Analysis of zz-www.sudokuoftheday.co.uk-20060320-absurd-base.sdk

Contents

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

level: medium

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

position: .......5.8...6...96....2..1.....37...6..84....716............3..8...1..52..549.6. initial

Autosolve

position: .....865.8...67..96...52..1..8..37.6.6.78451..716.5......8.6.3..86..1..52..549.6. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # I1: 2,4 => SOL
* DIS # H6: 2,4 => CTR => H6: 8,9
* PRF # H8: 2,4 => SOL
* DIS # B4: 2 => CTR => B4: 4,5
* DIS # A7: 4,5 => CTR => A7: 1,7,9
* DIS # C5: 3,9 => CTR => C5: 2
* DIS # A1: 3,9 => CTR => A1: 1,4,7
* PRF # I6: 3,4 => SOL
* DIS # A1: 3,4 => CTR => A1: 1,7,9
* DIS # E4: 2,9 => CTR => E4: 1
* DIS # H6: 2,9 => CTR => H6: 4,8
* DIS # I6: 2,3 => CTR => I6: 4,8
* DIS # C5: 9 => CTR => C5: 2,3
* PRF # I1: 2,3 => SOL
* DIS # C1: 3,7 => CTR => C1: 2,4,9
* PRF # E8: 7 => SOL
* CNT  16 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 # I1: 2,4 => SOL
* STA I1: 2,4
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

