Friday, December 20

Solving a diabolical Sudoku.


Solving a diabolical Sudoku. 
Starting with number 1 use pencil markings for any 2 numbers that must be candidates in each block, which I find is the most efficient way to solve difficult puzzles. Progress through the numbers. You may be able to crack open Yesterdays Age Diabolical Sudoku easier than I can, so why not give it a try. This puzzle fell into place relatively easily.
 
Firstly the Puzzle as it appeared in the Age
1
2
3
4
5
6
7
8
9
 
 
 
 
 
 
 
 
 
A
9
4
 
 
 
 
 
 
7
 
 
 
 
 
 
 
 
 
B
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
C
3
 
 
4
 
6
2
 
 
 
 
 
 
 
 
 
 
 
D
2
 
 
 
3
 
4
 
 
 
 
 
 
 
 
 
 
 
E
 
5
 
 
 
9
 
 
 
 
 
 
 
 
 
 
 
 
F
6
 
9
1
 
 
5
 
 
 
 
 
 
 
 
 
 
 
G
 
 
4
7
 
 
 
 
 
 
 
 
 
 
 
 
 
 
H
8
 
 
 
6
 
 
 
4
 
 
 
 
 
 
 
 
 
I
5
6
 
9
 
2
8
 
1
 
 
Step 1
Starting with Number 1 insert pencil markings for candidates only appearing twice in any block.  Where single numbers only appear those candidates can be filled in immediately. The Puzzle below has these numbers included with the pencil mark above to indicate how they were quickly ascertained. I show resultant pencil marks for the pairs that emerge and the solution to complete the left hand column.
1
2
3
4
5
6
7
8
9
 
 
 
 
 
 
 
 
 
A
9
4
 
 
 
 
 
 
7
17
 
 
 
 
 
 
4
 
B
7
 
 
 
 
 
 
4
 
 
 
 
 
7
 
 
 
 
C
3
 
 
4
7
6
2
 
 
 
 
 
56
 
5
 
9
9
D
2
 
 
 
3
 
4
 
 
4
 
 
 
 
 
 
 
 
E
4
5
 
 
 
9
 
 
 
 
 
 
 
 
4
 
 
 
F
6
 
9
1
 
4
5
 
 
17
9
 
 
8
8
 
 
 
G
1
 
4
7
 
 
 
 
 
 
9
 
 
 
1
 
 
 
H
8
 
 
 
6
1
 
 
4
 
 
37
 
 
 
 
37
 
I
5
6
 
9
4
2
8
 
1
 
Step 2
We are now in a position to partially solve the puzzle using some basic logic.  Cell G5 must be a 5 due to the two pairs in E5 and F5.  The only numbers that can go into H4 is 3, H5 is 6, G6 is 8, B5 is 9 and A5 is 1. The puzzle partially solved is as follows. 
1
2
3
4
5
6
7
8
9
 
 
 
 
 
 
 
 
 
A
9
4
 
 
1
 
 
 
7
17
 
 
 
 
 
 
4
 
B
7
 
 
 
9
 
 
4
 
 
 
 
 
7
 
 
 
 
C
3
 
 
4
7
6
2
 
 
 
 37
37
56
 
5
 
9
9
D
2
 
 
 
3
 
4
 
 
4
 
 
 
 
 
 
 
 
E
4
5
 
 
 
9
 
 
 
 
 
 
 
 
4
 
 
 
F
6
 
9
1
 
4
5
 
 
17
9
 
 
8
8
 
 
 
G
1
 
4
7
5
8
 
 
 
 
9
 
 
 
1
 
 
 
H
8
 
 
3
6
1
 
 
4
 
 
37
 
 
 
 
37
 
I
5
6
 
9
4
2
8
 
1
  
Step 3
By inserting pencil marks we find only number 5 can be included in cell H8. The only number that can be included in cell D6 is 7.
On the B row there is a hidden pair of 5 and 6 in the 3rd and last cells so that that B6 must be 3
17
125
12568
28
 
35
16
4
568
7
 
 
 
9
 
 
4
 
   
A 6 then becomes 5, B6 a 3.
Step 4 – Eliminating missing numbers. After reconfiguring the worksheet you find that from the 2 pairs in D2 and D 3 you end up with a further 2 pairs of 3 and 7 in Cells E3 and F2.
F2 then becomes 7 and E3,  3 by virtue of the hidden pairs of 2 and 3 in F8 and F9.
You can now solve the bottom box as the remaining numbers of 7, 9, and 7 respectively will only go into cells I3, H2 and G 2.
We are now getting close to solving the puzzle which I will list as it stands now as follows:
 
