Analysis of zz-www.sudokuoftheday.co.uk-20060724-absurd-base.sdk

Contents

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

level: medium

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

position: .2..3..6.....8.3.....7.45.....6....9.9...2.58....912...54...81....8436..3......9. initial

Autosolve

position: .2.13596.....8.3.....7.458....658..9.9..72.58....912.6.54...813...8436.53..51..9. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C9: 7,8 => CTR => C9: 2,6
* PRF # F7: 7 => SOL
* PRF # H2: 4,7 => SOL
* PRF # I9: 4,7 => SOL
* PRF # I2: 1,2 => SOL
* DIS # B6: 3,4 => CTR => B6: 7,8
* PRF # G4: 1,4 => SOL
* DIS # A5: 6 => CTR => A5: 1,4
* DIS # B9: 6,7 => CTR => B9: 8
* DIS # C9: 6,7 => CTR => C9: 2,8
* PRF # F7: 6,7 => SOL
* DIS # A2: 6,7 => CTR => A2: 1,4,5
* PRF # A8: 1,7 => SOL
* DIS # C8: 1,7 => CTR => C8: 2,9
* PRF # F7: 6,7 => SOL
* DIS # B9: 6,7 => CTR => B9: 8
* DIS # C9: 6,7 => CTR => C9: 2,8
* PRF # I9: 4 => SOL
* PRF # H2: 4 => SOL
* PRF # I9: 4,7 => SOL
* PRF # G4: 1 => SOL
* CNT  21 HDP CHAINS /  53 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 # C9: 7,8 => CTR => C9: 2,6
* DIS C9: 2,6 # F7: 6,9 => CTR => F7: 7
* PRF C9: 2,6 + F7: 7 => SOL
* STA C9: 2,6 + F7: 7
* CNT   3 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

