  => 13 pairs (_) / F4 = 1  =>  0 pairs (X)
B7,B8: 1.. / B7 = 1  => 20 pairs (_) / B8 = 1  =>  0 pairs (*)
E4,E7: 1.. / E4 = 1  => 13 pairs (_) / E7 = 1  =>  0 pairs (X)
D1,D2: 2.. / D1 = 2  => 21 pairs (_) / D2 = 2  =>  0 pairs (X)
A4,C4: 2.. / A4 = 2  =>  0 pairs (X) / C4 = 2  => 17 pairs (_)
A3,G3: 2.. / A3 = 2  =>  0 pairs (X) / G3 = 2  => 17 pairs (_)
B2,B8: 2.. / B2 = 2  =>  0 pairs (*) / B8 = 2  =>  0 pairs (X)
C1,A3: 3.. / C1 = 3  => 17 pairs (_) / A3 = 3  =>  0 pairs (X)
A4,C4: 3.. / A4 = 3  => 17 pairs (_) / C4 = 3  =>  0 pairs (X)
G7,I7: 3.. / G7 = 3  => 16 pairs (_) / I7 = 3  =>  0 pairs (X)
A3,A4: 3.. / A3 = 3  =>  0 pairs (X) / A4 = 3  => 17 pairs (_)
C1,C4: 3.. / C1 = 3  => 17 pairs (_) / C4 = 3  =>  0 pairs (X)
B7,C9: 4.. / B7 = 4  =>  0 pairs (*) / C9 = 4  =>  0 pairs (X)
C9,F9: 4.. / C9 = 4  => 20 pairs (_) / F9 = 4  =>  0 pairs (*)
B2,B7: 4.. / B2 = 4  => 20 pairs (_) / B7 = 4  =>  0 pairs (*)
G2,G3: 5.. / G2 = 5  => 17 pairs (_) / G3 = 5  =>  0 pairs (X)
D6,E6: 5.. / D6 = 5  => 16 pairs (_) / E6 = 5  =>  0 pairs (X)
A7,A9: 5.. / A7 = 5  =>  0 pairs (X) / A9 = 5  => 14 pairs (_)
A9,F9: 5.. / A9 = 5  => 14 pairs (_) / F9 = 5  =>  0 pairs (X)
D2,D6: 5.. / D2 = 5  =>  0 pairs (X) / D6 = 5  => 16 pairs (_)
H2,I2: 6.. / H2 = 6  =>  0 pairs (X) / I2 = 6  => 16 pairs (_)
A7,A8: 6.. / A7 = 6  => 16 pairs (_) / A8 = 6  =>  0 pairs (X)
I7,H8: 6.. / I7 = 6  =>  0 pairs (X) / H8 = 6  => 16 pairs (_)
A7,I7: 6.. / A7 = 6  => 16 pairs (_) / I7 = 6  =>  0 pairs (X)
A8,H8: 6.. / A8 = 6  =>  0 pairs (X) / H8 = 6  => 16 pairs (_)
H2,H8: 6.. / H2 = 6  =>  0 pairs (X) / H8 = 6  => 16 pairs (_)
I2,I7: 6.. / I2 = 6  => 16 pairs (_) / I7 = 6  =>  0 pairs (X)
A2,A3: 7.. / A2 = 7  => 14 pairs (_) / A3 = 7  =>  0 pairs (*)
D6,E6: 7.. / D6 = 7  =>  0 pairs (X) / E6 = 7  => 16 pairs (_)
D8,F8: 7.. / D8 = 7  =>  0 pairs (X) / F8 = 7  => 19 pairs (_)
F3,F8: 7.. / F3 = 7  =>  0 pairs (X) / F8 = 7  => 19 pairs (_)
E1,E2: 8.. / E1 = 8  =>  0 pairs (X) / E2 = 8  => 14 pairs (_)
C8,C9: 8.. / C8 = 8  => 15 pairs (_) / C9 = 8  =>  0 pairs (X)
C8,H8: 8.. / C8 = 8  => 15 pairs (_) / H8 = 8  =>  0 pairs (X)
E4,F4: 9.. / E4 = 9  =>  0 pairs (X) / F4 = 9  => 13 pairs (_)
* DURATION: 0:00:39.028178  START: 03:33:22.135998  END: 03:34:01.164176 2019-05-01
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B2,B7,B8,C4,D6,D8,E4,E6,F4,G7,G9,H3)
* 15...6........3....861......6.4..758875362941491..8632..78...2.....3.4.5.3.62...7
* PAIR B2: 2,4 BLK 1
C1: 2,4,3,9                              # reduction candidate for 2,4
C1: 2,4 => CTR
* 15.9.68737.92835163861.729426341975887536294149157863261789..2.9..73146553.62.187
C1: 3,9                                  # 16 pairs
C2: 2,4,9                                # reduction candidate for 2,4
C2: 2,4                                  # 20 pairs
* PAIR H3: 7,9 BLK 3
