Analysis of zz-www.sudokuoftheday.co.uk-20060623-absurd-base.sdk

Contents

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

level: medium

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

position: ...176.2.51...48.......8......3.59......1..4.6.........5.....8..79..1....8.6..3.5 initial

Autosolve

position: ...17652.51...48.6.6...8......3659....5.1.64.6......5..56..3.8.379..1.6..8.6..3.5 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A3: 2,7 => CTR => A3: 4,9
* DIS # D5: 2,9 => CTR => D5: 7,8
* DIS # D6: 2,9 => CTR => D6: 4,7,8
* PRF # I3: 4,9 => SOL
* DIS # A1: 4,9 => CTR => A1: 8
* PRF # I4: 1,7 => SOL
* DIS # I6: 1,7 => CTR => I6: 2,3,8
* DIS # C4: 1,7 => CTR => C4: 4,8
* DIS # H3: 1,7 => CTR => H3: 3,9
* DIS # H9: 1,7 => CTR => H9: 9
* DIS # H9: 1,7 => CTR => H9: 9
* PRF # G3: 1,7 => SOL
* CNT  12 HDP CHAINS /  34 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 # A3: 2,7 => CTR => A3: 4,9
* DIS A3: 4,9 # D5: 2,9 => CTR => D5: 7,8
* DIS A3: 4,9 + D5: 7,8 # D6: 2,9 => CTR => D6: 4,7,8
* DIS A3: 4,9 + D5: 7,8 + D6: 4,7,8 # D7: 2,9 => CTR => D7: 4,7
* PRF A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 # I3: 4,9 => SOL
* STA A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 + I3: 4,9
* CNT   5 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