.2..3..6.....8.3.....7.45.....6....9.9...2.58....912...54...81....8436..3......9. initial
.2.13596.....8.3.....7.458....658..9.9..72.58....912.6.54...813...8436.53..51..9. autosolve
428135967567289341931764582243658179196372458875491236654927813719843625382516794 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (16)
C1: 7,8
D2: 2,9
F2: 6,9
E3: 2,6
I1: 4,7
I3: 1,2
D5: 3,4
D6: 3,4
G5: 1,4
A7: 6,7
B8: 1,7
D7: 2,9
E7: 2,6
F9: 6,7
H8: 2,7
G9: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I2,I3: 1.. / I2 = 1  =>  0 pairs (*) / I3 = 1  =>  0 pairs (X)
G4,G5: 1.. / G4 = 1  =>  0 pairs (*) / G5 = 1  =>  0 pairs (X)
D2,E3: 2.. / D2 = 2  =>  0 pairs (*) / E3 = 2  =>  0 pairs (X)
A4,C4: 2.. / A4 = 2  => 16 pairs (_) / C4 = 2  =>  0 pairs (X)
D7,E7: 2.. / D7 = 2  => 24 pairs (_) / E7 = 2  =>  0 pairs (*)
H8,I9: 2.. / H8 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
E3,I3: 2.. / E3 = 2  => 24 pairs (_) / I3 = 2  =>  0 pairs (*)
C9,I9: 2.. / C9 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
A4,A8: 2.. / A4 = 2  => 16 pairs (_) / A8 = 2  =>  0 pairs (X)
D2,D7: 2.. / D2 = 2  =>  0 pairs (*) / D7 = 2  =>  0 pairs (X)
E3,E7: 2.. / E3 = 2  => 24 pairs (_) / E7 = 2  =>  0 pairs (*)
H2,H8: 2.. / H2 = 2  => 24 pairs (_) / H8 = 2  =>  0 pairs (*)
B3,C3: 3.. / B3 = 3  => 16 pairs (_) / C3 = 3  => 17 pairs (_)
D5,D6: 3.. / D5 = 3  => 16 pairs (_) / D6 = 3  =>  0 pairs (X)
H4,H6: 3.. / H4 = 3  => 17 pairs (_) / H6 = 3  => 17 pairs (_)
C5,D5: 3.. / C5 = 3  =>  0 pairs (X) / D5 = 3  => 16 pairs (_)
D5,D6: 4.. / D5 = 4  =>  0 pairs (X) / D6 = 4  => 16 pairs (_)
G9,I9: 4.. / G9 = 4  => 21 pairs (_) / I9 = 4  =>  0 pairs (*)
A1,I1: 4.. / A1 = 4  => 19 pairs (_) / I1 = 4  => 21 pairs (_)
A2,C2: 5.. / A2 = 5  => 16 pairs (_) / C2 = 5  => 26 pairs (_)
A6,C6: 5.. / A6 = 5  => 26 pairs (_) / C6 = 5  => 16 pairs (_)
A2,A6: 5.. / A2 = 5  => 16 pairs (_) / A6 = 5  => 26 pairs (_)
C2,C6: 5.. / C2 = 5  => 26 pairs (_) / C6 = 5  => 16 pairs (_)
F2,E3: 6.. / F2 = 6  => 24 pairs (_) / E3 = 6  =>  0 pairs (*)
A5,C5: 6.. / A5 = 6  =>  0 pairs (X) / C5 = 6  => 16 pairs (_)
E3,E7: 6.. / E3 = 6  =>  0 pairs (*) / E7 = 6  =>  0 pairs (X)
F7,F9: 7.. / F7 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
A7,F7: 7.. / A7 = 7  => 24 pairs (_) / F7 = 7  =>  0 pairs (*)
G4,G9: 7.. / G4 = 7  => 21 pairs (_) / G9 = 7  =>  0 pairs (*)
A1,C1: 8.. / A1 = 8  => 21 pairs (_) / C1 = 8  => 18 pairs (_)
B9,C9: 8.. / B9 = 8  => 19 pairs (_) / C9 = 8  =>  0 pairs (X)
A1,A6: 8.. / A1 = 8  => 21 pairs (_) / A6 = 8  => 18 pairs (_)
B6,B9: 8.. / B6 = 8  =>  0 pairs (X) / B9 = 8  => 19 pairs (_)
A3,C3: 9.. / A3 = 9  => 16 pairs (_) / C3 = 9  => 17 pairs (_)
D2,F2: 9.. / D2 = 9  => 24 pairs (_) / F2 = 9  =>  0 pairs (*)
A8,C8: 9.. / A8 = 9  => 17 pairs (_) / C8 = 9  => 16 pairs (_)
D7,F7: 9.. / D7 = 9  =>  0 pairs (*) / F7 = 9  =>  0 pairs (X)
A3,A8: 9.. / A3 = 9  => 16 pairs (_) / A8 = 9  => 17 pairs (_)
C3,C8: 9.. / C3 = 9  => 17 pairs (_) / C8 = 9  => 16 pairs (_)
D2,D7: 9.. / D2 = 9  => 24 pairs (_) / D7 = 9  =>  0 pairs (*)
F2,F7: 9.. / F2 = 9  =>  0 pairs (*) / F7 = 9  =>  0 pairs (X)
* DURATION: 0:00:49.519497  START: 01:14:52.865423  END: 01:15:42.384920 2019-05-01
* CP COUNT: (41)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,C1,D2,D5,D6,D7,E3,E7,F2,F9,G5,G9,H8,I1,I3)
* .2.13596.....8.3.....7.458....658..9.9..72.58....912.6.54...813...8436.53..51..9.
* PAIR C1: 7,8 BLK 1
A1: 7,8,4                                # reduction candidate for 7,8
A1: 7,8                                  # 21 pairs
A1: 4                                    # 19 pairs
* PAIR C1: 7,8 COL C
C6: 7,8,3,5                              # reduction candidate for 7,8
C6: 7,8                                  # 26 pairs
C9: 7,8,2,6                              # reduction candidate for 7,8
C9: 7,8 => CTR
