Analysis of zz-www.sudokuoftheday.co.uk-20190323-absurd-base.sdk

Contents

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

level: medium

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

position: .49....1.8..........6.....4..1....95..56..8..7....962...872..5....38.2..3...5..8. initial

Autosolve

position: 54926..188......62..6.....4..1....95..56..8..78.5.962...872..5..5.38.2..3.295..8. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B2: 3,7 => CTR => B2: 1
* DIS # F2: 3,7 => CTR => F2: 5
* DIS # B3: 1,2 => CTR => B3: 3,7
* DIS # F2: 3,7 => CTR => F2: 5
* DIS # E3: 3,7 => CTR => E3: 9
* DIS # F3: 3,7 => CTR => F3: 5,8
* DIS # G4: 3,7 => CTR => G4: 4
* PRF # G4: 4 => SOL
* DIS # E3: 3,7 => CTR => E3: 9
* DIS # F3: 3,7 => CTR => F3: 5,8
* PRF # H5: 3,7 => SOL
* DIS # H5: 4 => CTR => H5: 3,7
* PRF # E6: 1 => SOL
* PRF # I5: 1,3 => SOL
* PRF # E6: 1,3 => SOL
* DIS # E6: 4 => CTR => E6: 1,3
* DIS # F9: 1,6 => CTR => F9: 4
* DIS # A8: 9 => CTR => A8: 1,6
* DIS # H5: 3 => CTR => H5: 4,7
* PRF # I7: 6,9 => SOL
* DIS # B9: 1 => CTR => B9: 6,7
* CNT  21 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:

* DIS # B2: 3,7 => CTR => B2: 1
* DIS B2: 1 # G4: 3,7 => CTR => G4: 4
* PRF B2: 1 + G4: 4 => SOL
* STA B2: 1 + G4: 4
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

