Analysis of zz-www.sudokuoftheday.co.uk-20060325-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.............261...6.43.....7...3..952.681...1.....57..3...2...856.....6...9.. initial

Autosolve

position: ..5.............261...6.43....67...37.952.681...1.....57..3..62...8563....6...9.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A6: 3,4 => CTR => A6: 2,6,8
* DIS # B6: 3,4 => CTR => B6: 2,5,6,8
* PRF # F7: 1 => SOL
* DIS # D1: 2,7 => CTR => D1: 3,4,9
* DIS # B9: 1,4 => CTR => B9: 3,8
* DIS # F3: 2,7 => CTR => F3: 5,8,9
* PRF # C7: 4 => SOL
* DIS # H8: 1 => CTR => H8: 4,7
* CNT   8 HDP CHAINS /  39 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 # A6: 3,4 => CTR => A6: 2,6,8
* DIS A6: 2,6,8 # B6: 3,4 => CTR => B6: 2,5,6,8
* PRF A6: 2,6,8 + B6: 2,5,6,8 # F7: 1 => SOL
* STA A6: 2,6,8 + B6: 2,5,6,8 + F7: 1
* CNT   3 HDP CHAINS /  16 HYP OPENED

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

Details

Positions

..5.............261...6.43.....7...3..952.681...1.....57..3...2...856.....6...9.. initial
..5.............261...6.43....67...37.952.681...1.....57..3..62...8563....6...9.. autosolve
635492178497318526128765439851674293749523681263189754574931862912856347386247915 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
B5: 3,4
F5: 3,4
G4: 2,5
D7: 4,9
D9: 2,7
E9: 1,4
F9: 2,7
G7: 1,8
I8: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B4,C4: 1.. / B4 = 1  => 10 pairs (_) / C4 = 1  => 11 pairs (_)
F7,E9: 1.. / F7 = 1  =>  0 pairs (*) / E9 = 1  =>  0 pairs (X)
G4,G6: 2.. / G4 = 2  => 10 pairs (_) / G6 = 2  => 12 pairs (_)
D9,F9: 2.. / D9 = 2  =>  8 pairs (_) / F9 = 2  =>  0 pairs (X)
D1,D2: 3.. / D1 = 3  =>  9 pairs (_) / D2 = 3  => 15 pairs (_)
F5,F6: 3.. / F5 = 3  => 11 pairs (_) / F6 = 3  => 11 pairs (_)
A9,B9: 3.. / A9 = 3  =>  9 pairs (_) / B9 = 3  => 13 pairs (_)
B5,F5: 3.. / B5 = 3  => 11 pairs (_) / F5 = 3  => 11 pairs (_)
C2,C6: 3.. / C2 = 3  => 10 pairs (_) / C6 = 3  => 11 pairs (_)
B5,F5: 4.. / B5 = 4  => 11 pairs (_) / F5 = 4  => 11 pairs (_)
F2,F3: 5.. / F2 = 5  => 14 pairs (_) / F3 = 5  => 10 pairs (_)
G2,I3: 5.. / G2 = 5  => 10 pairs (_) / I3 = 5  => 14 pairs (_)
B4,B6: 5.. / B4 = 5  => 13 pairs (_) / B6 = 5  => 10 pairs (_)
H9,I9: 5.. / H9 = 5  => 11 pairs (_) / I9 = 5  => 14 pairs (_)
F2,G2: 5.. / F2 = 5  => 14 pairs (_) / G2 = 5  => 10 pairs (_)
F3,I3: 5.. / F3 = 5  => 10 pairs (_) / I3 = 5  => 14 pairs (_)
A1,B1: 6.. / A1 = 6  => 13 pairs (_) / B1 = 6  =>  9 pairs (_)
A6,B6: 6.. / A6 = 6  =>  9 pairs (_) / B6 = 6  => 13 pairs (_)
A1,A6: 6.. / A1 = 6  => 13 pairs (_) / A6 = 6  =>  9 pairs (_)
B1,B6: 6.. / B1 = 6  =>  9 pairs (_) / B6 = 6  => 13 pairs (_)
C2,C3: 7.. / C2 = 7  => 14 pairs (_) / C3 = 7  => 10 pairs (_)
D9,F9: 7.. / D9 = 7  =>  0 pairs (X) / F9 = 7  =>  8 pairs (_)
H8,I8: 7.. / H8 = 7  => 14 pairs (_) / I8 = 7  => 10 pairs (_)
G7,I9: 8.. / G7 = 8  => 14 pairs (_) / I9 = 8  =>  0 pairs (X)
C7,G7: 8.. / C7 = 8  =>  0 pairs (X) / G7 = 8  => 14 pairs (_)
A8,B8: 9.. / A8 = 9  =>  9 pairs (_) / B8 = 9  => 11 pairs (_)
D7,F7: 9.. / D7 = 9  => 15 pairs (_) / F7 = 9  => 16 pairs (_)
F4,H4: 9.. / F4 = 9  => 18 pairs (_) / H4 = 9  => 13 pairs (_)
* DURATION: 0:00:25.698332  START: 21:53:10.362378  END: 21:53:36.060710 2019-04-30
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,D7,D9,E9,F5,F9,G4,G7,I8)
* ..5.............261...6.43....67...37.952.681...1.....57..3..62...8563....6...9..
* PAIR B5: 3,4 BLK 4
A6: 3,4,2,6,8                            # reduction candidate for 3,4
A6: 3,4 => CTR
* 6.5.............261...6.43..5167.2.37.952.681.621.....57..3..62294856317.16.4.958
