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## FILL IN THE OPTIONS FOR THE UNSOLVED CELLS …
Now your grid should look like Example #32.2 below:
## STEPS 1-8 …
There are no Step 1-5 clues, so we will proceed with Step 6. STEP 6: DAN’S YES-NO CHALLENGE There are 3 circumstances that establish the potential for a Step 6 exercise: In column 6 we find just 2 unsolved cells that contain the number 1 as an option … C6R4 & C6R7. 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 #32.3 below:
One of these two yellow cells must be a 1. We will consider them as “driver cells” which “drive” the exercise. We will mark C6R4 with a “Y” and mark C6R7 with a lower case “y” to keep track of the exercise as per Example #32.4 below. If C6R4=1 (marked with a Y), then C1R4 cannot be a 1 and we mark it below with a “N” for no. The only other cell in box 4 that can now be a 1 is C3R6, which we mark as a Y. Then C3R7=N & C3R8=N. If C6R7=1(marked as a y), then C1R7 & C3R7 are not a 1 and we mark them with a n.
We will continue with another Step 6 exercise. In column 7 of Example #32.5 below we find just 2 unsolved cells that contain #4 as an option … C7R4 & C7R7. These cells are not in the same box, thereby qualifying as a candidate for a Step 6 exercise.
One of these two yellow cells 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 C7R4 is the 4, and see which other cells cannot be a 4. Then we will assume C7R7 is the 4, and see which other cells cannot be a 4. What happens if we find a cell or cells that cannot be a 4 regardless of which cell in column 7 is a 4? Quite simply it means that that cell cannot be a 4 and you can eliminate the 4 from that cell or those cells. We will mark C7R4 with a “Y” and mark C7R7 with a lower case “y” to keep track of the exercise as per Example #32.6 below. If C7R4=4 (marked with a Y), then C6R4, C4R4 & C1R4 cannot be a 4 and we mark them below with a “N” for no. If C7R7=4 (marked as a y), then C6R7 is not a 4 and we mark it with a n. The only other cell in box 8 that could be a 4 is C4R8 and we mark it with a y. Then C4R6 & C4R4 are not a 4 and we mark them with a n. Now look at C4R4 with its “N,n” designation. It is not a 4 regardless of which yellow cell is a 4. Therefore, you can remove a 4 as an option from C4R4.
Now your grid should look like Example #32.7 below:
## STEP 7: DAN’S CLOSE RELATIONSHIP CHALLENGETo begin this exercise, we choose any unsolved cell with just 2 options. We will choose C2R6 with options 46, which will be our “driver cell”. We will choose a sequence of 4,6 as indicated below in Example #32.8. Logic: If C2R6=4, then we know that the adjacent cells cannot be a 4. We will indicate this by marking these cells with a “N4” per example below. If C2R6=6, then not all of the cells marked with a N4 can be a 4, therefore some of these cells are not a 4 regardless if C2R6 is a 4 or 6. So we will track the 6 to see the outcome of the N4 cells. We will perform this track in the 3rd level of the unsolved cells. As we establish a value for a cell we will eliminate that option from the adjacent cells. To start C2R6=6. Right off we know that C3R6=1. Then C3R8=9. C3R1=3. C1R1=9. Then C1R4=4. C1R5=7 & C2R5=9 (highlighted in green). We will pause here to see what we have learned. Logic: If C2R6=4, then C1R5 & C2R5 are not a 4. If C2R6=6, then C1R5=7 & C2R5=9. So regardless if C2R6 is a 4 or 6, C1R5 & C2R5 are not a 4. Since C2R6 has to be a 4 or 6, C1R5 & C2R5 cannot be a 4 and the 4 can be eliminated from these two cells.
Do we need to stop here? NO. Track the 6 further to see what happens. Example #32.9 below shows the tracking continued.
Check out box 8 above in Example #32.9. Two cells have a 1 as their outcome of tracking the 6 in C2R6. This is a conflict! What does this mean? It means that C2R6 cannot be a 6. C2R6=4. Now your grid should look like Example #37.10 below:
The only cell in column 1 that can now be a 4 is C1R3. C1R3=4. C6R4 & C6R5 form a Step 2 Interaction. One of those cells must be a 4; therefore, C6R7 cannot be a 4. Now C4R8 is the only cell in box 8 that can be a 4. C4R8=4. From this point the puzzle is easily solved, giving you Example #32.11 below:
Hope you enjoyed this puzzle. It was a good exercise of Steps 6 & 7. May the gentle winds of Sudoku be at your back.
By Dan LeKander, Wellesley Island
[See Jessy Kahn’s Book Review, “3 Advanced Sudoku Techniques…” by Dan LeKander, June issue of TI Life.]
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