Analysis of zz-www.sudokuoftheday.co.uk-20190418-absurd-base.sdk

Contents

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

level: medium

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

position: ...6....33.6..89..7.9.3..2....1...5.5.7.62.39....9....6......1..537..2..2....6... initial

Autosolve

position: .256.9..33.62.89..78943.62.96.143.5.5.7862.39.3.597.6.6...2..1..537..2962....6... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E2: 1,7 => SOL
* DIS # G1: 1,7 => CTR => G1: 4,8
* DIS # E2: 7 => CTR => E2: 1,5
* DIS # I2: 4,7 => CTR => I2: 1,5
* DIS # I2: 4,7 => CTR => I2: 1,5
* DIS # I4: 7 => CTR => I4: 2,8
* DIS # C9: 4,8 => CTR => C9: 1
* PRF # I7: 7 => SOL
* PRF # E9: 5 => SOL
* PRF # A8: 4 => SOL
* CNT  10 HDP CHAINS /  47 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 # E2: 1,7 => SOL
* STA E2: 1,7
* CNT   1 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

...6....33.6..89..7.9.3..2....1...5.5.7.62.39....9....6......1..537..2..2....6... initial
.256.9..33.62.89..78943.62.96.143.5.5.7862.39.3.597.6.6...2..1..537..2962....6... autosolve
125679843346218975789435621962143758517862439834597162698324517453781296271956384 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
A1: 1,4
B2: 1,4
E1: 1,7
F3: 1,5
H2: 4,7
I3: 1,5
C4: 2,8
B5: 1,4
G4: 7,8
G5: 1,4
B7: 7,9
C7: 4,8
B9: 7,9
D7: 3,9
F7: 4,5
E8: 1,8
F8: 1,4
D9: 3,9
G7: 3,5
G9: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B2: 1.. / A1 = 1  =>  0 pairs (*) / B2 = 1  =>  0 pairs (X)
A8,C9: 1.. / A8 = 1  =>  0 pairs (X) / C9 = 1  => 23 pairs (_)
F3,I3: 1.. / F3 = 1  => 13 pairs (_) / I3 = 1  =>  0 pairs (*)
B5,G5: 1.. / B5 = 1  =>  0 pairs (*) / G5 = 1  =>  0 pairs (X)
C9,E9: 1.. / C9 = 1  => 23 pairs (_) / E9 = 1  =>  0 pairs (X)
B2,B5: 1.. / B2 = 1  =>  0 pairs (X) / B5 = 1  =>  0 pairs (_)
C6,C9: 1.. / C6 = 1  =>  0 pairs (X) / C9 = 1  => 23 pairs (_)
F3,F8: 1.. / F3 = 1  => 13 pairs (_) / F8 = 1  =>  0 pairs (*)
C4,C6: 2.. / C4 = 2  => 24 pairs (_) / C6 = 2  => 10 pairs (_)
I4,I6: 2.. / I4 = 2  => 10 pairs (_) / I6 = 2  => 24 pairs (_)
C4,I4: 2.. / C4 = 2  => 24 pairs (_) / I4 = 2  => 10 pairs (_)
C6,I6: 2.. / C6 = 2  => 10 pairs (_) / I6 = 2  => 24 pairs (_)
D7,D9: 3.. / D7 = 3  =>  0 pairs (*) / D9 = 3  =>  0 pairs (X)
G7,G9: 3.. / G7 = 3  => 13 pairs (_) / G9 = 3  =>  0 pairs (*)
D7,G7: 3.. / D7 = 3  =>  0 pairs (*) / G7 = 3  =>  0 pairs (X)
D9,G9: 3.. / D9 = 3  => 13 pairs (_) / G9 = 3  =>  0 pairs (*)
A1,B2: 4.. / A1 = 4  =>  0 pairs (X) / B2 = 4  =>  0 pairs (_)
F7,F8: 4.. / F7 = 4  =>  0 pairs (*) / F8 = 4  =>  0 pairs (X)
B5,G5: 4.. / B5 = 4  =>  0 pairs (X) / G5 = 4  =>  0 pairs (_)
A8,F8: 4.. / A8 = 4  =>  0 pairs (*) / F8 = 4  =>  0 pairs (X)
B2,B5: 4.. / B2 = 4  =>  0 pairs (*) / B5 = 4  =>  0 pairs (X)
E2,F3: 5.. / E2 = 5  => 13 pairs (_) / F3 = 5  =>  0 pairs (*)
I2,I3: 5.. / I2 = 5  =>  0 pairs (*) / I3 = 5  =>  0 pairs (X)
F7,E9: 5.. / F7 = 5  => 13 pairs (_) / E9 = 5  =>  0 pairs (*)
G7,G9: 5.. / G7 = 5  =>  0 pairs (*) / G9 = 5  =>  0 pairs (X)
E2,I2: 5.. / E2 = 5  => 13 pairs (_) / I2 = 5  =>  0 pairs (*)
F3,I3: 5.. / F3 = 5  =>  0 pairs (*) / I3 = 5  =>  0 pairs (X)
F7,G7: 5.. / F7 = 5  => 13 pairs (_) / G7 = 5  =>  0 pairs (*)
E9,G9: 5.. / E9 = 5  =>  0 pairs (*) / G9 = 5  =>  0 pairs (X)
E2,E9: 5.. / E2 = 5  => 13 pairs (_) / E9 = 5  =>  0 pairs (*)
F3,F7: 5.. / F3 = 5  =>  0 pairs (*) / F7 = 5  =>  0 pairs (X)
E1,E2: 7.. / E1 = 7  => 21 pairs (_) / E2 = 7  =>  0 pairs (X)
G4,I4: 7.. / G4 = 7  => 20 pairs (_) / I4 = 7  =>  0 pairs (X)
B7,B9: 7.. / B7 = 7  => 13 pairs (_) / B9 = 7  =>  0 pairs (*)
B7,I7: 7.. / B7 = 7  => 13 pairs (_) / I7 = 7  =>  0 pairs (*)
G1,G4: 7.. / G1 = 7  =>  0 pairs (X) / G4 = 7  => 20 pairs (_)
G1,H1: 8.. / G1 = 8  => 25 pairs (_) / H1 = 8  => 22 pairs (_)
E8,E9: 8.. / E8 = 8  => 26 pairs (_) / E9 = 8  => 10 pairs (_)
C7,I7: 8.. / C7 = 8  => 27 pairs (_) / I7 = 8  => 10 pairs (_)