* 827135964...986327.3.724581...6587.9.9..72158....912.6.54269813...843675368517492
C9: 2,6                                  # 20 pairs
* PAIR F2: 6,9 COL F
F7: 6,9,7                                # reduction candidate for 6,9
F7: 7 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
F7: 6,9                                  # 24 pairs
* PAIR I1: 4,7 BLK 3
H2: 4,7,2                                # reduction candidate for 4,7
H2: 4,7 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
H2: 2                                    # 24 pairs
I2: 4,7,1,2                              # reduction candidate for 4,7
I2: 4,7                                  # 24 pairs
* PAIR I1: 4,7 ROW 1
A1: 4,7,8                                # reduction candidate for 4,7
A1: 8                                    # 21 pairs
A1: 4,7                                  # 18 pairs
* PAIR I1: 4,7 COL I
I9: 4,7,2                                # reduction candidate for 4,7
I9: 4,7 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
I9: 2                                    # 24 pairs
* PAIR I3: 1,2 BLK 3
I2: 1,2,4,7                              # reduction candidate for 1,2
I2: 1,2 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
I2: 4,7                                  # 24 pairs
* PAIR D6: 3,4 ROW 6
B6: 3,4,7,8                              # reduction candidate for 3,4
B6: 3,4 => CTR
* 428135967567289341.1.7645822..658.39.96372458835491276654927813...843625382516794
B6: 7,8                                  # 17 pairs
H6: 3,4,7                                # reduction candidate for 3,4
H6: 3,4                                  # 18 pairs
* PAIR G5: 1,4 BLK 6
G4: 1,4,7                                # reduction candidate for 1,4
G4: 1,4 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
G4: 7                                    # 21 pairs
* PAIR G5: 1,4 ROW 5
A5: 1,4,6                                # reduction candidate for 1,4
A5: 6 => CTR
* .2.13596....98632.936724581.42658739693472158...391246754269813219843675368517492
A5: 1,4                                  # 16 pairs
* PAIR A7: 6,7 BLK 7
B9: 6,7,8                                # reduction candidate for 6,7
B9: 6,7 => CTR
* 827135964...986327.3.724581.7.6581.9.9..72.58.8..912.6.54269813...843675368517492
B9: 8                                    # 19 pairs
C9: 6,7,2,8                              # reduction candidate for 6,7
C9: 6,7 => CTR
* .2.13596....98632..63724581...6587.9691.72.58....912.6.54269813...843675386517492
C9: 2,8                                  # 17 pairs
* PAIR A7: 6,7 ROW 7
F7: 6,7,9                                # reduction candidate for 6,7
F7: 6,7 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
F7: 9                                    # 24 pairs
* PAIR A7: 6,7 COL A
A2: 6,7,1,4,5                            # reduction candidate for 6,7
A2: 6,7 => CTR
* 827135964645.893.1...764582...658..9.96372.585..4912.6754926813.1.8436.53..51..9.
A2: 1,4,5                                # 16 pairs
* PAIR B8: 1,7 BLK 7
A8: 1,7,2,9                              # reduction candidate for 1,7
A8: 1,7 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
A8: 2,9                                  # 17 pairs
C8: 1,7,2,9                              # reduction candidate for 1,7
C8: 1,7 => CTR
* .2.13596..6.2893.113976458224.658..9.96372158...4912.66549278139..843625382516.9.
C8: 2,9                                  # 17 pairs
* PAIR B8: 1,7 COL B
B2: 1,7,4,6                              # reduction candidate for 1,7
B2: 1,7                                  # 24 pairs
B4: 1,7,3,4                              # reduction candidate for 1,7
B4: 1,7                                  # 20 pairs
* PAIR F9: 6,7 BLK 8
F7: 6,7,9                                # reduction candidate for 6,7
F7: 6,7 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
