goldie5218 wrote:just how to find/identify an x-wing??

I will attempt to, step-by-step, explain how to identify an x-wing. There are two challenges to identifying an x-wing, especially when playing on paper.

- Having a correct set of pencilmarks is crucial. Make sure you haven't accidentally eliminated candidates that cannot be eliminated. Similarly, sometimes an x-wing doesn't appear until all possible placements/eliminations have been made.
- When do you start looking for an x-wing? This is very difficult to answer. I find it comes down to experience: once you are sure that the puzzle has reached at point where no more placements/eliminations can be made, start looking candidate-by-candidate for an x-wing.

In the list of steps I wrote

above, enough eliminations have been made after step #6 that an x-wing has appeared in the candidate 6's. As I noted above, the first six steps are likely the fastest way to reach the x-wing in the candidate 6's. However, there are still other placements/eliminations that can be made which do not affect the x-wing: r2c1=3, r3c2=5, r8c2=3, r7c5=1, eliminate candidate 8's from r2c8, r2c9, r7c7, and r7c8, eliminate candidate 9's from r8c1 and r8c9. If you do not understand how the first six steps were made, or how I made these additional placements and eliminations,

you are not ready to tackle x-wings: you should study, understand, and master the simpler techniques (such as

candidate restrictions,

pairs,

triples) before attempting puzzles that require advanced techniques (such as

x-wing,

swordfish,

colouring,

forcing chains).

I will begin after step #6 has been applied. The candidates now appear as follows.

- Code: Select all
` . . . | . . . | . . . 2 2 . | . . . | . . . . . . | . . . | . . .`

. . 1 | . . . | . . 1 . . . | . . . | . . . 3 . . | . . . | . 3 3

. . 1 | . . . | 1 . 1 . . . | . . . | . . . . 3 . | . . . | 3 3 3

-------+-------+------- -------+-------+------- -------+-------+-------

1 . . | . . 1 | . . 1 . . . | 2 . . | . 2 2 . . . | 3 . . | . 3 3

1 . . | . 1 1 | . . 1 . . . | . . . | . . . . . . | 3 . . | . 3 3

1 . . | . . 1 | 1 . 1 . . . | 2 . . | . 2 2 . . . | . . . | . . .

-------+-------+------- -------+-------+------- -------+-------+-------

. . . | . 1 . | . . . 2 2 . | . . . | . 2 . . . . | . . . | . . .

. . . | . . . | . . . 2 2 . | . . . | . . 2 3 3 . | . . . | 3 . 3

. . . | . . . | . . . . . . | . . . | . . . . . . | . . . | 3 3 3

. . . | . . 4 | . 4 . . . . | . . . | . . . 6 6 6 | . . 6 | 6 . .

. . . | . . . | . . . . . . | . . . | . . . . . 6 | 6 . . | . . .

. . . | . 4 . | . 4 4 . 5 . | . . . | . . . . . 6 | . . . | 6 . .

-------+-------+------- -------+-------+------- -------+-------+-------

4 . 4 | 4 . 4 | . . . . . . | . . . | . . . 6 6 6 | . . . | . 6 .

. . . | . . . | . . . 5 5 . | . . . | . 5 . 6 6 . | . . . | . 6 .

4 . . | 4 . 4 | . . . 5 5 . | . . . | 5 5 . . . . | . . . | . . .

-------+-------+------- -------+-------+------- -------+-------+-------

4 . 4 | 4 4 . | . 4 . . . . | 5 . . | 5 5 . . . . | . . . | . . .

4 . . | 4 4 4 | . . 4 . . . | . . . | . . . 6 6 . | 6 . 6 | . . .

. . 4 | 4 . . | . 4 4 . . . | 5 . . | 5 5 . . . 6 | 6 . . | . . .

. 7 7 | . . 7 | 7 7 . . . . | . . . | 8 8 . 9 9 9 | . . . | . 9 .

. . 7 | 7 7 . | . 7 7 . . . | 8 8 . | . 8 8 . . 9 | . . . | . 9 9

. . 7 | . 7 . | 7 7 7 . . . | . . . | . . . . . . | . . . | . . .

-------+-------+------- -------+-------+------- -------+-------+-------

. 7 7 | 7 . 7 | . 7 7 . 8 8 | 8 . . | . 8 8 . . . | . . . | . . .

. 7 . | 7 7 7 | . 7 7 . 8 . | 8 8 . | . 8 8 9 9 . | . 9 9 | . . .

. 7 . | 7 . 7 | 7 7 7 . 8 . | 8 . . | 8 8 8 9 9 . | . . 9 | . . .

-------+-------+------- -------+-------+------- -------+-------+-------

. . . | 7 7 . | 7 7 . . 8 8 | . . . | 8 8 . 9 9 9 | . 9 . | . 9 .

. . . | 7 7 7 | 7 . 7 . 8 . | . . . | 8 . 8 9 9 . | . 9 9 | . . 9

. . . | . . . | . . . . . . | . . . | . . . . . 9 | . . . | . 9 9

I will immediately focus on the candidate 6's and explain how to identify the x-wing. However, it should be noted that when solving a puzzle I would have to use this identification process for each candidate (unless I luckily decided to examine the candidate 6's first).

Now would be a good time to review the conditions for an x-wing. To paraphrase from angusj's

description: Given a specific candidate, the x-wing pattern requires

either two rows containing exactly two cells with this candidate in each row, and these candidates must share the same two columns

or two columns containing exactly two cells with this candidate in each column, and these candidates must share the same two rows.

It usually doesn't matter if you examine rows or columns first. Personally, in my head, I find it easier to examine columns first. So, to start, I am looking for columns that contain exactly two candidate 6's. It is easy enough to see that columns 6, 7, and 8 each have exactly two candidate 6's. Now I need to check if any of these three columns share the same two rows. Columns 6 and 7 share only row 1. Columns 7 and 8 do not share any rows. Columns 6 and 7 do not share any rows. Because we can't find two columns (that each contain exactly two candidate 6's) that share the same two rows, we cannot find an x-wing by looking at the columns.

So lets look for rows that contain exactly two candidate 6's. It is easy enough to see that rows 2, 3, and 9 each have exactly two candidate 6's. Check if any of these three rows share the same two columns. Rows 2 and 3 share only column 3. Rows 3 and 9 share only column 3. However, rows 2 and 9 share columns 3 and 4! We have found two rows containing exactly two cells with candidate 6's in each row, and the candidate 6's share the same two columns. We have identified the x-wing!

Well, that was a lot of typing. I do hope I haven't made any mistakes, which will only add to any confusion surrounding x-wings. And I hope this helped.

I think the most difficult part of identifying an x-wing is deciding when to start looking: only begin the search once you are sure that no more placements/eliminations can be made by other techniques.

Fixed: Grammar and spelling.