.49....1.8..........6.....4..1....95..56..8..7....962...872..5....38.2..3...5..8. initial
54926..188......62..6.....4..1....95..56..8..78.5.962...872..5..5.38.2..3.295..8. autosolve
549263718813475962276198534621837495935642871784519623498721356157386249362954187 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (17)
C2: 3,7
A3: 1,2
F1: 3,7
D2: 1,4
D3: 1,8
G1: 3,7
G2: 5,9
G3: 5,9
H3: 3,7
C6: 3,4
D4: 4,8
I6: 1,3
C8: 4,7
F8: 1,6
H8: 4,7
I8: 6,9
I9: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  =>  0 pairs (X) / D3 = 1  => 19 pairs (_)
E5,E6: 1.. / E5 = 1  => 18 pairs (_) / E6 = 1  =>  0 pairs (*)
I5,I6: 1.. / I5 = 1  =>  0 pairs (*) / I6 = 1  =>  0 pairs (X)
G7,G9: 1.. / G7 = 1  => 24 pairs (_) / G9 = 1  => 20 pairs (_)
B2,D2: 1.. / B2 = 1  => 19 pairs (_) / D2 = 1  =>  0 pairs (X)
E5,I5: 1.. / E5 = 1  => 18 pairs (_) / I5 = 1  =>  0 pairs (*)
E6,I6: 1.. / E6 = 1  =>  0 pairs (*) / I6 = 1  =>  0 pairs (X)
A8,F8: 1.. / A8 = 1  => 22 pairs (_) / F8 = 1  => 19 pairs (_)
A3,B3: 2.. / A3 = 2  => 22 pairs (_) / B3 = 2  =>  0 pairs (X)
F4,F5: 2.. / F4 = 2  => 20 pairs (_) / F5 = 2  => 21 pairs (_)
G1,H3: 3.. / G1 = 3  =>  0 pairs (X) / H3 = 3  => 24 pairs (_)
G7,I7: 3.. / G7 = 3  =>  0 pairs (*) / I7 = 3  =>  0 pairs (X)
F1,G1: 3.. / F1 = 3  => 24 pairs (_) / G1 = 3  =>  0 pairs (X)
C2,C6: 3.. / C2 = 3  =>  0 pairs (*) / C6 = 3  =>  0 pairs (X)
H3,H5: 3.. / H3 = 3  => 24 pairs (_) / H5 = 3  =>  0 pairs (X)
D2,E2: 4.. / D2 = 4  => 19 pairs (_) / E2 = 4  =>  0 pairs (X)
G4,H5: 4.. / G4 = 4  =>  0 pairs (*) / H5 = 4  =>  0 pairs (X)
A7,C8: 4.. / A7 = 4  =>  0 pairs (*) / C8 = 4  =>  0 pairs (X)
F7,F9: 4.. / F7 = 4  =>  0 pairs (X) / F9 = 4  => 19 pairs (_)
C6,E6: 4.. / C6 = 4  =>  0 pairs (*) / E6 = 4  =>  0 pairs (X)
C8,H8: 4.. / C8 = 4  =>  0 pairs (X) / H8 = 4  =>  0 pairs (_)
F9,G9: 4.. / F9 = 4  => 19 pairs (_) / G9 = 4  =>  0 pairs (X)
C6,C8: 4.. / C6 = 4  =>  0 pairs (*) / C8 = 4  =>  0 pairs (X)
D2,D4: 4.. / D2 = 4  => 19 pairs (_) / D4 = 4  =>  0 pairs (X)
H5,H8: 4.. / H5 = 4  =>  0 pairs (X) / H8 = 4  =>  0 pairs (_)
F2,F3: 5.. / F2 = 5  => 15 pairs (_) / F3 = 5  =>  0 pairs (X)
G2,G3: 5.. / G2 = 5  =>  0 pairs (X) / G3 = 5  => 15 pairs (_)
F2,G2: 5.. / F2 = 5  => 15 pairs (_) / G2 = 5  =>  0 pairs (X)
F3,G3: 5.. / F3 = 5  =>  0 pairs (X) / G3 = 5  => 15 pairs (_)
A4,B4: 6.. / A4 = 6  => 19 pairs (_) / B4 = 6  => 20 pairs (_)
G1,H3: 7.. / G1 = 7  => 24 pairs (_) / H3 = 7  =>  0 pairs (X)
C8,B9: 7.. / C8 = 7  =>  0 pairs (*) / B9 = 7  =>  0 pairs (X)
F1,G1: 7.. / F1 = 7  =>  0 pairs (X) / G1 = 7  => 24 pairs (_)
C8,H8: 7.. / C8 = 7  =>  0 pairs (*) / H8 = 7  =>  0 pairs (X)
C2,C8: 7.. / C2 = 7  =>  0 pairs (X) / C8 = 7  =>  0 pairs (_)
I5,I9: 7.. / I5 = 7  => 22 pairs (_) / I9 = 7  =>  0 pairs (*)
D3,F3: 8.. / D3 = 8  =>  0 pairs (X) / F3 = 8  => 19 pairs (_)
D4,F4: 8.. / D4 = 8  => 19 pairs (_) / F4 = 8  =>  0 pairs (X)
D3,D4: 8.. / D3 = 8  =>  0 pairs (X) / D4 = 8  => 19 pairs (_)
F3,F4: 8.. / F3 = 8  => 19 pairs (_) / F4 = 8  =>  0 pairs (X)
E2,E3: 9.. / E2 = 9  =>  0 pairs (X) / E3 = 9  => 15 pairs (_)
G2,G3: 9.. / G2 = 9  => 15 pairs (_) / G3 = 9  =>  0 pairs (X)
A5,B5: 9.. / A5 = 9  => 19 pairs (_) / B5 = 9  => 19 pairs (_)
I7,I8: 9.. / I7 = 9  =>  0 pairs (X) / I8 = 9  => 18 pairs (_)
E2,G2: 9.. / E2 = 9  =>  0 pairs (X) / G2 = 9  => 15 pairs (_)
E3,G3: 9.. / E3 = 9  => 15 pairs (_) / G3 = 9  =>  0 pairs (X)
A8,I8: 9.. / A8 = 9  =>  0 pairs (X) / I8 = 9  => 18 pairs (_)
B5,B7: 9.. / B5 = 9  => 19 pairs (_) / B7 = 9  => 19 pairs (_)
* DURATION: 0:00:58.596454  START: 04:44:14.260810  END: 04:45:12.857264 2019-05-01
* CP COUNT: (48)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C2,C6,C8,D2,D3,D4,F1,F8,G1,G2,G3,H3,H8,I6,I8,I9)
* 54926..188......62..6.....4..1....95..56..8..78.5.962...872..5..5.38.2..3.295..8.
* PAIR C2: 3,7 BLK 1
