Analysis of zz-www.sudokuoftheday.co.uk-20060608-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: .7..9....9...2576...1...3.....6.....1.52...8..4..8......84..9166...3..7..2....... initial

Autosolve

position: .7..9....9...2576...1...3.....6.....1.52...8..4..8......84.291661..3..7..2....... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 3,8 => CTR => A1: 2,4,5
* DIS # D2: 3,8 => CTR => D2: 1
* DIS # B4: 3,8 => CTR => B4: 9
* DIS # C1: 3,4 => CTR => C1: 2,6
* PRF # E4: 4,7 => SOL
* DIS # F5: 4,7 => CTR => F5: 3,9
* DIS # I5: 4,7 => CTR => I5: 3,9
* DIS # E3: 4,7 => CTR => E3: 6
* PRF # E3: 6 => SOL
* DIS # A7: 3,5 => CTR => A7: 7
* PRF # A7: 7 => SOL
* DIS # C9: 7 => CTR => C9: 4,9
* DIS # E9: 5,7 => CTR => E9: 1,6
* PRF # A7: 5,7 => SOL
* DIS # A7: 3 => CTR => A7: 5,7
* DIS # E4: 5,7 => CTR => E4: 1,4
* PRF # E4: 1,4 => SOL
* DIS # D9: 8,9 => CTR => D9: 1,5,7
* DIS # F9: 8,9 => CTR => F9: 1,6,7
* CNT  19 HDP CHAINS /  38 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 # A1: 3,8 => CTR => A1: 2,4,5
* DIS A1: 2,4,5 # D2: 3,8 => CTR => D2: 1
* DIS A1: 2,4,5 + D2: 1 # B4: 3,8 => CTR => B4: 9
* DIS A1: 2,4,5 + D2: 1 + B4: 9 # F3: 4,6 => CTR => F3: 7,8
* DIS A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 # D9: 5,9 => CTR => D9: 7,8
* PRF A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 # E4: 4,7 => SOL
* STA A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 + E4: 4,7
* CNT   6 HDP CHAINS /   8 HYP OPENED

