De må gjette svaret på utslagsspørsmålet.

Here De means formal you, not they.

In Norwegian, lowercase de normally means they, but capitalized De is the old-fashioned or very formal polite form of you. It can refer to one person or more than one person, so context tells you whether it is singular or plural.

So in this sentence, De is a polite way of addressing someone directly.

Not very common in everyday speech.

Most modern Norwegian speakers would usually say:

Du må gjette svaret på utslagsspørsmålet.
if speaking to one person informally, or

Dere må gjette svaret på utslagsspørsmålet.
if speaking to more than one person.

Using De today often sounds very formal, distant, old-fashioned, or deliberately polite. You may still see it in older texts, in some formal service language, or in situations where someone wants to sound especially courteous.

Because må is a modal verb, and modal verbs in Norwegian are followed by the bare infinitive, without å.

So you say:

De må gjette

not

De må å gjette

This is the same pattern you get with other modal verbs:

kan gjette = can guess
skal gjette = shall / will guess
vil gjette = want to guess
bør gjette = should guess

Here må means must or have to. It expresses necessity, obligation, or a requirement.

So the sentence is telling the person that guessing the answer is something they are required to do.

In other contexts, må can also mean something like must in the sense of logical deduction, as in Det må være riktig = That must be correct, but in this sentence it is clearly the obligation meaning.

Because the sentence refers to a specific answer: the answer to a particular question.

Svar is the noun answer.
It is a neuter noun:

et svar = an answer
svaret = the answer

Here, the context makes it specific. It is not just any answer; it is the answer connected to utslagsspørsmålet. That is why Norwegian uses the definite form svaret.

Because Norwegian says svaret på noe, literally the answer on something, where English says the answer to something.

So this is just a normal preposition pattern in Norwegian:

svaret på spørsmålet = the answer to the question

Even though English uses to, Norwegian uses på after svar/svaret in this construction.

This is a very common thing language learners run into: prepositions often do not match English word-for-word.

Utslagsspørsmålet is a compound noun. Norwegian usually writes compound nouns as one word.

It is made up of:

utslag + spørsmål

In this context, utslagsspørsmål means a tie-breaker question or a deciding question — a question used to determine the result when something is otherwise equal.

The definite form is:

utslagsspørsmålet = the tie-breaker question

The last part of the compound, spørsmål, determines the grammatical behavior of the whole word. Since spørsmål is neuter, the definite singular ending is -et, giving utslagsspørsmålet.

The sentence follows a very normal Norwegian main-clause pattern:

De = subject
må = finite verb / modal verb
gjette = infinitive main verb
svaret = direct object
på utslagsspørsmålet = prepositional phrase modifying svaret

So the structure is essentially:

Subject + finite verb + infinitive + object + prepositional phrase

Norwegian main clauses normally place the finite verb in the second position, and that is exactly what happens here with må.

Yes, if you only saw the form by itself, you might wonder about that, because de usually means they.

But in this sentence, the capital D strongly suggests formal you, not they. Also, the meaning of the sentence makes much more sense as a direct instruction to someone.

If it were they, the normal spelling would be de må gjette svaret på utslagsspørsmålet with a lowercase d.