H1: 7,9,8                                # reduction candidate for 7,9
H1: 7,9                                  # 22 pairs
H2: 7,9,1,6,8                            # reduction candidate for 7,9
H2: 7,9 => CTR
* 15...628....2.31.6.861..5...6.4..758875362941491..86326.78..329....3.46553.62.817
H2: 1,6,8                                # 14 pairs
* PAIR H3: 7,9 ROW 3
A3: 7,9,2,3                              # reduction candidate for 7,9
A3: 7,9 => SOLVED
* 153296874924783516786145293362419758875362941491578632647851329218937465539624187
A3: 2,3                                  # 18 pairs
E3: 7,9,4,5                              # reduction candidate for 7,9
E3: 7,9 => CTR
* 15...628.7..2.316..8619.57..6.419758875362941491..86329.78..3266..93741553.621897
E3: 4,5                                  # 15 pairs
F3: 7,9,4,5                              # reduction candidate for 7,9
F3: 7,9                                  # 26 pairs
* PAIR A4: 2,3 COL A
A3: 2,3,7,9                              # reduction candidate for 2,3
A3: 7,9 => SOLVED
* 153296874924783516786145293362419758875362941491578632647851329218937465539624187
A3: 2,3                                  # 18 pairs
* PAIR C4: 2,3 COL C
C1: 2,3,4,9                              # reduction candidate for 2,3
C1: 4,9 => CTR
* 15.2.68737..9835163861.729426341975887536294149157863261789..2.9..73146553.62.187
C1: 2,3                                  # 18 pairs
* PAIR E4: 1,9 COL E
E7: 1,9,4,5                              # reduction candidate for 1,9
E7: 1,9                                  # 26 pairs
E7: 4,5                                  # 19 pairs
* PAIR F4: 1,9 COL F
F7: 1,9,4,5                              # reduction candidate for 1,9
F7: 1,9 => SOLVED
* 153296874924783516786145293362419758875362941491578632647851329218937465539624187
F7: 4,5                                  # 15 pairs
F8: 1,9,7                                # reduction candidate for 1,9
F8: 1,9 => CTR
* 15...6.7.7....3..6.861.7.9..6.4..7588753629414915786326.78.532992873146553.62...7
F8: 7                                    # 19 pairs
F9: 1,9,4,5                              # reduction candidate for 1,9
F9: 1,9 => CTR
* 15...62...4.2.31..2861..573362419758875362941491578632.178.5326628937415534621897
F9: 4,5                                  # 17 pairs
* PAIR D6: 5,7 COL D
D2: 5,7,2,9                              # reduction candidate for 5,7
D2: 5,7 => SOLVED
* 153296874924783516786145293362419758875362941491578632647851329218937465539624187
D2: 2,9                                  # 17 pairs
* PAIR E6: 5,7 COL E
E2: 5,7,4,8,9                            # reduction candidate for 5,7
E2: 5,7 => CTR
* 153.862.4...253..62861..5.33624..7588753629414915786326.78.5329928731465534629..7
E2: 4,8,9                                # 14 pairs
E3: 5,7,4,9                              # reduction candidate for 5,7
