Analysis of zz-www.sudokuoftheday.co.uk-20060319-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: .....6...27...3..6..3...8.1.8...1.5....3.74.2....2.....6.4....89.......3.21....7. initial

Autosolve

position: ...2.673.27...3..66.3...821.82..135....3.74.2.3..2.....6.4....89.......3.21....7. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 4,5 => CTR => A1: 1,8
* DIS # B1: 4,5 => CTR => B1: 1,9
* DIS # A7: 5,7 => CTR => A7: 3
* DIS # C6: 5,7 => CTR => C6: 4,6,9
* DIS # B1: 4,5 => CTR => B1: 1,9
* CNT   5 HDP CHAINS /  42 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 # A1: 4,5 => CTR => A1: 1,8
* DIS A1: 1,8 # B1: 4,5 => CTR => B1: 1,9
* DIS A1: 1,8 + B1: 1,9 # A7: 5,7 => CTR => A7: 3
* PRF A1: 1,8 + B1: 1,9 + A7: 3 # C8: 5,7 => SOL
* STA A1: 1,8 + B1: 1,9 + A7: 3 + C8: 5,7
* CNT   4 HDP CHAINS /  24 HYP OPENED

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

Details

Positions

.....6...27...3..6..3...8.1.8...1.5....3.74.2....2.....6.4....89.......3.21....7. initial
...2.673.27...3..66.3...821.82..135....3.74.2.3..2.....6.4....89.......3.21....7. autosolve
194286735278153946653974821782641359516397482439825167367412598945768213821539674 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
I1: 4,5
G2: 5,9
H2: 4,9
A4: 4,7
A5: 1,5
D4: 6,9
I4: 7,9
G6: 1,6
I6: 7,9
C7: 5,7
B8: 4,5
H7: 1,9
I9: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B1: 1.. / A1 = 1  => 19 pairs (_) / B1 = 1  => 14 pairs (_)
D2,E2: 1.. / D2 = 1  => 15 pairs (_) / E2 = 1  => 15 pairs (_)
B1,B5: 1.. / B1 = 1  => 14 pairs (_) / B5 = 1  => 19 pairs (_)
D2,D8: 1.. / D2 = 1  => 15 pairs (_) / D8 = 1  => 15 pairs (_)
F7,F8: 2.. / F7 = 2  => 14 pairs (_) / F8 = 2  => 14 pairs (_)
G7,G8: 2.. / G7 = 2  => 14 pairs (_) / G8 = 2  => 14 pairs (_)
F7,G7: 2.. / F7 = 2  => 14 pairs (_) / G7 = 2  => 14 pairs (_)
F8,G8: 2.. / F8 = 2  => 14 pairs (_) / G8 = 2  => 14 pairs (_)
A7,A9: 3.. / A7 = 3  => 13 pairs (_) / A9 = 3  =>  0 pairs (X)
E7,E9: 3.. / E7 = 3  =>  0 pairs (X) / E9 = 3  => 13 pairs (_)
A7,E7: 3.. / A7 = 3  => 13 pairs (_) / E7 = 3  =>  0 pairs (X)
A9,E9: 3.. / A9 = 3  =>  0 pairs (X) / E9 = 3  => 13 pairs (_)
I1,H2: 4.. / I1 = 4  =>  0 pairs (X) / H2 = 4  => 12 pairs (_)
E4,F6: 4.. / E4 = 4  => 13 pairs (_) / F6 = 4  => 14 pairs (_)
H8,I9: 4.. / H8 = 4  =>  0 pairs (X) / I9 = 4  => 12 pairs (_)
A4,E4: 4.. / A4 = 4  => 14 pairs (_) / E4 = 4  => 13 pairs (_)
A9,I9: 4.. / A9 = 4  =>  0 pairs (X) / I9 = 4  => 12 pairs (_)
F3,F6: 4.. / F3 = 4  => 13 pairs (_) / F6 = 4  => 14 pairs (_)
H2,H8: 4.. / H2 = 4  => 12 pairs (_) / H8 = 4  =>  0 pairs (X)
I1,I9: 4.. / I1 = 4  =>  0 pairs (X) / I9 = 4  => 12 pairs (_)
I1,G2: 5.. / I1 = 5  => 12 pairs (_) / G2 = 5  =>  0 pairs (X)
I1,I9: 5.. / I1 = 5  => 12 pairs (_) / I9 = 5  =>  0 pairs (X)
C5,C6: 6.. / C5 = 6  => 14 pairs (_) / C6 = 6  =>  0 pairs (X)
D4,E4: 6.. / D4 = 6  => 15 pairs (_) / E4 = 6  => 17 pairs (_)
C5,H5: 6.. / C5 = 6  => 14 pairs (_) / H5 = 6  =>  0 pairs (X)
D3,E3: 7.. / D3 = 7  => 13 pairs (_) / E3 = 7  => 16 pairs (_)
I4,I6: 7.. / I4 = 7  => 14 pairs (_) / I6 = 7  => 13 pairs (_)
A4,I4: 7.. / A4 = 7  => 13 pairs (_) / I4 = 7  => 14 pairs (_)