A6: 2,6,8                                #  9 pairs
B6: 3,4,2,5,6,8                          # reduction candidate for 3,4
B6: 3,4 => CTR
* .65........3....261.7.6.43.85167.2.37.952.6816.21.....578.3.162..48563.7..6...9..
B6: 2,5,6,8                              #  9 pairs
C6: 3,4,2,8                              # reduction candidate for 3,4
C6: 3,4                                  # 14 pairs
* PAIR B5: 3,4 COL B
B1: 3,4,2,6,8,9                          # reduction candidate for 3,4
B1: 3,4                                  # 17 pairs
B2: 3,4,8,9                              # reduction candidate for 3,4
B2: 3,4                                  # 11 pairs
B9: 3,4,1,8                              # reduction candidate for 3,4
B9: 3,4                                  # 11 pairs
* PAIR F5: 3,4 BLK 5
F6: 3,4,8,9                              # reduction candidate for 3,4
F6: 3,4                                  # 13 pairs
F6: 8,9                                  # 12 pairs
* PAIR G4: 2,5 BLK 6
G6: 2,5,7                                # reduction candidate for 2,5
G6: 2,5                                  # 14 pairs
G6: 7                                    # 10 pairs
* PAIR G4: 2,5 ROW 4
B4: 2,5,1,4,8                            # reduction candidate for 2,5
B4: 2,5                                  # 14 pairs
B4: 1,4,8                                # 10 pairs
* PAIR D7: 4,9 BLK 8
F7: 4,9,1                                # reduction candidate for 4,9
F7: 1 => SOLVED
* 635492178497318526128765439851674293749523681263189754574931862912856347386247915
F7: 4,9                                  # 14 pairs
* PAIR D7: 4,9 COL D
D1: 4,9,2,3,7                            # reduction candidate for 4,9
D1: 4,9                                  # 18 pairs
D2: 4,9,3,7                              # reduction candidate for 4,9
D2: 4,9                                  # 11 pairs
* PAIR D9: 2,7 COL D
D1: 2,7,3,4,9                            # reduction candidate for 2,7
D1: 2,7 => CTR
* ..5.4.8.949738..261..96.43....674.93749523681..31987..5784391629.485637...6.1.9..
D1: 3,4,9                                #  9 pairs
D3: 2,7,9                                # reduction candidate for 2,7
D3: 2,7                                  # 10 pairs
* PAIR E9: 1,4 BLK 8
F7: 1,4,9                                # reduction candidate for 1,4
F7: 9                                    # 16 pairs
F7: 1,4                                  # 15 pairs
* PAIR E9: 1,4 ROW 9
B9: 1,4,3,8                              # reduction candidate for 1,4
B9: 1,4 => CTR
* ..5...81.....8152618..6543..5167.2.3739524681...193745578439162912856374346.1.958
B9: 3,8                                  # 10 pairs
H9: 1,4,5                                # reduction candidate for 1,4
H9: 1,4                                  # 14 pairs
* PAIR E9: 1,4 COL E
E1: 1,4,8,9                              # reduction candidate for 1,4
E1: 1,4                                  # 15 pairs
E2: 1,4,8,9                              # reduction candidate for 1,4
E2: 1,4                                  # 14 pairs
* PAIR F9: 2,7 COL F
F1: 2,7,1,4,8,9                          # reduction candidate for 2,7
F1: 2,7                                  # 10 pairs
F3: 2,7,5,8,9                            # reduction candidate for 2,7
F3: 2,7 => CTR
* ..5.4179......5.261...6.435...67...37.952.681...19....57..39.62...8563....6.1.95.
F3: 5,8,9                                #  9 pairs
* PAIR G7: 1,8 ROW 7
C7: 1,8,4                                # reduction candidate for 1,8
C7: 4 => SOLVED
* 635492178497318526128765439851674293749523681263189754574931862912856347386247915
