Sudoku Puzzle #44

Your September Sudoku puzzle brings you another challenge, now that the River has calmed …

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 C2R9=6. C4R4=6.

Now your grid should look like Example #44.1 below:

NOT-SO-OBVIOUS ANSWERS … There are none.

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

In box 7 (lower left-hand grid of 3 x 3 cells) a 1 can exist only in C1R7 or C2R7; therefore, a 1 cannot exist as an option in C4R7, C5R7, C7R7 or C9R7. We already know a 1 cannot exist in C5R7 & C9R7, so pencil a small 1 in the bottom of C4R7 & C7R7 to indicate they cannot be a 1.

In box 3 a 1 can only exist in C8R1 of C8R3; therefore, a 1 cannot exist in C8R8 or C8R9.

In box 5 a 4 can only exist in C4R5 or C5R5; therefore, a 4 cannot exist in C1R5, C2R5, C7R5 or C8R5.

In box 7 an 8 can only exist in C3R8 or C3R9; therefore, an 8 cannot exist in C3R1, C3R3, C3R4 or C3R6.

Now your grid should look like Example #44.2 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 #44.3 below:

STEPS 1-8

We will begin with Step 1, identifying Pairs, Triplets, Quads & Quints. We will search each row, column and box. Can you spot any Step 1 clues in Example #44.3 above?

Take a close look at row 5. C2R5 & C8R5 are the only 2 cells in row 5 that can contain the 2 options 7 and 9 and are thus, a hidden pair; therefore, we can eliminate the other options from these two cells.

Now your grid should look like Example #44.4 below:

Can we identify any other Step 1-5 clues? In box 4 we see that a 2 only exists in C2R4 & C3R4; therefore, one of those two cells must be a 2. This precludes C6R4 from being a 2. Now your grid should look like Example #44.5 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 6 we find just 2 unsolved cells that contain the option 7 … C6R1 & C6R9. These cells are not in the same box, thereby qualifying as a candidate for a Step 6 exercise. These cells are highlighted in yellow in Example #44.6 below:

One of these two yellow cells 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 C6R1 is the 7 and see which other cells cannot be a 7. Then we will assume C6R9 is the 7 and see which other cells cannot be a 7.

We will mark C6R1 with a “Y” and mark C6R9 with a lower case “y” to keep track of the exercise as per Example #44.7 below.

We will start by assuming C6R1=7. Then, as marked above, C2R1 and C3R1 are not a 7 (marked with a “N”). Then, C2R2=Y, C2R4 & C2R5=N, C3R4=Y, C8R4 & C9R4=N, C8R5=Y, and then C8R9=N.

Now we will assume C6R9=7 (y for yes). Then, C8R9 & C9R9=n, C9R7=y, and then C9R4=n.

We now see in Example #44.7 above that two cells have a “N,n” designation. What does that mean? Since we know one of the two yellow highlighted cells must be a 7 and that C9R4 and C8R9 are not a 7 regardless of which yellow cell is a 7, then 7 cannot be an option for those two cells.

Now your grid should look like Example #44.8 below:

We still need more clues to solve the puzzle, so we will perform another Step 6 exercise.

In Example #44.9 below we have selected C3R3 & C3R6 (highlighted in yellow) as the driver cells, since they are the only two cells in column 3 with a 9 as an option.

Again, first we assume C3R3 is the 9. Then, C4R3 & C6R3=N. C4R2=Y. C4R7 & C4R8=N. C6R8=Y. C8R8 & C9R8=N. C9R7=Y. C9R6=N. C8R5=Y.

Next, we assume C3R6 is the 9. Then, C9R6=n. C8R5=y.

We find C9R6 & C8R8 have a “N,n” designation, so the 9 can be removed from those cells. We also find C8R5 has a “Y,y” designation, so it is a 9 regardless of which starter cell is the 9. C8R5=9.

Now your grid should look like Example #44.10 below:

From this point the puzzle is easily solved. C2R5=7. C3R1=7. C4R4=7 and so forth.

Your final grid should now look like Example #44.11 below:

Again, Step 6 has leveled the playing field!

May the gentle winds of Sudoku be at your back.

Dan LeKander