B2: 3,7,1                                # reduction candidate for 3,7
B2: 3,7 => CTR
* 54926..188..14.962..689.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8.
B2: 1                                    # 19 pairs
B3: 3,7,1,2                              # reduction candidate for 3,7
B3: 3,7                                  # 19 pairs
* PAIR C2: 3,7 ROW 2
E2: 3,7,4,9                              # reduction candidate for 3,7
E2: 3,7                                  # 19 pairs
F2: 3,7,5                                # reduction candidate for 3,7
F2: 3,7 => CTR
* 54926..188...9.562..68.59.4..14.8.95..56.28..78.5.962...872..5..5.38.2..3.295..8.
F2: 5                                    # 15 pairs
* PAIR A3: 1,2 BLK 1
B3: 1,2,3,7                              # reduction candidate for 1,2
B3: 1,2 => CTR
* 54926..188...45962..6.9.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8.
B3: 3,7                                  # 19 pairs
* PAIR F1: 3,7 BLK 2
E2: 3,7,4,9                              # reduction candidate for 3,7
E2: 3,7                                  # 19 pairs
F2: 3,7,5                                # reduction candidate for 3,7
F2: 3,7 => CTR
* 54926..188...9.562..68.59.4..14.8.95..56.28..78.5.962...872..5..5.38.2..3.295..8.
F2: 5                                    # 15 pairs
E3: 3,7,9                                # reduction candidate for 3,7
E3: 3,7 => CTR
* 54926..188..49.562..6..59.4..1..8.95..56.28..78.5.962...872..5..5.38.2..3.295..8.
E3: 9                                    # 15 pairs
F3: 3,7,5,8                              # reduction candidate for 3,7
F3: 3,7 => CTR
* 54926..188....5962..689.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8.
F3: 5,8                                  # 18 pairs
* PAIR F1: 3,7 COL F
F4: 3,7,2,8                              # reduction candidate for 3,7
F4: 3,7                                  # 21 pairs
F5: 3,7,2                                # reduction candidate for 3,7
F5: 3,7                                  # 20 pairs
* PAIR G1: 3,7 COL G
G4: 3,7,4                                # reduction candidate for 3,7
G4: 3,7 => CTR
* 54926.7188.7....62..6....344618.2395..56..847783549621..872..53.5438.27937295..86
G4: 4 => SOLVED
* 549263718813475962276198534621837495935642871784519623498721356157386249362954187
* PAIR H3: 3,7 ROW 3
B3: 3,7,1,2                              # reduction candidate for 3,7
B3: 3,7                                  # 19 pairs
E3: 3,7,9                                # reduction candidate for 3,7
E3: 3,7 => CTR
* 54926..188..49.562..6..59.4..1..8.95..56.28..78.5.962...872..5..5.38.2..3.295..8.
E3: 9                                    # 15 pairs
F3: 3,7,5,8                              # reduction candidate for 3,7
F3: 3,7 => CTR
* 54926..188....5962..689.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8.
F3: 5,8                                  # 18 pairs
* PAIR H3: 3,7 COL H
H5: 3,7,4                                # reduction candidate for 3,7
H5: 3,7 => SOLVED
* 549263718813475962276198534621837495935642871784519623498721356157386249362954187
H5: 4 => CTR
* 5492637188.7..5962..6.975344618...95..56..84.78.5.962...872..5..5438.27.37295..86
* PAIR C6: 3,4 ROW 6
E6: 3,4,1                                # reduction candidate for 3,4
E6: 1 => SOLVED
* 549263718813475962276198534621837495935642871784519623498721356157386249362954187
E6: 3,4                                  # 18 pairs
* PAIR I6: 1,3 BLK 6
I5: 1,3,7                                # reduction candidate for 1,3
I5: 1,3 => SOLVED
* 549263718813475962276198534621837495935642871784519623498721356157386249362954187
I5: 7                                    # 22 pairs
* PAIR I6: 1,3 ROW 6
E6: 1,3,4                                # reduction candidate for 1,3
E6: 1,3 => SOLVED
* 549263718813475962276198534621837495935642871784519623498721356157386249362954187
