Y Wings are a fairly advanced Sudoku solving technique that allows you to eliminate candidates in particular rows or columns of the grid. This is why it’s known as a candidate eliminator strategy.
Similar to the X Wing strategy, Y Wings involves identifying a particular pattern of candidates in the grid but unlike X Wing, it only involves three different cells, not four.
That’s why this strategy is also referred to as “bent triples” or an “XY Wing.”
While this pattern is not always the easiest to spot, it is sometimes necessary to solve harder Sudoku puzzles.
So what is this pattern and how can you use the Y Wing Sudoku strategy to solve puzzles?
The Y Wing Pattern
The Y-Wing pattern consists of three different cells that each contain two of three possible candidates. For example, ab, ac, and bc.
That is, the three possible candidates we’re working with are a, b, and c, and two of these three candidates are the only possible candidates in three cells.
These three cells must also form the Y pattern so that only one of the three cells ‘sees’ (that is, shares a column, row, or 3×3 region) with the other two.
See the example below of the structure of the Y pattern to help visualize this.
In this example, we’ve got three cells that contain the possible candidates a, b, and c.
It’s important to know that each of these cells can only contain one of the candidates. They cannot contain any digit other than the two candidates shown above.
A couple of red lines have been added to show how this pattern gets the name Y Wing.
The other important point to note is that only one of these cells ‘sees’ both of the other two. In this case, it’s the ‘ab’ cell.
What this pattern means
If we think about the implications of this pattern, it becomes clear that while the cell ‘ab’ could contain either ‘a’ or ‘b’, either ‘ac’ or ‘bc’ must contain a ‘c’.
It is not possible that neither ‘ac’ nor ‘bc’ contains a ‘c’.
This is because of ‘ac’ contained ‘a’ and and ‘bc’ contained ‘b’ then by the rules of Sudoku, there would be not possible solution to the cell ‘ab’.
Taking this logic a step further, we can then eliminate the digit ‘c’ from any cell that sees both ‘ac’ and ‘bc’ as we know one of these cells contains a ‘c’.
In this particular example, that means ‘c’ can be eliminated from the highlighted cell below.
Using the Y Wing Strategy to Solve Puzzles
Now that you know what the Y pattern looks like, let’s take a look at how it can solve Sudokus with the example puzzle below.
In this example, some of the cells have had all their possible candidates pencil marked in.
If you look closely, you’ll see there’s a Y Wing in columns 2 and 3 with the candidates 3, 4, and 8. This is shown below.
Now that we’ve identified a Y Wing, the next step is to determine which of the three cells sess both of the other two.
In this case, it’s the top cell with the candidates 3 and 8.
This means one of the other two cells must contain a 4.
Taking this a step further, we can now eliminate 4 from any cells that see both of these two cells (the ‘4, 8’ and the ‘3, 4’).
Therefore we can eliminate 4 as a possible candidate from the cell in column 3, row 8 (highlighted below).
Now that this cell only contains the candidates 3 and 8, another Y Wing has formed. This time horizontally instead of vertically making it a bit harder to spot.
This is why it may be more helpful to think of Y Wings as ‘bent triples’ instead.
Using this newly revealed Y Wing, we can now able to eliminate the 4 as a candidate from the cell in column 6, row 7.
Meaning that we can now resolve this cell as being a 9.
Summary
As you may now appreciate, the Sudoku Y Wing strategy is an advanced solving technique that is not always easy to spot.
Because of this, you won’t need to use it to solve simple puzzles with an easy rating. But as you move up in difficulty, you are likely to encounter times you need to use Y Wings to solve the puzzle.
And now that you know what to look for, you’ll be able to tackle these harder Sudokus.
