Analysis of zz-www.sudokuoftheday.co.uk-20060825-absurd-base.sdk

Contents

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006

level: medium

Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006

position: 43...57.29...634....7.............1....39...8.59....6.....2.8..14.6...2....8....9 initial

Autosolve

position: 436..57.29..7634....7............91....39...8.59....6..9..2.8..1486.9.2....8....9 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H3: 5,8 => CTR => H3: 3,9
* DIS # B2: 1,8 => CTR => B2: 2
* DIS # F3: 4,8 => CTR => F3: 2
* DIS # E4: 4,8 => CTR => E4: 5,7
* DIS # E6: 4,8 => CTR => E6: 1,7
* DIS # H3: 8,9 => CTR => H3: 3,5
* DIS # H3: 5,8 => CTR => H3: 3,9
* DIS # C2: 2 => CTR => C2: 1,5
* DIS # I3: 3,5 => CTR => I3: 1,6
* DIS # H9: 5,7 => CTR => H9: 3,4
* DIS # A7: 3,5 => CTR => A7: 6,7
* DIS # H7: 3,5 => CTR => H7: 4,7
* DIS # I3: 3,5 => CTR => I3: 1,6
* DIS # H7: 3,5 => CTR => H7: 4,7
* PRF # I8: 3,5 => SOL
* DIS # I8: 7 => CTR => I8: 3,5
* DIS # H9: 3,5 => CTR => H9: 4,7
* DIS # E8: 3,5 => CTR => E8: 7
* PRF # E8: 7 => SOL
* CNT  19 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 # H3: 5,8 => CTR => H3: 3,9
* DIS H3: 3,9 # B2: 1,8 => CTR => B2: 2
* PRF H3: 3,9 + B2: 2 # I3: 6 => SOL
* STA H3: 3,9 + B2: 2 + I3: 6
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

