Analysis of zz-www.sudokuoftheday.co.uk-20060706-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...5.1..3...2.69...83......86.7.2..9..5....3..92....7......86..9..6....5......4 initial

Autosolve

position: 92..6531883...2.69...839...5.86.7923.9..5....3..92....7...9..86.89..6.3..5..8..94 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C2: 4,7 => CTR => C2: 5
* DIS # C3: 6,7 => CTR => C3: 1,4,5
* DIS # D2: 4,7 => CTR => D2: 1
* DIS # D5: 1,4 => CTR => D5: 3
* PRF # C7: 1,4 => SOL
* DIS # D7: 1,4 => CTR => D7: 2,3,5
* DIS # D7: 1,3 => CTR => D7: 2,4,5
* DIS # D9: 1,3 => CTR => D9: 2,7
* DIS # F5: 1,3 => CTR => F5: 4,8
* CNT   9 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 # C2: 4,7 => CTR => C2: 5
* DIS C2: 5 # C3: 6,7 => CTR => C3: 1,4
* DIS C2: 5 + C3: 1,4 # D2: 4,7 => CTR => D2: 1
* DIS C2: 5 + C3: 1,4 + D2: 1 # E8: 7 => CTR => E8: 1,4
* PRF C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # C7: 1,4 => SOL
* STA C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 + C7: 1,4
* CNT   5 HDP CHAINS /  26 HYP OPENED

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

Details

Positions

.2...5.1..3...2.69...83......86.7.2..9..5....3..92....7......86..9..6....5......4 initial
92..6531883...2.69...839...5.86.7923.9..5....3..92....7...9..86.89..6.3..5..8..94 autosolve
927465318835172469461839572548617923192358647376924851714593286289746135653281794 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
C1: 4,7
B3: 6,7
D1: 4,7
H3: 5,7
B4: 1,4
B6: 6,7
E4: 1,4
G5: 6,8
H5: 4,7
I5: 1,7
G6: 6,8
B7: 1,4
F9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A3,C3: 1.. / A3 = 1  => 15 pairs (_) / C3 = 1  => 15 pairs (_)
D2,E2: 1.. / D2 = 1  => 15 pairs (_) / E2 = 1  =>  0 pairs (X)
I5,I6: 1.. / I5 = 1  => 14 pairs (_) / I6 = 1  => 15 pairs (_)
B4,E4: 1.. / B4 = 1  =>  0 pairs (X) / E4 = 1  => 18 pairs (_)
B4,B7: 1.. / B4 = 1  =>  0 pairs (X) / B7 = 1  => 18 pairs (_)
G3,I3: 2.. / G3 = 2  => 23 pairs (_) / I3 = 2  => 14 pairs (_)
A5,C5: 2.. / A5 = 2  => 17 pairs (_) / C5 = 2  => 17 pairs (_)
I3,I8: 2.. / I3 = 2  => 14 pairs (_) / I8 = 2  => 23 pairs (_)
D5,F5: 3.. / D5 = 3  => 13 pairs (_) / F5 = 3  =>  0 pairs (X)
C7,C9: 3.. / C7 = 3  => 16 pairs (_) / C9 = 3  => 18 pairs (_)
G2,G3: 4.. / G2 = 4  => 16 pairs (_) / G3 = 4  => 16 pairs (_)
H5,H6: 4.. / H5 = 4  => 14 pairs (_) / H6 = 4  => 15 pairs (_)
C1,D1: 4.. / C1 = 4  =>  0 pairs (X) / D1 = 4  => 17 pairs (_)
B4,E4: 4.. / B4 = 4  => 18 pairs (_) / E4 = 4  =>  0 pairs (X)
B4,B7: 4.. / B4 = 4  => 18 pairs (_) / B7 = 4  =>  0 pairs (X)
C2,C3: 5.. / C2 = 5  => 14 pairs (_) / C3 = 5  =>  0 pairs (X)
H6,I6: 5.. / H6 = 5  => 15 pairs (_) / I6 = 5  => 16 pairs (_)
D7,D8: 5.. / D7 = 5  => 14 pairs (_) / D8 = 5  => 15 pairs (_)
C2,G2: 5.. / C2 = 5  => 14 pairs (_) / G2 = 5  =>  0 pairs (X)
D7,G7: 5.. / D7 = 5  => 14 pairs (_) / G7 = 5  => 15 pairs (_)
H3,H6: 5.. / H3 = 5  => 16 pairs (_) / H6 = 5  => 15 pairs (_)
G5,G6: 6.. / G5 = 6  => 12 pairs (_) / G6 = 6  => 16 pairs (_)
A9,C9: 6.. / A9 = 6  => 14 pairs (_) / C9 = 6  => 19 pairs (_)
B3,B6: 6.. / B3 = 6  => 14 pairs (_) / B6 = 6  =>  0 pairs (X)
C1,D1: 7.. / C1 = 7  => 17 pairs (_) / D1 = 7  =>  0 pairs (X)
D9,G9: 7.. / D9 = 7  => 18 pairs (_) / G9 = 7  => 16 pairs (_)
B3,B6: 7.. / B3 = 7  =>  0 pairs (X) / B6 = 7  => 14 pairs (_)
E2,E8: 7.. / E2 = 7  => 17 pairs (_) / E8 = 7  => 17 pairs (_)
F5,F6: 8.. / F5 = 8  => 12 pairs (_) / F6 = 8  => 16 pairs (_)
G5,G6: 8.. / G5 = 8  => 16 pairs (_) / G6 = 8  => 12 pairs (_)
F5,G5: 8.. / F5 = 8  => 12 pairs (_) / G5 = 8  => 16 pairs (_)