.......5.8...6...96....2..1.....37...6..84....716............3..8...1..52..549.6. initial
.....865.8...67..96...52..1..8..37.6.6.78451..716.5......8.6.3..86..1..52..549.6. autosolve
714938652825167349693452871548213796962784513371695284159826437486371925237549168 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (12)
H2: 2,4
A4: 4,5
A5: 3,9
A6: 3,4
E6: 2,9
I5: 2,3
B9: 1,3
C9: 3,7
E7: 2,7
D8: 2,3
G9: 1,8
I9: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D4,E4: 1.. / D4 = 1  =>  0 pairs (X) / E4 = 1  => 14 pairs (_)
G7,G9: 1.. / G7 = 1  =>  0 pairs (X) / G9 = 1  =>  0 pairs (_)
B2,D2: 1.. / B2 = 1  =>  0 pairs (X) / D2 = 1  => 14 pairs (_)
B9,G9: 1.. / B9 = 1  =>  0 pairs (X) / G9 = 1  =>  0 pairs (_)
A1,A7: 1.. / A1 = 1  =>  0 pairs (X) / A7 = 1  =>  0 pairs (_)
E1,E4: 1.. / E1 = 1  =>  0 pairs (X) / E4 = 1  => 14 pairs (_)
B4,C5: 2.. / B4 = 2  =>  0 pairs (X) / C5 = 2  => 12 pairs (_)
C5,I5: 2.. / C5 = 2  => 12 pairs (_) / I5 = 2  =>  0 pairs (X)
D4,D8: 2.. / D4 = 2  => 12 pairs (_) / D8 = 2  => 14 pairs (_)
B9,C9: 3.. / B9 = 3  =>  0 pairs (*) / C9 = 3  =>  0 pairs (X)
D8,E8: 3.. / D8 = 3  => 12 pairs (_) / E8 = 3  => 14 pairs (_)
E1,E8: 3.. / E1 = 3  => 12 pairs (_) / E8 = 3  => 14 pairs (_)
B2,C2: 5.. / B2 = 5  => 15 pairs (_) / C2 = 5  => 12 pairs (_)
A4,B4: 5.. / A4 = 5  => 12 pairs (_) / B4 = 5  =>  0 pairs (X)
A4,A7: 5.. / A4 = 5  => 12 pairs (_) / A7 = 5  =>  0 pairs (X)
C2,C7: 5.. / C2 = 5  => 12 pairs (_) / C7 = 5  => 15 pairs (_)
I1,H3: 7.. / I1 = 7  =>  0 pairs (X) / H3 = 7  =>  0 pairs (_)
E7,E8: 7.. / E7 = 7  => 14 pairs (_) / E8 = 7  =>  0 pairs (*)
C3,H3: 7.. / C3 = 7  =>  0 pairs (X) / H3 = 7  =>  0 pairs (_)
C9,I9: 7.. / C9 = 7  =>  0 pairs (*) / I9 = 7  =>  0 pairs (X)
H3,H8: 7.. / H3 = 7  =>  0 pairs (*) / H8 = 7  =>  0 pairs (X)
G3,H3: 8.. / G3 = 8  =>  0 pairs (*) / H3 = 8  =>  0 pairs (X)
G9,I9: 8.. / G9 = 8  =>  0 pairs (X) / I9 = 8  =>  0 pairs (_)
H3,H6: 8.. / H3 = 8  =>  0 pairs (X) / H6 = 8  =>  0 pairs (_)
I6,I9: 8.. / I6 = 8  =>  0 pairs (X) / I9 = 8  =>  0 pairs (_)
A5,C5: 9.. / A5 = 9  => 13 pairs (_) / C5 = 9  =>  0 pairs (X)
* DURATION: 0:00:28.696205  START: 20:01:33.006126  END: 20:02:01.702331 2019-04-30
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A6,B9,C9,D8,E6,E7,G9,H2,I5,I9)
* .....865.8...67..96...52..1..8..37.6.6.78451..716.5......8.6.3..86..1..52..549.6.
* PAIR H2: 2,4 BLK 3
I1: 2,4,3,7                              # reduction candidate for 2,4
I1: 2,4 => SOLVED
* 714938652825167349693452871548213796962784513371695284159826437486371925237549168
I1: 3,7                                  # 13 pairs
G2: 2,4,3                                # reduction candidate for 2,4
G2: 2,4                                  # 18 pairs
* PAIR H2: 2,4 ROW 2
B2: 2,4,1,3,5                            # reduction candidate for 2,4
B2: 2,4                                  # 16 pairs
C2: 2,4,3,5                              # reduction candidate for 2,4
C2: 2,4                                  # 17 pairs
* PAIR H2: 2,4 COL H
H4: 2,4,9                                # reduction candidate for 2,4
H4: 2,4                                  # 18 pairs
H6: 2,4,8,9                              # reduction candidate for 2,4
H6: 2,4 => CTR
* .....865.8...67..96...52.81..8..37.6.6.78451..716.5......8.6.3..86..1.752.7549.68
H6: 8,9                                  # 13 pairs
H8: 2,4,7,9                              # reduction candidate for 2,4
H8: 2,4 => SOLVED
* 714938652825167349693452871548213796962784513371695284159826437486371925237549168
H8: 7,9                                  # 13 pairs
* PAIR A4: 4,5 BLK 4
B4: 4,5,2                                # reduction candidate for 4,5
B4: 2 => CTR
* .....865.8...67..96...52..1528..3746.6.784512471625......876234.862319752..549.6.
B4: 4,5                                  # 12 pairs
* PAIR A4: 4,5 COL A
A7: 4,5,1,7,9                            # reduction candidate for 4,5
A7: 4,5 => CTR
* 1.7..865.8..167..96...52.71..8.137.69627845133716.5.8....876.3.786..1..5213549867
A7: 1,7,9                                # 12 pairs
* PAIR A5: 3,9 BLK 4
C5: 3,9,2                                # reduction candidate for 3,9
C5: 3,9 => CTR
* .....865.8...67..96...52..1.28..37.6.6.784512.71625......8762344862319752.7549168
C5: 2                                    # 12 pairs
* PAIR A5: 3,9 COL A
A1: 3,9,1,4,7                            # reduction candidate for 3,9
A1: 3,9 => CTR
* .....865.8...67..96...52..1..8..37.6.6.78451..716.5...1..8.6.3.786..1..523.549.6.
A1: 1,4,7                                # 13 pairs
* PAIR A6: 3,4 ROW 6
G6: 3,4,2,8,9                            # reduction candidate for 3,4
