Learn Swedish: Mysteriet kan vi inte lösa, men vi letar efter något nytt. - The mystery we cannot solve, but we are looking for something new.

Because it describes the word något (something). Words like något, inget (nothing), and allt (everything) act as neuter words in Swedish. Any adjective describing them must take the neuter -t ending, so ny becomes nytt.

Why is the word order Mysteriet kan vi and not Mysteriet vi kan?

This is the V2 (verb-second) rule. Because the sentence starts with the object Mysteriet (The mystery) to emphasize it, the verb kan must take the second spot. The subject vi is then pushed to the third position.

Why does inte come after the subject vi here?

In a main clause, the negation inte comes after the first verb. Because the V2 rule swapped the subject and verb to make it kan vi, the word inte falls in right after the subject: ...kan vi inte...

Do I always need to use efter with letar?

Yes, when you want to say you are looking for a specific thing or person, the set phrase is letar efter. The verb letar on its own just means the general action of searching.