F6,G6: 8.. / F6 = 8  => 16 pairs (_) / G6 = 8  => 12 pairs (_)
* DURATION: 0:00:37.475730  START: 00:25:38.411722  END: 00:26:15.887452 2019-05-01
* CP COUNT: (32)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B6,B7,C1,D1,E4,F9,G5,G6,H3,H5,I5)
* 92..6531883...2.69...839...5.86.7923.9..5....3..92....7...9..86.89..6.3..5..8..94
* PAIR C1: 4,7 BLK 1
C2: 4,7,5                                # reduction candidate for 4,7
C2: 4,7 => CTR
* 92..6531883...2569165839472548617923.9135864737692485171.593286489..6.35.5..8..94
C2: 5                                    # 14 pairs
C3: 4,7,1,5,6                            # reduction candidate for 4,7
C3: 4,7                                  # 18 pairs
* PAIR C1: 4,7 COL C
C5: 4,7,1,2,6                            # reduction candidate for 4,7
C5: 4,7                                  # 20 pairs
C6: 4,7,1,6                              # reduction candidate for 4,7
C6: 4,7                                  # 18 pairs
* PAIR B3: 6,7 BLK 1
C3: 6,7,1,4,5                            # reduction candidate for 6,7
C3: 6,7 => CTR
* 924765318835..27691..8394525.86.7923.9..5....3..92...57...9..86.89.76.3..5..8..94
C3: 1,4,5                                # 13 pairs
* PAIR D1: 4,7 BLK 2
D2: 4,7,1                                # reduction candidate for 4,7
D2: 4,7 => CTR
* 92..6531883..12.69...839...518647923.9..5....3..92....74..9..86.89476.3..5..8.794
D2: 1                                    # 15 pairs
E2: 4,7,1                                # reduction candidate for 4,7
E2: 4,7                                  # 15 pairs
* PAIR D1: 4,7 COL D
D8: 4,7,1,2,5                            # reduction candidate for 4,7
D8: 4,7                                  # 20 pairs
D8: 1,2,5                                # 13 pairs
* PAIR H3: 5,7 BLK 3
G2: 5,7,4                                # reduction candidate for 5,7
G2: 5,7                                  # 16 pairs
G3: 5,7,2,4                              # reduction candidate for 5,7
G3: 5,7                                  # 18 pairs
I3: 5,7,2                                # reduction candidate for 5,7
I3: 5,7                                  # 23 pairs
* PAIR H3: 5,7 ROW 3
C3: 5,7,1,4,6                            # reduction candidate for 5,7
C3: 5,7                                  # 19 pairs
C3: 1,4,6                                # 14 pairs
* PAIR H3: 5,7 COL H
H6: 5,7,4                                # reduction candidate for 5,7
H6: 4                                    # 15 pairs
H6: 5,7                                  # 14 pairs
* PAIR B4: 1,4 BLK 4
A5: 1,4,2,6                              # reduction candidate for 1,4
A5: 1,4                                  # 18 pairs
C5: 1,4,2,6,7                            # reduction candidate for 1,4
C5: 1,4                                  # 20 pairs
C6: 1,4,6,7                              # reduction candidate for 1,4
C6: 1,4                                  # 15 pairs
* PAIR B6: 6,7 BLK 4
C5: 6,7,1,2,4                            # reduction candidate for 6,7
C5: 6,7                                  # 19 pairs
C6: 6,7,1,4                              # reduction candidate for 6,7
C6: 6,7                                  # 15 pairs
* PAIR E4: 1,4 BLK 5
D5: 1,4,3                                # reduction candidate for 1,4
D5: 1,4 => CTR
* 924765318837142569.6.839...548617923.9.45387137192864571..94.86489.76132.5..81794
D5: 3                                    # 13 pairs
F5: 1,4,3,8                              # reduction candidate for 1,4