A8,E8: 8.. / A8 = 8  => 10 pairs (_) / E8 = 8  => 26 pairs (_)
A6,A8: 8.. / A6 = 8  => 26 pairs (_) / A8 = 8  => 10 pairs (_)
H1,H9: 8.. / H1 = 8  => 22 pairs (_) / H9 = 8  => 25 pairs (_)
B7,B9: 9.. / B7 = 9  =>  0 pairs (*) / B9 = 9  =>  0 pairs (X)
D7,D9: 9.. / D7 = 9  => 13 pairs (_) / D9 = 9  =>  0 pairs (*)
B7,D7: 9.. / B7 = 9  =>  0 pairs (*) / D7 = 9  =>  0 pairs (X)
B9,D9: 9.. / B9 = 9  => 13 pairs (_) / D9 = 9  =>  0 pairs (*)
* DURATION: 0:01:11.024725  START: 05:23:35.201358  END: 05:24:46.226083 2019-05-01
* CP COUNT: (46)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B5,B7,B9,C4,C7,D7,D9,E1,E8,F3,F7,F8,G4,G5,G7,G9,H2,I3)
* .256.9..33.62.89..78943.62.96.143.5.5.7862.39.3.597.6.6...2..1..537..2962....6...
* PAIR A1: 1,4 ROW 1
G1: 1,4,7,8                              # reduction candidate for 1,4
G1: 7,8                                  # 25 pairs
G1: 1,4                                  # 10 pairs
* PAIR A1: 1,4 COL A
A6: 1,4,8                                # reduction candidate for 1,4
A6: 1,4                                  # 10 pairs
A8: 1,4,8                                # reduction candidate for 1,4
A8: 1,4                                  # 26 pairs
* PAIR B2: 1,4 ROW 2
I2: 1,4,5,7                              # reduction candidate for 1,4
I2: 5,7                                  # 21 pairs
I2: 1,4                                  # 14 pairs
* PAIR E1: 1,7 BLK 2
E2: 1,7,5                                # reduction candidate for 1,7
E2: 1,7 => SOLVED
* 125679843346218975789435621962143758517862439834597162698324517453781296271956384
E2: 5                                    # 13 pairs
* PAIR E1: 1,7 ROW 1
G1: 1,7,4,8                              # reduction candidate for 1,7
G1: 1,7 => CTR
* 42561978331627894578943562.96.143.5.547862139.3.59746.6...2..1..537.42962....6...
G1: 4,8                                  # 23 pairs
* PAIR F3: 1,5 BLK 2
E2: 1,5,7                                # reduction candidate for 1,5
E2: 7 => CTR
* .256.9..33.627894578943562196.143.5.547862139.3.59746.6...2451.4537812962.1.563.4
E2: 1,5                                  # 21 pairs
* PAIR H2: 4,7 BLK 3
G1: 4,7,1,8                              # reduction candidate for 4,7
G1: 4,7                                  # 25 pairs
H1: 4,7,8                                # reduction candidate for 4,7
H1: 4,7                                  # 25 pairs
I2: 4,7,1,5                              # reduction candidate for 4,7
I2: 4,7 => CTR
* 125679.8334625897.78943162596.143.5.5.7862.39.3.597.616...2531..537.42962.13865..
I2: 1,5                                  # 21 pairs
* PAIR H2: 4,7 COL H
H9: 4,7,8                                # reduction candidate for 4,7
H9: 8                                    # 25 pairs
H9: 4,7                                  # 22 pairs
* PAIR I3: 1,5 BLK 3
I2: 1,5,4,7                              # reduction candidate for 1,5
I2: 4,7 => CTR
* 125679.8334625897.78943162596.143.5.5.7862.39.3.597.616...2531..537.42962.13865..
I2: 1,5                                  # 21 pairs
* PAIR C4: 2,8 BLK 4
C6: 2,8,1,4                              # reduction candidate for 2,8
C6: 1,4                                  # 26 pairs
C6: 2,8                                  # 10 pairs
* PAIR C4: 2,8 ROW 4
I4: 2,8,7                                # reduction candidate for 2,8
I4: 7 => CTR
* .256.9..33.62.89..78943.62.9621438575.7862.39.3.597.6267.92.31..537..29629.3.657.
I4: 2,8                                  # 20 pairs
* PAIR B5: 1,4 BLK 4
A6: 1,4,8                                # reduction candidate for 1,4
A6: 1,4                                  # 10 pairs
C6: 1,4,2,8                              # reduction candidate for 1,4
C6: 1,4                                  # 26 pairs
* PAIR G4: 7,8 BLK 6
I4: 7,8,2                                # reduction candidate for 7,8
I4: 7,8                                  # 24 pairs