C7: 1,8                                  # 14 pairs
* PAIR G7: 1,8 COL G
G1: 1,8,7                                # reduction candidate for 1,8
G1: 1,8                                  # 11 pairs
G2: 1,8,5,7                              # reduction candidate for 1,8
G2: 1,8                                  # 15 pairs
* PAIR I8: 4,7 BLK 9
H8: 4,7,1                                # reduction candidate for 4,7
H8: 1 => CTR
* .65...798....8.1261...6.435.1.67954374952368165314....571.3.862...856317..6.1.9..
H8: 4,7                                  # 15 pairs
* PAIR I8: 4,7 COL I
I6: 4,7,5,9                              # reduction candidate for 4,7
I6: 4,7                                  # 13 pairs
I6: 5,9                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060325-absurd-base-pr-000.dot
* REASONING
* DIS # A6: 3,4 => CTR => A6: 2,6,8
* DIS # B6: 3,4 => CTR => B6: 2,5,6,8
* PRF # F7: 1 => SOL
* DIS # D1: 2,7 => CTR => D1: 3,4,9
* DIS # B9: 1,4 => CTR => B9: 3,8
* DIS # F3: 2,7 => CTR => F3: 5,8,9
* PRF # C7: 4 => SOL
* DIS # H8: 1 => CTR => H8: 4,7
* CNT   8 HDP CHAINS /  39 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B5,D7,D9,E9,F5,F9,G4,G7,I8)
* ..5.............261...6.43....67...37.952.681...1.....57..3..62...8563....6...9..
* PAIR B5: 3,4 BLK 4
A6: 3,4,2,6,8                            # reduction candidate for 3,4
A6: 3,4 => CTR
* 6.5.............261...6.43..5167.2.37.952.681.621.....57..3..62294856317.16.4.958
B6: 3,4,2,5,6,8                          # reduction candidate for 3,4
B6: 3,4 => CTR
* .65........3....261.7.6.43.85167.2.37.952.6816.21.....578.3.162..48563.7..6...9..
C6: 3,4,2,8                              # reduction candidate for 3,4
C6: 3,4                                  # 14 pairs
* RESTART
* PAIR B5: 3,4 BLK 4
C6: 3,4,2,8                              # reduction candidate for 3,4
C6: 3,4                                  # 14 pairs
C6: 2,8                                  # 13 pairs
* PAIR B5: 3,4 COL B
B1: 3,4,2,6,8,9                          # reduction candidate for 3,4
B1: 3,4                                  # 18 pairs
B2: 3,4,8,9                              # reduction candidate for 3,4
B2: 3,4                                  # 11 pairs
B9: 3,4,1,8                              # reduction candidate for 3,4
B9: 3,4                                  # 11 pairs
* PAIR F5: 3,4 BLK 5
F6: 3,4,8,9                              # reduction candidate for 3,4
F6: 3,4                                  # 13 pairs
F6: 8,9                                  # 12 pairs
* PAIR G4: 2,5 BLK 6
G6: 2,5,7                                # reduction candidate for 2,5
G6: 2,5                                  # 14 pairs
G6: 7                                    # 10 pairs
* PAIR G4: 2,5 ROW 4
B4: 2,5,1,4,8                            # reduction candidate for 2,5
B4: 2,5                                  # 14 pairs
B4: 1,4,8                                # 10 pairs
* PAIR D7: 4,9 BLK 8
F7: 4,9,1                                # reduction candidate for 4,9
F7: 1 => SOLVED
* 635492178497318526128765439851674293749523681263189754574931862912856347386247915
* DURATION: 0:00:09.634574  START: 21:53:57.258015  END: 21:54:06.892589 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060325-absurd-base-pr-001.dot
* REASONING
* DIS # A6: 3,4 => CTR => A6: 2,6,8
* DIS A6: 2,6,8 # B6: 3,4 => CTR => B6: 2,5,6,8
* PRF A6: 2,6,8 + B6: 2,5,6,8 # F7: 1 => SOL
* STA A6: 2,6,8 + B6: 2,5,6,8 + F7: 1
* CNT   3 HDP CHAINS /  16 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060325, absurd

