Zapeli smo na zadnjoj zagonetki.

The dictionary form is zapeti.

In this sentence, zapeti means to get stuck. With zagonetka (riddle / puzzle), it is usually understood figuratively: we reached that riddle and could not continue or solve it easily.

So Zapeli smo means we got stuck or we were stuck, depending on context.

This is the normal Croatian past tense formation.

It is made from:

• the past participle: zapeli
• the auxiliary verb biti (to be): smo = we are / we have in this tense construction

Together, zapeli smo means we got stuck / we were stuck.

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

Here, smo already tells you the subject is we.

So:

• Zapeli smo na zadnjoj zagonetki. = We got stuck on the last riddle.
• Mi smo zapeli na zadnjoj zagonetki. also works, but mi adds emphasis, like we in contrast to someone else.

The past participle in Croatian agrees with the subject in number and gender.

• zapeli smo = we (masculine plural, or a mixed group, or unspecified gender)
• zapele smo = we (all female)

So zapeli smo is the normal default form if the group is mixed or if gender is not being specified.

Because smo is a clitic. Croatian clitics normally cannot stand in the first position of a sentence.

That is why:

• Zapeli smo na zadnjoj zagonetki. is correct.
• Smo zapeli na zadnjoj zagonetki. is not natural/standard as a sentence start.

You can also say:

• Mi smo zapeli na zadnjoj zagonetki.
• Na zadnjoj zagonetki smo zapeli.

In each case, smo comes after the first stressed word or phrase.

Here na is used in the expression zapeti na nečemu, which means to get stuck on something.

After na, the noun is in the locative here:

• na zadnjoj zagonetki

This literally feels like on the last riddle, but in English we naturally say stuck on the last riddle.

A useful rule:

• na + accusative often expresses movement onto
• na + locative often expresses being on / at something

Here the idea is not movement, but the point where you got stuck, so locative is used.

Because both words are in the locative singular.

The basic form is:

• zadnja zagonetka = the last riddle

After na in this sentence, that changes to:

• na zadnjoj zagonetki

So:

• zadnja → zadnjoj
• zagonetka → zagonetki

The adjective must agree with the noun in:

• gender: feminine
• number: singular
• case: locative

Yes. Both are correct.

• zadnji = last
• posljednji = last / final

In many situations, they are interchangeable:

• na zadnjoj zagonetki
• na posljednjoj zagonetki

Both sound natural. Posljednji can sometimes sound a bit more explicitly final in sequence, but zadnji is extremely common in everyday Croatian.

In this sentence, it is normally figurative.

With a puzzle or riddle, zapeti usually means:

• you cannot solve it
• you cannot continue past it
• it is blocking your progress

So it is not about being physically stuck. It is about being mentally stuck on that riddle.

A rough English-friendly pronunciation is:

ZAH-peh-lee smo na ZAHD-nyoy za-go-NET-kee

A few helpful notes:

• z = like z in zoo
• e = short e as in bet
• lj in zadnjoj is a soft sound, roughly like ly in million
• j is pronounced like English y
• stress is not marked in normal writing, but for a learner the approximation above is good enough to start with