Analysis of zz-www.sudokuoftheday.co.uk-20060506-absurd-base.sdk

Contents

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

level: medium

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

position: 6...1934.5.3.....84......1...6........4.27.6.......7.......19...72.9.5......73.2. initial

Autosolve

position: 62..1934.5137...984......1.7.6.....2..4.27.6.2.....7.....2.197..72.9.5......73.2. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 7,8 => CTR => C3: 9
* DIS # C3: 7 => CTR => C3: 8,9
* DIS # B5: 8,9 => CTR => B5: 3,5
* DIS # B6: 8,9 => CTR => B6: 3,5
* DIS # D3: 5,8 => CTR => D3: 3,6
* DIS # E3: 5,8 => CTR => E3: 3,6
* DIS # D4: 5,8 => CTR => D4: 1,3,4,9
* DIS # D5: 5,8 => CTR => D5: 1,3,9
* DIS # D6: 5,8 => CTR => D6: 1,3,4,6,9
* DIS # E7: 4,6 => CTR => E7: 5,8
* PRF # G4: 1,8 => SOL
* DIS # D5: 1,8 => CTR => D5: 3,5,9
* PRF # G9: 4 => SOL
* DIS # A8: 3,8 => CTR => A8: 1
* DIS # E7: 4,6 => CTR => E7: 5,8
* DIS # C9: 1,9 => CTR => C9: 5,8
* DIS # E7: 4,6 => CTR => E7: 5,8
* DIS # D9: 4,6 => CTR => D9: 5,8
* DIS # A8: 3,8 => CTR => A8: 1
* CNT  19 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 # C3: 7,8 => CTR => C3: 9
* DIS C3: 9 # E7: 4,6 => CTR => E7: 5,8
* PRF C3: 9 + E7: 5,8 # G4: 1,8 => SOL
* STA C3: 9 + E7: 5,8 + G4: 1,8
* CNT   3 HDP CHAINS /  16 HYP OPENED

