Soduko Puzzle #51 by Dan LeKander

T. I. LIFE PUZZLE FOR APRIL 2019

 A humbling Sudoku puzzle? A beast? Give it a go and decide for yourself!

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.

Also, see Sudoku Puzzle Challenge… February 2016, March 2016, April 2016, May 2016, June 2016, July 2016, August 2016, September 2016, October 2016, November 2016,  December 2016, January 2017, February 2017, March 2017 , April 2017,  May 2017, June 2017, July 2017, August 2017, September 2017, October 2017, November 2017 ,  December 2017, January 2018, February 2018, March 2018, April 2018. May 2018, June 2018, July 2018, August 2018, September 2018 , October 2018, November 2018, December 2018, January 2019, February 2019 and March 2019.

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 …

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

OBVIOUS ANSWERS …

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 answer is C1R3 (cell in column 1, row 3) = 3.  C3R2=1.   C7R7=8.  Now your grid should look like Example 51.1 below:

NOT-SO-OBVIOUS ANSWERS … there are none.

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

The only cell in box 5 (center, middle box of 9x9 cells) that can be a 4 is C4R4 or C4R5; therefore, a 4 cannot exist in C4R1, C4R2 or C4R3.  Indicate this by placing a small 4 in the bottom of those three cells, as per example below.  

The only cells in box 9 that can be a 3 are C7R9 or C9R9; therefore, a 3 cannot exist in C4R9 or C6R9.

The options for C1R1, C2R1 & C3R1 must be 4, 5 & 8, which become an obvious triplet; therefore, a 4, 5 & 8 cannot exist in any other unsolved cells in row 1.

Now your grid should look like Example #51.2 below:

FILL IN THE OPTIONS FOR THE UNSOLVED CELLS …

Once you fill in the options for the unsolved cells, your grid should look like Example #51.3 below:

STEPS 1-8

We search all rows, columns & boxes in Step 1 for Pairs, Triplets & Quads. In row 8 only 2 unsolved cells contain the 2 options 7 & 9, a hidden pair. We change the options for C1R8 & C5R8 to 79. Now your grid should look like Example # 51.4 below:

There are no additional Step 1-5 clues.  

We will now move 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 row 8 we find just 2 unsolved cells that contain the option 7 … C1R8 & C5R8.  

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 #51.5 below:

Do you agree that one of these two yellow cells in row 8 must be a 7?   We will consider them as “driver cells” which “drive” the exercise.

Here is the logic. We will perform two exercises. First, we will assume C1R8 is the 7 and see which other cells cannot be a 7. Then we will assume C5R8 is the 7 and see which other cells cannot be a 7.  

We will mark C1R8 with a “Y” and mark C5R8 with a lower case “y” to keep track of the exercise as per Example #51.6 below.  

We start by assuming C1R8=7. Then, as marked above, C3R7, C1R4, & C1R6 are not a 7 (marked with a “N”). Now the only cell in box 4 that can be a 7 is C3R4, so we will mark it as a “Y”. Then, C7R4=N.  C9R4=N.  C9R6=Y.  C9R1=N.  C9R3=N.  C7R3=Y.  C4R3=N.  C5R3=N.   C4R1=Y.  C4R7=N.

Now we will assume C5R8=7 (y for yes).  Then, C5R3=n.  C4R7=n.

We now see in Example #51.6 above that …

·         2 cells have an N,n designation, meaning that they cannot be a 7 regardless of which driver cell is a 7.  Therefore, you can remove a 7 as an option from those cells.

·        This leaves only C5R8 as the only cell in box 8 that can be a 7.  C5R8=7.  

·        C1R8=9.  

Now your grid should look like Example #51.7 below:

You can now see in Example #51.7 above that C3R5=9.  C8R6=9.  C8R1=6.  C7R2=9.  C4R1=9.  C5R9=9.  C6R1=2.  C4R2=5.  C5R2=8. From this point the puzzle is easily solved, giving us Example #51.8 below:

Step 6 was once again magical and the first attempt led us to a solution to the puzzle!  

May the gentle winds of Sudoku be at your back,

Dan LeKander

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 #51!

I suggest you purchase Dan’s book a “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.  Remember when your teacher said – no such thing as a silly question – as we can all learn together.

As always, I want to thank Dan…and his proofreader… Peggy! I am hoping you will enjoy our Sudoku and at the same time join me in thanking Dan - Bravo to you both…

Posted in: Volume 14, Issue 4, April 2019, Sports