G6: 3,4                                  # 14 pairs
I6: 3,4,2,8                              # reduction candidate for 3,4
I6: 3,4 => SOLVED
* 714938652825167349693452871548213796962784513371695284159826437486371925237549168
I6: 2,8                                  # 13 pairs
* PAIR A6: 3,4 COL A
A1: 3,4,1,7,9                            # reduction candidate for 3,4
A1: 3,4 => CTR
* .....865.8...67..96...52..1..8..37.6.6.78451..716.5...1..8.6.3.786..1..523.549.6.
A1: 1,7,9                                # 13 pairs
* PAIR E6: 2,9 BLK 5
D4: 2,9,1                                # reduction candidate for 2,9
D4: 2,9                                  # 14 pairs
E4: 2,9,1                                # reduction candidate for 2,9
E4: 2,9 => CTR
* 7...1865.815.67..96...52.715.81.37.6.6.78451..716.5.8.15.876.3..86231..5237549168
E4: 1                                    # 14 pairs
* PAIR E6: 2,9 ROW 6
G6: 2,9,3,4,8                            # reduction candidate for 2,9
G6: 2,9                                  # 14 pairs
H6: 2,9,4,8                              # reduction candidate for 2,9
H6: 2,9 => CTR
* .....865.8...67..96...52.81..8..37.6.6.78451..716.5......8.6.3..86..1.752.7549.68
H6: 4,8                                  # 13 pairs
* PAIR I5: 2,3 BLK 6
G6: 2,3,4,8,9                            # reduction candidate for 2,3
G6: 2,3                                  # 15 pairs
I6: 2,3,4,8                              # reduction candidate for 2,3
I6: 2,3 => CTR
* 7...386548...673296.3.528715.8213796.627845133716954821..826937.863712.5237549168
I6: 4,8                                  # 13 pairs
* PAIR I5: 2,3 ROW 5
C5: 2,3,9                                # reduction candidate for 2,3
C5: 9 => CTR
* .....865.8...67..96...52..1.28..37.6.69784512.71625......8762344862319752.7549168
C5: 2,3                                  # 13 pairs
* PAIR I5: 2,3 COL I
I1: 2,3,4,7                              # reduction candidate for 2,3
I1: 2,3 => SOLVED
* 714938652825167349693452871548213796962784513371695284159826437486371925237549168
I1: 4,7                                  # 13 pairs
* PAIR B9: 1,3 COL B
B1: 1,3,2,4,9                            # reduction candidate for 1,3
B1: 1,3                                  # 16 pairs
B2: 1,3,2,4,5                            # reduction candidate for 1,3
B2: 1,3                                  # 14 pairs
* PAIR C9: 3,7 COL C
C1: 3,7,2,4,9                            # reduction candidate for 3,7
C1: 3,7 => CTR
* 7.3..865.8...673.96..352871..8..37.6.6.78451..716.5.8.1..826.37.86.71..52.7549168
C1: 2,4,9                                # 12 pairs
C3: 3,7,4,9                              # reduction candidate for 3,7
C3: 3,7                                  # 14 pairs
* PAIR E7: 2,7 BLK 8
E8: 2,7,3                                # reduction candidate for 2,7
E8: 3                                    # 14 pairs
E8: 2,7                                  # 12 pairs
* PAIR E7: 2,7 ROW 7
I7: 2,7,4                                # reduction candidate for 2,7
I7: 4                                    # 18 pairs
I7: 2,7                                  # 13 pairs
* PAIR D8: 2,3 BLK 8
E8: 2,3,7                                # reduction candidate for 2,3
E8: 7 => SOLVED
* 714938652825167349693452871548213796962784513371695284159826437486371925237549168
E8: 2,3                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060320-absurd-base-pr-000.dot
* REASONING
* PRF # I1: 2,4 => SOL
* DIS # H6: 2,4 => CTR => H6: 8,9
* PRF # H8: 2,4 => SOL
* DIS # B4: 2 => CTR => B4: 4,5
* DIS # A7: 4,5 => CTR => A7: 1,7,9
* DIS # C5: 3,9 => CTR => C5: 2
* DIS # A1: 3,9 => CTR => A1: 1,4,7
* PRF # I6: 3,4 => SOL
* DIS # A1: 3,4 => CTR => A1: 1,7,9
* DIS # E4: 2,9 => CTR => E4: 1
* DIS # H6: 2,9 => CTR => H6: 4,8
* DIS # I6: 2,3 => CTR => I6: 4,8
* DIS # C5: 9 => CTR => C5: 2,3
* PRF # I1: 2,3 => SOL
* DIS # C1: 3,7 => CTR => C1: 2,4,9
* PRF # E8: 7 => SOL
* CNT  16 HDP CHAINS /  47 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,A6,B9,C9,D8,E6,E7,G9,H2,I5,I9)
* .....865.8...67..96...52..1..8..37.6.6.78451..716.5......8.6.3..86..1..52..549.6.
* PAIR H2: 2,4 BLK 3
I1: 2,4,3,7                              # reduction candidate for 2,4
I1: 2,4 => SOLVED
* 714938652825167349693452871548213796962784513371695284159826437486371925237549168
* DURATION: 0:00:01.778152  START: 20:02:28.200583  END: 20:02:29.978735 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060320-absurd-base-pr-001.dot
* REASONING
* PRF # I1: 2,4 => SOL
* STA I1: 2,4
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060320, absurd

