cecbevwr, in another

thread (which might be the one you were referring to) I wrote a long explanation of identifying an x-wing, which you may find helpful.

I will attempt to provide a similar explanation for how to identify an x-wing in the

second grid (your progress grid) that you provided. I offer this explanation only to demonstrate why there

is not an x-wing in the candidate 1's or 3's using the cells r1c7, r1c9, r9c7, and r9c9, and why there

is an x-wing in the candidate 8's. Remember, the x-wing technique

is not required to solve this puzzle, as

pointed out by su_doku.

First, here is the set of pencilmarks for the puzzle as it stands.

- Code: Select all
` {12} 4 {123} | 9 5 7 | {1238} {136} {2368}`

{17} {137} 6 | 4 {38} 2 | {13578} {13} 9

5 8 {2379} | 1 {3} 6 | {2347} {34} {237}

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

{1479} 6 5 | 8 2 {14} | {1347} {1349} {37}

8 {1237} {12347} | 6 9 {14} | {12347} {134} 5

{1249} {129} {1249} | 5 7 3 | {124} 8 {26}

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

3 5 8 | 7 1 9 | 6 2 4

6 {27} {27} | 3 4 8 | 9 5 1

{149} {19} {149} | 2 6 5 | {38} 7 {38}

Clearly there cannot be an x-wing in the candidate 1's using the cells r1c7, r1c9, r9c7, and r9c9 because the 1 at r8c9 has eliminated the candidate 1's from the cells r1c9, r9c7, and r9c9.

Next, lets look at the candidate 3's.

- Code: Select all
` . . 3 | . . . | 3 3 3`

. 3 . | . 3 . | 3 3 .

. . 3 | . 3 . | 3 3 3

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

. . . | . . . | 3 3 3

. 3 3 | . . . | 3 3 .

. . . | . . . | . . .

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

. . . | . . . | . . .

. . . | . . . | . . .

. . . | . . . | 3 . 3

I will again 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 3's. Only columns 2 and 5 each have exactly two candidate 3's. However, columns 2 and 5 share only row 2. Because we can't find two columns (that each contain exactly two candidate 3'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 3's. Only row 9 has exactly two candidate 3's. Because we can find only one row that contains exactly two candidate 3's, we cannot find an x-wing by looking at the rows.

Therefore there is not an x-wing in the candidate 3's.

Finally, lets look at the candidate 8's.

- Code: Select all
` . . . | . . . | 8 . 8`

. . . | . 8 . | 8 . .

. . . | . . . | . . .

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

. . . | . . . | . . .

. . . | . . . | . . .

. . . | . . . | . . .

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

. . . | . . . | . . .

. . . | . . . | . . .

. . . | . . . | 8 . 8

To start, I am looking for columns that contain exactly two candidate 8's. Only column 9 has exactly two candidate 8's. Because we can find only one column that contains exactly two candidate 8's, we cannot find an x-wing by looking at the columns.

So lets look for rows that contain exactly two candidate 8's. It is easy enough to see that rows 1, 2, and 9 each have exactly two candidate 8's. Check if any of these three rows share the same two columns. Rows 1 and 2 share only column 7. Rows 2 and 9 share only column 7. However, rows 1 and 9 share columns 7 and 9! We have found two rows containing exactly two cells with candidate 8's in each row, and the candidate 8's share the same two columns. We have identified the x-wing!

The x-wing lets us deduce that if an 8 is in cell r1c7 then an 8 is in cell r9c9, or if an 8 is in cell r1c9 then an 8 is in cell r9c7. Therefore, the only cells in column 7 that can contain candidate 8's are r1c7 and r9c7. Therefore the candidate 8 can be eliminated from r2c7. The only candidate 8 remaining in row 2 is at r2c5. (The reason the x-wing technique is not required is because the candidate 8 at r2c5 is the

only candidate 8 remaining in box 2. This is generally easier to spot than an x-wing.)

Make sure you understand and have mastered the simpler techniques (such as

candidate restrictions,

pairs,

triples) before trying to tackle puzzles that require advanced techniques (such as

x-wing,

swordfish,

colouring,

forcing chains).

Use of the x-wing, swordfish, colouring, and forcing chain techniques should be a last resort only, especially if you are playing on paper. These techniques rely heavily on having a complete, minimal, and accurate set of pencilmarks. If you make a mistake with your pencilmarks or haven't eliminated enough of them, it becomes much more difficult (in some cases, impossible) to apply these techniques.