...176.2.51...48.......8......3.59......1..4.6.........5.....8..79..1....8.6..3.5 initial
...17652.51...48.6.6...8......3659....5.1.64.6......5..56..3.8.379..1.6..8.6..3.5 autosolve
843176529512934876967258134428365917795812643631749258256493781379581462184627395 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
C2: 2,7
D2: 2,9
I1: 4,9
B4: 2,4
H4: 1,7
D8: 5,8
E8: 5,8
G7: 1,7
G8: 2,4
I8: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G8,I8: 2.. / G8 = 2  => 25 pairs (_) / I8 = 2  =>  0 pairs (*)
B4,I4: 2.. / B4 = 2  =>  0 pairs (*) / I4 = 2  =>  0 pairs (X)
G6,G8: 2.. / G6 = 2  =>  0 pairs (*) / G8 = 2  =>  0 pairs (X)
B1,C1: 3.. / B1 = 3  =>  0 pairs (X) / C1 = 3  => 12 pairs (_)
E2,E3: 3.. / E2 = 3  => 11 pairs (_) / E3 = 3  => 10 pairs (_)
H2,H3: 3.. / H2 = 3  => 10 pairs (_) / H3 = 3  => 11 pairs (_)
I5,I6: 3.. / I5 = 3  => 11 pairs (_) / I6 = 3  => 13 pairs (_)
E2,H2: 3.. / E2 = 3  => 11 pairs (_) / H2 = 3  => 10 pairs (_)
E3,H3: 3.. / E3 = 3  => 10 pairs (_) / H3 = 3  => 11 pairs (_)
B5,I5: 3.. / B5 = 3  => 13 pairs (_) / I5 = 3  => 11 pairs (_)
C1,C6: 3.. / C1 = 3  => 12 pairs (_) / C6 = 3  =>  0 pairs (X)
D6,E6: 4.. / D6 = 4  => 10 pairs (_) / E6 = 4  => 18 pairs (_)
G8,I8: 4.. / G8 = 4  =>  0 pairs (*) / I8 = 4  =>  0 pairs (X)
B1,B4: 4.. / B1 = 4  =>  0 pairs (*) / B4 = 4  =>  0 pairs (X)
D6,D7: 4.. / D6 = 4  => 10 pairs (_) / D7 = 4  => 18 pairs (_)
G3,G8: 4.. / G3 = 4  => 25 pairs (_) / G8 = 4  =>  0 pairs (*)
D3,E3: 5.. / D3 = 5  =>  8 pairs (_) / E3 = 5  => 12 pairs (_)
D8,E8: 5.. / D8 = 5  => 12 pairs (_) / E8 = 5  =>  8 pairs (_)
D3,D8: 5.. / D3 = 5  =>  8 pairs (_) / D8 = 5  => 12 pairs (_)
E3,E8: 5.. / E3 = 5  => 12 pairs (_) / E8 = 5  =>  8 pairs (_)
D7,F9: 7.. / D7 = 7  =>  0 pairs (X) / F9 = 7  => 15 pairs (_)
C2,H2: 7.. / C2 = 7  => 12 pairs (_) / H2 = 7  => 19 pairs (_)
F9,H9: 7.. / F9 = 7  => 15 pairs (_) / H9 = 7  =>  0 pairs (X)
A1,C1: 8.. / A1 = 8  => 12 pairs (_) / C1 = 8  =>  0 pairs (X)
D8,E8: 8.. / D8 = 8  =>  8 pairs (_) / E8 = 8  => 12 pairs (_)
E6,E8: 8.. / E6 = 8  =>  8 pairs (_) / E8 = 8  => 12 pairs (_)
I7,H9: 9.. / I7 = 9  =>  0 pairs (X) / H9 = 9  => 19 pairs (_)
* DURATION: 0:00:31.350461  START: 00:02:50.852930  END: 00:03:22.203391 2019-05-01
* CP COUNT: (27)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C2,D2,D8,E8,G7,G8,H4,I1,I8)
* ...17652.51...48.6.6...8......3659....5.1.64.6......5..56..3.8.379..1.6..8.6..3.5
* PAIR C2: 2,7 BLK 1
A3: 2,7,4,9                              # reduction candidate for 2,7
A3: 2,7 => CTR
* ...17652451...48.6.64..8....4.3659.2..5.1.64.6......5..56..3.8.379..1.6..8.6..3.5
A3: 4,9                                  # 13 pairs
C3: 2,7,4                                # reduction candidate for 2,7
C3: 2,7                                  # 13 pairs
* PAIR D2: 2,9 BLK 2
E2: 2,9,3                                # reduction candidate for 2,9
E2: 2,9                                  # 10 pairs
D3: 2,9,5                                # reduction candidate for 2,9
D3: 2,9                                  # 12 pairs
E3: 2,9,3,5                              # reduction candidate for 2,9
E3: 2,9                                  # 10 pairs
* PAIR D2: 2,9 COL D
D5: 2,9,7,8                              # reduction candidate for 2,9
D5: 2,9 => CTR
* ...176524517..48.6.6.5.87.1.4.365912..5.1.64.6......5..567.3189379851.6..8.6..375
D5: 7,8                                  # 11 pairs
D6: 2,9,4,7,8                            # reduction candidate for 2,9
D6: 2,9 => CTR
* ...17652.51...48.6.6...8......3659....5.1.64.6...4..5..564.3.8.379.81.6..8.6.73.5
D6: 4,7,8                                # 10 pairs
D7: 2,9,4,7                              # reduction candidate for 2,9
D7: 2,9                                  # 13 pairs
* PAIR I1: 4,9 BLK 3
I3: 4,9,1,7                              # reduction candidate for 4,9
I3: 4,9 => SOLVED
* 843176529512934876967258134428365917795812643631749258256493781379581462184627395
I3: 1,7                                  # 11 pairs
* PAIR I1: 4,9 ROW 1
A1: 4,9,8                                # reduction candidate for 4,9
A1: 4,9 => CTR
* 43817652951...48.696..58431841365972..5.1.6436.3....58.56..3.8.379.81264.8.6..3.5
A1: 8                                    # 12 pairs
B1: 4,9,3                                # reduction candidate for 4,9
B1: 4,9                                  # 12 pairs
* PAIR H4: 1,7 BLK 6
I4: 1,7,2,8                              # reduction candidate for 1,7
I4: 1,7 => SOLVED
* 843176529512934876967258134428365917795812643631749258256493781379581462184627395