D3,D8: 7.. / D3 = 7  => 13 pairs (_) / D8 = 7  => 16 pairs (_)
H5,H6: 8.. / H5 = 8  => 15 pairs (_) / H6 = 8  => 17 pairs (_)
C8,A9: 8.. / C8 = 8  => 18 pairs (_) / A9 = 8  => 16 pairs (_)
E5,H5: 8.. / E5 = 8  => 17 pairs (_) / H5 = 8  => 15 pairs (_)
A1,A9: 8.. / A1 = 8  => 18 pairs (_) / A9 = 8  => 16 pairs (_)
G2,H2: 9.. / G2 = 9  => 12 pairs (_) / H2 = 9  =>  0 pairs (X)
I4,I6: 9.. / I4 = 9  => 13 pairs (_) / I6 = 9  => 14 pairs (_)
H2,H7: 9.. / H2 = 9  =>  0 pairs (X) / H7 = 9  => 12 pairs (_)
* DURATION: 0:00:38.398651  START: 20:00:04.280139  END: 20:00:42.678790 2019-04-30
* CP COUNT: (36)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B8,C7,D4,G2,G6,H2,H7,I1,I4,I6,I9)
* ...2.673.27...3..66.3...821.82..135....3.74.2.3..2.....6.4....89.......3.21....7.
* PAIR I1: 4,5 ROW 1
A1: 4,5,1,8                              # reduction candidate for 4,5
A1: 4,5 => CTR
* 4192867352781539466539748217826413591963.7482534.2.16736.41..9894.768213821.3.674
A1: 1,8                                  # 14 pairs
B1: 4,5,1,9                              # reduction candidate for 4,5
B1: 4,5 => CTR
* 148296735275..3946693...821.82..135.519387462.36.2.18.36741..98954.....3821.3..74
B1: 1,9                                  # 14 pairs
C1: 4,5,8,9                              # reduction candidate for 4,5
C1: 4,5                                  # 24 pairs
E1: 4,5,8,9                              # reduction candidate for 4,5
E1: 4,5                                  # 22 pairs
* PAIR G2: 5,9 COL G
G7: 5,9,1,2                              # reduction candidate for 5,9
G7: 5,9                                  # 18 pairs
G9: 5,9,6                                # reduction candidate for 5,9
G9: 5,9                                  # 16 pairs
* PAIR A4: 4,7 BLK 4
A6: 4,7,1,5                              # reduction candidate for 4,7
A6: 4,7                                  # 16 pairs
C6: 4,7,5,6,9                            # reduction candidate for 4,7
C6: 4,7                                  # 20 pairs
* PAIR A5: 1,5 BLK 4
B5: 1,5,9                                # reduction candidate for 1,5
B5: 1,5                                  # 21 pairs
A6: 1,5,4,7                              # reduction candidate for 1,5
A6: 1,5                                  # 20 pairs
* PAIR A5: 1,5 COL A
A1: 1,5,4,8                              # reduction candidate for 1,5
A1: 1,5                                  # 19 pairs
A1: 4,8                                  # 15 pairs
* PAIR D4: 6,9 BLK 5
E4: 6,9,4                                # reduction candidate for 6,9
E4: 6,9                                  # 14 pairs
E4: 4                                    # 13 pairs
* PAIR D4: 6,9 COL D
D9: 6,9,5,8                              # reduction candidate for 6,9
D9: 6,9                                  # 16 pairs
D9: 5,8                                  # 16 pairs
* PAIR G6: 1,6 BLK 6
H5: 1,6,8                                # reduction candidate for 1,6
H5: 1,6                                  # 17 pairs
H6: 1,6,8                                # reduction candidate for 1,6
H6: 1,6                                  # 15 pairs
* PAIR G6: 1,6 COL G
G8: 1,6,2,5                              # reduction candidate for 1,6