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

Details

Positions

6...1934.5.3.....84......1...6........4.27.6.......7.......19...72.9.5......73.2. initial
62..1934.5137...984......1.7.6.....2..4.27.6.2.....7.....2.197..72.9.5......73.2. autosolve
627819345513742698489635217796154832854327169231968754345281976172496583968573421 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
C1: 7,8
B3: 8,9
D1: 5,8
E2: 4,6
I1: 5,7
G2: 2,6
G3: 2,6
I3: 5,7
G5: 1,8
A7: 3,8
B7: 4,6
C7: 5,8
B9: 4,6
H8: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A5,C6: 1.. / A5 = 1  =>  0 pairs (X) / C6 = 1  => 15 pairs (_)
D4,G4: 1.. / D4 = 1  => 16 pairs (_) / G4 = 1  =>  0 pairs (X)
A8,I8: 1.. / A8 = 1  => 17 pairs (_) / I8 = 1  =>  0 pairs (X)
C6,C9: 1.. / C6 = 1  => 15 pairs (_) / C9 = 1  =>  0 pairs (X)
F2,F3: 2.. / F2 = 2  => 11 pairs (_) / F3 = 2  => 13 pairs (_)
G2,G3: 2.. / G2 = 2  => 13 pairs (_) / G3 = 2  => 11 pairs (_)
F2,G2: 2.. / F2 = 2  => 11 pairs (_) / G2 = 2  => 13 pairs (_)
F3,G3: 2.. / F3 = 2  => 13 pairs (_) / G3 = 2  => 11 pairs (_)
D3,E3: 3.. / D3 = 3  => 14 pairs (_) / E3 = 3  => 15 pairs (_)
A7,A8: 3.. / A7 = 3  => 16 pairs (_) / A8 = 3  =>  0 pairs (X)
A7,I7: 3.. / A7 = 3  => 16 pairs (_) / I7 = 3  =>  0 pairs (X)
E2,F2: 4.. / E2 = 4  => 14 pairs (_) / F2 = 4  => 13 pairs (_)
G4,I6: 4.. / G4 = 4  => 17 pairs (_) / I6 = 4  =>  0 pairs (*)
B7,B9: 4.. / B7 = 4  => 14 pairs (_) / B9 = 4  => 18 pairs (_)
G4,G9: 4.. / G4 = 4  => 17 pairs (_) / G9 = 4  =>  0 pairs (*)
I1,I3: 5.. / I1 = 5  => 12 pairs (_) / I3 = 5  =>  0 pairs (X)
H4,H6: 5.. / H4 = 5  => 16 pairs (_) / H6 = 5  => 15 pairs (_)
C7,C9: 5.. / C7 = 5  => 12 pairs (_) / C9 = 5  =>  0 pairs (X)
E7,D9: 5.. / E7 = 5  =>  0 pairs (X) / D9 = 5  => 12 pairs (_)
D1,I1: 5.. / D1 = 5  =>  0 pairs (X) / I1 = 5  => 12 pairs (_)
B5,D5: 5.. / B5 = 5  => 14 pairs (_) / D5 = 5  =>  0 pairs (X)
C7,E7: 5.. / C7 = 5  => 12 pairs (_) / E7 = 5  =>  0 pairs (X)
C9,D9: 5.. / C9 = 5  =>  0 pairs (X) / D9 = 5  => 12 pairs (_)
G2,G3: 6.. / G2 = 6  => 11 pairs (_) / G3 = 6  => 13 pairs (_)
B7,B9: 6.. / B7 = 6  => 18 pairs (_) / B9 = 6  => 14 pairs (_)
C1,C3: 7.. / C1 = 7  => 12 pairs (_) / C3 = 7  =>  0 pairs (X)
I1,I3: 7.. / I1 = 7  =>  0 pairs (X) / I3 = 7  => 12 pairs (_)
C1,I1: 7.. / C1 = 7  => 12 pairs (_) / I1 = 7  =>  0 pairs (X)
C3,I3: 7.. / C3 = 7  =>  0 pairs (X) / I3 = 7  => 12 pairs (_)
H8,G9: 8.. / H8 = 8  =>  0 pairs (*) / G9 = 8  =>  0 pairs (X)
C1,D1: 8.. / C1 = 8  =>  0 pairs (X) / D1 = 8  => 12 pairs (_)
B3,C3: 9.. / B3 = 9  =>  0 pairs (X) / C3 = 9  => 13 pairs (_)
I5,I6: 9.. / I5 = 9  => 20 pairs (_) / I6 = 9  =>  0 pairs (X)
A9,C9: 9.. / A9 = 9  => 16 pairs (_) / C9 = 9  =>  0 pairs (X)
B4,D4: 9.. / B4 = 9  => 15 pairs (_) / D4 = 9  =>  0 pairs (X)
A5,A9: 9.. / A5 = 9  =>  0 pairs (X) / A9 = 9  => 16 pairs (_)
* DURATION: 0:00:40.557231  START: 22:57:07.919532  END: 22:57:48.476763 2019-04-30
* CP COUNT: (36)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,B7,B9,C1,C7,D1,E2,G2,G3,G5,H8,I1,I3)
* 62..1934.5137...984......1.7.6.....2..4.27.6.2.....7.....2.197..72.9.5......73.2.
* PAIR C1: 7,8 BLK 1
C3: 7,8,9                                # reduction candidate for 7,8
C3: 7,8 => CTR
* 62..1934.5137...9849.....1.7.69..1.2..4.278692.91..7.4.4.2.197..7249658.961.7342.
C3: 9                                    # 13 pairs
* PAIR B3: 8,9 BLK 1
C3: 8,9,7                                # reduction candidate for 8,9
C3: 7 => CTR
* 6285193475137...98497....157.69..1.2.54.278692.91..7.4.4.2.197..72.9.58.....7342.
C3: 8,9                                  # 12 pairs
* PAIR B3: 8,9 COL B
B4: 8,9,3,5                              # reduction candidate for 8,9
B4: 8,9                                  # 17 pairs
B5: 8,9,3,5                              # reduction candidate for 8,9
B5: 8,9 => CTR
* 62.8193455137...984.9..52177.69....2..4527.632.....7.93..25197..72.9.53...5.7382.
B5: 3,5                                  # 15 pairs
B6: 8,9,3,5                              # reduction candidate for 8,9
B6: 8,9 => CTR
* 62..1934.5137...984......1.7.69..1.21.4.278692..16.7348452.197..7249658.96..73421
B6: 3,5                                  # 15 pairs
* PAIR D1: 5,8 BLK 2
