Otkako smo zapeli na zagonetki, moramo surađivati i pažljivo gledati.

Here otkako means since, in the time sense: from the moment when ... until now.

So:

Otkako smo zapeli na zagonetki, ...
= Since we got stuck on the puzzle/riddle, ...

It is different from kad, which usually just means when.

• Kad smo zapeli... = When we got stuck...
• Otkako smo zapeli... = Ever since we got stuck...

So otkako emphasizes that something started at that moment and is still relevant now.

Smo zapeli is the Croatian perfect tense, a very common past tense.

It is built with:

• a present form of biti (to be)
• plus the past participle

Here:

• smo = we are / auxiliary for we
• zapeli = past participle of zapeti

So:

smo zapeli = we got stuck / we have got stuck

This is the normal way Croatian expresses many completed past actions in everyday language.

Because the participle has to agree with the subject in number and sometimes gender.

The subject is understood as we. In the past tense, Croatian often shows gender in the participle:

• mi smo zapeli = we got stuck
  used for a masculine group or a mixed group
• mi smo zapele = we got stuck
  used if the speakers are all female

So zapeli is the masculine/mixed plural form.

The verb zapeti can mean different things in different contexts, but zapeti na + location/topic/problem often means to get stuck on something.

So:

• zapeti na zagonetki = to get stuck on a riddle/puzzle

This is a very natural way to express being unable to move forward with a problem.

Zagonetki is in the locative singular, because it follows the preposition na in this expression.

The noun is:

• nominative: zagonetka
• locative: zagonetki

So:

• na zagonetki

Even though English says on the riddle/puzzle only metaphorically, Croatian also uses na here in the idiomatic sense stuck on a problem.

This is something worth learning as a chunk:

• zapeti na nečemu = to get stuck on something

Because Croatian often drops subject pronouns when they are already clear from the verb form.

Here the verbs already show we:

• smo = we in the past construction
• moramo = we must / we have to

So mi is unnecessary unless the speaker wants emphasis.

Compare:

• Moramo surađivati. = We have to cooperate.
• Mi moramo surađivati. = We have to cooperate.
  with extra emphasis, like we in particular

Because morati works like a modal verb meaning must / have to, and it is followed by an infinitive.

So:

• moramo surađivati = we have to cooperate
• moramo gledati = we have to look

In this sentence, one moramo controls both infinitives:

• moramo surađivati i pažljivo gledati

That is completely normal in Croatian, just like in English:

• We have to cooperate and look carefully.

Because the sentence talks about ongoing, repeated, or sustained action, not one single completed act.

• surađivati = to cooperate in an ongoing sense
• gledati = to look/watch in an ongoing sense

That fits the meaning well: they need to keep cooperating and keep looking carefully.

If perfective verbs were used instead, the meaning would shift more toward a single completed result, which would sound less natural here.

Here pažljivo is an adverb, meaning carefully.

It comes from the adjective:

• pažljiv = careful, attentive

Adverbs often end in -o:

• pažljiv → pažljivo

So:

• pažljivo gledati = to look carefully

It describes how they must look.

In this sentence, pažljivo most naturally modifies gledati:

• moramo surađivati i pažljivo gledati = we have to cooperate and look carefully

Grammatically and semantically, it belongs most directly to gledati, not to surađivati.

If the speaker wanted carefully to apply to both actions, they would usually phrase it differently.

Yes. Croatian word order is fairly flexible, though some orders sound more natural than others depending on emphasis.

The given sentence is neutral and natural:

Otkako smo zapeli na zagonetki, moramo surađivati i pažljivo gledati.

But other versions are possible, for example:

• Moramo surađivati i pažljivo gledati otkako smo zapeli na zagonetki.

That version is grammatical, but it sounds less natural for neutral speech because the time clause is often placed first when it sets the context.

So the original order is a good default.

Because gledati means to look or to watch, while vidjeti means to see.

Here the idea is about making an effort with your eyes or attention:

• pažljivo gledati = to look carefully

But vidjeti is more about the result of perception:

• vidjeti = to see

So Croatian uses gledati because the sentence is about actively observing, not just passively seeing something.