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

Details

Positions

.7..9....9...2576...1...3.....6.....1.52...8..4..8......84..9166...3..7..2....... initial
.7..9....9...2576...1...3.....6.....1.52...8..4..8......84.291661..3..7..2....... autosolve
276394158983125764451867392892641537165273489347589621738452916614938275529716843 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
B2: 3,8
C2: 3,4
D3: 7,8
E5: 4,7
G5: 4,6
B7: 3,5
C8: 4,9
E7: 5,7
F8: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,I2: 1.. / D2 = 1  => 13 pairs (_) / I2 = 1  =>  0 pairs (X)
E4,E9: 1.. / E4 = 1  =>  0 pairs (X) / E9 = 1  =>  0 pairs (_)
G8,I8: 2.. / G8 = 2  =>  9 pairs (_) / I8 = 2  =>  9 pairs (_)
A7,B7: 3.. / A7 = 3  =>  0 pairs (X) / B7 = 3  =>  0 pairs (_)
H9,I9: 3.. / H9 = 3  =>  9 pairs (_) / I9 = 3  => 10 pairs (_)
C2,I2: 4.. / C2 = 4  =>  0 pairs (X) / I2 = 4  => 14 pairs (_)
E4,D6: 5.. / E4 = 5  =>  0 pairs (X) / D6 = 5  =>  0 pairs (_)
B3,B7: 5.. / B3 = 5  =>  0 pairs (*) / B7 = 5  =>  0 pairs (X)
C1,B3: 6.. / C1 = 6  =>  0 pairs (*) / B3 = 6  =>  0 pairs (X)
B5,C6: 6.. / B5 = 6  =>  0 pairs (*) / C6 = 6  =>  0 pairs (X)
G5,G6: 6.. / G5 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
E9,F9: 6.. / E9 = 6  =>  0 pairs (X) / F9 = 6  =>  0 pairs (_)
C1,F1: 6.. / C1 = 6  =>  0 pairs (*) / F1 = 6  =>  0 pairs (X)
B5,G5: 6.. / B5 = 6  =>  0 pairs (*) / G5 = 6  =>  0 pairs (X)
C6,G6: 6.. / C6 = 6  =>  0 pairs (X) / G6 = 6  =>  0 pairs (_)
B3,B5: 6.. / B3 = 6  =>  0 pairs (X) / B5 = 6  =>  0 pairs (_)
C1,C6: 6.. / C1 = 6  =>  0 pairs (*) / C6 = 6  =>  0 pairs (X)
E3,E9: 6.. / E3 = 6  =>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
A7,E7: 7.. / A7 = 7  =>  0 pairs (*) / E7 = 7  =>  0 pairs (X)
A4,B4: 8.. / A4 = 8  => 10 pairs (_) / B4 = 8  =>  0 pairs (X)
H3,I3: 9.. / H3 = 9  =>  9 pairs (_) / I3 = 9  =>  9 pairs (_)
B4,B5: 9.. / B4 = 9  => 10 pairs (_) / B5 = 9  =>  0 pairs (X)
C8,C9: 9.. / C8 = 9  =>  0 pairs (X) / C9 = 9  => 16 pairs (_)
* DURATION: 0:00:23.260523  START: 23:42:40.349334  END: 23:43:03.609857 2019-04-30
* CP COUNT: (23)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B7,C2,C8,D3,E5,E7,F8,G5)
* .7..9....9...2576...1...3.....6.....1.52...8..4..8......84.291661..3..7..2.......
* PAIR B2: 3,8 BLK 1
A1: 3,8,2,4,5                            # reduction candidate for 3,8
A1: 3,8 => CTR
* .7..9....9.4.2576...1...3.....65....1.524.68..46.8......8472916619538.7.427.16...
A1: 2,4,5                                #  9 pairs
* PAIR B2: 3,8 ROW 2
D2: 3,8,1                                # reduction candidate for 3,8
D2: 3,8 => CTR
* .7..9....9.4.25761..1...3.....65....1.524.68..46.8......8472916619538.7.427.16...
D2: 1                                    # 13 pairs
* PAIR B2: 3,8 COL B
B4: 3,8,9                                # reduction candidate for 3,8
B4: 3,8 => CTR
* .7..96...9...2576..61...3.....6.....1952..68..46.8.....5847291661..3..7..2..6....
B4: 9                                    # 10 pairs
* PAIR C2: 3,4 BLK 1
A1: 3,4,2,5,8                            # reduction candidate for 3,4
A1: 3,4                                  # 15 pairs
C1: 3,4,2,6                              # reduction candidate for 3,4
C1: 3,4 => CTR
* .7..96...9...2576..61...3.....6.....1.52..68..46.8.....5847291661..3..7..2..6....
C1: 2,6                                  # 10 pairs
* PAIR D3: 7,8 BLK 2
F3: 7,8,4,6                              # reduction candidate for 7,8
F3: 7,8                                  # 17 pairs
F3: 4,6                                  # 10 pairs
* PAIR D3: 7,8 COL D
D9: 7,8,1,5,9                            # reduction candidate for 7,8
D9: 7,8                                  # 18 pairs
D9: 1,5,9                                #  9 pairs
* PAIR E5: 4,7 BLK 5
E4: 4,7,1,5                              # reduction candidate for 4,7
E4: 4,7 => SOLVED
* 276394158983125764451867392892641537165273489347589621738452916614938275529716843
E4: 1,5                                  # 10 pairs
F4: 4,7,1,3,9                            # reduction candidate for 4,7
F4: 4,7                                  # 12 pairs
F5: 4,7,3,9                              # reduction candidate for 4,7
F5: 4,7 => CTR
* .7..9....9...2576..61...3.....6.....1.52..68..46.8.....5847291661..3..7..2..6....
F5: 3,9                                  # 10 pairs
* PAIR E5: 4,7 ROW 5
I5: 4,7,3,9                              # reduction candidate for 4,7
I5: 4,7 => CTR
* .7..9....9...2576..61...3.....6.....1.52..68..46.8.....5847291661..3..7..2..6....
I5: 3,9                                  # 10 pairs
* PAIR E5: 4,7 COL E
E3: 4,7,6                                # reduction candidate for 4,7
E3: 4,7 => CTR
* .76.9.1..98.125764.51.463..89.614...16527.48..4758.6.1738452916614.3..7.529.6.8..
E3: 6 => SOLVED
* 276394158983125764451867392892641537165273489347589621738452916614938275529716843