43...57.29...634....7.............1....39...8.59....6.....2.8..14.6...2....8....9 initial
436..57.29..7634....7............91....39...8.59....6..9..2.8..1486.9.2....8....9 autosolve
436185792921763485587942136362458917714396258859217364693524871148679523275831649 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
A3: 5,8
B3: 1,8
D1: 1,9
E1: 1,8
E3: 4,8
H1: 8,9
H2: 5,8
I2: 1,5
G3: 1,6
G5: 2,5
H5: 5,7
G6: 2,3
C7: 3,5
I7: 1,6
G8: 3,5
G9: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,E1: 1.. / D1 = 1  => 16 pairs (_) / E1 = 1  =>  0 pairs (X)
B5,C5: 1.. / B5 = 1  => 18 pairs (_) / C5 = 1  =>  0 pairs (X)
I7,G9: 1.. / I7 = 1  => 22 pairs (_) / G9 = 1  => 14 pairs (_)
C2,C5: 1.. / C2 = 1  => 18 pairs (_) / C5 = 1  =>  0 pairs (X)
G3,G9: 1.. / G3 = 1  => 22 pairs (_) / G9 = 1  => 14 pairs (_)
B2,C2: 2.. / B2 = 2  => 18 pairs (_) / C2 = 2  =>  0 pairs (X)
D3,F3: 2.. / D3 = 2  =>  0 pairs (X) / F3 = 2  => 17 pairs (_)
G5,G6: 2.. / G5 = 2  =>  0 pairs (*) / G6 = 2  =>  0 pairs (X)
H3,I3: 3.. / H3 = 3  => 18 pairs (_) / I3 = 3  =>  0 pairs (X)
E8,E9: 3.. / E8 = 3  =>  0 pairs (X) / E9 = 3  => 18 pairs (_)
G6,G8: 3.. / G6 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
C4,C5: 4.. / C4 = 4  =>  0 pairs (X) / C5 = 4  => 19 pairs (_)
I4,I6: 4.. / I4 = 4  => 21 pairs (_) / I6 = 4  => 18 pairs (_)
H7,H9: 4.. / H7 = 4  => 19 pairs (_) / H9 = 4  => 17 pairs (_)
C5,F5: 4.. / C5 = 4  => 19 pairs (_) / F5 = 4  =>  0 pairs (X)
C2,A3: 5.. / C2 = 5  =>  0 pairs (X) / A3 = 5  => 16 pairs (_)
D4,E4: 5.. / D4 = 5  =>  0 pairs (X) / E4 = 5  => 23 pairs (_)
G5,H5: 5.. / G5 = 5  =>  0 pairs (X) / H5 = 5  =>  0 pairs (_)
D4,D7: 5.. / D4 = 5  =>  0 pairs (X) / D7 = 5  => 23 pairs (_)
G5,G8: 5.. / G5 = 5  =>  0 pairs (X) / G8 = 5  =>  0 pairs (_)
G3,I3: 6.. / G3 = 6  => 14 pairs (_) / I3 = 6  => 22 pairs (_)
F4,F5: 6.. / F4 = 6  => 16 pairs (_) / F5 = 6  => 19 pairs (_)
I7,G9: 6.. / I7 = 6  => 14 pairs (_) / G9 = 6  => 22 pairs (_)
A7,I7: 6.. / A7 = 6  => 22 pairs (_) / I7 = 6  => 14 pairs (_)
G3,G9: 6.. / G3 = 6  => 14 pairs (_) / G9 = 6  => 22 pairs (_)
I3,I7: 6.. / I3 = 6  => 22 pairs (_) / I7 = 6  => 14 pairs (_)
E8,I8: 7.. / E8 = 7  =>  0 pairs (*) / I8 = 7  =>  0 pairs (X)
E1,H1: 8.. / E1 = 8  => 16 pairs (_) / H1 = 8  =>  0 pairs (X)
B2,H2: 8.. / B2 = 8  =>  0 pairs (X) / H2 = 8  => 17 pairs (_)
D1,D3: 9.. / D1 = 9  =>  0 pairs (X) / D3 = 9  => 16 pairs (_)
H1,H3: 9.. / H1 = 9  => 16 pairs (_) / H3 = 9  =>  0 pairs (X)
D1,H1: 9.. / D1 = 9  =>  0 pairs (X) / H1 = 9  => 16 pairs (_)
D3,H3: 9.. / D3 = 9  => 16 pairs (_) / H3 = 9  =>  0 pairs (X)
* DURATION: 0:00:37.398474  START: 02:04:03.912128  END: 02:04:41.310602 2019-05-01
* CP COUNT: (33)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,C7,D1,E1,E3,G3,G5,G6,G8,G9,H1,H2,H5,I2,I7)
* 436..57.29..7634....7............91....39...8.59....6..9..2.8..1486.9.2....8....9
* PAIR A3: 5,8 ROW 3
H3: 5,8,3,9                              # reduction candidate for 5,8
H3: 5,8 => CTR
* 436..57929..7634....79.2..3......91....39...8.59...36..9..2.8.6148639527...8....9
H3: 3,9                                  # 17 pairs
* PAIR B3: 1,8 BLK 1
B2: 1,8,2                                # reduction candidate for 1,8
B2: 1,8 => CTR
* 436.157829.27634.55.7........4..691...1394..8.59.7..64.9..2.8..1486.9.27...8....9
B2: 2                                    # 18 pairs
* PAIR E1: 1,8 COL E
E6: 1,8,4,7                              # reduction candidate for 1,8
E6: 1,8                                  # 19 pairs
E6: 4,7                                  # 17 pairs
* PAIR E3: 4,8 BLK 2
F3: 4,8,2                                # reduction candidate for 4,8
F3: 4,8 => CTR
* 436..57.29..7634....72...93......91....39...8.59...36..9..2.8.6148639527...8....9
F3: 2                                    # 17 pairs
* PAIR E3: 4,8 COL E
E4: 4,8,5,7                              # reduction candidate for 4,8
E4: 4,8 => CTR
* 436.15782982763451517...693...5..91...1394578.59....6..9..2.8..1486.9.2....8....9
E4: 5,7                                  # 17 pairs
E6: 4,8,1,7                              # reduction candidate for 4,8
E6: 4,8 => CTR
* 436.15782982763451517...693......91...1394578.59....6..9..2.8..1486.9.2....8....9
E6: 1,7                                  # 17 pairs
* PAIR H1: 8,9 BLK 3
H3: 8,9,3,5                              # reduction candidate for 8,9
H3: 8,9 => CTR
* 436..57.29..7634....7.....3......91....39...8.59...36..9..2.8.6148639527...8....9
H3: 3,5                                  # 17 pairs
* PAIR H2: 5,8 BLK 3
H3: 5,8,3,9                              # reduction candidate for 5,8
H3: 5,8 => CTR
* 436..57929..7634....79.2..3......91....39...8.59...36..9..2.8.6148639527...8....9
H3: 3,9                                  # 17 pairs
* PAIR I2: 1,5 BLK 3
I3: 1,5,3,6                              # reduction candidate for 1,5
I3: 3,6                                  # 17 pairs
I3: 1,5                                  # 17 pairs