E6: 4 => CTR
* 54926.7188.74...62..61.8534..1....95..561.8..78.549621..872..5..5438.27.37295..86
* PAIR F8: 1,6 BLK 8
F7: 1,6,4                                # reduction candidate for 1,6
F7: 1,6                                  # 19 pairs
F9: 1,6,4                                # reduction candidate for 1,6
F9: 1,6 => CTR
* 549263718837....62..6....34..1...395..56..847783549621..8724153154386279372951486
F9: 4                                    # 19 pairs
* PAIR F8: 1,6 ROW 8
A8: 1,6,9                                # reduction candidate for 1,6
A8: 9 => CTR
* 54926..188.3....62..6.....4.31...495.956..87.7845.962.418726359957381246362954187
A8: 1,6                                  # 18 pairs
* PAIR H8: 4,7 BLK 9
G9: 4,7,1                                # reduction candidate for 4,7
G9: 4,7                                  # 24 pairs
G9: 1                                    # 20 pairs
* PAIR H8: 4,7 COL H
H5: 4,7,3                                # reduction candidate for 4,7
H5: 3 => CTR
* 5492673188..4...62..61.8574..187.495..5612837784539621..872..53.5.38.2493.2954786
H5: 4,7                                  # 24 pairs
* PAIR I8: 6,9 BLK 9
I7: 6,9,3                                # reduction candidate for 6,9
I7: 6,9 => SOLVED
* 549263718813475962276198534621837495935642871784519623498721356157386249362954187
I7: 3                                    # 22 pairs
* PAIR I8: 6,9 ROW 8
A8: 6,9,1                                # reduction candidate for 6,9
A8: 1                                    # 22 pairs
A8: 6,9                                  # 19 pairs
* PAIR I9: 6,7 ROW 9
B9: 6,7,1                                # reduction candidate for 6,7
B9: 1 => CTR
* 549267318873145962126893574..14...95..56..8..78.5.962...872..5..5738.24.312954786
B9: 6,7                                  # 20 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190323-absurd-base-pr-000.dot
* REASONING
* DIS # B2: 3,7 => CTR => B2: 1
* DIS # F2: 3,7 => CTR => F2: 5
* DIS # B3: 1,2 => CTR => B3: 3,7
* DIS # F2: 3,7 => CTR => F2: 5
* DIS # E3: 3,7 => CTR => E3: 9
* DIS # F3: 3,7 => CTR => F3: 5,8
* DIS # G4: 3,7 => CTR => G4: 4
* PRF # G4: 4 => SOL
* DIS # E3: 3,7 => CTR => E3: 9
* DIS # F3: 3,7 => CTR => F3: 5,8
* PRF # H5: 3,7 => SOL
* DIS # H5: 4 => CTR => H5: 3,7
* PRF # E6: 1 => SOL
* PRF # I5: 1,3 => SOL
* PRF # E6: 1,3 => SOL
* DIS # E6: 4 => CTR => E6: 1,3
* DIS # F9: 1,6 => CTR => F9: 4
* DIS # A8: 9 => CTR => A8: 1,6
* DIS # H5: 3 => CTR => H5: 4,7
* PRF # I7: 6,9 => SOL
* DIS # B9: 1 => CTR => B9: 6,7
* CNT  21 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C2,C6,C8,D2,D3,D4,F1,F8,G1,G2,G3,H3,H8,I6,I8,I9)
* 54926..188......62..6.....4..1....95..56..8..78.5.962...872..5..5.38.2..3.295..8.
* PAIR C2: 3,7 BLK 1
B2: 3,7,1                                # reduction candidate for 3,7
B2: 3,7 => CTR
* 54926..188..14.962..689.5.4..14.8.95..56.284.7845.962.4.872..5..5738.2..3.295..8.
* RESTART
* PAIR F1: 3,7 COL F
F4: 3,7,2                                # reduction candidate for 3,7
F4: 3,7                                  # 21 pairs
F5: 3,7,2                                # reduction candidate for 3,7
F5: 3,7                                  # 20 pairs
* PAIR G1: 3,7 COL G
G4: 3,7,4                                # reduction candidate for 3,7
G4: 3,7 => CTR
* 54926..1881.4.59622.61985.4..18...95..56..84.78.5.962...872..5..5438.27.37295..86
G4: 4 => SOLVED
* 549263718813475962276198534621837495935642871784519623498721356157386249362954187
* DURATION: 0:00:05.427743  START: 04:45:48.166728  END: 04:45:53.594471 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20190323-absurd-base-pr-001.dot
* REASONING
* DIS # B2: 3,7 => CTR => B2: 1
* DIS B2: 1 # G4: 3,7 => CTR => G4: 4
* PRF B2: 1 + G4: 4 => SOL
* STA B2: 1 + G4: 4
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2019, 20190323, absurd