G8: 1,6                                  # 17 pairs
G8: 2,5                                  # 14 pairs
* PAIR I6: 7,9 ROW 6
C6: 7,9,4,5,6                            # reduction candidate for 7,9
C6: 7,9                                  # 16 pairs
C6: 4,5,6                                # 15 pairs
* PAIR C7: 5,7 BLK 7
A7: 5,7,3                                # reduction candidate for 5,7
A7: 5,7 => CTR
* 814296735275..3946693...821.82..135..5.3.74.2.3..2.....6743.198948...263321...574
A7: 3                                    # 13 pairs
C8: 5,7,4,8                              # reduction candidate for 5,7
C8: 5,7                                  # 23 pairs
* PAIR C7: 5,7 ROW 7
E7: 5,7,1,3,9                            # reduction candidate for 5,7
E7: 5,7                                  # 16 pairs
E7: 1,3,9                                # 13 pairs
* PAIR C7: 5,7 COL C
C6: 5,7,4,6,9                            # reduction candidate for 5,7
C6: 5,7 => CTR
* .1924673527...3946643...821482..1357.963.74.2.3..24..9.6.4...98954.....3821....74
C6: 4,6,9                                # 14 pairs
* PAIR B8: 4,5 BLK 7
C8: 4,5,7,8                              # reduction candidate for 4,5
C8: 4,5                                  # 18 pairs
A9: 4,5,3,8                              # reduction candidate for 4,5
A9: 4,5                                  # 20 pairs
* PAIR B8: 4,5 COL B
B1: 4,5,1,9                              # reduction candidate for 4,5
B1: 4,5 => CTR
* 148296735275..3946693...821.82..135.519387462.36.2.18.36741..98954.....3821.3..74
B1: 1,9                                  # 14 pairs
B3: 4,5,9                                # reduction candidate for 4,5
B3: 4,5                                  # 16 pairs
* PAIR H7: 1,9 BLK 9
G7: 1,9,2,5                              # reduction candidate for 1,9
G7: 1,9                                  # 18 pairs
G7: 2,5                                  # 14 pairs
* PAIR H7: 1,9 ROW 7
E7: 1,9,3,5,7                            # reduction candidate for 1,9
E7: 3,5,7                                # 15 pairs
E7: 1,9                                  # 15 pairs
* PAIR I9: 4,5 ROW 9
A9: 4,5,3,8                              # reduction candidate for 4,5
A9: 4,5                                  # 20 pairs
A9: 3,8                                  # 13 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060319-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 4,5 => CTR => A1: 1,8
* DIS # B1: 4,5 => CTR => B1: 1,9
* DIS # A7: 5,7 => CTR => A7: 3
* DIS # C6: 5,7 => CTR => C6: 4,6,9
* DIS # B1: 4,5 => CTR => B1: 1,9
* CNT   5 HDP CHAINS /  42 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A5,B8,C7,D4,G2,G6,H2,H7,I1,I4,I6,I9)
* ...2.673.27...3..66.3...821.82..135....3.74.2.3..2.....6.4....89.......3.21....7.
* PAIR I1: 4,5 ROW 1
A1: 4,5,1,8                              # reduction candidate for 4,5
A1: 4,5 => CTR
* 4192867352781539466539748217826413591963.7482534.2.16736.41..9894.768213821.3.674
B1: 4,5,1,9                              # reduction candidate for 4,5
B1: 4,5 => CTR
* 148296735275..3946693...821.82..135.519387462.36.2.18.36741..98954.....3821.3..74
