Slično smo riješili prvi trag.

Here slično is an adverb, meaning similarly, in a similar way, or like that too.

It comes from the adjective sličan / slična / slično = similar, but in this sentence it is not describing a noun. It is describing how the action was done:

• Slično smo riješili prvi trag. = We solved the first clue in a similar way.

So this is not neuter adjective agreement here; it is an adverbial use.

Croatian commonly forms the past tense with:

• the auxiliary biti in the present tense
• plus the l-participle

So:

• smo = we are/have as an auxiliary
• riješili = past participle of riješiti

Together, smo riješili means we solved / we have solved.

This is the normal Croatian past-tense pattern:

• ja sam riješio/riješila
• ti si riješio/riješila
• mi smo riješili/riješile

Because smo is a clitic. Croatian clitics usually go in the second position in the sentence or clause.

In:

• Slično smo riješili prvi trag.

the first element is Slično, so the clitic smo comes right after it.

This is very typical in Croatian. Compare:

• Prvi trag smo riješili slično.
• Jučer smo riješili prvi trag.

In each case, smo tends to come after the first stressed element.

Riješili is the masculine plural form of the participle.

Croatian past participles agree with the subject in gender and number.

So:

• mi smo riješili = we solved
  used for a group of men or a mixed-gender group, and often also as the default when gender is not specified
• mi smo riješile = we solved
  used if the speakers are all female

So the sentence assumes either:

• the speakers are male/mixed, or
• masculine plural is being used as the default form.

It is in the accusative singular, because it is the direct object of riješiti.

The verb riješiti means to solve, and the thing being solved goes in the accusative.

So:

• riješiti trag = to solve the clue/trace

Why does it look the same as the nominative?

Because trag is a masculine inanimate noun, and for many masculine inanimate nouns:

• nominative singular = accusative singular

So:

• prvi trag can be nominative
• prvi trag can also be accusative

In this sentence, it is accusative because it is the object.

It actually is changing correctly for the noun it goes with.

Prvi agrees with trag in:

• gender: masculine
• number: singular
• case: accusative

Because trag is masculine inanimate, the accusative singular form of the adjective is the same as the nominative singular:

• prvi trag

Compare with a masculine animate noun, where the accusative would look different:

• nominative: prvi čovjek
• accusative: prvog čovjeka

So prvi stays in this form because of the noun type.

The infinitive is riješiti.

This is a perfective verb, usually meaning to solve, to resolve, or to finish solving something.

The corresponding imperfective verb is usually:

• rješavati = to be solving, to solve repeatedly, to work on solving

So roughly:

• riješiti = solve, complete the solution
• rješavati = solve/process over time, be solving

In this sentence, riješiti fits well because it refers to a completed action.

Literally, trag often means trace, track, or trail.

But depending on context, it can also be used for something like a clue or lead, especially in puzzles, mysteries, hunts, or investigations.

So if the meaning given to the learner is clue, that is probably coming from the context rather than from the most basic dictionary meaning alone.

Yes. Croatian word order is fairly flexible, although not completely free.

This sentence:

• Slično smo riješili prvi trag.

emphasizes how the clue was solved: similarly / in a similar way.

Other possible orders include:

• Prvi trag smo riješili slično.
• Prvi trag riješili smo slično.
• Riješili smo prvi trag slično.

These versions may sound slightly different in emphasis or style, but the basic meaning can stay similar.

The version with Slično first highlights the manner right away.

Yes. That is exactly how it often works.

Slično usually refers back to something already known from the context:

• another method
• another example
• another clue
• a previous action

So this sentence often implies something like:

• We solved the first clue in a similar way (as the other one / as before).

Croatian often leaves that comparison unspoken if it is obvious from context.

Usually it can correspond to either, depending on context.

• Smo riješili is the standard Croatian past tense form.
• In English, you might translate it as:
  • we solved
  • we have solved

Croatian does not make the same everyday distinction that English does between simple past and present perfect in all contexts.

So the sentence could be translated naturally as either one, depending on the situation.

Then the participle would change to the feminine plural:

• Slično smo riješile prvi trag.

Everything else stays the same.

That is because only the participle agrees with the subject’s gender here.

Yes. That means essentially the same thing:

• Na sličan način smo riješili prvi trag.
• Slično smo riješili prvi trag.

The version with na sličan način is a bit more explicit:

• literally in a similar way

The sentence with just slično is shorter and very natural.