Sudoku Puzzle #48

By: Dan LeKander

Volume 14, Issue 1, January 2019

As we begin a  new year, let’s pause and ask ourselves how we would evaluate our Sudoku  skills. You could be a beginner through expert. Regardless of your  skill level, 2019 will be the year of the Sudoku Challenge and learning!  All 12 of the puzzles for 2019 have been selected and each will  represent a serious challenge.

If you are an expert, sharpen your pencil and enjoy. If you are a  beginner or at an intermediate level, you have the opportunity to learn the skills necessary to solve extreme puzzles. So, buckle up, and enjoy  the ride.

DAN’S 8-STEP APPROACH TO SOLVING ALL SUDOKU PUZZLES

Once you have completed the puzzle, to the extent that you have  filled-in all obvious answers and have written all potential options  across the top of the unsolved cells (PUZZLE PREPARATION), Dan  recommends the following Steps to complete the puzzle.

Step 1:  Sudoku Pairs, Triplets and Quads – September 2015

Step 2:  Turbos & Interaction – October 2015

Step 3:  Sudoku Gordonian Rectangles and Polygons – November 2015

Step 4:  XY-Wings & XYZ Wings – December 2015

Step 5:  X-Wings – January 2016

Step 6:  DAN’S YES/NO CHALLENGE

Step 7:  DAN’S CLOSE RELATIONSHIP CHALLENGE

Step 8:  AN EXPANSION OF STEP 7

Steps 1-5 are relatively common techniques and are explained in  the TI LIFE articles above. Steps 6-8 are covered in detail, in Dan’s  book.

As a reminder, the basic rules of Sudoku are that the numbers 1-9  must be contained and cannot be repeated in a row, column, or box, and  there can only be one solution to the puzzle.

PUZZLE PREPARATION

Prior to utilizing techniques first complete the 4 Steps of Puzzle Preparation …

3. MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS
4. FILL IN THE OPTIONS FOR THE UNSOLVED CELLS

Start with the 1’s to see if there are any obvious 1-choice answers. Then navigate the 2’s through 9’s.

The first obvious answer is C1R6 (cell in column 1, row 6) = 1.  C3R4=5. C5R8=8. You may ask why this last obvious answer is obvious.  Good point. If you examine this cell’s options you see that an 8 is the  only option available. Catch it now or catch it later.

NOT-SO-OBVIOUS ANSWERS … there are none.

MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS

In box 3 (upper right box of 3 x 3 cells) C9R1 & C9R3 are the  only two cells that can have the option 6; therefore, a 6 cannot exist  in C9R7 or C9R9. Pencil a small 6 in the bottom of those two cells to  indicate they cannot be a 6. This will be handy when you fill in options  for the unsolved cells.

Also, there has to be an obvious triplet in C2R4, C2R5 and C2R6.  These cells can only have options 6, 7 & 8. So, we will move ahead  and enter those options now, to remind us that the rest of the unsolved  cells in column 2 cannot be a 6, 7 or 8.

Now your grid should look like Example #48.1 below:

FILL IN THE OPTIONS FOR THE UNSOLVED CELLS …

Once you fill in the options for the unsolved cells, your grid should look like Example #48.2 below:

STEPS 1-8

There are no Step 1-5 clues.

We will pause here for a moment to examine Example #48.2. For a puzzle that requires 81 answers, we only have 20 given answers at this point, not much to work with! Why will we be able to solve this puzzle? The answer to that question is that there is always a weak link or links in a puzzle, such that when exposed, the puzzle is easily solved. Exposing weak links is exactly what Dan’s Steps 6-8 accomplish. So, make sure you fully comprehend these techniques. Each puzzle this year requires at least one successful Step 6-8, and some of the puzzles require more than one, as you have witnessed in previous articles.

We will now move to Step 6: Dan’s Yes-No Challenge.

There are 3 circumstances that establish the potential for a Step 6 exercise:

1. Look for just 2 unsolved cells in a box that contain the same option where these 2 cells are not in the same row or column.
2. Look for just 2 unsolved cells in a column that contain the same option where these 2 cells are not in the same box.
3. Look for just 2 unsolved cells in a row that contain the same option where these 2 cells are not in the same box.

We will start by searching the 1’s to see if there is a potential Step 6 clue, and then navigate through the 2-9’s.

In column 2 we find just 2 unsolved cells that contain the option 3 … C2R1 & C2R9. These cells are not in the same box, thereby qualifying as a candidate for a Step 6 exercise. The options in these cells are highlighted in yellow in Example #48.3 below:

Example #48.3

Do you agree that one of these two yellow cells in column 2 must be a 3? We will consider them as “driver cells” which “drive” the exercise.

Here is the logic. We will perform two exercises. First, we  will assume C2R1 is the 3 and see which other cells cannot be a 3. Then  we will assume C2R9 is the 3 and see which other cells cannot be a 3.

We will mark C2R1 with a “Y” and mark C2R9 with a lower case “y” to keep track of the exercise as per Example #48.4 below.

We will start by assuming C2R1=3. Then, as marked above, C1R1, C1R2,  C5R1 & C6R1 are not a 3 (marked with a “N”). Now the only cell in  box 2 that can be a 3 is C6R2, so we will mark it as a “Y”. Then,  C6R4=N. C6R5=N. C5R5=Y. C7R5=N. C9R5=N. C9R4=Y. C9R9=N. C7R8=Y. C1R8=N.

Now we will assume C2R9=3 (y for yes). Then, C1R8=n. C9R9=n. C7R8=y. C7R5=n.

We now see in Example #47.7 above that C1R8, C7R5 & C9R9 all have  a “N,n” designations. What does that mean? Since we know one of the two  yellow highlighted cells in column 2 must be a 3, the N,n cells cannot  be a 3 regardless of which starter cell is a 3. We eliminate the 3 as an  option from these cells.

We also see in Example #48.4 that C7R8 has a Y,y designation. It  follows that this cell is a 3 regardless of which starter cell is a 3;  therefore, C7R8=3.

Now your grid should look like Example #48.5 below:

It now follows that C1R8=6, C6R8=1, C8R8=9, C3R8=4, C2R7=2, C2R1  & C2R9 have options 39; therefore, C2R3=4. C4R2=4. C5R6=4. C9R4=4.  C7R7=4 and so forth.

From this point the puzzle is easily solved. Your final grid should now look like Example #48.6 below:

One Step 6 exercise exposed the weak link and allowed an easy finish to an extreme puzzle!

May the gentle winds of Sudoku be at your back,

Dan LeKander, Wellesley Island

Editor’s note:

In January 2016, we published a final article in his series – but  many of us enjoy using “Dan’s Steps,” so when he asked if we would like a  puzzle to solve every month … this editor said an enthusiastic… Yes,  please! Now we are several years later and on Puzzle #48!

I suggest you purchase Dan’s book as a Christmas gift: “3 Advanced Sudoku Techniques, That Will Change Your Game Forever!”

The book is available online at amazon.com and on ebay.com.

Purchase of a book includes a 50-page blank grid pad, 33 black and two green tokens, to assist with Step 6.…

Most importantly, I ask that you leave comments on any part  of his series and throughout the year.  Remember when your teacher said  – no such thing as a silly question – as we can all learn together.

As always, I want to thank Dan…and his proofreader… Peggy! I am  hoping you will enjoy our Sudoku and at the same time join me in thanking Dan - Bravo to you both… Hope to see you on the beach!

Posted in: Volume 14, Issue 1, January 2019, Sports