* PAIR B7: 3,5 BLK 7
A7: 3,5,7                                # reduction candidate for 3,5
A7: 3,5 => CTR
* .7..96...9...2576...1...3.....6.....1.524.68..46.8......847291661..3..7..2.......
A7: 7 => SOLVED
* 276394158983125764451867392892641537165273489347589621738452916614938275529716843
* PAIR C8: 4,9 BLK 7
C9: 4,9,7                                # reduction candidate for 4,9
C9: 7 => CTR
* .7..9....9...2576...1...3.....65....1.524.68..46.8......8472916619538.7.427.16...
C9: 4,9                                  # 18 pairs
* PAIR E7: 5,7 BLK 8
D9: 5,7,1,8,9                            # reduction candidate for 5,7
D9: 5,7                                  # 23 pairs
E9: 5,7,1,6                              # reduction candidate for 5,7
E9: 5,7 => CTR
* .7..9....9...2576...1.6.3.....61....16524..8..4..8......84.291661..3..7..2.......
E9: 1,6                                  # 10 pairs
* PAIR E7: 5,7 ROW 7
A7: 5,7,3                                # reduction candidate for 5,7
A7: 5,7 => SOLVED
* 276394158983125764451867392892641537165273489347589621738452916614938275529716843
A7: 3 => CTR
* .7..96...9...2576...1...3.....6.....1.524.68..46.8....35847291661..3..7..2.......
* PAIR E7: 5,7 COL E
E4: 5,7,1,4                              # reduction candidate for 5,7
E4: 5,7 => CTR
* .76.9....9...2576...1.6.3.....6.....16524..8..4..8......84.291661..3..7..2..16...
E4: 1,4 => SOLVED
* 276394158983125764451867392892641537165273489347589621738452916614938275529716843
* PAIR F8: 8,9 BLK 8
D8: 8,9,5                                # reduction candidate for 8,9
D8: 8,9                                  # 23 pairs
D9: 8,9,1,5,7                            # reduction candidate for 8,9
D9: 8,9 => CTR
* .76.9....9...2576...1.6.3.....65....16524..8..4..8......847291661.53..7..2..16...
D9: 1,5,7                                #  9 pairs
F9: 8,9,1,6,7                            # reduction candidate for 8,9
F9: 8,9 => CTR
* .7..9....9...2576...1...3.....61....1.52...8..4.58......845291661..3..7.52..6....
F9: 1,6,7                                #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060608-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 3,8 => CTR => A1: 2,4,5
* DIS # D2: 3,8 => CTR => D2: 1
* DIS # B4: 3,8 => CTR => B4: 9
* DIS # C1: 3,4 => CTR => C1: 2,6
* PRF # E4: 4,7 => SOL
* DIS # F5: 4,7 => CTR => F5: 3,9
* DIS # I5: 4,7 => CTR => I5: 3,9
* DIS # E3: 4,7 => CTR => E3: 6
* PRF # E3: 6 => SOL
* DIS # A7: 3,5 => CTR => A7: 7
* PRF # A7: 7 => SOL
* DIS # C9: 7 => CTR => C9: 4,9
* DIS # E9: 5,7 => CTR => E9: 1,6
* PRF # A7: 5,7 => SOL
* DIS # A7: 3 => CTR => A7: 5,7
* DIS # E4: 5,7 => CTR => E4: 1,4
* PRF # E4: 1,4 => SOL
* DIS # D9: 8,9 => CTR => D9: 1,5,7
* DIS # F9: 8,9 => CTR => F9: 1,6,7
* CNT  19 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B7,C2,C8,D3,E5,E7,F8,G5)
* .7..9....9...2576...1...3.....6.....1.52...8..4..8......84.291661..3..7..2.......
* PAIR B2: 3,8 BLK 1
A1: 3,8,2,4,5                            # reduction candidate for 3,8
A1: 3,8 => CTR
* .7..9....9.4.2576...1...3.....65....1.524.68..46.8......8472916619538.7.427.16...
* PAIR B2: 3,8 ROW 2
D2: 3,8,1                                # reduction candidate for 3,8
D2: 3,8 => CTR
* .7..9....9.4.25761..1...3.....65....1.524.68..46.8......8472916619538.7.427.16...
* PAIR B2: 3,8 COL B
B4: 3,8,9                                # reduction candidate for 3,8
B4: 3,8 => CTR
* .7..96...9..12576..61...3.....6.....1952..68..46.8.....5847291661..3..7..2..61...
* PAIR RESTART
* PAIR D3: 7,8 BLK 2
F3: 7,8,4,6                              # reduction candidate for 7,8
F3: 4,6 => CTR
* .7..96...9..12576..61.743..89.6.....13524.68..46.8......84.291661..3..7..2.......
* PAIR D3: 7,8 COL D
D9: 7,8,5,9                              # reduction candidate for 7,8
D9: 5,9 => CTR
* .7.39....983125764..1...3..89.65....1.524.68..46.8......847291661..3..7..2..16...
* PAIR RESTART
* PAIR E5: 4,7 BLK 5
E4: 4,7,1,5                              # reduction candidate for 4,7
E4: 4,7 => SOLVED
* 276394158983125764451867392892641537165273489347589621738452916614938275529716843
* DURATION: 0:00:07.626379  START: 23:43:22.705853  END: 23:43:30.332232 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060608-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 3,8 => CTR => A1: 2,4,5
* DIS A1: 2,4,5 # D2: 3,8 => CTR => D2: 1
* DIS A1: 2,4,5 + D2: 1 # B4: 3,8 => CTR => B4: 9
* DIS A1: 2,4,5 + D2: 1 + B4: 9 # F3: 4,6 => CTR => F3: 7,8
* DIS A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 # D9: 5,9 => CTR => D9: 7,8
* PRF A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 # E4: 4,7 => SOL
* STA A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 + E4: 4,7
* CNT   6 HDP CHAINS /   8 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060608, absurd

