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Y-WingSTEP 0/5

Introduction

The Y-Wing strategy uses three cells containing two candidates each. By connecting these candidates in the right way, we can eliminate one digit from other cells.

We are looking for a cell with exactly two candidates. This is our pivot - the central element of the entire pattern.
Next, we look for two cells that see the pivot and also contain exactly two candidates.
The two side cells must share one common candidate. This is the digit we will be able to eliminate later.

The name Y-Wing comes from the characteristic arrangement of the three cells. Let's see how this relationship works in a concrete example.

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Y-WingSTEP 1/5

Finding the Pivot

Let's start by finding the central cell. We will focus on the candidates 3 and 5.

In Row 1, Column 3, there are exactly two candidates: 3 and 5.
This cell is our pivot. If one of these candidates turns out to be impossible, the other one must remain.

Now we need to find two cells that connect the pivot to another common candidate.

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Y-WingSTEP 2/5

Finding the Pincers

We are looking for two cells that see our pivot. Each of them must share one of the pivot's candidates.

In Row 2, Column 1, we have candidates 5 and 8. This cell sees the pivot through the same 3×3 box and shares candidate 5 with it.
In Row 8, Column 3, we have candidates 3 and 8. This cell sees the pivot through Column 3 and shares candidate 3 with it.
Notice that both pincer cells share a common candidate: 8. This is the candidate we will eliminate.

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Y-WingSTEP 3/5

Analysis

We do not need to know whether the pivot contains 3 or 5. In both cases, one of the pincers will be forced to contain the common candidate 8.

If Row 1, Column 3 = 3, then Row 8, Column 3 = 8, because its other possibility was 3.
If, on the other hand, Row 1, Column 3 = 5, then Row 2, Column 1 = 8, because its other possibility was 5.
In both cases, at least one of the pincers must contain the digit 8.

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Y-WingSTEP 4/5

Making the Elimination

Since one of the two pincers must contain the digit 8, we can eliminate 8 from every cell that sees both pincers.

The cell Row 8, Column 1 sees the pincer at Row 2, Column 1 through Column 1 and the pincer at Row 8, Column 3 through Row 8.
Therefore, candidate 8 is impossible in this cell and can be eliminated.

This is the essence of Y-Wing: we do not know which pincer will contain the common candidate, but we know that one of them must contain it. Therefore, we can eliminate it from every cell that sees both pincers.

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Y-WingSTEP 5/5

Forcing the Digit

After removing candidate 8 from the cell Row 8, Column 1, let's check the remaining possibilities for the digit 8 in this row.

Row 7, Column 4 already contains the digit 8, so Row 8 cannot contain another 8 in Column 4.
Row 9, Column 9 also contains the digit 8, so that position is already occupied.
After taking the previous elimination into account, only one possible position remains for the digit 8: Row 8, Column 3.

So we enter 8 into Row 8, Column 3. This is a direct result of the elimination made using the Y-Wing strategy.

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