Solution

position: 714938652825167349693452871548213796962784513371695284159826437486371925237549168 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:

* PRF # I1: 2,4 => SOL
* INC # I1: 3,7 => UNS
* INC # G2: 2,4 => UNS
* INC # B2: 2,4 => UNS
* INC # C2: 2,4 => UNS
* INC # H4: 2,4 => UNS
* DIS # H6: 2,4 => CTR => H6: 8,9
* INC # H6: 8,9 => UNS
* PRF # H8: 2,4 => SOL
* INC # H8: 7,9 => UNS
* INC # B4: 4,5 => UNS
* DIS # B4: 2 => CTR => B4: 4,5
* DIS # A7: 4,5 => CTR => A7: 1,7,9
* INC # A7: 1,7,9 => UNS
* DIS # C5: 3,9 => CTR => C5: 2
* INC # C5: 2 => UNS
* DIS # A1: 3,9 => CTR => A1: 1,4,7
* INC # A1: 1,4,7 => UNS
* INC # G6: 3,4 => UNS
* PRF # I6: 3,4 => SOL
* INC # I6: 2,8 => UNS
* DIS # A1: 3,4 => CTR => A1: 1,7,9
* INC # A1: 1,7,9 => UNS
* INC # D4: 2,9 => UNS
* DIS # E4: 2,9 => CTR => E4: 1
* INC # E4: 1 => UNS
* INC # G6: 2,9 => UNS
* DIS # H6: 2,9 => CTR => H6: 4,8
* INC # H6: 4,8 => UNS
* INC # G6: 2,3 => UNS
* DIS # I6: 2,3 => CTR => I6: 4,8
* INC # I6: 4,8 => UNS
* INC # C5: 2,3 => UNS
* DIS # C5: 9 => CTR => C5: 2,3
* PRF # I1: 2,3 => SOL
* INC # I1: 4,7 => UNS
* INC # B1: 1,3 => UNS
* INC # B2: 1,3 => UNS
* DIS # C1: 3,7 => CTR => C1: 2,4,9
* INC # C1: 2,4,9 => UNS
* INC # C3: 3,7 => UNS
* INC # E8: 2,7 => UNS
* INC # E8: 3 => UNS
* INC # I7: 2,7 => UNS
* INC # I7: 4 => UNS
* INC # E8: 2,3 => UNS
* PRF # E8: 7 => SOL
* CNT  47 HDP CHAINS /  47 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # I1: 2,4 => SOL
* STA I1: 2,4
* CNT   1 HDP CHAINS /   1 HYP OPENED