813554 wrote:I mean, I can detect skyscrapers or X-wings more easily. When see 2 digits in a row or column with a strong link, I can see the the patterns

X-Wings and Skyscrapers are easier to see exactly because both of their strong links are on either two rows or two columns. However, all the other X-Chains of length 4 have also two strong links (and one weak link), but they're just located differently:

X-Wing: both on rows or columns (weak links in opposite types of line)

Skyscraper: both on rows or columns (weak link in opposite type of line)

2-String Kite: one on a row, one on a column (weak link in a box)

Empty Rectangle: one on a row/column, one in a box (weak link on a row/column)

but for this example, I have to follow the chain twice for each number (r1c2 and r2c1 in this case). In other examples it's enough to follow the chain once and I can eliminate some candidates. In this, I have to assume that r1c2 is 9, follow the chain, then I assume that r2c1 is 9 this time and follow the chain again.

I don't quite understand. r1c2 sees the victim directly, so there's no chain needed for the case r1c2=9. You only need to follow the chain for the opposite case, i.e. if r1c2<>9 (-> r2c1=9). That's what the AIC depicts:

(9)r1c2 = r2c1 - r4c1 = (9)r4c4 => -9 r1c4

It can be read as follows: if r1c2=9 then r1c4<>4; else r2c1=9 -> r4c1<>9 -> r4c4=9 -> r1c4<>9. Thus, regardless of the truth value of r1c2, there can't be a 9 in r1c4. The chain works similarly the other way around too, i.e. if you start with r4c4. What it proves is that one or both of the chain ends must be a 9, and thus no cell weakly linked to both of them can't be a 9.

As a forcing chain (like you see it) it looks like:

(9)r1c2 - (9)r1c4

||

(9)r2c1 - r4c1 = r4c4 - (9)r1c4

=> -9 r1c4

But anyway, your reply really helped me, I saw it more clearly and I think I'll be able to see these patterns with less effort in time. Thank you.

You're welcome.