Sudoku Puzzle #31

Do you think Mother Nature was a bit confused this year at the River, by switching summer and fall?

Having arrived in Florida after hurricane Irma cast her anger, it occurred to me that Florida and the River both have the same start to their busy seasons. High water at the River dampened the economic outlook and cost property owners. Hurricane Irma will affect property owners and businesses for months, if not years, to come. Simply a coincidence in the same year, or are more extreme weather conditions the norm?

You might ask what this introduction has to do with Sudoku. One possible explanation is that Sudoku can be a “positive distraction”, much unlike the weather this year.

Puzzle #31 is another opportunity to hone our Sudoku skills, with the ultimate goal of being able to solve any Sudoku puzzle. So, give it a go, or follow along with me below.

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 C4R7 (cell in column 4, row 7) =5. C4R8=9.

NOT-SO-OBVIOUS ANSWERS … none.

NUMBERS IN CELLS THAT CANNOT EXIST …

In box 8 (bottom center grid of 3 x 3 cells) a 2 can exist only in cells C6R7, C6R8 or C6R9; therefore, a 2 cannot exist in C6R5 or C6R6. On your grid, mark the bottom of these two cells with a “2”, indicating that a 2 cannot be an option.

In box 3 a 4 can only exist in cells C1R1 or C9R3; therefore, a 4 cannot exist in C9R7 & C9R9.

In box 8 an 8 can only exist in cells C6R7 or C6R9; therefore an 8 cannot exist in C6R1, C6R3, C6R5 & C6R6. Now your grid should look like Example #31.1 below:

FILL IN THE OPTIONS FOR THE UNSOLVED CELLS … after considering the options that cannot exist, your grid should now look like Example #31.2 below:

STEPS 1-8 …

STEP 1 … PAIRS, TRIPLETS & QUADS

Can you spot an example? Carefully search each row, column & box.

Do you need a hint? Ok, what is different about row 4?

C4R4 & C9R4 are the only 2 cells in row 4 that have 1 & 7 as options; therefore, you can reduce the options in those 2 cells to 17. This is an example of a “hidden pair”. Now your grid should look like Example #31.3 below:

There are no other Step 1-5 clues, so we will move on to Step 6.

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.

In column 3 we find just 2 unsolved cells that contain #1 as an option … C3R1 & C3R9. 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 #31.4 below:

One of these two cells must be a 1. We will consider them as “starter cells” which “drive” the exercise.

Here is the theory. We will perform two exercises. First, we will assume C3R1 is the 1, and see which other cells cannot be a 1. Then we will assume C3R9 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 column 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 C3R1 with a “Y” and mark C3R9 with a lower case “y” to keep track of the exercise as per Example #31.4 above.

Starting with C3R1 we see that if it is a 1 (Y for yes), then C4R1 & C6R1 are not a 1. We will mark these two cells with a “N” indicating they cannot be a 1 if C3R1 is a 1 (see Example #31.5 below). The only other cell in box 2 that now could be a 1 is C4R2 so we will mark it with a Y. If C4R2 is a 1, then C4R4 & C4R5 are not a 1. The only other cell in box 5 that could be a 1 is C6R5, so we will mark it with a Y. Then C7R5=N. Then C9R4=Y. Then C9R9=N.

Now we will switch to C3R9 and assume it is the 1. Then C7R9 & C9R9 cannot be a 1 and we mark them with a “n”. The only other cell in box 9 that can be a 1 is C7R8 and we will mark it with a “y”. Then C7R5 is a “n”. Then C9R4=y. Then C4R4=n.

Now take a close look at Example #31.5 below. Cells C4R4, C7R5 & C9R9 have a “N,n” designation. We have proven that these 3 cells are not a 1 regardless of which starter cell in column 1 is a 1, so the 1 can now be eliminated from those cells as an option. Conversely, cell C9R4 has a “Y,y” designation, meaning it is a 1 regardless of which starter cell is a 1. Therefore, C9R4=1.

 Now your grid should look like Example #31.6 below:

You can now clearly see that C4R4=7. Then C6R3=7. C2R2=7. C3R7=7. C7R8=7. C9R6=7. C1R8=1 (only cell in row 8 that has a 1 as an option). C3R1=1. C4R2=1. C6R5=1. C7R9=1. That retires the 1’s and 7’s. C8R8=6. C1R7=6. C6R6=6. C7R5=6. C3R4=6. C5R2=6. C9R3=6. C5R1=5. C9R1=4. C6R1=3. C4R1=8. C4R3=4. C4R5=2. C4R6=3. C5R4=8. C5R6=4. C5R8=3. C3R5=5. C8R5=8. C2R5=4. From this point the puzzle is easily solved, giving you the final version Example #31.7 below:

May this Sudoku puzzle add to your future Sudoku success & may the gentle winds of Sudoku be at your back.

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 31! How many have you completed?

[See Jessy Kahn’s Book Review, “3 Advanced Sudoku Techniques…” by Dan LeKander, June issue of TI Life.]