Learn Finnish: Me luimme jännittävän arvoituksen jostakin kirjasta. - We read an exciting mystery from some book.

The base word is jokin (some/something). When this pronoun changes case, the case ending is actually inserted in the middle, right before the -kin suffix. Since we are saying 'from some book', we need the elative case (-sta). The root jo- plus -sta- plus -kin gives us jostakin.

Could we use a form of joku instead of jokin here?

No, because kirja (book) is an inanimate object. In standard Finnish, jokin is used for things and animals, while joku is used for people. Since a book is a thing, you must use the elative form of jokin (jostakin). If you were talking about a person, you would use the elative of joku, which is jostakusta. Keep in mind that in spoken Finnish, people often use joku for everything, but standard written Finnish requires this distinction.

Why do the words jännittävä and arvoitus end in -n?

They form the object of the sentence: 'an exciting mystery'. Because the action of reading it is seen as a complete action, the object takes the accusative case, which looks identical to the genitive case with its -n ending. The adjective jännittävä (exciting) must match the noun arvoitus (mystery) and take the same ending.

How does the spelling of arvoitus change to arvoituksen?