Bilmece kronometre durmadan çözüldü.

Because çözüldü is the passive/intransitive form.

• çözdü = he/she/it solved
• çözüldü = it was solved / it got solved

It breaks down like this:

• çöz- = solve
• -ül- = passive/inchoative marker here
• -dü = past tense

So bilmece çözüldü means the riddle was solved, not someone solved the riddle in an active way.

In an active sentence, yes, you would often get bilmeceyi:

• Birisi bilmeceyi çözdü = Someone solved the riddle

But in this sentence the verb is passive: çözüldü. In Turkish, the thing affected by a passive verb becomes the grammatical subject, and subjects normally appear in the bare nominative form, with no ending.

So:

• bilmece çözüldü = the riddle was solved

That is why you see bilmece, not bilmeceyi.

Durmadan comes from:

• durmak = to stop
• -madan / -meden = without doing

So:

• durmadan = without stopping

Very often, durmadan also works like an adverb meaning nonstop, continuously, or without interruption.

By itself, durmadan means without stopping.

To mean before stopping, Turkish normally says:

• durmadan önce = before stopping

This is important, because English speakers sometimes see -madan and wonder if it can mean before on its own. Normally, it does not. The before meaning usually needs önce.

This is probably the hardest part of the sentence.

Kronometre is a bare noun here, and it is not marked as:

• an object
• an instrument like kronometreyle = with a stopwatch

So it seems to be part of a compressed side phrase: kronometre durmadan.

That can suggest something like:

• with the stopwatch not stopping
• while the stopwatch was still running

If the intended meaning were specifically with a stopwatch, Turkish would normally say kronometreyle or kronometre ile.

It is understandable, but many learners are right to feel that it is not very transparent.

One reason is that -madan/-meden clauses most naturally share their subject with the main clause. But here:

• the main clause subject is bilmece
• kronometre seems to act like the subject of durmadan

That makes the sentence feel compressed, and a bit unusual out of context.

Depending on the intended meaning, Turkish might use a clearer version such as:

• Bilmece, kronometre durmadan önce çözüldü.
• Bilmece, kronometre çalışırken çözüldü.

So if this part feels awkward to parse, that is normal.

Because Turkish passives often leave the agent unstated when it is unknown, obvious, or not important.

So:

• Bilmece çözüldü = The riddle was solved

The sentence focuses on the result, not on who did it.

If Turkish wants to state the doer, it often switches to an active sentence instead of using a passive with an explicit by-phrase.

Yes. Turkish word order is flexible, although the verb usually stays at the end.

In this sentence:

• Bilmece comes first, so the riddle is the starting point/topic
• çözüldü stays at the end, which is normal for Turkish

A different order could change the emphasis, for example:

• Kronometre durmadan bilmece çözüldü.

The basic meaning can stay similar, but the focus shifts depending on which part comes earlier.