I4: 2,8                                  # 11 pairs
G6: 1,7,2                                # reduction candidate for 1,7
G6: 1,7                                  # 25 pairs
I6: 1,7,2,3,8                            # reduction candidate for 1,7
I6: 1,7 => CTR
* 84317652951...48.696..587.4.2.3659.8.95.1.643638...251.56..3.87379.81462.8.6.7395
I6: 2,3,8                                # 10 pairs
* PAIR H4: 1,7 ROW 4
A4: 1,7,4,8                              # reduction candidate for 1,7
A4: 1,7                                  # 13 pairs
C4: 1,7,4,8                              # reduction candidate for 1,7
C4: 1,7 => CTR
* 9.8176524517234896.6.958137..136597.7.581.64.6..74..5.156423789379581.6..8.697315
C4: 4,8                                  # 11 pairs
* PAIR H4: 1,7 COL H
H3: 1,7,3,9                              # reduction candidate for 1,7
H3: 1,7 => CTR
* ..317652.517..4836.6.538.7.7.83659129.5712648621489753.56..3187379851.6.18.6.7395
H3: 3,9                                  # 11 pairs
H9: 1,7,9                                # reduction candidate for 1,7
H9: 1,7 => CTR
* ...17652451...48.6.6...8....4.3659.2..5.1.64.6......5..56..3.89379..1.6..8.6..3.5
H9: 9                                    # 19 pairs
* PAIR G7: 1,7 BLK 9
I7: 1,7,9                                # reduction candidate for 1,7
I7: 1,7                                  # 19 pairs
H9: 1,7,9                                # reduction candidate for 1,7
H9: 1,7 => CTR
* ...17652451...48.6.6...8....4.3659.2..5.1.64.6......5..56..3.89379..1.6..8.6..3.5
H9: 9                                    # 19 pairs
* PAIR G7: 1,7 COL G
G3: 1,7,4                                # reduction candidate for 1,7
G3: 1,7 => SOLVED
* 843176529512934876967258134428365917795812643631749258256493781379581462184627395
G3: 4                                    # 25 pairs
G6: 1,7,2                                # reduction candidate for 1,7
G6: 1,7                                  # 25 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060623-absurd-base-pr-000.dot
* REASONING
* DIS # A3: 2,7 => CTR => A3: 4,9
* DIS # D5: 2,9 => CTR => D5: 7,8
* DIS # D6: 2,9 => CTR => D6: 4,7,8
* PRF # I3: 4,9 => SOL
* DIS # A1: 4,9 => CTR => A1: 8
* PRF # I4: 1,7 => SOL
* DIS # I6: 1,7 => CTR => I6: 2,3,8
* DIS # C4: 1,7 => CTR => C4: 4,8
* DIS # H3: 1,7 => CTR => H3: 3,9
* DIS # H9: 1,7 => CTR => H9: 9
* DIS # H9: 1,7 => CTR => H9: 9
* PRF # G3: 1,7 => SOL
* CNT  12 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C2,D2,D8,E8,G7,G8,H4,I1,I8)
* ...17652.51...48.6.6...8......3659....5.1.64.6......5..56..3.8.379..1.6..8.6..3.5
* PAIR C2: 2,7 BLK 1
A3: 2,7,4,9                              # reduction candidate for 2,7
A3: 2,7 => CTR
* ...17652451...48.6.64..8....4.3659.2..5.1.64.6......5..56..3.8.379..1.6..8.6..3.5
* RESTART
* PAIR D2: 2,9 BLK 2
E2: 2,9,3                                # reduction candidate for 2,9
E2: 2,9                                  # 11 pairs
D3: 2,9,5                                # reduction candidate for 2,9
D3: 2,9                                  # 15 pairs
E3: 2,9,3,5                              # reduction candidate for 2,9
E3: 2,9                                  # 14 pairs
* PAIR D2: 2,9 COL D
D5: 2,9,7,8                              # reduction candidate for 2,9
D5: 2,9 => CTR
* ...176524517..48.64625.87.1.4.365912..5.1.64.6......5..567.3189379851.6..8.6..375
D6: 2,9,4,7,8                            # reduction candidate for 2,9
D6: 2,9 => CTR
* ...17652.51...48.6.6...8......3659....5.1.64.6...4..5..564.3.8.379.81.6..8.6.73.5
D7: 2,9,4,7                              # reduction candidate for 2,9
D7: 2,9 => CTR
* ..317652.51.294836.62538.7.7483659129.5712648621489753256943187379851.6.184627395
* RESTART
* PAIR RESTART
* PAIR I1: 4,9 BLK 3
I3: 4,9,1,7                              # reduction candidate for 4,9
I3: 4,9 => SOLVED
* 843176529512934876967258134428365917795812643631749258256493781379581462184627395
* DURATION: 0:00:07.163437  START: 00:03:44.802585  END: 00:03:51.966022 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060623-absurd-base-pr-001.dot
* REASONING
* DIS # A3: 2,7 => CTR => A3: 4,9
* DIS A3: 4,9 # D5: 2,9 => CTR => D5: 7,8
* DIS A3: 4,9 + D5: 7,8 # D6: 2,9 => CTR => D6: 4,7,8
* DIS A3: 4,9 + D5: 7,8 + D6: 4,7,8 # D7: 2,9 => CTR => D7: 4,7
* PRF A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 # I3: 4,9 => SOL
* STA A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 + I3: 4,9
* CNT   5 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060623, absurd

