XY Wing is my favorite technique. I'm not sure why. I guess it's because the logic is just so perfect!
First, let me describe what it is.
In order for this to work, the cell in the middle of the "Y" (green) must intersect both of the cells on its wings (blue), while the two wing cells may not intersect each other.
Additionally, the green cell's two pencil marks must appear in each of the blue cells' pencil marks, along with a third pencil mark shared by the blue cells only. Notice how the green cell has 2 and 7. Also notice: one of the wings has a 2, and the other, a 7. The other candidate in each of the wings is the same: a 1.
Bear with me, I promise I am going somewhere with this!
Suppose the green cell ended up being "7". This would make the right blue cell a 1. Or perhaps the middle cell is "2"? This would make the left blue cell a 1. In either case, one of the blue cells is going to be 1.
Now that we know with 100% certainty that one of the wing (blue) cells is a 1, we can assume that any cell that intersects both of the blue cells cannot possibly be a 1!
Let's take a look at the same example again:
See two cells colored pink? These two cells intersect both of the blue cells.
Since the green cell dictates that one of the blue cells is going to be "1", we can remove the "1" pencil mark from the pink cells. We have, through logic, eliminated 1 as a candidate for the pink cells.
This creates a Lone Single in the right pink cell, solving it.
OK, you say — pretty cool logic indeed. But how could I ever find a situation like this? Well, I'll tell you — it's a bit easier than it may seem…
If you are working on a puzzle and find yourself stuck — you can find any more naked pairs, hidden singles, or omissions — maybe it's time to look for an XY Wing:
So, find any cells that intersect both of them and remove the candidates!
9 videos|46 docs
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1. What is an XY Wing in Sudoku? | ![]() |
2. How do you identify an XY Wing structure in a Sudoku puzzle? | ![]() |
3. Can you give an example of how to apply the XY Wing technique in a Sudoku puzzle? | ![]() |
4. Are there any limitations to using the XY Wing technique? | ![]() |
5. How does the XY Wing technique compare to other advanced Sudoku techniques? | ![]() |