I4: 2                                    # 10 pairs
* PAIR G4: 7,8 COL G
G1: 7,8,1,4                              # reduction candidate for 7,8
G1: 7,8                                  # 25 pairs
G1: 1,4                                  # 10 pairs
* PAIR G5: 1,4 BLK 6
G6: 1,4,8                                # reduction candidate for 1,4
G6: 1,4                                  # 25 pairs
I6: 1,4,2,8                              # reduction candidate for 1,4
I6: 1,4                                  # 10 pairs
* PAIR G5: 1,4 COL G
G1: 1,4,7,8                              # reduction candidate for 1,4
G1: 7,8                                  # 25 pairs
G1: 1,4                                  # 10 pairs
* PAIR C7: 4,8 BLK 7
A8: 4,8,1                                # reduction candidate for 4,8
A8: 4,8                                  # 23 pairs
C9: 4,8,1                                # reduction candidate for 4,8
C9: 4,8 => CTR
* 4256791833162589..7894316259621437585.7862.39.31597.626...2..1.1537842962...165..
C9: 1                                    # 23 pairs
* PAIR C7: 4,8 ROW 7
I7: 4,8,7                                # reduction candidate for 4,8
I7: 7 => SOLVED
* 125679843346218975789435621962143758517862439834597162698324517453781296271956384
I7: 4,8                                  # 13 pairs
* PAIR C7: 4,8 COL C
C6: 4,8,1,2                              # reduction candidate for 4,8
C6: 4,8                                  # 28 pairs
C6: 1,2                                  # 14 pairs
* PAIR E8: 1,8 BLK 8
E9: 1,8,5                                # reduction candidate for 1,8
E9: 5 => SOLVED
* 125679843346218975789435621962143758517862439834597162698324517453781296271956384
E9: 1,8                                  # 13 pairs
* PAIR E8: 1,8 ROW 8
A8: 1,8,4                                # reduction candidate for 1,8
A8: 4 => SOLVED
* 125679843346218975789435621962143758517862439834597162698324517453781296271956384
A8: 1,8                                  # 13 pairs
* PAIR F8: 1,4 ROW 8
A8: 1,4,8                                # reduction candidate for 1,4
A8: 1,4                                  # 26 pairs
A8: 8                                    # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190418-absurd-base-pr-000.dot
* REASONING
* PRF # E2: 1,7 => SOL
* DIS # G1: 1,7 => CTR => G1: 4,8
* DIS # E2: 7 => CTR => E2: 1,5
* DIS # I2: 4,7 => CTR => I2: 1,5
* DIS # I2: 4,7 => CTR => I2: 1,5
* DIS # I4: 7 => CTR => I4: 2,8
* DIS # C9: 4,8 => CTR => C9: 1
* PRF # I7: 7 => SOL
* PRF # E9: 5 => SOL
* PRF # A8: 4 => SOL
* CNT  10 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B2,B5,B7,B9,C4,C7,D7,D9,E1,E8,F3,F7,F8,G4,G5,G7,G9,H2,I3)
* .256.9..33.62.89..78943.62.96.143.5.5.7862.39.3.597.6.6...2..1..537..2962....6...
* PAIR A1: 1,4 ROW 1
G1: 1,4,7,8                              # reduction candidate for 1,4
G1: 7,8                                  # 25 pairs
G1: 1,4                                  # 10 pairs
* PAIR A1: 1,4 COL A
A6: 1,4,8                                # reduction candidate for 1,4
A6: 1,4                                  # 10 pairs
A8: 1,4,8                                # reduction candidate for 1,4
A8: 1,4                                  # 26 pairs
* PAIR B2: 1,4 ROW 2
I2: 1,4,5,7                              # reduction candidate for 1,4
I2: 5,7                                  # 21 pairs
I2: 1,4                                  # 14 pairs
* PAIR E1: 1,7 BLK 2
E2: 1,7,5                                # reduction candidate for 1,7
E2: 1,7 => SOLVED
* 125679843346218975789435621962143758517862439834597162698324517453781296271956384
* DURATION: 0:00:06.836691  START: 05:25:27.543263  END: 05:25:34.379954 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190418-absurd-base-pr-001.dot
* REASONING
* PRF # E2: 1,7 => SOL
* STA E2: 1,7
* CNT   1 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2019, 20190418, absurd

