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XY-Wing

For this pattern to occur, a number of criteria must be met. First you need three fields which contain exactly two candidates. The cumulative list of candidates for the three fields must contain exactly three candidates (which means that if the three fields of the group were together in a logical unit, it would be a Naked Triplet).
But unlike the Triplet there are no options here. The candidates are precisely distributed in the fields in the pattern xy-xz-yz. In addition, they are not in just one logical unit, but in two. Here, the X-branch (xz) is in one logical unit and the Y-branch (yz) in another. The two logical units, in turn, have an intersection, and this field is the root field (xy). Thus, the root field has a direct relationship to each of the two branches, while the branches have no relationship to each other (relationship means sharing a logical unit - row, column or block). This is important - the branches can have no relationship to or be dependent on each other.

If these criteria are fulfilled, the candidate z can be eliminated from all fields that share a logical unit with both the X-branch and the Y-branch.
You might say that these are all of those fields which would be alternative positions for the root field , if only they had the right candidate.

Reasoning:
We are talking about a field that shares a logical unit with both the X-branch and the Y-branch, and about the candidate z. Recall the distribution xy-xz-yz - were this hypothetical fourth field to be filled in with the candidate z, then z would be eliminated in both branches. That would result in the distribution xy-x-y. Now that the two branches contain both x and y, x and y can be eliminated from the root field - because the root field shares logical units with both branches. Then the root field would have no more candidates.
And because that cannot be, z is not possible in the hypothetical fourth field and can therefor be eliminated from the candidate list.

An example will explain it better than words.

In this picture there are three examples of an XY-Wing.

The pink field is the root field, x = 5, y = 8.
Both branches are green, z = 3.

In the yellow field the 3 can be eliminated as a candidate, because a 3 in this field would lead to a 5 and an 8 in the two branches.
This means that no more candidates would remain for the root field.

Sudoku example XY-Wing

The pink field is the root field, x = 3, y = 8.
The two branches are green, z = 5.

Hence the 5 can be eliminated as a candidate in the yellow field.

The yellow field can thus be filled in with the 9.

Sudoku example XY-Wing

The root field is pink, x = 1, y = 3.
The two branches are green, z = 2.

Consequently, the 2 can be eliminated as a candidate in the yellow field.

Another completed field!

Sudoku example XY-Wing
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