F5: 1,4                                  # 17 pairs
F6: 1,4,8                                # reduction candidate for 1,4
F6: 1,4                                  # 12 pairs
* PAIR E4: 1,4 COL E
E2: 1,4,7                                # reduction candidate for 1,4
E2: 1,4                                  # 17 pairs
E8: 1,4,7                                # reduction candidate for 1,4
E8: 1,4                                  # 17 pairs
* PAIR H5: 4,7 BLK 6
H6: 4,7,5                                # reduction candidate for 4,7
H6: 4,7                                  # 16 pairs
H6: 5                                    # 15 pairs
* PAIR H5: 4,7 ROW 5
C5: 4,7,1,2,6                            # reduction candidate for 4,7
C5: 4,7                                  # 20 pairs
C5: 1,2,6                                # 15 pairs
* PAIR I5: 1,7 BLK 6
I6: 1,7,5                                # reduction candidate for 1,7
I6: 5                                    # 16 pairs
I6: 1,7                                  # 15 pairs
* PAIR I5: 1,7 ROW 5
C5: 1,7,2,4,6                            # reduction candidate for 1,7
C5: 1,7                                  # 17 pairs
C5: 2,4,6                                # 15 pairs
* PAIR B7: 1,4 BLK 7
C7: 1,4,2,3                              # reduction candidate for 1,4
C7: 1,4 => SOLVED
* 927465318835172469461839572548617923192358647376924851714593286289746135653281794
C7: 2,3                                  # 14 pairs
A8: 1,4,2                                # reduction candidate for 1,4
A8: 1,4                                  # 16 pairs
* PAIR B7: 1,4 ROW 7
D7: 1,4,2,3,5                            # reduction candidate for 1,4
D7: 1,4 => CTR
* 92..65318835..2469...8392..5.86.7923.9.35....3..92....7.2.93586.89576132.53281794
D7: 2,3,5                                # 13 pairs
F7: 1,4,3                                # reduction candidate for 1,4
F7: 1,4                                  # 16 pairs
* PAIR F9: 1,3 BLK 8
D7: 1,3,2,4,5                            # reduction candidate for 1,3
D7: 1,3 => CTR
* 92.465318835712469...8392..51864792329.1538.73..9286.1742.9.586.89576132.53281794
D7: 2,4,5                                # 13 pairs
F7: 1,3,4                                # reduction candidate for 1,3
F7: 1,3                                  # 20 pairs
D9: 1,3,2,7                              # reduction candidate for 1,3
D9: 1,3 => CTR
* 92..6531883...2.6916.839...548617923.9.453871371928645713.94586489576132.5.381794
D9: 2,7                                  # 14 pairs
* PAIR F9: 1,3 ROW 9
C9: 1,3,2,6                              # reduction candidate for 1,3
C9: 2,6                                  # 17 pairs
C9: 1,3                                  # 17 pairs
* PAIR F9: 1,3 COL F
F5: 1,3,4,8                              # reduction candidate for 1,3
F5: 1,3 => CTR
* 924765318837142569.6.839...548617923.9.45387137192864571..94.86489.76.32.5..81794
F5: 4,8                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060706-absurd-base-pr-000.dot
* REASONING
* DIS # C2: 4,7 => CTR => C2: 5
* DIS # C3: 6,7 => CTR => C3: 1,4,5
* DIS # D2: 4,7 => CTR => D2: 1
* DIS # D5: 1,4 => CTR => D5: 3
* PRF # C7: 1,4 => SOL
* DIS # D7: 1,4 => CTR => D7: 2,3,5
* DIS # D7: 1,3 => CTR => D7: 2,4,5
* DIS # D9: 1,3 => CTR => D9: 2,7
* DIS # F5: 1,3 => CTR => F5: 4,8
* CNT   9 HDP CHAINS /  53 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,B6,B7,C1,D1,E4,F9,G5,G6,H3,H5,I5)
* 92..6531883...2.69...839...5.86.7923.9..5....3..92....7...9..86.89..6.3..5..8..94
