#anyhow keep solving sudokus everyone!

[capitalismwasamistake]

More sudoku! @two-hundred-percent-trash asked for an explanation on the Y-Wing! Here you go, bestie ^_^

If you missed my previous sudoku post, you might want to check it out for the sake of notation and a primer on the X-Wing, since we'll be comparing the two.

The Y-Wing is a beginner technique slightly harder than the X-Wing that uses three cells instead of four, but in return is less versatile. Let's look at the example:

Here the green cell R4C3, is the "body" of our Y-Wing, and the yellow cell R4C7 and the red cell R7C3 are our "wings" (those are not their actual names, but exact terminology is less intuitive imo). The plain cell, R7C7, is our target cell.

How do we identify a Y-Wing? With the X-Wing it was easy, you had two pairs that contained the same digit. Here it's a bit more complicated. To have a Y-Wing, the following needs to be true: each wing has a digit in common with the body, and the wings have a digit in common with each other. As you can see, here the green and yellow cell both have a 1, and the green and red cell both have a 2. The yellow and red cell both have a 5.

So what does a Y-Wing tell us? First, you identify your target cell - that's the cell that both wings "see", in which case R7C7. Once we have the target cell, we start thinking about the state of affairs.

Let's imagine the green cell is a 1. What happens then? Well, if that happens, the yellow cell is a 5. Which means that the target cell cannot be a 5 and must be a 7.

Now about the other possibility - the green cell is a two. If that happens, the red cell is a 5. Therefore the target cell once again cannot be a 5 and must be a 7.

Therefore, not matter the "yellow" or "red" state of affairs, our target cell cannot be a 5.

So what the Y-Wing tells us is that the target cell cannot contain the digit common to both wings!

Why is it less versatile? If you remember the X-Wing clears up a digit from all cells between your two pairs - the Y-Wing only affects the target cell. Nevertheless, you're more likely to encounter a Y-Wing in a sudoku than an X-Wing (because it requires less cells), even though it's harder to identify.

Bonus: you could think about it backwards! Let's focus on the target cell instead of the body of the Y-Wing. We start thinking of those states of affairs. If the target cell is 7, nothing happens to the coloured cells. But if the target cell is 5, disaster! The yellow cell is a 1, and the red cell is a 2. But then the green cell can be neither a 1 nor a 2, therefore it cannot be anything! So now you can claim that the plain cell cannot be 5. This is a less optimal way to do it, because the target cell may contain more than only 2 options, so you have more to get through, and also requires you to actually do the "state of affairs" contemplation, whereas once you're proficient with the Y-Wing you can just remember to eliminate the digit common to the wings from the target cell. Still, to some people the reverse method may be more intuitive!

Hope that makes it clear!

Example image created with F-Puzzles Sudoku Setter