# Sudoku Puzzle #55 and Bonus Puzzle #56

### By: Dan LeKander

Volume 14, Issue 7, July 2019

Puzzle #54

## PUZZLE PREPARATION

Prior to utilizing techniques first complete the 5 Steps of Puzzle Preparation …

1. FILL IN DATA FROM OBSERVATIONS
4. MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS
5. FILL IN THE OPTIONS FOR THE UNSOLVED CELLS

After many months of puzzles, I decided to modify the Puzzle Preparation steps somewhat, and probably should have done it long ago.  The frequency of application is often enough to warrant a new Step 1.

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 –  See September 2015

Step 2:  Turbos & Interaction – See October 2015

Step 3:  Sudoku Gordonian Rectangles and Polygons – See November 2015

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

Step 5:  X-Wings –  See 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.

Now to continue ...

## DATA FROM OBSERVATIONS …

We see that the only two cells in box 6 (right center box of 9 x 9 cells) that can have options 18, which are C9R4 & C9R5.
Additionally, take a close look at Row 6.  There are only two cells that can have options 7 and 9, which are C2R6 & C6R6.  We will mark then as such.
Also, in row 1 only two cells can have the options 7 and 9, which are C6R1 & C9R1.  We will mark them as such.

We have now identified three obvious pairs, which will greatly improve solving this puzzle.

Now your grid should look like Example #55.1 below:

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 C6R7=8.  C5R9=3.
There is now an obvious triplet 126 as options in C4R8, C5R8 & C6R8.
Now your grid should look like Example #55.2 below:

The only choice for C8R8 is 5.  C8R8=5.  Now the only choice for C3R8 is 4.  C3R8=4.
Now your grid should look like Example #55.3 below:

## MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS …

The only cells in box 1 that can be a 1 are C2R2 or C2R3; therefore, a 1 cannot exist in C2R7 or C2R9.  Indicate this by placing a small 1 in the bottom of those two cells, as per Example #55.4 below.

## FILL IN THE OPTIONS FOR THE UNSOLVED CELLS

Once you fill in the options for the remaining unsolved cells, your grid should look like Example #55.5 below:

## STEPS 1-8

We have already identified all pairs, triplets & quads, so we will move on to Interaction.  Note that in row 2 the option 8 is only present in C1R2 & C2R2; therefore, one of these two cells must be an 8.  You can eliminate the 8 as an option for all other cells in box 1.  Now your grid should look like Example #55.6 below:

There are no additional Step 1 – 5 clues, so we will now proceed 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 7 … C2R6 & 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 #55.7 below:

Do you agree that one of these two yellow cells in column 2 must be a 7?   We will consider them “driver cells” which “drive” the exercise.
Here is the logic.  We will perform two exercises.  First, we will assume C2R6 is the 7 and see which other cells cannot be a 7.  Then we will assume C2R9 is the 7 and see which other cells cannot be a 7.
We will mark C2R6 with a “Y” and mark C2R9 with a lower case “y” to keep track of the exer-cise as per Example #55.8 below.

We start by assuming C2R6=7.  Then, as marked above, C6R6 is not a 7 (marked with a “N”).  C5R5=Y.  C5R2=N.  C6R1=Y.  C9R1=N.  C7R2=Y.  C7R9=N.  C9R8=Y.
Now we will assume C2R9=7 (y for yes).  Then, C7R9=n.  C9R8=y.  C9R1=n.  C7R2=y.  C5R2=n.   C6R1=y.  C6R6=n.   C5R5=y.
We now see in Example #54.8 above that …
• 4 cells have an N,n designation, meaning that it cannot be a 7 regardless of which driver cell is a 7; therefore, you can remove a 7 as an option from those 4 cells.
• 4 cell has a Y,y designation, meaning it is a 7 regardless of which driver cell is a 7.
• It now follows that C6R1=7, C9R8=7, C9R1=9, C6R6=9. C2R6=7.  C1R8=9. C7R2=7.

Now your grid should look like Example # 55.9 below:

From this point the puzzle is easily solved, giving us Example #55.10 below:

## Bonus Puzzle #56

Hint … Steps 6-8 are not required!

May the gentle winds of Sudoku be at your back,

By Dan LeKander

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 #55 and # 56!

I suggest you purchase Dan’s book: “3 Advanced Sudoku Techniques, That Will Change Your Game Forever!” Purchase of a book includes a 50-page blank grid pad, 33 black and two green tokens, to assist with Step 6.…

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

Most importantly, I ask that you leave comments on any part of his series and throughout the year.

And now we are halfway through 2019... many puzzles later... I want to thank Dan…and his proofreader… Peggy! I am hoping you will enjoy our monthly Sudoku and at the same time join me in saluting Dan - Bravo to you both…(Mind you sometimes I am not so polite when I can't solve the puzzle...)

Be sure to read the review of Dan's book by Jesse Kahn published in Jun 2015.

Posted in: Volume 14, Issue 7, July 2019, Sports