Sudoku Puzzle #47

T. I. LIFE PUZZLE FOR DECEMBER 2018

This holiday Sudoku Puzzle will warm your heart and take your mind off any inclement weather. So grab a hot cup of coffee or tea & tackle this very difficult puzzle with your knowledge of advanced Sudoku techniques.

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.

There are no obvious answers.

NOT-SO-OBVIOUS ANSWERS … We notice that the 6 and 7 in column 9 prevent C9R7 (cell in column 9 row7), C9R8 & C9R9 from being a 6 or 7. You now have two cells in box 9 (lower right grid of 9 cells) that can be a 6 or 7, which are C7R8 & C8R9. We will insert a 6 & 7 in those cells as their options per Example #47.1 below:

We can clearly see that the only remaining options for C9R7, C9R8 & C9R9 are 3, 5 & 9. Since there is already a 3 and 9 in row 8, C9R8 must be a 5. C9R7 & C9R9 must have options 3 & 9. Now your grid should look like Example #47.2 below:

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

In box 4 C1R6 & C3R4 are the only two cells that can have options 7 & 9, another obvious pair. Mark those cells with options 79.

In box 7 a 1 can exist only in C3R7 or C3R8; therefore, a 1 cannot exist as an option in C3R5. Pencil a small 1 in the bottom of C3R5 to indicate it cannot be a 1.

In box 2 a 3 & 6 can only exist in C5R1 or C5R2; therefore, mark those cells with options 36.

Now your grid should look like Example #47.3 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 #47.4 below:

STEPS 1-8

There are no Step 1 clues. Moving to Step 2: Interaction & Turbos examine Box 4 carefully. We find the only unsolved cells with the option 3 are C1R5 & C3R5, creating an Interaction in that no other cells in row 5 can have a 3 as an option. We eliminate the 3 from C4R5, C7R5 & C8R5. Now your grid should look like Example #47.5 below:

There are no other 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 column 2 we find just 2 unsolved cells that contain the option 4 … C2R1 & C2R9. 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 #47.6 below:

Do you agree that one of these two yellow cells in column 2 must be a 4? We will consider them as “driver cells” which “drive” the exercise.

Here is the logic. We will perform two exercises. First, we will assume C2R1 is the 4 and see which other cells cannot be a 4. Then we will assume C2R9 is the 4 and see which other cells cannot be a 4.

We will mark C2R1 with a “Y” and mark C2R9 with a lower case “y” to keep track of the exercise as per Example #47.7 below.

We will start by assuming C2R1=4. Then, as marked above, C1R1, C1R3, C7R1 & C9R1 are not a 4 (marked with a “N”). Now the only cell in box 3 that can be a 4 is C7R3, so we will mark it as a “Y”. Then, C7R4=N. C7R5=N. C9R4=Y. C5R4=N. C6R4=N. C6R5=Y. C6R9=N.

Now we will assume C2R9=4 (y for yes). Then, C5R9 & C6R9=n. C5R8=y. C5R4=n.

We now see in Example #47.7 above that C5R4 & C6R9 have a “N,n” designation. What does that mean? Since we know one of the two yellow highlighted cells in column 2 must be a 4, the N,n cells cannot be a 4 regardless of which starter cell is a 4. We eliminate the 4 as an option from these cells.

Now your grid should look like Example #47.8 below:

We need further clues to solve the puzzle, so we will look for another Step 6 clue. In column 2 we find just 2 unsolved cells that contain the option 8 … C2R2 & C2R9. 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 #47.9 below:

We will start by assuming C2R2=8 and marking that cell with a “Y” for yes. Then, as indicated above, C8R2 & C9R2 =N. C8R3=Y. C8R5 & C8R6=N. C9R6=Y. C5R6=N. C6R5=Y. C6R9=N.

Now we will assume C2R9=8 (y for yes). Then, C5R9 & C6R9=n. C5R8=y. C5R6=n. C6R5=y. C8R5=n.

We now see in Example #47.9 above that C5R6, C6R9 & C8R5 have a “N,n” designation. We eliminate the 8 as an option from these cells. C6R5 has a Y,y designation. So, C6R5=8.

Now your grid should look like Example #47.10 below:

It now follows that C6R4=4. C7R5=4. C9R1=4. C1R3=4. C1R8=6. C7R8=7. C8R9=6. C4R7=6. C4R8=1, and so forth.

From this point the puzzle is easily solved. Your final grid should now look like Example #47.11 below:

Wishing you and yours a very happy holiday season.

May the gentle winds of Sudoku be at your back,

Dan LeKander