D3: 5,8,3,6                              # reduction candidate for 5,8
D3: 5,8 => CTR
* 6278193455137...9848953..177.618.4.2854.2716.2.1...7..3.825197.172.9853.9.5.73821
D3: 3,6                                  # 15 pairs
E3: 5,8,3,6                              # reduction candidate for 5,8
E3: 5,8 => CTR
* 62.5193475137...984..3...1.7.61..4.2.549271632.1...7.93..2.197..72.9.53.9.5.73821
E3: 3,6                                  # 15 pairs
F3: 5,8,2,6                              # reduction candidate for 5,8
F3: 5,8                                  # 14 pairs
* PAIR D1: 5,8 COL D
D4: 5,8,1,3,4,9                          # reduction candidate for 5,8
D4: 5,8 => CTR
* 62..1934.5137...98489....17796...1.21.4.278692.8...7.4...2.197..72.9.58.9...7342.
D4: 1,3,4,9                              # 14 pairs
D5: 5,8,1,3,9                            # reduction candidate for 5,8
D5: 5,8 => CTR
* 6278193455137...98489365.1.7.6...4.2..4.2716.2.19..7.33.825197.172.9853.9.5.73821
D5: 1,3,9                                # 14 pairs
D6: 5,8,1,3,4,6,9                        # reduction candidate for 5,8
D6: 5,8 => CTR
* 62..1934.5137...984.93...1779613.482854927163231...7593.825197.172.9853.9.5.73821
D6: 1,3,4,6,9                            # 14 pairs
D9: 5,8,4,6                              # reduction candidate for 5,8
D9: 5,8                                  # 17 pairs
* PAIR E2: 4,6 BLK 2
F2: 4,6,2                                # reduction candidate for 4,6
F2: 4,6                                  # 13 pairs
F2: 2                                    # 11 pairs
* PAIR E2: 4,6 COL E
E6: 4,6,3,5,8                            # reduction candidate for 4,6
E6: 4,6                                  # 17 pairs
E7: 4,6,5,8                              # reduction candidate for 4,6
E7: 4,6 => CTR
* 62.8193455137...984......177.6.....2.54.27.6.2.....7..8.52.1973372.985.....573.2.
E7: 5,8                                  # 16 pairs
* PAIR G2: 2,6 ROW 2
F2: 2,6,4                                # reduction candidate for 2,6
F2: 2,6                                  # 14 pairs
F2: 4                                    # 13 pairs
* PAIR G3: 2,6 ROW 3
F3: 2,6,5,8                              # reduction candidate for 2,6
F3: 2,6                                  # 15 pairs
F3: 5,8                                  # 14 pairs
* PAIR G5: 1,8 BLK 6
G4: 1,8,4                                # reduction candidate for 1,8
G4: 1,8 => SOLVED
* 627819345513742698489635217796154832854327169231968754345281976172496583968573421
G4: 4                                    # 17 pairs
* PAIR G5: 1,8 ROW 5
A5: 1,8,9                                # reduction candidate for 1,8
A5: 1,8                                  # 16 pairs
D5: 1,8,3,5,9                            # reduction candidate for 1,8
D5: 1,8 => CTR
* 62..1934.5137...984......1.7.69....2.54.27.632.....7.93..2.197..72.9.53.....7382.
D5: 3,5,9                                # 14 pairs
* PAIR G5: 1,8 COL G
G9: 1,8,4                                # reduction candidate for 1,8
G9: 4 => SOLVED
* 627819345513742698489635217796154832854327169231968754345281976172496583968573421
G9: 1,8                                  # 17 pairs
* PAIR A7: 3,8 BLK 7
A8: 3,8,1                                # reduction candidate for 3,8
A8: 3,8 => CTR
* 62..1934.5137...984......1.7.6...4.2.54.27.6.2.....7.....2.197..72.9.5.1....73.2.
A8: 1                                    # 17 pairs
* PAIR B7: 4,6 ROW 7
E7: 4,6,5,8                              # reduction candidate for 4,6
E7: 4,6 => CTR
* 62.8193455137...984......177.6.....2.54.27.6.2.....7..8.52.1973372.985.....573.2.
E7: 5,8                                  # 16 pairs
I7: 4,6,3                                # reduction candidate for 4,6
I7: 4,6                                  # 16 pairs
* PAIR C7: 5,8 BLK 7
C9: 5,8,1,9                              # reduction candidate for 5,8
C9: 1,9 => CTR
* 6278193455137...98498....177.69..1.29541278632.....7....52.197..72.9.58.8.9573.2.
C9: 5,8                                  # 16 pairs
* PAIR C7: 5,8 ROW 7
E7: 5,8,4,6                              # reduction candidate for 5,8
E7: 4,6 => CTR
