1. The X-wing technique

The X-Wing Technique

Hello and welcome to the X-Wing technique course!

The X-Wing technique will work on your concentration, your ability to analyze the grid, and it will be quite fun to do.

The X-Wing

Let's take a close look at the R2 and R4 lines that are selected. We can see that there are only two cells in each row that have the candidate number 8.

Finally, if we look closely, these four cells form an X since they are perfectly aligned.

If cell R2-C5 is an 8, then cell R4-C7 is necessarily an 8. Otherwise, if R2-C7 is an 8, then R4-C5 is necessarily an 8.

In any case, it is impossible for any other companion cells other than these four cells to be an 8, so we can safely remove all candidates.

The X-Wing technique is to look for four cells that are aligned (that form an X), and that have the same candidate that does not appear anywhere else in the same row or column. This common candidate is called the fish digit.

A second example, but this time in a column

We saw earlier an example of an X-Wing where the rows were the base set.

This time we'll see an example with the columns as the basis set.

If we look at columns C5 and C7, we see that for both columns, only two cells have the number 3 as a candidate.

Since these four cells form an X (or rectangle), then we can apply the X-Wing technique and remove all the 3 number candidates from the other cells in the same house.

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