# Sudoku Puzzle #54 by Dan LeKander

### By: Dan LeKander

Volume 14, Issue 6, June 2019

Tame the lion!

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 – September 2015

Step 2:  Turbos & Interaction – October 2015

Step 3:  Sudoku Gordonian Rectangles and Polygons – November 2015

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

Step 5:  X-Wings – 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.

As a reminder, the basic rules of Sudoku are that the numbers 1-9 must be contained and cannot be repeated in a row, column, or box, and there can only be one solution to the puzzle.

PUZZLE PREPARATION
Prior to utilizing techniques, first complete the 4 Steps of Puzzle Preparation …

3. MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS
4. FILL IN THE OPTIONS FOR THE UNSOLVED CELLS

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 answers are C5R7=3.  C6R9=9.   Now your grid should look like Example 54.1 below:

NOT-SO-OBVIOUS ANSWERS … there are none.

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

The only cells in box 4 (left, middle box of 9x9 cells) that can be a 1 are C1R6 or C3R6; therefore, a 1 cannot exist in C4R6, C5R6 or C6R6. Indicate this by placing a small 1 in the bottom of those three cells, as per Example #54.2 below.

The only cells in box 3 that can be a 7 are C7R2 or C9R2; therefore, a 7 cannot exist in C5R2 or C6R2. The options for the unsolved cells in box 8 are 1,2,7, an obvious triplet; therefore the 1,2 & 7 cannot exist anywhere else in column 4.

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 #54.3 below:

STEPS 1-8
First, we will search for pairs, triplets, quads & quints.  Can you spot any?
Take a closer look at column 8, what do you find?   You either spot a quint 12469 contained in only 5 cells, realizing that C8R & C8R7 must be 58.  Or you notice that only two cells in column 8 contain options 58, a hidden pair.  In either case, the result is the same, giving us Example #54.4 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 4 we find just 2 unsolved cells that contain the option 5 … C4R1 & C4R6.  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 #54.5 below:

Do you agree that one of these two yellow cells in column 4 must be a 5?   We will consider them “driver cells” which “drive” the exercise.

Here is the logic.  We will perform two exercises.  First, we will assume C4R1 is the 5 and see which other cells cannot be a 5.  Then we will assume C4R6 is the 5 and see which other cells cannot be a 5.

We will mark C4R1 with a “Y” and mark C4R6 with a lower case “y” to keep track of the exercise as per Example #54.6 below.

We start by assuming C4R1=5.  Then, as marked above, C2R1 is not a 5 (marked with a “N”).  C5R1=N.  C5R2=N.  Now the only cell in box 1 that can be a 5 is C1R2, so we will mark it as a “Y”.  Then, C1R7=N & C1R9=N.  Then, C2R7=Y.  C8R7=N & C9R7=N.  C9R9=Y.  C9R6=N.  C8R5=Y.  C5R5=N.

Now we will assume C4R6=1 (y for yes).  Then, C5R5=n.  C9R6=n.  C8R5=y.  C8R7=n.

We now see in Example #54.6 above that …
• 3 cells have an N,n designation, meaning that it cannot be a 5 regardless of which driver cell is a 5; therefore, you can remove a 5 as an option from those 3 cells.
• 1 cell has a Y,y designation, meaning it is a 5 regardless of which driver cell is a 5.  C8R5=5.

Now your grid should look like Example # 54.7 below:

You can now see in Example #54.7 above that C3R9=8.  C2R3=8.  C4R3=4.  C6R2=8.  C4R4=6.

From this point the puzzle is easily solved, giving us Example #54.8 below:

Step 6 is a very powerful technique.   In many cases this technique can essentially solve the puzzle for you, taming of the lion without much effort!

May the gentle winds of Sudoku be at your back,

By Dan LeKander, Wellesley Island

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 #54!

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...)

Dan LeKander

Posted in: Volume 14, Issue 6, June 2019, Sports