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Now your grid should look like Example #34.2 below:
## STEPS 1-5## STEP 1: PAIRS, TRIPLETS, QUADSSearch each row, column & box. Do you spot any Step 1 clues? Ok, can you find an obvious pair, triplet or quad? Ok, check our row 8. What clue do you find? Right, there are 4 unsolved cells that contain only some or all of the 4 options 2678. This is an “Obvious Quad”. Looks like cells C3R8, C7R8, C8R8 & C9R8 have a monopoly on the options 2678; therefore, no other cell in row 8 may have the options 2678. After removing these options from C2R8, C5R8 & C6R8 you find that C6R8 now only has the one option. C6R8=5. Now your grid should look like Example #34.3 below:
Now ask yourself if the 5 in C6R8 has produced any new clues? Yes, look at C6R4, C6R5 & C6R6. There are
Now we will move on to Step 2. ## STEP 2: INTERACTIONS & TURBOSWhat do you notice about row 3? The only 2 cells in that row that can be a 3, are C4R3 & C5R3. So, can any other cell in box 2 have a 3 as an option? No! You may now delete the 3 as an option from C3R1, C4R1, C3R2 & C4R2. Now your grid should look like Example #34.5 below:
There are no other Step 1-5 clues, so we will move on to Step 6.
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 row 1 we find just 2 unsolved cells that contain the option 4 … C1R3 & C1R7. 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 #34.6 below:
One of these two yellow cells must be a 4. We will consider them as “ Here is the We will mark C1R3 with a “Y” and mark C1R7 with a lower case “y” to keep track of the exercise as per Example #34.7 below. If C1R3=4 (marked with a Y), then C7R3 and C8R3 cannot be a 4 and we mark them below with a “N” for no. The only other choice for a 4 is C8R1 and we will mark it with a Y. Then C8R5=N & C8R6=N. Then C7R5=Y. Then C5R5=N. Then C4R6=Y and C4R7=N. If C1R7=4 (marked as a y), then C4R7=n and C5R7=n. Then C5R8=y. Then C5R5=n. Then C4R6=y. Then C8R6=n.
Now your grid should look like Example #34.8 below:
Well, that was helpful. So where do we go from here? Did the Step 6 results provide any other clues? First of all, check out box 6. The only cell that can be a 9 is C9R6. C9R6=9. Then C9R1=3. C3R1=6. “Easy pickins” from here. Your finished grid should look like Example #34.9 below:
Step 6 has a tendency to bring difficult Sudoku puzzles to submission, time and time again. It is an exercise of looking past the complexity of a problem and instead, focusing on a subtle aspect of what can and cannot be. I sincerely hope you appreciate this exercise as it took a considerable amount of time to develop and to understand the intricacies of its influence on a puzzle. 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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