F7: 9                                    # 24 pairs
* PAIR F9: 6,7 ROW 9
B9: 6,7,8                                # reduction candidate for 6,7
B9: 6,7 => CTR
* 827135964...986327.3.724581.7.6581.9.9..72.58.8..912.6.54269813...843675368517492
B9: 8                                    # 19 pairs
C9: 6,7,2,8                              # reduction candidate for 6,7
C9: 6,7 => CTR
* .2.13596....98632..63724581...6587.9691.72.58....912.6.54269813...843675386517492
C9: 2,8                                  # 17 pairs
* PAIR H8: 2,7 BLK 9
I9: 2,7,4                                # reduction candidate for 2,7
I9: 4 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
I9: 2,7                                  # 21 pairs
* PAIR H8: 2,7 ROW 8
A8: 2,7,1,9                              # reduction candidate for 2,7
A8: 2,7                                  # 17 pairs
C8: 2,7,1,9                              # reduction candidate for 2,7
C8: 2,7                                  # 18 pairs
* PAIR H8: 2,7 COL H
H2: 2,7,4                                # reduction candidate for 2,7
H2: 4 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
H2: 2,7                                  # 21 pairs
* PAIR G9: 4,7 BLK 9
I9: 4,7,2                                # reduction candidate for 4,7
I9: 4,7 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
I9: 2                                    # 24 pairs
* PAIR G9: 4,7 COL G
G4: 4,7,1                                # reduction candidate for 4,7
G4: 1 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
G4: 4,7                                  # 18 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060724-absurd-base-pr-000.dot
* REASONING
* DIS # C9: 7,8 => CTR => C9: 2,6
* PRF # F7: 7 => SOL
* PRF # H2: 4,7 => SOL
* PRF # I9: 4,7 => SOL
* PRF # I2: 1,2 => SOL
* DIS # B6: 3,4 => CTR => B6: 7,8
* PRF # G4: 1,4 => SOL
* DIS # A5: 6 => CTR => A5: 1,4
* DIS # B9: 6,7 => CTR => B9: 8
* DIS # C9: 6,7 => CTR => C9: 2,8
* PRF # F7: 6,7 => SOL
* DIS # A2: 6,7 => CTR => A2: 1,4,5
* PRF # A8: 1,7 => SOL
* DIS # C8: 1,7 => CTR => C8: 2,9
* PRF # F7: 6,7 => SOL
* DIS # B9: 6,7 => CTR => B9: 8
* DIS # C9: 6,7 => CTR => C9: 2,8
* PRF # I9: 4 => SOL
* PRF # H2: 4 => SOL
* PRF # I9: 4,7 => SOL
* PRF # G4: 1 => SOL
* CNT  21 HDP CHAINS /  53 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B8,C1,D2,D5,D6,D7,E3,E7,F2,F9,G5,G9,H8,I1,I3)
* .2.13596.....8.3.....7.458....658..9.9..72.58....912.6.54...813...8436.53..51..9.
* PAIR C1: 7,8 BLK 1
A1: 7,8,4                                # reduction candidate for 7,8
A1: 7,8                                  # 21 pairs
A1: 4                                    # 19 pairs
* PAIR C1: 7,8 COL C
C6: 7,8,3,5                              # reduction candidate for 7,8
C6: 7,8                                  # 26 pairs
C9: 7,8,2,6                              # reduction candidate for 7,8
C9: 7,8 => CTR
* 827135964...986327.3.724581...6587.9.9..72158....912.6.54269813...843675368517492
* RESTART
* PAIR RESTART
* PAIR C1: 7,8 BLK 1
A1: 7,8,4                                # reduction candidate for 7,8
A1: 7,8                                  # 29 pairs
A1: 4                                    # 20 pairs
* PAIR F2: 6,9 COL F
F7: 6,9,7                                # reduction candidate for 6,9
F7: 6,9 => CTR
* .2.13596....98632.963724581...6587.969.472158.7.391246754269813.1.843675386517492
F7: 7 => SOLVED
* 428135967567289341931764582243658179196372458875491236654927813719843625382516794
* DURATION: 0:00:06.498091  START: 01:16:19.664482  END: 01:16:26.162573 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060724-absurd-base-pr-001.dot
* REASONING
* DIS # C9: 7,8 => CTR => C9: 2,6
* DIS C9: 2,6 # F7: 6,9 => CTR => F7: 7
* PRF C9: 2,6 + F7: 7 => SOL
* STA C9: 2,6 + F7: 7
* CNT   3 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060724, absurd

