Happy New Year everyone! Time to sharpen our pencils and break out the Sudoku puzzles. Speaking of puzzles, the puzzle this month might get us off to a good start for 2018.
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.
See TI Life Puzzle Preparation:
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 per 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 and December 2017.
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.
Prior to utilizing techniques first complete the 4 Steps of Puzzle Preparation …
- FILL IN OBVIOUS ANSWERS
- FILL IN NOT-SO-OBVIOUS ANSWERS
- MARK UNSOLVED CELLS WITH OPTIONS THAT CANNOT EXIST IN THOSE CELLS
- 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 C3R5=2 (cell in column 3, row 5). C9R8=5. C7R9=4.
NOT-SO-OBVIOUS ANSWERS …
There are none.
NUMBERS IN CELLS THAT CANNOT EXIST …
In box 4 (middle left hand box of 3X3 cells) an 8 can only exist in C2R4, C2R5 or C2R6; therefore, an 8 cannot exist in C2R7, C2R8 or C2R9. Mark a small “8” in pencil in the bottom of those three cells to indicate they cannot be an 8, in preparation for the next step.
FILL IN THE OPTIONS FOR THE UNSOLVED CELLS …
When you arrive at C5R3 you find that the only choice for the cell is an 8. C5R3=8. Also, please keep in mind that C8R7, C8R8 & C8R9 form a triplet 278; therefore, no other unsolved cell in column 8 can have a 2, 7 or 8 as an option.
After filling in the options for the remaining unsolved cells, your grid should look like Example #33.1 below:
Well, this sure looks intimidating, right? Let’s see if we can find the inherent weakness in this puzzle, the hidden clue that once revealed, will break down the barriers!
Steps 1-5 reveal no clues! It looks like we may be in some kind of trouble here. Let’s see if Step 6 can help us.
STEP 6: DAN’S YES-NO CHALLENGE
There are 3 circumstances that establish the potential for a Step 6 exercise:
- 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.
- Look for just 2 unsolved cells in a column that contain the same option where these 2 cells are not in the same box.
- 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 row 3, we find just 2 unsolved cells that contain #1 as an option … C1R3 & C7R3. These cells are not in the same box, thereby qualifying as a candidate for a Step 6 exercise. These cells are highlighted below in Example #33.2 below:
One of these two yellow cells must be a 1. We will consider them as “driver cells” which “drive” the exercise.
Here is the logic. We will perform two exercises. First, we will assume C1R3 is the 1, and see which other cells cannot be a 1. Then we will assume C7R3 is the 1, and see which other cells cannot be a 1. What happens if we find a cell or cells that cannot be a 1 regardless of which cell in row 3 is a 1? Quite simply it means that that cell cannot be a 1 and you can eliminate the 1 from that cell or those cells.
We will mark C1R3 with a “Y” and mark C7R3 with a lower case “y” to keep track of the exercise as per Example #33.3 below.
If C1R3=1 (marked with a Y), then C1R7 cannot be a 1 and we mark it below with a “N” for no.
If C7R3=1(marked as a y), then C7R5 & C7R6 are not a 1 and we mark them with a n. The only other cell in box 6 that can be a 1 is C8R6. Mark it with a y. Then C5R6=n and C6R6=n. Then C6R5=y. Then C6R7=n and C6R9=n. Then C5R7=y, and C1R7=n.
Now look at C1R7 with its “N,n” designation. It is not a 1 regardless of which yellow cell is a 1. Therefore, you can remove a 1 as an option from C1R7.
Now your grid should look like Example #33.4 below:
Example # 33.4
Having deleted the 1 in C1R7 gives us just 2 cells in box 7 that can be a 1, C2R7 & C2R9; therefore, just one of these cells in column 2 must be a 1. This sets up a Step 2 Interaction, eliminating the 1 as an option in C2R2. Since there are no more Step 1-5 clues, we will look for another Step 6 potential. In Example #33.5 below we have highlighted 2 more cells that are a potential Step 6 exercise.
The 2 yellow highlighted cells are the only 2 cells in row 3 that have a 9 as an option, and they are not in the same box, thus qualifying for a Step 6 exercise. We will first assume C1R3 is a 9 and mark it with a Y as per above example. Next, we will assume C9R3 is a 9 and mark it with a y. Track each of the 2 yellow cells with the yes’s and no’s and you have the result of a “N,n” designation in C1R8. So C1R8 is not a 9 regardless of which yellow cell is a 9, eliminating the 9 as an option from C1R8. This gives you Example #33.6 below:
So, has this Step 6 been more productive? Let’s look at column 1. C1R3 is now the only cell in column 1 that can be a 9. C1R3=9. Then C9R3=7, C4R3=5, and you are off to the races in solving this puzzle. Now your completed grid should look like Example #33.7 below:
Hope you enjoyed this puzzle. It is yet another example of how a Step 6 exercise exposed the weakness in a puzzle that looked so difficult. See you on February 15, 2018.
May the gentle winds of Sudoku be at your back.
Do you tackle a Sudoku on your cottage veranda, sailboat cockpit, or at a campsite? And now in January… how about the beach!
TI Life is taking full advantage of Dan LeKander, from Wellesley Island, who is a Sudoku expert and author of “3 Advanced Sudoku Techniques – That Will Change Your Game Forever!”
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 in January 2018.
I suggest you purchase Dan’s book, “3 Advanced Sudoku Techniques, That Will Change Your Game Forever!”
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.
Dan’s book is available online, amazon.com and on ebay.com.
Purchase of a book includes a 50-page blank grid pad, 33 black and two green tokens, to assist with Step 6.…
As always, I want to thank Dan… what a lot of work he puts into our TI Life articles!
By Dan LeKander, Wellesley Island
Dan LeKander and his wife, Peggy, have been seasonal residents of Fineview, on Wellesley Island, NY, since 1983. In addition to being a Sudoku addict, Dan explores the 1000 Islands to enjoy the wildlife, beauty and of course, Catch-and Release bass fishing.
Editor’s Note: Wow; Number 33! How many have you completed?
[See Jessy Kahn’s Book Review, “3 Advanced Sudoku Techniques…” by Dan LeKander, June issue of TI Life.]