* PAIR I2: 1,5 ROW 2
C2: 1,5,2                                # reduction candidate for 1,5
C2: 2 => CTR
* 436.157829.27634.55.7........4..691...1394..8.59.7..64.9..2.8..1486.9.27...8....9
C2: 1,5                                  # 18 pairs
* PAIR G3: 1,6 BLK 3
I3: 1,6,3,5                              # reduction candidate for 1,6
I3: 3,5 => CTR
* 436..57.29..7634.1.17...6.5..4..6913..1394.78359.7826479..218.61486.9327562837149
I3: 1,6                                  # 17 pairs
* PAIR H5: 5,7 COL H
H7: 5,7,3,4                              # reduction candidate for 5,7
H7: 5,7                                  # 21 pairs
H9: 5,7,3,4                              # reduction candidate for 5,7
H9: 5,7 => CTR
* 4361857929.1763485587942631..245.91..1439.258.5921.364.93521846148679523265834179
H9: 3,4                                  # 17 pairs
* PAIR G6: 2,3 ROW 6
A6: 2,3,7,8                              # reduction candidate for 2,3
A6: 2,3                                  # 19 pairs
A6: 7,8                                  # 18 pairs
* PAIR C7: 3,5 BLK 7
A7: 3,5,6,7                              # reduction candidate for 3,5
A7: 3,5 => CTR
* 436..57.29.17634.5587.426.1......91..1439..78.59....6.3951278461486.9.27..28.4159
A7: 6,7                                  # 17 pairs
A9: 3,5,2,6,7                            # reduction candidate for 3,5
A9: 3,5                                  # 22 pairs
C9: 3,5,2                                # reduction candidate for 3,5
C9: 3,5                                  # 21 pairs
* PAIR C7: 3,5 ROW 7
H7: 3,5,4,7                              # reduction candidate for 3,5
H7: 3,5 => CTR
* 436..57.29..76348...7....3....5..91....39.578.59...26..93.2.85.148659327...83..49
H7: 4,7                                  # 18 pairs
* PAIR I7: 1,6 COL I
I3: 1,6,3,5                              # reduction candidate for 1,6
I3: 3,5 => CTR
* 436..57.29..7634.1.17...6.5..4..6913..1394.78359.7826479..218.61486.9327562837149
I3: 1,6                                  # 17 pairs
* PAIR G8: 3,5 BLK 9
H7: 3,5,4,7                              # reduction candidate for 3,5
H7: 3,5 => CTR
* 436..57.29..76348...7....3....5..91....39.578.59...26..93.2.85.148659327...83..49
H7: 4,7                                  # 18 pairs
I8: 3,5,7                                # reduction candidate for 3,5
I8: 3,5 => SOLVED
* 436185792921763485587942136362458917714396258859217364693524871148679523275831649
I8: 7 => CTR
* 436..57.29..7634....7....3....5..91....39.578.59...26..9..2.8..148659327...83...9
H9: 3,5,4,7                              # reduction candidate for 3,5
H9: 3,5 => CTR
* 436..57.29..76348...7...63....5..91...439.578.59...26..9.12.84.148659327...834159
H9: 4,7                                  # 17 pairs
* PAIR G8: 3,5 ROW 8
E8: 3,5,7                                # reduction candidate for 3,5
E8: 3,5 => CTR
* 436..57.29..7634....7....3....5..91....39.578.59...26..9..2.8..148659327...83...9
E8: 7 => SOLVED
* 436185792921763485587942136362458917714396258859217364693524871148679523275831649
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060825-absurd-base-pr-000.dot
* REASONING
* DIS # H3: 5,8 => CTR => H3: 3,9
* DIS # B2: 1,8 => CTR => B2: 2
* DIS # F3: 4,8 => CTR => F3: 2
* DIS # E4: 4,8 => CTR => E4: 5,7
* DIS # E6: 4,8 => CTR => E6: 1,7
* DIS # H3: 8,9 => CTR => H3: 3,5
* DIS # H3: 5,8 => CTR => H3: 3,9
* DIS # C2: 2 => CTR => C2: 1,5
* DIS # I3: 3,5 => CTR => I3: 1,6
* DIS # H9: 5,7 => CTR => H9: 3,4
* DIS # A7: 3,5 => CTR => A7: 6,7
* DIS # H7: 3,5 => CTR => H7: 4,7
* DIS # I3: 3,5 => CTR => I3: 1,6
* DIS # H7: 3,5 => CTR => H7: 4,7
* PRF # I8: 3,5 => SOL
* DIS # I8: 7 => CTR => I8: 3,5
* DIS # H9: 3,5 => CTR => H9: 4,7
* DIS # E8: 3,5 => CTR => E8: 7
* PRF # E8: 7 => SOL
* CNT  19 HDP CHAINS /  43 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,C7,D1,E1,E3,G3,G5,G6,G8,G9,H1,H2,H5,I2,I7)
* 436..57.29..7634....7............91....39...8.59....6..9..2.8..1486.9.2....8....9
* PAIR A3: 5,8 ROW 3
H3: 5,8,3,9                              # reduction candidate for 5,8
H3: 5,8 => CTR
* 436..57929..7634....79.2..3......91....39...8.59...36..9..2.8.6148639527...8....9
* PAIR RESTART
* PAIR B3: 1,8 BLK 1
B2: 1,8,2                                # reduction candidate for 1,8
B2: 1,8 => CTR
* 436.157829.27634.55.7........4..691...1394..8.59.7..64.9..2.8..1486.9.27...8....9
* PAIR I2: 1,5 BLK 3
I3: 1,5,6                                # reduction candidate for 1,5
I3: 6 => SOLVED
* 436185792921763485587942136362458917714396258859217364693524871148679523275831649
* DURATION: 0:00:05.245983  START: 02:05:07.248326  END: 02:05:12.494309 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060825-absurd-base-pr-001.dot
* REASONING
* DIS # H3: 5,8 => CTR => H3: 3,9
* DIS H3: 3,9 # B2: 1,8 => CTR => B2: 2
* PRF H3: 3,9 + B2: 2 # I3: 6 => SOL
* STA H3: 3,9 + B2: 2 + I3: 6
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060825, absurd

