Hello and welcome to the XY wing technique course!
The XY wing technique is a technique that is often compared to the hooks of an eagle and its prey. The objective is to find the hook cells and proceed to eliminate the prey.
First, we start by finding a column with a cell having only two candidates, called pivot. The candidates in the cell are called X and Y. In the example below, the pivot is cell R5-C5.
Next, we look for two other cells that also have two candidates and belong to the same house as the pivot.
These two cells are called pins. One of the clamps must have X and Z as candidates and the other clamp must have Y and Z. In other words, the three cells must be related by common candidates.
In our example grid, Z is equal to 7. The clamps are cells R5-C2 and R8-C5 and the pivot is cell R5-C5.
For the pivot cell, there are only two possible options, the number 6 or 9.
If the correct candidate is 6, then let's see what the consequences would be.
If the correct candidate is the number 9, then the possible combination reverses.
In either case, one of the R5-C2 or R8-C5 clamps must be a 7.
Therefore, any column that is companion to both R5-C2 or R8-C5 clamps cannot be a 7.
In this case, we can safely remove all 7s from the companion cells.
In the previous example, the wing was shaped like an X, which may make you think of the X-wing technique, but in reality, it doesn't have to be.
Let's take another example where this time R7-C1 is the pivot.
The R2-C1 and R9-C3 cells are clamps.
All companion cells in R2-C1 and R9-C3 clamps cannot contain a 3. In this case, it is safe to delete candidates from cells containing a 3.
Cells R2-C3 and R3-C3, with candidate 3 deleted, are in the same house of both R2-C1 and R9-C3 clamps.
The XY wings must involve three companion cells that have only two candidates each, so start by looking for three companion cells that have only two candidates.
Once found, make sure the candidates follow the XY, XZ and YZ rule.
If you find this scenario, look for companion cells in XZ and YZ cells, and eliminate the Z candidates from them.