C1: 4,5,8,9                              # reduction candidate for 4,5
C1: 4,5                                  # 24 pairs
E1: 4,5,8,9                              # reduction candidate for 4,5
E1: 4,5                                  # 22 pairs
* PAIR RESTART
* PAIR I1: 4,5 ROW 1
C1: 4,5,8,9                              # reduction candidate for 4,5
C1: 4,5                                  # 24 pairs
E1: 4,5,8,9                              # reduction candidate for 4,5
E1: 4,5                                  # 22 pairs
* PAIR G2: 5,9 COL G
G7: 5,9,1,2                              # reduction candidate for 5,9
G7: 5,9                                  # 20 pairs
G9: 5,9,6                                # reduction candidate for 5,9
G9: 5,9                                  # 18 pairs
* PAIR A4: 4,7 BLK 4
A6: 4,7,1,5                              # reduction candidate for 4,7
A6: 4,7                                  # 17 pairs
C6: 4,7,5,6,9                            # reduction candidate for 4,7
C6: 4,7                                  # 25 pairs
* PAIR A5: 1,5 BLK 4
B5: 1,5,9                                # reduction candidate for 1,5
B5: 1,5                                  # 22 pairs
A6: 1,5,4,7                              # reduction candidate for 1,5
A6: 1,5                                  # 25 pairs
* PAIR D4: 6,9 BLK 5
E4: 6,9,4                                # reduction candidate for 6,9
E4: 4                                    # 25 pairs
E4: 6,9                                  # 15 pairs
* PAIR D4: 6,9 COL D
D9: 6,9,5,8                              # reduction candidate for 6,9
D9: 6,9                                  # 18 pairs
D9: 5,8                                  # 18 pairs
* PAIR G6: 1,6 BLK 6
H5: 1,6,8                                # reduction candidate for 1,6
H5: 1,6                                  # 19 pairs
H6: 1,6,8                                # reduction candidate for 1,6
H6: 1,6                                  # 17 pairs
* PAIR G6: 1,6 COL G
G8: 1,6,2,5                              # reduction candidate for 1,6
G8: 1,6                                  # 19 pairs
G8: 2,5                                  # 16 pairs
* PAIR I6: 7,9 ROW 6
C6: 7,9,4,5,6                            # reduction candidate for 7,9
C6: 7,9                                  # 17 pairs
C6: 4,5,6                                # 17 pairs
* PAIR C7: 5,7 BLK 7
A7: 5,7,3                                # reduction candidate for 5,7
A7: 5,7 => CTR
* 814296735275..3946693...821.82..135..5.3.74.2.3..2.....6743.198948...263321...574
C8: 5,7,4,8                              # reduction candidate for 5,7
C8: 5,7 => SOLVED
* 194286735278153946653974821782641359516397482439825167367412598945768213821539674
* DURATION: 0:00:16.421918  START: 20:01:07.536465  END: 20:01:23.958383 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060319-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 4,5 => CTR => A1: 1,8
* DIS A1: 1,8 # B1: 4,5 => CTR => B1: 1,9
* DIS A1: 1,8 + B1: 1,9 # A7: 5,7 => CTR => A7: 3
* PRF A1: 1,8 + B1: 1,9 + A7: 3 # C8: 5,7 => SOL
* STA A1: 1,8 + B1: 1,9 + A7: 3 + C8: 5,7
* CNT   4 HDP CHAINS /  24 HYP OPENED

