# Sudoku Puzzles #83, #84 & #85

### By: Dan LeKander

Volume 16, Issue 6, June 2021

In addition to our “Clueless” puzzle series and the feature puzzle for June, there is a special puzzle I would like to share with you.   If you are up for it, you will be sufficiently challenged.

### 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 #83 have any more clues?

(The answer follows below after the conclusion of Puzzle #85, the feature puzzle for June)

### Challenge Puzzle

The next puzzle represents a formidable challenge to all who have mastered Steps 6 & 7.  It is one of the most difficult 17-given puzzles I’ve experienced in the last few years (unless, of course, I made it more difficult than it really is).  Solve this puzzle on your own, and if you are successful, you will earn an A+  . . .

### Feature Puzzle

The “Impossible” Series continues with Puzzle #85, the feature puzzle for June …

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 PREPARATION

Prior to utilizing Steps 1-8, 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, until we conclude all Puzzle Preparation Step 1-4 clues.

The first thing we observe is that C1R1 & C2R2 have options 68.
Next, C4R4 & C5R4 have options 29.
C8R8 & C9R7 have options 89.   Then, C7R9, C8R9 & C9R9 have options 267.  However, there is already a 2 & 6 in column 8; therefore, C8R9=7.
C1R9, C2R9, C4R9 & C5R9 are limited to options 1345.
In box 3 the option 3 can only exist in C7R2 or C8R2; therefore, a 3 cannot exist as an option in C3R2.

Now your grid should look like Example #85.1 below:

This concludes Puzzle Preparation steps 1-4.  We will now fill in the options for the unsolved cells, giving us Example #85.2 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 #85.3 below we find two unsolved cells in column 3 that are not in the same box having a 1 as an option, C3R5 & C3R7 which become our “driver” cells.  One of these two cells must be a 1.

We start with C3R5 and assume it 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.  We then assume C3R7 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 C3R5 or C3R7 is the 1 in column three.

We can see from the exercise above that two cells have N,n designations, thus, they cannot have a 1 as an option.  We also see that the only cell in box 4 that can now be a 1 is C3R5.   Thus, C3R5=1.  You can now see that the only unsolved cells in box four that can be a 4 are C2R4 & C2R5.   Thus, a 4 cannot exist as an option in C2R8 or C2R9 (Interaction), leaving C3R8 the only cell in box 7 or column 3 that can be a 4.   C3R8=4.  From this point the 4’s cash out, and the puzzle has a relatively simple conclusion per Example #85.4 below:

In the event you are too busy to dedicate a few hours to these puzzles, you could print out the article and save it for a rainy day.

Best of summer to you!

May the gentle winds of Sudoku be at your back.

By Dan LeKander

Clue for Puzzle #83 … focus your attention on row 4.   What do you observe?

Cells C6R4, C7R4, C8R4 & C9R4 cannot have options 4, 6 or 8.   That leaves 3 unsolved cells in row 4 that now must have options 468.   There is already a 4 & 6 in column 1; therefore, C1R4=8.

Editor's Note

Editor's Note:  Summer 2021!

Dan and his proofreader (and, as they say, better half) Peggy, give us a new challenge each month.

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 6, June 2021, Sports