Sudoku Puzzle #45

Experience the power of the 6 with puzzle #45!

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 C6R3=9 (cell in column 6, row 3). C3R4=9.

Now your grid should look like Example #45.1 below:

NOT-SO-OBVIOUS ANSWERS … There are none.

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

In box 2 (top, middle grid of 3 x 3 cells) a 2 can exist only in C4R1 or C6R1; therefore, a 2 cannot exist as an option in C2R1, C3R1, C7R1 or C9R1. Pencil a small 2 in the bottom of those 4 cells to indicate they cannot be a 2.

In box 4 a 4 can only exist in C1R4 of C1R6; therefore, a 4 cannot exist in C1R2, C1R3, C1R8 or C1R9.

In box 4 a 5 can only exist in C2R5 or C3R5; therefore, a 5 cannot exist in C4R5, C6R5, C8R5 or C9R5. We will not put a “5” in the bottom of C4R5 or C8R5 because the 5 in C4R2 & C8R1 precludes C4R5 & C8R1 from being a 5.

In box 9 a 5 can only exist in C7R8 or C7R9; therefore, a 5 cannot exist in C7R4 or C7R6.

Now your grid should look like Example #45.2 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 #45.3 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 #45.3 above?

Take a close look at row 1. Can you spot a Step 1 clue?

Row 1 has a hidden pair & a quint. Take your choice. Personally, I spotted the quint before the hidden pair. In any event, C3R1 & C7R1 are the only two cells in row 1 that contain the options 6 & 7. Therefore, all other options for those two cells can be eliminated. Now your grid should look like Example #45.4 below:

Next, we will search for any other Step 1-5 clues. In looking at Example #45.4 above, you see that with changing C3R1 & C7R1 to options 67 that the only choice for a 1 in row 1 is C4R1, C5R1 or C6R1; therefore, a 1 cannot exist as an option in box 2 in C5R3 and the 1 can be eliminated from C5R3. This is an example of a Step 2 Interaction. Now your grid should look like Example #45.5 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 1 we find just 2 unsolved cells that contain the option 6 … C1R3 & C1R9. 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 #45.6 below:

Do you agree that one of these two yellow cells in column 1 must be a 6? 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 6 and see which other cells cannot be a 6. Then we will assume C1R9 is the 6 and see which other cells cannot be a 6. Then we will attempt to identify any cell or cells that cannot be a 6 regardless of which cell in column 1 is a 6.

We will mark C1R3 with a “Y” and mark C1R9 with a lower case “y” to keep track of the exercise as per Example #45.7 below.

We will start by assuming C1R3=6. Then, as marked above, C7R3 and C8R3 are not a 6 (marked with a “N”). Then, C7R1=Y. C7R4=N.

Now we will assume C1R9=9 (y for yes). Then, C4R9 & C5R9=n, C4R7=y, and then C4R4 & C4R5=n. C5R4=y and C7R4=n.

We now see in Example #45.7 above that C7R4 has a “N,n” designation. What does that mean? Since we know one of the two yellow highlighted cells in column 1 must be a 6 and that C7dR4 is not a 6 regardless of which yellow cell is a 6, then 6 cannot be an option for C7R4.

Now your grid should look like Example #45.8 below:

Now notice in box 6 a 6 exists as an option only in C8R4 & C8R5. Therefore, we have created an Interaction and the 6 in C8R3 can be eliminated. Now your grid should look like Example #45.9 below:

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

In Example #45.10 below we have selected C1R2 & C1R8 as the driver cells, as they are the only two cells in column 1 with a 7 as an option.

Again, first we assume C1R2 is the 7. Then, C8R2=N. C7R1=Y. C7R6=N.

Next, we assume C1R8 is the 7. Then, C5R8 & C6R8=n. C6R7=y. C6R5 & C6R6=n. C5R6=y. C7R6=n. C7R1=y.

We find C7R6 has a “N,n” designation, so the 7 can be removed from that cell. We also find C7R1 has a “Y,y” designation, so it is a 7 regardless of which starter cell is the 7. C7R1=7.

Now your grid should look like Example #45.11 below:

It follows that C3R1=6. C7R3=6. C1R9=6. C4R7=6. C8R5=6. C8R6=7. C6R5=7. C5R8=7. C3R7=7. C1R2=7. That completes the 7 & 8’s. From this point the puzzle is easily solved.

Your final grid should now look like Example #45.12 below:

May the gentle winds of Sudoku be at your back.

Dan LeKander