E3: 5,7                                  # 15 pairs
* PAIR B7: 1,4 ROW 7
E7: 1,4,5,9                              # reduction candidate for 1,4
E7: 1,4                                  # 18 pairs
F7: 1,4,5,9                              # reduction candidate for 1,4
F7: 1,4                                  # 18 pairs
* PAIR A9: 5,9 BLK 7
A7: 5,9,6                                # reduction candidate for 5,9
A7: 5,9 => CTR
* 15...628....2.316..861..5...6.4..758875362941491..8632..78..3266...3.4.5.3.62.8.7
A7: 6                                    # 16 pairs
* PAIR A9: 5,9 ROW 9
F9: 5,9,1,4                              # reduction candidate for 5,9
F9: 5,9 => CTR
* 15...6....4...3....861.7.9..6.419758875362941491.78632.178.4329.28.314.5.3462...7
F9: 1,4                                  # 15 pairs
* PAIR D8: 7,9 BLK 8
F8: 7,9,1                                # reduction candidate for 7,9
F8: 1 => CTR
* 15...6........3....861.7.9..6.4..758875362941491.78632..78...29...731465.3.629..7
F8: 7,9                                  # 20 pairs
* PAIR D8: 7,9 COL D
D1: 7,9,2                                # reduction candidate for 7,9
D1: 7,9 => CTR
* 15...6....492.3..6.861......6.4..7588753629414915786326178..329928731465534629..7
D1: 2                                    # 21 pairs
D2: 7,9,2,5                              # reduction candidate for 7,9
D2: 7,9                                  # 18 pairs
* PAIR G9: 1,8 BLK 9
H8: 1,8,6,9                              # reduction candidate for 1,8
H8: 1,8 => CTR
* 15...628.7..2.316..861..57..6.4..758875362941491..8632..78..3266...3741553.621897
H8: 6,9                                  # 16 pairs
H9: 1,8,9                                # reduction candidate for 1,8
H9: 1,8                                  # 19 pairs
* PAIR G9: 1,8 COL G
G2: 1,8,2,5                              # reduction candidate for 1,8
G2: 1,8 => CTR
* 153.862.4749253..62861..5.33624..7588753629414915786326178.5329928731465534629..7
G2: 2,5                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190207-absurd-base-pr-000.dot
* REASONING
* DIS # C1: 2,4 => CTR => C1: 3,9
* DIS # H2: 7,9 => CTR => H2: 1,6,8
* PRF # A3: 7,9 => SOL
* DIS # E3: 7,9 => CTR => E3: 4,5
* PRF # A3: 7,9 => SOL
* DIS # C1: 4,9 => CTR => C1: 2,3
* PRF # F7: 1,9 => SOL
* DIS # F8: 1,9 => CTR => F8: 7
* DIS # F9: 1,9 => CTR => F9: 4,5
* PRF # D2: 5,7 => SOL
* DIS # E2: 5,7 => CTR => E2: 4,8,9
* DIS # A7: 5,9 => CTR => A7: 6
* DIS # F9: 5,9 => CTR => F9: 1,4
* DIS # F8: 1 => CTR => F8: 7,9
* DIS # D1: 7,9 => CTR => D1: 2
* DIS # H8: 1,8 => CTR => H8: 6,9
* DIS # G2: 1,8 => CTR => G2: 2,5
* CNT  17 HDP CHAINS /  44 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B2,B7,B8,C4,D6,D8,E4,E6,F4,G7,G9,H3)
* 15...6........3....861......6.4..758875362941491..8632..78...2.....3.4.5.3.62...7
* PAIR B2: 2,4 BLK 1
C1: 2,4,3,9                              # reduction candidate for 2,4