* PAIR C1: 4,7 BLK 1
C2: 4,7,5                                # reduction candidate for 4,7
C2: 4,7 => CTR
* 92..6531883...2569165839472548617923.9135864737692485171.593286489..6.35.5..8..94
C3: 4,7,1,6                              # reduction candidate for 4,7
C3: 4,7                                  # 18 pairs
* RESTART
* PAIR C1: 4,7 BLK 1
C3: 4,7,1,6                              # reduction candidate for 4,7
C3: 4,7                                  # 18 pairs
C3: 1,6                                  # 15 pairs
* PAIR C1: 4,7 COL C
C5: 4,7,1,2,6                            # reduction candidate for 4,7
C5: 4,7                                  # 20 pairs
C6: 4,7,1,6                              # reduction candidate for 4,7
C6: 4,7                                  # 18 pairs
* PAIR B3: 6,7 BLK 1
C3: 6,7,1,4                              # reduction candidate for 6,7
C3: 6,7 => CTR
* 924765318835..27691..8394525.86.7923.9..5....3..92...57...9..86.89.76.3..5..8..94
* PAIR D1: 4,7 BLK 2
D2: 4,7,1                                # reduction candidate for 4,7
D2: 4,7 => CTR
* 92..65318835.12.69...839...518647923.9..5....3..92....74..9..86.89476.3..5..8.794
* RESTART
* PAIR D1: 4,7 COL D
D8: 4,7,2,5                              # reduction candidate for 4,7
D8: 4,7                                  # 18 pairs
D8: 2,5                                  # 18 pairs
* PAIR H3: 5,7 BLK 3
G3: 5,7,2,4                              # reduction candidate for 5,7
G3: 5,7                                  # 18 pairs
I3: 5,7,2                                # reduction candidate for 5,7
I3: 5,7                                  # 25 pairs
* PAIR H3: 5,7 COL H
H6: 5,7,4                                # reduction candidate for 5,7
H6: 5,7                                  # 18 pairs
H6: 4                                    # 17 pairs
* PAIR B4: 1,4 BLK 4
A5: 1,4,2,6                              # reduction candidate for 1,4
A5: 1,4                                  # 22 pairs
C5: 1,4,2,6,7                            # reduction candidate for 1,4
C5: 1,4                                  # 19 pairs
C6: 1,4,6,7                              # reduction candidate for 1,4
C6: 1,4                                  # 19 pairs
* PAIR B6: 6,7 BLK 4
C5: 6,7,1,2,4                            # reduction candidate for 6,7
C5: 6,7                                  # 19 pairs
C6: 6,7,1,4                              # reduction candidate for 6,7
C6: 6,7                                  # 19 pairs
* PAIR E4: 1,4 BLK 5
F5: 1,4,3,8                              # reduction candidate for 1,4
F5: 1,4                                  # 19 pairs
F6: 1,4,8                                # reduction candidate for 1,4
F6: 1,4                                  # 16 pairs
* PAIR E4: 1,4 COL E
E8: 1,4,7                                # reduction candidate for 1,4
E8: 7 => CTR
* 92..653188351.2.69...839...5.8617923.9..5....3..92....71..9..86.89.7613..5..81794
* PAIR RESTART
* PAIR E4: 1,4 BLK 5
F5: 1,4,8                                # reduction candidate for 1,4
F5: 1,4                                  # 19 pairs
F6: 1,4,8                                # reduction candidate for 1,4
F6: 1,4                                  # 15 pairs
* PAIR B7: 1,4 BLK 7
C7: 1,4,2,3                              # reduction candidate for 1,4
C7: 1,4 => SOLVED
* 927465318835172469461839572548617923192358647376924851714593286289746135653281794
* DURATION: 0:00:20.152878  START: 00:26:50.507567  END: 00:27:10.660445 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060706-absurd-base-pr-001.dot