* 62.8193455137...984......177.6.....2.54.27.6.2.....7..8.52.1973372.985.....573.2.
E7: 5,8                                  # 16 pairs
* PAIR B9: 4,6 ROW 9
D9: 4,6,5,8                              # reduction candidate for 4,6
D9: 4,6 => CTR
* 62781934551374..984895...177.61.5482854.2716.2.1.8.75.3.825197.172.9853.9.5.73821
D9: 5,8                                  # 17 pairs
I9: 4,6,1                                # reduction candidate for 4,6
I9: 4,6                                  # 20 pairs
* PAIR H8: 3,8 ROW 8
A8: 3,8,1                                # reduction candidate for 3,8
A8: 3,8 => CTR
* 62..1934.5137...984......1.7.6...4.2.54.27.6.2.....7.....2.197..72.9.5.1....73.2.
A8: 1                                    # 17 pairs
* PAIR H8: 3,8 COL H
H4: 3,8,5                                # reduction candidate for 3,8
H4: 3,8                                  # 15 pairs
H6: 3,8,5                                # reduction candidate for 3,8
H6: 3,8                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060506-absurd-base-pr-000.dot
* REASONING
* DIS # C3: 7,8 => CTR => C3: 9
* DIS # C3: 7 => CTR => C3: 8,9
* DIS # B5: 8,9 => CTR => B5: 3,5
* DIS # B6: 8,9 => CTR => B6: 3,5
* DIS # D3: 5,8 => CTR => D3: 3,6
* DIS # E3: 5,8 => CTR => E3: 3,6
* DIS # D4: 5,8 => CTR => D4: 1,3,4,9
* DIS # D5: 5,8 => CTR => D5: 1,3,9
* DIS # D6: 5,8 => CTR => D6: 1,3,4,6,9
* DIS # E7: 4,6 => CTR => E7: 5,8
* PRF # G4: 1,8 => SOL
* DIS # D5: 1,8 => CTR => D5: 3,5,9
* PRF # G9: 4 => SOL
* DIS # A8: 3,8 => CTR => A8: 1
* DIS # E7: 4,6 => CTR => E7: 5,8
* DIS # C9: 1,9 => CTR => C9: 5,8
* DIS # E7: 4,6 => CTR => E7: 5,8
* DIS # D9: 4,6 => CTR => D9: 5,8
* DIS # A8: 3,8 => CTR => A8: 1
* CNT  19 HDP CHAINS /  53 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B3,B7,B9,C1,C7,D1,E2,G2,G3,G5,H8,I1,I3)
* 62..1934.5137...984......1.7.6.....2..4.27.6.2.....7.....2.197..72.9.5......73.2.
* PAIR C1: 7,8 BLK 1
C3: 7,8,9                                # reduction candidate for 7,8
C3: 7,8 => CTR
* 62..1934.5137...9849.....1.7.69..1.2..4.278692.91..7.4.4.2.197..7249658.961.7342.
* PAIR E2: 4,6 BLK 2
F2: 4,6,2                                # reduction candidate for 4,6
F2: 4,6                                  # 17 pairs
F2: 2                                    # 11 pairs
* PAIR E2: 4,6 COL E
E6: 4,6,3,5,8                            # reduction candidate for 4,6
E6: 4,6                                  # 17 pairs
E7: 4,6,5,8                              # reduction candidate for 4,6
E7: 4,6 => CTR
* 6278193455137...98489....177.6.....2..4.27.6.2.....7....52.197..72.9853.9..57382.
* RESTART
* PAIR E2: 4,6 COL E
E6: 4,6,3,5,8                            # reduction candidate for 4,6
E6: 3,5,8                                # 18 pairs
E6: 4,6                                  # 17 pairs
* PAIR RESTART
* PAIR E2: 4,6 BLK 2
F2: 4,6,2                                # reduction candidate for 4,6
F2: 4,6                                  # 19 pairs
F2: 2                                    # 13 pairs
* PAIR E2: 4,6 COL E
E6: 4,6,3,5,8                            # reduction candidate for 4,6
E6: 3,5,8                                # 18 pairs
E6: 4,6                                  # 17 pairs
* PAIR G2: 2,6 ROW 2
F2: 2,6,4                                # reduction candidate for 2,6
F2: 4                                    # 19 pairs
F2: 2,6                                  # 15 pairs
* PAIR G3: 2,6 ROW 3
F3: 2,6,5                                # reduction candidate for 2,6
F3: 2,6                                  # 21 pairs
F3: 5                                    # 15 pairs
* PAIR G5: 1,8 BLK 6
G4: 1,8,4                                # reduction candidate for 1,8
G4: 1,8 => SOLVED
* 627819345513742698489635217796154832854327169231968754345281976172496583968573421
* DURATION: 0:00:12.731741  START: 22:58:20.833971  END: 22:58:33.565712 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060506-absurd-base-pr-001.dot
* REASONING
* DIS # C3: 7,8 => CTR => C3: 9
* DIS C3: 9 # E7: 4,6 => CTR => E7: 5,8
* PRF C3: 9 + E7: 5,8 # G4: 1,8 => SOL
* STA C3: 9 + E7: 5,8 + G4: 1,8
* CNT   3 HDP CHAINS /  16 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060506, absurd