Solution

position: 276394158983125764451867392892641537165273489347589621738452916614938275529716843 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 # A1: 3,8 => CTR => A1: 2,4,5
* INC # A1: 2,4,5 => UNS
* DIS # D2: 3,8 => CTR => D2: 1
* INC # D2: 1 => UNS
* DIS # B4: 3,8 => CTR => B4: 9
* INC # B4: 9 => UNS
* INC # A1: 3,4 => UNS
* DIS # C1: 3,4 => CTR => C1: 2,6
* INC # C1: 2,6 => UNS
* INC # F3: 7,8 => UNS
* INC # F3: 4,6 => UNS
* INC # D9: 7,8 => UNS
* INC # D9: 1,5,9 => UNS
* PRF # E4: 4,7 => SOL
* INC # E4: 1,5 => UNS
* INC # F4: 4,7 => UNS
* DIS # F5: 4,7 => CTR => F5: 3,9
* INC # F5: 3,9 => UNS
* DIS # I5: 4,7 => CTR => I5: 3,9
* INC # I5: 3,9 => UNS
* DIS # E3: 4,7 => CTR => E3: 6
* PRF # E3: 6 => SOL
* DIS # A7: 3,5 => CTR => A7: 7
* PRF # A7: 7 => SOL
* INC # C9: 4,9 => UNS
* DIS # C9: 7 => CTR => C9: 4,9
* INC # D9: 5,7 => UNS
* DIS # E9: 5,7 => CTR => E9: 1,6
* INC # E9: 1,6 => UNS
* PRF # A7: 5,7 => SOL
* DIS # A7: 3 => CTR => A7: 5,7
* DIS # E4: 5,7 => CTR => E4: 1,4
* PRF # E4: 1,4 => SOL
* INC # D8: 8,9 => UNS
* DIS # D9: 8,9 => CTR => D9: 1,5,7
* INC # D9: 1,5,7 => UNS
* DIS # F9: 8,9 => CTR => F9: 1,6,7
* INC # F9: 1,6,7 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 3,8 => CTR => A1: 2,4,5
* DIS A1: 2,4,5 # D2: 3,8 => CTR => D2: 1
* DIS A1: 2,4,5 + D2: 1 # B4: 3,8 => CTR => B4: 9
* INC A1: 2,4,5 + D2: 1 + B4: 9 # F3: 7,8 => UNS
* DIS A1: 2,4,5 + D2: 1 + B4: 9 # F3: 4,6 => CTR => F3: 7,8
* INC A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 # D9: 7,8 => UNS
* DIS A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 # D9: 5,9 => CTR => D9: 7,8
* PRF A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 # E4: 4,7 => SOL
* STA A1: 2,4,5 + D2: 1 + B4: 9 + F3: 7,8 + D9: 7,8 + E4: 4,7
* CNT   8 HDP CHAINS /   8 HYP OPENED