* REASONING
* DIS # C2: 4,7 => CTR => C2: 5
* DIS C2: 5 # C3: 6,7 => CTR => C3: 1,4
* DIS C2: 5 + C3: 1,4 # D2: 4,7 => CTR => D2: 1
* DIS C2: 5 + C3: 1,4 + D2: 1 # E8: 7 => CTR => E8: 1,4
* PRF C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # C7: 1,4 => SOL
* STA C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 + C7: 1,4
* CNT   5 HDP CHAINS /  26 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jul&YEAR=2006, 20060706, absurd

Solution

position: 927465318835172469461839572548617923192358647376924851714593286289746135653281794 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 # C2: 4,7 => CTR => C2: 5
* INC # C2: 5 => UNS
* INC # C3: 4,7 => UNS
* INC # C5: 4,7 => UNS
* INC # C6: 4,7 => UNS
* DIS # C3: 6,7 => CTR => C3: 1,4,5
* INC # C3: 1,4,5 => UNS
* DIS # D2: 4,7 => CTR => D2: 1
* INC # D2: 1 => UNS
* INC # E2: 4,7 => UNS
* INC # D8: 4,7 => UNS
* INC # D8: 1,2,5 => UNS
* INC # G2: 5,7 => UNS
* INC # G3: 5,7 => UNS
* INC # I3: 5,7 => UNS
* INC # C3: 5,7 => UNS
* INC # C3: 1,4,6 => UNS
* INC # H6: 5,7 => UNS
* INC # H6: 4 => UNS
* INC # A5: 1,4 => UNS
* INC # C5: 1,4 => UNS
* INC # C6: 1,4 => UNS
* INC # C5: 6,7 => UNS
* INC # C6: 6,7 => UNS
* DIS # D5: 1,4 => CTR => D5: 3
* INC # D5: 3 => UNS
* INC # F5: 1,4 => UNS
* INC # F6: 1,4 => UNS
* INC # E2: 1,4 => UNS
* INC # E8: 1,4 => UNS
* INC # H6: 4,7 => UNS
* INC # H6: 5 => UNS
* INC # C5: 4,7 => UNS
* INC # C5: 1,2,6 => UNS
* INC # I6: 1,7 => UNS
* INC # I6: 5 => UNS
* INC # C5: 1,7 => UNS
* INC # C5: 2,4,6 => UNS
* PRF # C7: 1,4 => SOL
* INC # C7: 2,3 => UNS
* INC # A8: 1,4 => UNS
* DIS # D7: 1,4 => CTR => D7: 2,3,5
* INC # D7: 2,3,5 => UNS
* INC # F7: 1,4 => UNS
* DIS # D7: 1,3 => CTR => D7: 2,4,5
* INC # D7: 2,4,5 => UNS
* INC # F7: 1,3 => UNS
* DIS # D9: 1,3 => CTR => D9: 2,7
* INC # D9: 2,7 => UNS
* INC # C9: 1,3 => UNS
* INC # C9: 2,6 => UNS
* DIS # F5: 1,3 => CTR => F5: 4,8
* INC # F5: 4,8 => UNS
* CNT  53 HDP CHAINS /  53 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C2: 4,7 => CTR => C2: 5
* INC C2: 5 # C3: 4,7 => UNS
* INC C2: 5 # C3: 4,7 => UNS
* INC C2: 5 # C3: 1,6 => UNS
* INC C2: 5 # C5: 4,7 => UNS
* INC C2: 5 # C6: 4,7 => UNS
* DIS C2: 5 # C3: 6,7 => CTR => C3: 1,4
* DIS C2: 5 + C3: 1,4 # D2: 4,7 => CTR => D2: 1
* INC C2: 5 + C3: 1,4 + D2: 1 # D8: 4,7 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # D8: 2,5 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # G3: 5,7 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # I3: 5,7 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # H6: 5,7 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # H6: 4 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # A5: 1,4 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # C5: 1,4 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # C6: 1,4 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # C5: 6,7 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # C6: 6,7 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # F5: 1,4 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # F6: 1,4 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 # E8: 1,4 => UNS
* DIS C2: 5 + C3: 1,4 + D2: 1 # E8: 7 => CTR => E8: 1,4
* INC C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # F5: 1,4 => UNS
* INC C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # F6: 1,4 => UNS
* PRF C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 # C7: 1,4 => SOL
* STA C2: 5 + C3: 1,4 + D2: 1 + E8: 1,4 + C7: 1,4
* CNT  26 HDP CHAINS /  26 HYP OPENED