# Sudoku Puzzles #110, #111, & #112

### By: Dan LeKander

Volume 17, Issue 6, June 2022

We continue with 3 puzzles each month.   There should be ample material for novices through seasoned veterans.  Enjoy!

### Clueless?

We start with a Sudoku puzzle in progress, where it appears there are no more obvious or not-so-obvious clues.  Can you find the hidden clue in Puzzle #110?  (Not an easy clue to find!)

### PUZZLE #110

(The answer follows after the conclusion of Puzzle #112, the feature puzzle for June)

Logic Puzzle
Difficult rating … 5/10
(rating based on puzzles not requiring advanced techniques)

Puzzle #111 does not require advanced techniques 6-8.   Please enjoy.

### Feature Puzzle, # 112

Difficult rating … 5/10
(rating based on puzzles requiring advanced techniques)
Print this puzzle and give it a go.

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
2. FILL IN OBVIOUS ANSWERS
3. FILL IN NOT-SO-OBVIOUS ANSWERS
4. MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS
5. FILL IN THE OPTIONS FOR THE UNSOLVED CELLS

We observe the following clues ... C4R1=1, C9R4=2, C7R4 & C7R5 have options 5 & 8, C7R6, C8R6 & C9R6 have options 1, 4 & 7, C1R6=3, C5R6=9, C2R6=6, C3R1=6, and C4R7 & C9R7 have options 6 & 9.  We also see that C6R1, C6R2, C6R3 & C6R5 can only have options 2, 4, 7 & 9, and therefore, C6R4, C6R8 & C6R9 can only have options 3, 5 & 6.

In box 2 an 8 can only exist as an option in C4R2 & C5R2; therefore, an 8 cannot exist as an op-tion in in C1R2, C2R2, C8R2 & C9R2.

In box 7 a 1 can only exist as an option in C2R8 or C2R9; therefore, a 1 cannot exist as an op-tion in C2R4 & C2R5.

In box 8 a 9 can only exist as an option in C4R7 & C4R8; therefore, a 9 cannot exist as an option in C4R2.

Now your grid looks like Example #112.1 Below:

This completes Puzzle Preparation Steps 1-4, so we will fill in the options for all unsolved cells.  Now your grid should look like Example #112.2 below:

There are no Step 6 viable exercises.

We will now proceed to Step 7, Dan’s Close Relationship Challenge.   We will pick C6R9 as our starter cell, with a sequence of 5,6.   We will annotate this on the 2nd level of this cell, as per Example #112.3 below.

We begin by asking ourselves that if this starter cell is a 5, what adjacent cells could not be a 5, annotating those cells as “N5”, again on the 2nd level of those cells.   This just simply means that if the starter cell is a 5, then those cells cannot be a 5.

Next, we assume the starter cell is a 6 and track the results through the puzzle.   If any N5 cell is a number other than 5, it means that cell is not a 5 regardless if the starter cell is a 5 or 6, and the 5 could be eliminated as an option from that cell.
Before we perform this exercise, we will list the potential outcomes . . .

• The tracking of the second number of the starter cell doesn’t reach the N9 cells, and therefore, the exercise is unsuccessful.

• The tracking of the second number goes entirely through the puzzle without a conflict, indicating that the 2nd number is correct for the starter cell and you have solved the puzzle.

• The tracking of the second number creates a conflict, such as a number showing up twice in a row, column or box.   Or it could show up by having no cell for a particular number in a row, column or box.  Regardless of how the conflict arises, it would mean the second number is incorrect for that cell, and therefore, the answer to the starter cell is the first number.

We will now track the 6 through the puzzle above on the third level of the unsolved cells to preserve the integrity of the original puzzle.    As you can see from the example above, in tracking the 6 through the puzzle, there is not an unsolved cell in row 8 that can be a 9.   This is a conflict!   If C6R9 cannot be a 6, then it must be a 5.  C6R9=5.

The puzzle is easily solved from this point and the solution is Example #112.4 below:

May the gentle winds of Sudoku be at your back.

Dan LeKander

Clue for Puzzle #110 …  did you find the clue?  If not, read on. In column 9, C9R1, C9R2, C9R3 & C9R6 cannot be a 2, 6 or 7.   The 3 remaining unsolved cells in column 9, C9R5, C9R7 & C9R8, must have options 2, 6 & 7.  Since there is already a 2 & 6 in row 8, C9R8=7.   This is a fun puzzle to finish.

### Editor's Note:  May 2022 - into the 100s

OK. TI Life GANG, here are Puzzles #101, #111, and #112.

"When we published the final article in Dan's Series of steps to learn the logic of Sudoku, I never in a zillion years thought that Dan would so graciously offer to do one or two puzzles for us each month - and he has done so without my asking. Now we are up to 3!

Then his wife, Peggy, does the proof reading and I only have to post in on TI Life. We would love to know how many you have solved.  (Some, darn it, have stumped me, but I look forward to them each month.)

Last month (May, 2022) someone wrote to ask how to fill them out online. Unfortunately, you need to print them yourself - but that is easy to do and I know you will have just as much fun.

And, 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. 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 17, Issue 6, June 2022, Sports