Solution

position: 549263718813475962276198534621837495935642871784519623498721356157386249362954187 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 # B2: 3,7 => CTR => B2: 1
* INC # B2: 1 => UNS
* INC # B3: 3,7 => UNS
* INC # E2: 3,7 => UNS
* DIS # F2: 3,7 => CTR => F2: 5
* INC # F2: 5 => UNS
* DIS # B3: 1,2 => CTR => B3: 3,7
* INC # B3: 3,7 => UNS
* INC # E2: 3,7 => UNS
* DIS # F2: 3,7 => CTR => F2: 5
* INC # F2: 5 => UNS
* DIS # E3: 3,7 => CTR => E3: 9
* INC # E3: 9 => UNS
* DIS # F3: 3,7 => CTR => F3: 5,8
* INC # F3: 5,8 => UNS
* INC # F4: 3,7 => UNS
* INC # F5: 3,7 => UNS
* DIS # G4: 3,7 => CTR => G4: 4
* PRF # G4: 4 => SOL
* INC # B3: 3,7 => UNS
* DIS # E3: 3,7 => CTR => E3: 9
* INC # E3: 9 => UNS
* DIS # F3: 3,7 => CTR => F3: 5,8
* INC # F3: 5,8 => UNS
* PRF # H5: 3,7 => SOL
* DIS # H5: 4 => CTR => H5: 3,7
* INC # E6: 3,4 => UNS
* PRF # E6: 1 => SOL
* PRF # I5: 1,3 => SOL
* INC # I5: 7 => UNS
* PRF # E6: 1,3 => SOL
* DIS # E6: 4 => CTR => E6: 1,3
* INC # F7: 1,6 => UNS
* DIS # F9: 1,6 => CTR => F9: 4
* INC # F9: 4 => UNS
* INC # A8: 1,6 => UNS
* DIS # A8: 9 => CTR => A8: 1,6
* INC # G9: 4,7 => UNS
* INC # G9: 1 => UNS
* INC # H5: 4,7 => UNS
* DIS # H5: 3 => CTR => H5: 4,7
* PRF # I7: 6,9 => SOL
* INC # I7: 3 => UNS
* INC # A8: 6,9 => UNS
* INC # A8: 1 => UNS
* INC # B9: 6,7 => UNS
* DIS # B9: 1 => CTR => B9: 6,7
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B2: 3,7 => CTR => B2: 1
* INC B2: 1 # F4: 3,7 => UNS
* INC B2: 1 # F5: 3,7 => UNS
* DIS B2: 1 # G4: 3,7 => CTR => G4: 4
* PRF B2: 1 + G4: 4 => SOL
* STA B2: 1 + G4: 4
* CNT   5 HDP CHAINS /   4 HYP OPENED