Learn Hardcore Finnish: Olen iloinen, koska löysin ratkaisun ongelmaan. - I am happy because I found a solution to the problem.

Olen is the 1st person singular present tense of olla (to be). Finnish verbs change form for person and number. For olla in the present tense:

olen (I am)
olet (you are)
on (he/she/it is)
olemme (we are)
olette (you pl. are)
ovat (they are)

You omit the pronoun minä (I) because the verb ending already tells you who the subject is.

What role does iloinen play in the sentence, and why isn’t it inflected?

Iloinen is a predicate adjective meaning “happy.” After a form of olla, the adjective stays in the nominative singular if the subject is singular. Since the understood subject is minä (I), we use the nominative singular iloinen. If the subject were plural (we), you’d say olemme iloisia (we are happy).

Why is there a comma before koska?

In Finnish, you normally separate a main clause from a subordinate clause with a comma. Here koska (because) introduces a subordinate clause that explains the reason. So: Olen iloinen, koska löysin…
The comma signals that what follows is the explanation.

What exactly does koska mean, and is it different from other “because” words?

Koska means “because” and introduces a reason clause. Other related words:

siksi että – also “because,” often a bit more formal or emphatic
kun – can mean “when” or sometimes “because” in spoken Finnish
Use koska for a clear causal link: “I am happy because I found a solution.”

How is löysin formed, and what tense is it?

Löysin is the past (preterite) tense, 1st person singular of löytää (to find). Löytää is a Type 4 verb:

Infinitive: löytää
Past stem: löysi-
Ending for “I”: -n
So löysin = “I found.”

Why is the direct object ratkaisun in the genitive?

In the simple past (preterite) of a transitive verb, a definite object takes the accusative form, which in the singular looks like the genitive.

Nominative (indefinite): ratkaisu (“a solution”)
Accusative/Genitive (definite): ratkaisun (“the solution”)
Because you’re talking about a specific solution you found, you use ratkaisun.

Why is ongelmaan in the illative case, and how do you form it?

Ongelmaan is the illative singular of ongelma (problem), meaning “into/to the problem.” Finnish uses the illative to express “to” in the sense of movement or direction. For most words ending in an -a or -ä, you add -an or -än:

ongelma + an → ongelmaan
This construction literally means “a solution into the problem,” idiomatically “a solution to the problem.”

Can you switch the order of the clauses?

Yes. If you put the reason clause first, you still use a comma: Koska löysin ratkaisun ongelmaan, olen iloinen.
The meaning stays the same, but you’ve emphasized the reason by mentioning it first.