Solution

position: 635492178497318526128765439851674293749523681263189754574931862912856347386247915 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 # A6: 3,4 => CTR => A6: 2,6,8
* INC # A6: 2,6,8 => UNS
* DIS # B6: 3,4 => CTR => B6: 2,5,6,8
* INC # B6: 2,5,6,8 => UNS
* INC # C6: 3,4 => UNS
* INC # B1: 3,4 => UNS
* INC # B2: 3,4 => UNS
* INC # B9: 3,4 => UNS
* INC # F6: 3,4 => UNS
* INC # F6: 8,9 => UNS
* INC # G6: 2,5 => UNS
* INC # G6: 7 => UNS
* INC # B4: 2,5 => UNS
* INC # B4: 1,4,8 => UNS
* INC # F7: 4,9 => UNS
* PRF # F7: 1 => SOL
* INC # D1: 4,9 => UNS
* INC # D2: 4,9 => UNS
* DIS # D1: 2,7 => CTR => D1: 3,4,9
* INC # D1: 3,4,9 => UNS
* INC # D3: 2,7 => UNS
* INC # F7: 1,4 => UNS
* INC # F7: 9 => UNS
* DIS # B9: 1,4 => CTR => B9: 3,8
* INC # B9: 3,8 => UNS
* INC # H9: 1,4 => UNS
* INC # E1: 1,4 => UNS
* INC # E2: 1,4 => UNS
* INC # F1: 2,7 => UNS
* DIS # F3: 2,7 => CTR => F3: 5,8,9
* INC # F3: 5,8,9 => UNS
* INC # C7: 1,8 => UNS
* PRF # C7: 4 => SOL
* INC # G1: 1,8 => UNS
* INC # G2: 1,8 => UNS
* INC # H8: 4,7 => UNS
* DIS # H8: 1 => CTR => H8: 4,7
* INC # I6: 4,7 => UNS
* INC # I6: 5,9 => UNS
* CNT  39 HDP CHAINS /  39 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A6: 3,4 => CTR => A6: 2,6,8
* DIS A6: 2,6,8 # B6: 3,4 => CTR => B6: 2,5,6,8
* INC A6: 2,6,8 + B6: 2,5,6,8 # C6: 3,4 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # C6: 3,4 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # C6: 2,8 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # B1: 3,4 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # B2: 3,4 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # B9: 3,4 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # F6: 3,4 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # F6: 8,9 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # G6: 2,5 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # G6: 7 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # B4: 2,5 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # B4: 1,4,8 => UNS
* INC A6: 2,6,8 + B6: 2,5,6,8 # F7: 4,9 => UNS
* PRF A6: 2,6,8 + B6: 2,5,6,8 # F7: 1 => SOL
* STA A6: 2,6,8 + B6: 2,5,6,8 + F7: 1
* CNT  16 HDP CHAINS /  16 HYP OPENED