Solution

position: 627819345513742698489635217796154832854327169231968754345281976172496583968573421 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 # C3: 7,8 => CTR => C3: 9
* INC # C3: 9 => UNS
* INC # C3: 8,9 => UNS
* DIS # C3: 7 => CTR => C3: 8,9
* INC # B4: 8,9 => UNS
* DIS # B5: 8,9 => CTR => B5: 3,5
* INC # B5: 3,5 => UNS
* DIS # B6: 8,9 => CTR => B6: 3,5
* INC # B6: 3,5 => UNS
* DIS # D3: 5,8 => CTR => D3: 3,6
* INC # D3: 3,6 => UNS
* DIS # E3: 5,8 => CTR => E3: 3,6
* INC # E3: 3,6 => UNS
* INC # F3: 5,8 => UNS
* DIS # D4: 5,8 => CTR => D4: 1,3,4,9
* INC # D4: 1,3,4,9 => UNS
* DIS # D5: 5,8 => CTR => D5: 1,3,9
* INC # D5: 1,3,9 => UNS
* DIS # D6: 5,8 => CTR => D6: 1,3,4,6,9
* INC # D6: 1,3,4,6,9 => UNS
* INC # D9: 5,8 => UNS
* INC # F2: 4,6 => UNS
* INC # F2: 2 => UNS
* INC # E6: 4,6 => UNS
* DIS # E7: 4,6 => CTR => E7: 5,8
* INC # E7: 5,8 => UNS
* INC # F2: 2,6 => UNS
* INC # F2: 4 => UNS
* INC # F3: 2,6 => UNS
* INC # F3: 5,8 => UNS
* PRF # G4: 1,8 => SOL
* INC # G4: 4 => UNS
* INC # A5: 1,8 => UNS
* DIS # D5: 1,8 => CTR => D5: 3,5,9
* INC # D5: 3,5,9 => UNS
* INC # G9: 1,8 => UNS
* PRF # G9: 4 => SOL
* DIS # A8: 3,8 => CTR => A8: 1
* INC # A8: 1 => UNS
* DIS # E7: 4,6 => CTR => E7: 5,8
* INC # E7: 5,8 => UNS
* INC # I7: 4,6 => UNS
* INC # C9: 5,8 => UNS
* DIS # C9: 1,9 => CTR => C9: 5,8
* INC # E7: 5,8 => UNS
* DIS # E7: 4,6 => CTR => E7: 5,8
* DIS # D9: 4,6 => CTR => D9: 5,8
* INC # D9: 5,8 => UNS
* INC # I9: 4,6 => UNS
* DIS # A8: 3,8 => CTR => A8: 1
* INC # A8: 1 => UNS
* INC # H4: 3,8 => UNS
* INC # H6: 3,8 => UNS
* CNT  53 HDP CHAINS /  53 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C3: 7,8 => CTR => C3: 9
* INC C3: 9 # F2: 4,6 => UNS
* INC C3: 9 # F2: 2 => UNS
* INC C3: 9 # E6: 4,6 => UNS
* DIS C3: 9 # E7: 4,6 => CTR => E7: 5,8
* INC C3: 9 + E7: 5,8 # E6: 4,6 => UNS
* INC C3: 9 + E7: 5,8 # E6: 3,5,8 => UNS
* INC C3: 9 + E7: 5,8 # F2: 4,6 => UNS
* INC C3: 9 + E7: 5,8 # F2: 2 => UNS
* INC C3: 9 + E7: 5,8 # E6: 4,6 => UNS
* INC C3: 9 + E7: 5,8 # E6: 3,5,8 => UNS
* INC C3: 9 + E7: 5,8 # F2: 2,6 => UNS
* INC C3: 9 + E7: 5,8 # F2: 4 => UNS
* INC C3: 9 + E7: 5,8 # F3: 2,6 => UNS
* INC C3: 9 + E7: 5,8 # F3: 5 => UNS
* PRF C3: 9 + E7: 5,8 # G4: 1,8 => SOL
* STA C3: 9 + E7: 5,8 + G4: 1,8
* CNT  16 HDP CHAINS /  16 HYP OPENED