Header Info

http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Mar&YEAR=2006, 20060319, absurd

Solution

position: 194286735278153946653974821782641359516397482439825167367412598945768213821539674 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 # A1: 4,5 => CTR => A1: 1,8
* INC # A1: 1,8 => UNS
* DIS # B1: 4,5 => CTR => B1: 1,9
* INC # B1: 1,9 => UNS
* INC # C1: 4,5 => UNS
* INC # E1: 4,5 => UNS
* INC # G7: 5,9 => UNS
* INC # G9: 5,9 => UNS
* INC # A6: 4,7 => UNS
* INC # C6: 4,7 => UNS
* INC # B5: 1,5 => UNS
* INC # A6: 1,5 => UNS
* INC # A1: 1,5 => UNS
* INC # A1: 4,8 => UNS
* INC # E4: 6,9 => UNS
* INC # E4: 4 => UNS
* INC # D9: 6,9 => UNS
* INC # D9: 5,8 => UNS
* INC # H5: 1,6 => UNS
* INC # H6: 1,6 => UNS
* INC # G8: 1,6 => UNS
* INC # G8: 2,5 => UNS
* INC # C6: 7,9 => UNS
* INC # C6: 4,5,6 => UNS
* DIS # A7: 5,7 => CTR => A7: 3
* INC # A7: 3 => UNS
* INC # C8: 5,7 => UNS
* INC # E7: 5,7 => UNS
* INC # E7: 1,3,9 => UNS
* DIS # C6: 5,7 => CTR => C6: 4,6,9
* INC # C6: 4,6,9 => UNS
* INC # C8: 4,5 => UNS
* INC # A9: 4,5 => UNS
* DIS # B1: 4,5 => CTR => B1: 1,9
* INC # B1: 1,9 => UNS
* INC # B3: 4,5 => UNS
* INC # G7: 1,9 => UNS
* INC # G7: 2,5 => UNS
* INC # E7: 1,9 => UNS
* INC # E7: 3,5,7 => UNS
* INC # A9: 4,5 => UNS
* INC # A9: 3,8 => UNS
* CNT  42 HDP CHAINS /  42 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 4,5 => CTR => A1: 1,8
* DIS A1: 1,8 # B1: 4,5 => CTR => B1: 1,9
* INC A1: 1,8 + B1: 1,9 # C1: 4,5 => UNS
* INC A1: 1,8 + B1: 1,9 # E1: 4,5 => UNS
* INC A1: 1,8 + B1: 1,9 # C1: 4,5 => UNS
* INC A1: 1,8 + B1: 1,9 # E1: 4,5 => UNS
* INC A1: 1,8 + B1: 1,9 # G7: 5,9 => UNS
* INC A1: 1,8 + B1: 1,9 # G9: 5,9 => UNS
* INC A1: 1,8 + B1: 1,9 # A6: 4,7 => UNS
* INC A1: 1,8 + B1: 1,9 # C6: 4,7 => UNS
* INC A1: 1,8 + B1: 1,9 # B5: 1,5 => UNS
* INC A1: 1,8 + B1: 1,9 # A6: 1,5 => UNS
* INC A1: 1,8 + B1: 1,9 # E4: 6,9 => UNS
* INC A1: 1,8 + B1: 1,9 # E4: 4 => UNS
* INC A1: 1,8 + B1: 1,9 # D9: 6,9 => UNS
* INC A1: 1,8 + B1: 1,9 # D9: 5,8 => UNS
* INC A1: 1,8 + B1: 1,9 # H5: 1,6 => UNS
* INC A1: 1,8 + B1: 1,9 # H6: 1,6 => UNS
* INC A1: 1,8 + B1: 1,9 # G8: 1,6 => UNS
* INC A1: 1,8 + B1: 1,9 # G8: 2,5 => UNS
* INC A1: 1,8 + B1: 1,9 # C6: 7,9 => UNS
* INC A1: 1,8 + B1: 1,9 # C6: 4,5,6 => UNS
* DIS A1: 1,8 + B1: 1,9 # A7: 5,7 => CTR => A7: 3
* PRF A1: 1,8 + B1: 1,9 + A7: 3 # C8: 5,7 => SOL
* STA A1: 1,8 + B1: 1,9 + A7: 3 + C8: 5,7
* CNT  24 HDP CHAINS /  24 HYP OPENED