Solution

position: 843176529512934876967258134428365917795812643631749258256493781379581462184627395 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 # A3: 2,7 => CTR => A3: 4,9
* INC # A3: 4,9 => UNS
* INC # C3: 2,7 => UNS
* INC # E2: 2,9 => UNS
* INC # D3: 2,9 => UNS
* INC # E3: 2,9 => UNS
* DIS # D5: 2,9 => CTR => D5: 7,8
* INC # D5: 7,8 => UNS
* DIS # D6: 2,9 => CTR => D6: 4,7,8
* INC # D6: 4,7,8 => UNS
* INC # D7: 2,9 => UNS
* PRF # I3: 4,9 => SOL
* INC # I3: 1,7 => UNS
* DIS # A1: 4,9 => CTR => A1: 8
* INC # A1: 8 => UNS
* INC # B1: 4,9 => UNS
* PRF # I4: 1,7 => SOL
* INC # I4: 2,8 => UNS
* INC # G6: 1,7 => UNS
* DIS # I6: 1,7 => CTR => I6: 2,3,8
* INC # I6: 2,3,8 => UNS
* INC # A4: 1,7 => UNS
* DIS # C4: 1,7 => CTR => C4: 4,8
* INC # C4: 4,8 => UNS
* DIS # H3: 1,7 => CTR => H3: 3,9
* INC # H3: 3,9 => UNS
* DIS # H9: 1,7 => CTR => H9: 9
* INC # H9: 9 => UNS
* INC # I7: 1,7 => UNS
* DIS # H9: 1,7 => CTR => H9: 9
* INC # H9: 9 => UNS
* PRF # G3: 1,7 => SOL
* INC # G3: 4 => UNS
* INC # G6: 1,7 => UNS
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A3: 2,7 => CTR => A3: 4,9
* INC A3: 4,9 # E2: 2,9 => UNS
* INC A3: 4,9 # D3: 2,9 => UNS
* INC A3: 4,9 # E3: 2,9 => UNS
* DIS A3: 4,9 # D5: 2,9 => CTR => D5: 7,8
* DIS A3: 4,9 + D5: 7,8 # D6: 2,9 => CTR => D6: 4,7,8
* DIS A3: 4,9 + D5: 7,8 + D6: 4,7,8 # D7: 2,9 => CTR => D7: 4,7
* PRF A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 # I3: 4,9 => SOL
* STA A3: 4,9 + D5: 7,8 + D6: 4,7,8 + D7: 4,7 + I3: 4,9
* CNT   8 HDP CHAINS /   8 HYP OPENED