Solution

position: 428135967567289341931764582243658179196372458875491236654927813719843625382516794 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:

* INC # A1: 7,8 => UNS
* INC # A1: 4 => UNS
* INC # C6: 7,8 => UNS
* DIS # C9: 7,8 => CTR => C9: 2,6
* INC # C9: 2,6 => UNS
* INC # F7: 6,9 => UNS
* PRF # F7: 7 => SOL
* PRF # H2: 4,7 => SOL
* INC # H2: 2 => UNS
* INC # I2: 4,7 => UNS
* INC # A1: 4,7 => UNS
* INC # A1: 8 => UNS
* PRF # I9: 4,7 => SOL
* INC # I9: 2 => UNS
* PRF # I2: 1,2 => SOL
* INC # I2: 4,7 => UNS
* DIS # B6: 3,4 => CTR => B6: 7,8
* INC # B6: 7,8 => UNS
* INC # H6: 3,4 => UNS
* PRF # G4: 1,4 => SOL
* INC # G4: 7 => UNS
* INC # A5: 1,4 => UNS
* DIS # A5: 6 => CTR => A5: 1,4
* DIS # B9: 6,7 => CTR => B9: 8
* INC # B9: 8 => UNS
* DIS # C9: 6,7 => CTR => C9: 2,8
* INC # C9: 2,8 => UNS
* PRF # F7: 6,7 => SOL
* INC # F7: 9 => UNS
* DIS # A2: 6,7 => CTR => A2: 1,4,5
* INC # A2: 1,4,5 => UNS
* PRF # A8: 1,7 => SOL
* INC # A8: 2,9 => UNS
* DIS # C8: 1,7 => CTR => C8: 2,9
* INC # C8: 2,9 => UNS
* INC # B2: 1,7 => UNS
* INC # B4: 1,7 => UNS
* PRF # F7: 6,7 => SOL
* INC # F7: 9 => UNS
* DIS # B9: 6,7 => CTR => B9: 8
* INC # B9: 8 => UNS
* DIS # C9: 6,7 => CTR => C9: 2,8
* INC # C9: 2,8 => UNS
* INC # I9: 2,7 => UNS
* PRF # I9: 4 => SOL
* INC # A8: 2,7 => UNS
* INC # C8: 2,7 => UNS
* INC # H2: 2,7 => UNS
* PRF # H2: 4 => SOL
* PRF # I9: 4,7 => SOL
* INC # I9: 2 => UNS
* INC # G4: 4,7 => UNS
* PRF # G4: 1 => SOL
* CNT  53 HDP CHAINS /  53 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 7,8 => UNS
* INC # A1: 4 => UNS
* INC # C6: 7,8 => UNS
* DIS # C9: 7,8 => CTR => C9: 2,6
* INC C9: 2,6 # A1: 7,8 => UNS
* INC C9: 2,6 # A1: 4 => UNS
* DIS C9: 2,6 # F7: 6,9 => CTR => F7: 7
* PRF C9: 2,6 + F7: 7 => SOL
* STA C9: 2,6 + F7: 7
* CNT   8 HDP CHAINS /   7 HYP OPENED