1
2
3
4
5
6
7
8
9
 
 
 
 
 
 
 
 
 
A
9
4
 
 
1
5
 
 
7
17
125
12568
28
 
35
16
4
568
B
7
 
 
 
9
3
 
4
 
 
 
 
 
7
 
 
 
 
C
3
 
 
4
7
6
2
 
 
 
 
 
56
 
7
 
9
9
D
2
 
 
5
3
7
4
 
 
4
 
 
 
28
 
 
 
 
E
4
5
3
6
 
9
 
 
 
 
 
 
 
28
4
 
 
 
F
6
7
9
1
 
4
5
 
 
17
9
 
 
 
8
 
 
 
G
1
 3
4
7
5
8
 
 
 
 
9
 
 
 
1
 
 
 
H
8
 9
2
3
6
1
 
5
4
 
 
37
 
 
 
 
37
 
I
5
6
 7
9
4
2
8
 
1
Step 5
From here on it amounts to standard Sudoku Logic and the puzzle can easily be solved.
The solution is as per below.  
 
1
2
3
4
5
6
7
8
9
 
 
 
 
 
 
 
 
 
A
9
4
6
2
1
5
3
8
7
17
125
12568
28
 
35
16
4
568
B
7
2
1
8
9
3
6
4
5
 
 
 
 
7
 
 
 
 
C
3
8
5
4
7
6
2
1
9
 
 
 
56
 
7
 
9
9
D
2
1
8
5
3
7
4
9
6
4
 
 
 
28
 
 
 
 
E
4
5
3
6
2
9
1
7
8
 
 
 
 
28
4
 
 
 
F
6
7
9
1
8
4
5
2
3
17
9
 
 
 
8
 
 
 
G
1
3
4
7
5
8
9
6
2
 
9
 
 
 
1
 
 
 
H
8
9
2
3
6
1
7
5
4
 
 
37
 
 
 
 
37
 
I
5
6
7
9
4
2
8
3
1
Posted by at

4 comments:

Tom said...

Not sure that I understand your system, but finished the entree quickly enough. Now for the main course?

2:55 AM
Lindsay Byrnes said...

Hi Tom,
I don't think this so called diabolical Sudoku was as difficult as some that come under that heading. As for a main course and to explain my technique one can visit
Learn- Sudoku.com and click on the more advanced option.
That is: for the narrative on all of their techniques. What I propose from inception is instead of including all of the candidates as pencil marks you only include those that can appear twice or once in any block of nine, of which there are of course 9 blocks. By lining up all the number 1's for instance and working your way through all the numbers you end up with a worksheet with potentially just naked singles, doubles and two squares in each block where the number must be in either cell. This makes the discovery of hidden singles, Naked Pairs, Naked Triplets & Quads, Omission, Hidden Pairs, Hidden Triplets and quads easier to discover along the way. The more advanced aspects of using x Wings and brute force were not necessary with this puzzle.
best wishes

2:14 PM
Tom said...

I did use 'Single's Chains' aka 'Simple Colouring' at one point to clear a 5. After that it was plain sailing. As you say, this so-called diabolical Sudoku wasn't as difficult as some. Thanks for the link; I'll peruse in due course.

In case you don't post again before 25th., I hope you and your family have a great and fire-free Christmas.

7:55 PM
Lindsay Byrnes said...

Hi Tom,
I reworked the puzzle to see where I could have used the Simple Colouring to get rid of the 5 you mentioned and in the process discovered there was a bit of basic logic from the pencil marks I had previously missed.
My solution is therefore overcomplicated.
If you keep inserting the pencil marks to ascertain those pairs or singles that can only occur in the blocks, what emerges are additional pairs and singles. From there the puzzle opens up to a solution.

We have given a number of Christmas concerts inclusive of that wonderful carol by John Rutter – The Candlelight Carol. I never get tired of singing it.
Despite the ever present risk of bush fires and temperatures yesterday of 44 degrees we are all singing songs such as 'In the Bleak Midwinter' by Harold Darke, interspersed with some Australian carols more in tune with the Australian landscape. The red dust is over the town, the grass in the paddock is brown, as we lift up our voices to sing... Christ Child....
A joyful and holy Christmas to you and yours.

11:59 PM

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