Utslagsrunden er vanskelig uten ledetråden.

Because Norwegian often puts the definite article at the end of the noun instead of using a separate word like English the.

• en utslagsrunde = a knockout round
• utslagsrunden = the knockout round

And:

• en ledetråd = a clue
• ledetråden = the clue

So the ending -en here is doing the job of English the.

Because Norwegian usually writes compound nouns as one word.

So:

• utslag
  • runde → utslagsrunde
• utslagsrunde
  • -n / -en definite ending → utslagsrunden

This is very normal in Norwegian. English often separates these ideas into two words, but Norwegian usually combines them:

• fotballkamp = football match
• skolebok = school book
• utslagsrunde = knockout round / elimination round

If you split compound nouns in Norwegian, it can look unnatural or even change the meaning.

The -s- is a linking element that often appears inside Norwegian compound nouns. It does not mean possession here.

So this is not the round of the knockout in a possessive sense. It is just the standard compound form:

• utslag
  • s
    • runde → utslagsrunde

This linking -s- is very common in Norwegian compounds, for example:

• arbeidsdag = workday
• fødselsdato = date of birth
• sannsynlighetsregning = probability calculation

Sometimes compounds use a linking -s-, and sometimes they do not. It is something you mostly learn word by word.

Because vanskelig is a predicative adjective here, meaning it comes after er and describes the subject:

• Utslagsrunden er vanskelig.

In this position, adjectives agree with the noun to some extent, but the basic form is often used with a singular common-gender noun like utslagsrunden.

Also, vanskelig is one of those adjectives whose neuter singular form looks the same as the basic form, so you do not see a change there either.

Compare:

• Runden er vanskelig.
• Spillet er vanskelig.
• Rundene er vanskelige.

The plural form changes to vanskelige, but the singular form here stays vanskelig.

Because the sentence is referring to a specific clue, not just any clue.

Compare these:

• uten ledetråden = without the clue
• uten en ledetråd = without a clue
• uten ledetråd = without clues / without any clue in a more general sense

So the original sentence suggests there is a particular clue already known from the context.

This is the same basic difference as in English:

• without the clue = a specific clue
• without a clue = any clue, not a specific one

Because in Norwegian, the definite article is usually attached to the noun itself.

So:

• ledetråden already means the clue
• utslagsrunden already means the knockout round

You normally do not add a separate the-word in front when the noun stands alone.

However, a separate word can appear in some cases, especially with adjectives or extra emphasis:

• den vanskelige utslagsrunden = the difficult knockout round
• den ledetråden = that clue / that particular clue

This is a common Norwegian pattern sometimes called double definiteness: a separate definite word plus a definite ending on the noun.

Yes. That sentence is also correct.

Norwegian allows you to move elements to the front for emphasis or style. If you put uten ledetråden first, the verb still has to stay in the second position, which is a major feature of Norwegian main clauses.

So you can have:

• Utslagsrunden er vanskelig uten ledetråden.
  Neutral word order.

• Uten ledetråden er utslagsrunden vanskelig.
  More emphasis on without the clue.

Both are grammatical. The second one highlights the condition more strongly.

Literally, ledetråd is something like guiding thread:

• lede = to lead / guide
• tråd = thread

So the image is of a thread that leads you in the right direction. That is why it means clue.

It is a very common and useful Norwegian word. You will see it in contexts like:

• Kan du gi meg en ledetråd? = Can you give me a clue?
• Politiet fulgte en viktig ledetråd. = The police followed an important clue.

So even though the literal image is different from English, the actual usage is very natural and common.