C1: 2,4 => CTR
* 15.9.68737.92835163861.729426341975887536294149157863261789..2.9..73146553.62.187
C2: 2,4,9                                # reduction candidate for 2,4
C2: 2,4                                  # 20 pairs
* RESTART
* PAIR B2: 2,4 BLK 1
C2: 2,4,9                                # reduction candidate for 2,4
C2: 9 => CTR
* 15...6....49..3..6.861......6.4..758875362941491..86326178..329.28.3.465534629..7
* PAIR F4: 1,9 COL F
F8: 1,9,7                                # reduction candidate for 1,9
F8: 1,9 => CTR
* 15.2.687.7.498351638615729426.4..7588753629414915786326.78.5329..873.46553.624187
F8: 7 => SOLVED
* 153296874924783516786145293362419758875362941491578632647851329218937465539624187
* DURATION: 0:00:05.782330  START: 03:34:27.861962  END: 03:34:33.644292 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190207-absurd-base-pr-001.dot
* REASONING
* DIS # C1: 2,4 => CTR => C1: 3,9
* DIS C1: 3,9 # C2: 9 => CTR => C2: 2,4
* DIS C1: 3,9 + C2: 2,4 # F8: 1,9 => CTR => F8: 7
* PRF C1: 3,9 + C2: 2,4 + F8: 7 => SOL
* STA C1: 3,9 + C2: 2,4 + F8: 7
* CNT   4 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Feb&YEAR=2019, 20190207, absurd

Solution

position: 153296874924783516786145293362419758875362941491578632647851329218937465539624187 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 # C1: 2,4 => CTR => C1: 3,9
* INC # C1: 3,9 => UNS
* INC # C2: 2,4 => UNS
* INC # H1: 7,9 => UNS
* DIS # H2: 7,9 => CTR => H2: 1,6,8
* INC # H2: 1,6,8 => UNS
* PRF # A3: 7,9 => SOL
* INC # A3: 2,3 => UNS
* DIS # E3: 7,9 => CTR => E3: 4,5
* INC # E3: 4,5 => UNS
* INC # F3: 7,9 => UNS
* INC # A3: 2,3 => UNS
* PRF # A3: 7,9 => SOL
* INC # C1: 2,3 => UNS
* DIS # C1: 4,9 => CTR => C1: 2,3
* INC # E7: 1,9 => UNS
* INC # E7: 4,5 => UNS
* PRF # F7: 1,9 => SOL
* INC # F7: 4,5 => UNS
* DIS # F8: 1,9 => CTR => F8: 7
* INC # F8: 7 => UNS
* DIS # F9: 1,9 => CTR => F9: 4,5
* INC # F9: 4,5 => UNS
* PRF # D2: 5,7 => SOL
* INC # D2: 2,9 => UNS
* DIS # E2: 5,7 => CTR => E2: 4,8,9
* INC # E2: 4,8,9 => UNS
* INC # E3: 5,7 => UNS
* INC # E7: 1,4 => UNS
* INC # F7: 1,4 => UNS
* DIS # A7: 5,9 => CTR => A7: 6
* INC # A7: 6 => UNS
* DIS # F9: 5,9 => CTR => F9: 1,4
* INC # F9: 1,4 => UNS
* INC # F8: 7,9 => UNS
* DIS # F8: 1 => CTR => F8: 7,9
* DIS # D1: 7,9 => CTR => D1: 2
* INC # D1: 2 => UNS
* INC # D2: 7,9 => UNS
* DIS # H8: 1,8 => CTR => H8: 6,9
* INC # H8: 6,9 => UNS
* INC # H9: 1,8 => UNS
* DIS # G2: 1,8 => CTR => G2: 2,5
* INC # G2: 2,5 => UNS
* CNT  44 HDP CHAINS /  44 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C1: 2,4 => CTR => C1: 3,9
* INC C1: 3,9 # C2: 2,4 => UNS
* INC C1: 3,9 # C2: 2,4 => UNS
* DIS C1: 3,9 # C2: 9 => CTR => C2: 2,4
* DIS C1: 3,9 + C2: 2,4 # F8: 1,9 => CTR => F8: 7
* PRF C1: 3,9 + C2: 2,4 + F8: 7 => SOL
* STA C1: 3,9 + C2: 2,4 + F8: 7
* CNT   6 HDP CHAINS /   5 HYP OPENED