# Sudoku Puzzles #70 & #80

### By: Dan LeKander

Volume 16, Issue 4, April 2021

Greetings friends of the River.  Get your Sudoku hat, hot cup of coffee and a sharp pencil ready for the April Sudoku puzzles.

Clueless?
As a bonus each month this year we will start with a Sudoku puzzle in progress, where it       appears there are no more obvious or not-so-obvious clues.  Does this puzzle #79 have any more clues?

(The answer follows below after the conclusion of Puzzle #80, the feature puzzle for April)

The Impossible Series continues.    See if you can solve this puzzle without any assistance!

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 7Steps  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.

## Puzzle #80

### PUZZLE PREPARATION

Prior to utilizing techniques 1-8 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

We will complete all of the first 4 steps in the order we observe them.
We will start with the 1’s and navigate through 2’s to 9’s, then repeat the process until we conclude all Puzzle Preparation Step 1-4 clues.

The first thing we observe is that C8R6 (cell in column 8, row 6) =6 (obvious answer).   Then, C3R1=7 and C2R2=8.  Looking at C5R7 we see the only number it can be is a 4.  Fill in the options for the remaining three cells in box 1.  Now the remaining unsolved cells in row 3 can have only options 1,3,5 and 9.  Fill in the options for those four cells.

Now your grid should look like Example #80.1 below:

In box six a 4 can only exist as an option in C7R5, C8R5 or C9R5; therefore, a 4 cannot exist as an option in C1R5, C2R5 and C3R5.  Indicate this by placing a small 4 in the bottom of those cells.

Now your grid should look like Example #80.2 below:

This concludes Puzzle Preparation steps 1-4.  We will now fill in the options for the unsolved cells, giving us Example #80.3 below:

### TECHNIQUES 1-5

There are no other Step 1-5 clues.

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

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.

In Example #80.4 below we find two unsolved cells in column 4 that are not in the same box having a 1 as an option, C4R3 & C4R5 which become our “driver” cells.  One of these two cells must be a 1.

We start with C4R3 and assume it is the 1 and assign a “Y”.  We then mark, as before in previous month article Step 6 exercises, the cells which can and cannot be a 1 with the Y’s and N’s.  We then assume C4R5 is the 1 and assign a “y”.  We then mark the cells which can and cannot be a 1 with the y’s and n’s.  Where we see a N,n indicates a cell that cannot be an 1 regardless of whether C4R3 or C4R5 is the 1 in column four.

We can see from the exercise above that three cells have N,n designations, thus, they cannot have a 1 as an option.  We also see that the only cell in box 2 that can now be a 1 is C4R3.   Thus, C4R3=1.  We will make those changes, giving us Example #80.5 below:

We can see from the example above that C5R2=2.  We can also see that C5R4=1, C5R8=7, C5R6=3 and C5R2=7.  From this point the puzzle is easily solved, giving us the Example 80.6 below:

Let’s pause here to ask ourselves some questions.   When searching for a Step 6 prospect in a puzzle is there an optimum number of given answers of numbers 1 through 9 that will en-hance a successful outcome?   In the puzzle above, we chose the number 1 to perform a Step 6 exercise.

How many completed cells were number 1?   In this case, three cells had number one as the answer.   This brings up the next question.   How often is a successful Step 6 per-formed with three cells containing the number chosen for the exercise?

To answer that question, I looked at all the articles in the last 16 months that contained a Step 6 exercise.   Out of the 16 monthly articles, 11 had Step 6 exercises.   Out of those 11, all 11 had three given an-swers for the digit chosen!   This brings up the next logical question.

Why are 3 given an-swers such a magical number?   Essentially, once you find a potential Step 6 exercise you have to track the “yes” and “no” cells through the puzzle.  If you have less than 2 given answers or more than 3 given answers for the digit, the track will generally not be productive.  So, the next time you perform a Step 6 exercise, check the digits 1-9 that have 3 given answers first.

May the gentle winds of Sudoku be at your back.

By Dan LeKander

Clue for Puzzle #79 … focus your attention to row 1.   What do you observe?
There is only one cell in row 1 that can have a 6 as an option.  C2R1=6.  It follows that C1R6=6, C8R5=6 and C7R9=6.

Editor's Note:  Can't believe #80...  Dan and his proofreader (and, as they say, better half) Peggy, give us a new challenge each month.

I copy the article - insert the examples and then realize just how much work goes into each one of the Dan's articles.  I have the easy job, his is difficult and then you, our readers, have the challenge.

It was back in January 2016, when we published a final article in Dan's Series of Steps to learn the logic of Sudoku –  he asked if we would like a puzzle to solve every month … this editor said an enthusiastic… Yes, please!

If you have not already done so, 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.…

I also encourage you to write to Dan and tell him how his system is helpful!

The book is available online at ebay.com.

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

Posted in: Volume 16, Issue 4, April 2021, sport