Photo © Ian Coristine/1000IslandsPhotoArt.com |
|||||||||||||||||||||||||

To begin this exercise, we will look for We will first examine box 5 (middle box of 3 X 3 cells). The options for cells C4R5, C5R5 & C6R5 can only be 1, 3 & 4, an obvious triplet. Insert the options into your grid for those 3 cells. The only cells in box 1 that can be a 4 & 6 are C2R1 & C2R2, an obvious pair. Insert the options 46 into those two cells. Now your grid should look like Example #41.2 below:
Now we will search for Not-Obvious answers. In row 5, the four unsolved cells without options can only be 2, 7, 8 & 9. C3R5 must therefore be a 7, as there are already a 2, 8 & 9 in column 3. In row 5, the three remaining unsolved cells now can only be 2, 8 & 9. C9R5 must be a 2, as there are already an 8 & 9 in column 9. Fill in the options 89 for C2R5 & C8R5, an obvious pair. Now your grid should look like Example #41.3 below:
There are no more “Not Obvious Answers”.
In box 9 a 4 can exist only in C7R7 or C7R8; therefore, a 4 cannot exist as an option in C7R4 or C7R6. Pencil a small 4 in the bottom of those two cells to indicate they cannot be a 4. Now your grid should look like Example #41.4 below:
Once you fill in the options for the unsolved cells, your grid should look like Example #41.5 below:
We will begin with The first pair we spot is in row 3. C5R3 & C7R3 are the only two unsolved cells in row 3 that can have options 89, a hidden pair; therefore, eliminate all other options for these 2 cells. Next, we see in row 9 that the only two unsolved cells that can have options 89 are C2R9 & C5R9, another hidden pair; therefore, you may eliminate all other options for those 2 cells. In column 2 we have created an obvious pair 89 in C2R5 & C2R9; therefore, you may remove the 8 & 9 as options for all other cells in column 2. And finally, we see in column 5 we have created an obvious pair 89 in C5R3 & C5R9; therefore, you may remove the 8 and 9 as options from all other unsolved cells in column 5. Now we will move on to
In continuing our search for other Step 2 clues and then searching Steps 3-5 we find no additional clues.
There are 3 circumstances that establish the potential for a Step 6 exercise: - 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**. - Look for
**just 2 unsolved****cells**in a**column**that contain the**same option**where these 2 cells are**not in the same box**. - 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 5 we find just 2 unsolved cells that contain the option 8 … C5R3 & C5R9. 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 #41.7 below:
One of these two yellow cells must be an 8. We will consider them as “ Here is the We will mark C5R3 with a “Y” and mark C1R7 with a lower case “y” to keep track of the exercise as per Example #41.8 below.
If C5R3=8 then C7R3 is not an 8, so we will mark that cell with a “N”. If this cell is not an 8, then C8R1 must be an 8 (only other cell in box 3 that could be an 8). Then C8R4 & C8R5 are N, C7R4=Y, then C2R5 is Y, C1R4 is N, C1R7 is Y and C2R9 is N (all as marked above). Now we will assume C5R9 is the 8. Then C2R9 is n, C1R7 is y, C2R5 is y, C1R4 is n, C8R5 is n. What does it mean if a cell is marked N,n? What does it mean if a cell is marked Y,y? We know that one of the 2 yellow cells must be an 8. We have gone through the exercise detailing what the other unsolved cells in the puzzle must be, depending on which yellow cells is an 8. So, a cell with a N,n designation means that it cannot be an 8 regardless of which yellow cell is an 8, so you can remove the 8 as an option from that cell. If a cell has a Y,y designation, it mean that regardless of which yellow cell is an 8, this cell is an 8. You may now assign an 8 as an answer to these 2 cells. We now see that C2R9=9, C2R5=8, C8R5=9, C5R9=8, C5R3=9 & C8R3=8. C1R4 options become 13; therefore, C3R4=4. Now your grid should look like Example #41.9 below:
You can now see that there are many more clues in the grid. For example, once you process the obvious pair 13 in row 4, C3R6=5, C2R6=2, C1R6=9. Its all downhill from here, leading to an easy solution, as per Example #41.10 below:
Looking back at Example #41.6 one would think this might be a very challenging puzzle! Indeed, it would without a powerful Enjoy the summer, hopefully at the River. May the gentle winds of Sudoku be at your back. Dan LeKander
Posted in: Sports
## CommentsThere are currently no comments, be the first to post one. |