Sudoku Puzzles #81 & #82

By: Dan LeKander

Volume 16, Issue 5, May 2021

More Sudoku fun is in store for you this May.  Please enjoy!

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 #81 have any more clues?   Hint … you will not see this type of clue often, so really focus on finding the clue!

(The answer follows below after the conclusion of Puzzle #82, the feature puzzle for May)

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 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 C7R9=2.  C1R2=6.  C7R8 & C8R8 must have options 58.

C9R7, C9R8 & C9R9 must have options 167.
C9R3, C9R5 & C9R6 must have options 349.  There is a 3 & 9 in row 6; therefore, C9R6=4.
C9R3 & C9R5 must have options 39.  There is a 9 in row 3; therefore, C9R5=9 & C9R3=3.
C1R4=9.
Options for C4R2 & C4R9 = 39.

In box 1 the only unsolved cells that can be a 5 are C2R2 & C2R3; therefore, a 5 cannot exist as an option in C2R5, C2R6, C2R7 & C2R9.

In box 5 the only unsolved cells that can be a 6 are C5R5 & C6R5; therefore, a 6 cannot exist as an option for C7R5 & C8R5.

Any more clues?

Take a look at row 1.  If any of the unsolved cells C5R1, C6R1, C7R1 or C8R1 cannot have options 489, then it will combine with C1R1, C1R2 & C3R1 to form a quad.  Check out C8R1.   Its options are 127.   We did not find a clue, but we are limiting the options for C5R1, C6R1 & C7R1 to 489.

Now your grid should look like Example #82.1 below:

This concludes Puzzle Preparation steps 1-4.  We will now fill in the options for the unsolved cells, giving us Example #82.2 below:

TECHNIQUES 1-5

In box 1, row 1 we find that a 3 must exist as an option in C1R1 or C2R1; therefore, a 3 cannot exist as an option in C2R2.  This is an example of an Interaction.

Now your grid should look like Example #82.3 below:

There are no other Step 1-5 clues.

There are no Step 6 productive exercises, so we will move on to Step 7:  Dan’s Close Relation-ship Challenge.

To begin a Step 7 exercise, we will pick any 2-digit unsolved cell to be our “driver cell”, and we will pick a sequence to follow.  We will pick C5R1 as our driver cell and conduct this exercise in Example #82.4 below:

You can see in the example above that we have chosen a sequence 4,8 for our driver cell C5R1.  If C5R1 is a 4, then the unsolved cells adjacent (in the same box, column or row) to C5R1 that have a 4 as an option cannot be a 4.

We will mark those 4 cells with a N4 to indicate this.

Here is the theory.

If C5R1 is really an 8, then not all of the cells marked N4 can be a 4.

We will track the 8 though the puzzle to see if we can determine the resulting value for the N4 cells.

We will track in the 3rd level of each cell to preserve the original puzzle in the 1st level. If any of them are not a 4, then we know that those cells are not a 4, regardless if C5R1 is a 4 or 8, and we will be able to remove the option 4 from those cells.

However, there are other events that might happen along the way.   So, let get started.

Assume C5R1=8.  C6R1=9.  C6R8=8.  C9R8=1.  C3R8=3.  C5R8=4.

We will pause here, noting that if C5R8=4, then C5R7 & C5R3 cannot be a 4.

We will remember this, because we will be able to remove the 4 as an option from those cells.

Continuing, C2R8=9.  C7R1=4.  C7R2=9.  C8R4=3.  C4R2=3.  C4R9=9.   We will pause here.

What do you notice in box 8?  No unsolved cell can have the option 3!  What does this mean?  Quite simply, it proves that C5R1 cannot be an 8, and therefore, C5R1=4.  It follows that C7R1=9, C6R1=8, and so forth, leading to an easy conclusion in Example #82.5 below:

May the gentle winds of Sudoku be at your back.

By Dan LeKander

Clue for Puzzle #81 … what do you observe in column 9?
C9R1, C9R2 & C9R3 cannot be a 3, 6 or7.  C9R4 cannot be a 3, 6 or 7.  The remaining unsolved cells in column 9 must contain the options 3, 6 and 7.  Options for C9R8 are 36.   The only cell in column 9 that can be a 7 is C9R9.   It follows that C1R7=7, C3R1=7 and C7R8=8.

Editor's Note:  Yes, you are reading this correctly: #81 & #82!

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 5, May 2021, Sports