Solution

position: 436185792921763485587942136362458917714396258859217364693524871148679523275831649 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 # H3: 5,8 => CTR => H3: 3,9
* INC # H3: 3,9 => UNS
* DIS # B2: 1,8 => CTR => B2: 2
* INC # B2: 2 => UNS
* INC # E6: 1,8 => UNS
* INC # E6: 4,7 => UNS
* DIS # F3: 4,8 => CTR => F3: 2
* INC # F3: 2 => UNS
* DIS # E4: 4,8 => CTR => E4: 5,7
* INC # E4: 5,7 => UNS
* DIS # E6: 4,8 => CTR => E6: 1,7
* INC # E6: 1,7 => UNS
* DIS # H3: 8,9 => CTR => H3: 3,5
* INC # H3: 3,5 => UNS
* DIS # H3: 5,8 => CTR => H3: 3,9
* INC # H3: 3,9 => UNS
* INC # I3: 1,5 => UNS
* INC # I3: 3,6 => UNS
* INC # C2: 1,5 => UNS
* DIS # C2: 2 => CTR => C2: 1,5
* INC # I3: 1,6 => UNS
* DIS # I3: 3,5 => CTR => I3: 1,6
* INC # H7: 5,7 => UNS
* DIS # H9: 5,7 => CTR => H9: 3,4
* INC # H9: 3,4 => UNS
* INC # A6: 2,3 => UNS
* INC # A6: 7,8 => UNS
* DIS # A7: 3,5 => CTR => A7: 6,7
* INC # A7: 6,7 => UNS
* INC # A9: 3,5 => UNS
* INC # C9: 3,5 => UNS
* DIS # H7: 3,5 => CTR => H7: 4,7
* INC # H7: 4,7 => UNS
* INC # I3: 1,6 => UNS
* DIS # I3: 3,5 => CTR => I3: 1,6
* DIS # H7: 3,5 => CTR => H7: 4,7
* INC # H7: 4,7 => UNS
* PRF # I8: 3,5 => SOL
* DIS # I8: 7 => CTR => I8: 3,5
* DIS # H9: 3,5 => CTR => H9: 4,7
* INC # H9: 4,7 => UNS
* DIS # E8: 3,5 => CTR => E8: 7
* PRF # E8: 7 => SOL
* CNT  43 HDP CHAINS /  43 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # H3: 5,8 => CTR => H3: 3,9
* DIS H3: 3,9 # B2: 1,8 => CTR => B2: 2
* INC H3: 3,9 + B2: 2 # I3: 1,5 => UNS
* PRF H3: 3,9 + B2: 2 # I3: 6 => SOL
* STA H3: 3,9 + B2: 2 + I3: 6
* CNT   4 HDP CHAINS /   4 HYP OPENED