Solution

position: 125679843346218975789435621962143758517862439834597162698324517453781296271956384 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 # G1: 1,4 => UNS
* INC # G1: 7,8 => UNS
* INC # A6: 1,4 => UNS
* INC # A8: 1,4 => UNS
* INC # I2: 1,4 => UNS
* INC # I2: 5,7 => UNS
* PRF # E2: 1,7 => SOL
* INC # E2: 5 => UNS
* DIS # G1: 1,7 => CTR => G1: 4,8
* INC # G1: 4,8 => UNS
* INC # E2: 1,5 => UNS
* DIS # E2: 7 => CTR => E2: 1,5
* INC # G1: 4,7 => UNS
* INC # H1: 4,7 => UNS
* DIS # I2: 4,7 => CTR => I2: 1,5
* INC # I2: 1,5 => UNS
* INC # H9: 4,7 => UNS
* INC # H9: 8 => UNS
* INC # I2: 1,5 => UNS
* DIS # I2: 4,7 => CTR => I2: 1,5
* INC # C6: 2,8 => UNS
* INC # C6: 1,4 => UNS
* INC # I4: 2,8 => UNS
* DIS # I4: 7 => CTR => I4: 2,8
* INC # A6: 1,4 => UNS
* INC # C6: 1,4 => UNS
* INC # I4: 7,8 => UNS
* INC # I4: 2 => UNS
* INC # G1: 7,8 => UNS
* INC # G1: 1,4 => UNS
* INC # G6: 1,4 => UNS
* INC # I6: 1,4 => UNS
* INC # G1: 1,4 => UNS
* INC # G1: 7,8 => UNS
* INC # A8: 4,8 => UNS
* DIS # C9: 4,8 => CTR => C9: 1
* INC # C9: 1 => UNS
* INC # I7: 4,8 => UNS
* PRF # I7: 7 => SOL
* INC # C6: 4,8 => UNS
* INC # C6: 1,2 => UNS
* INC # E9: 1,8 => UNS
* PRF # E9: 5 => SOL
* INC # A8: 1,8 => UNS
* PRF # A8: 4 => SOL
* INC # A8: 1,4 => UNS
* INC # A8: 8 => UNS
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 1,4 => UNS
* INC # G1: 7,8 => UNS
* INC # A6: 1,4 => UNS
* INC # A8: 1,4 => UNS
* INC # I2: 1,4 => UNS
* INC # I2: 5,7 => UNS
* PRF # E2: 1,7 => SOL
* STA E2: 1,7
* CNT   7 HDP CHAINS /   7 HYP OPENED