Questions & Answers about Lopulta he löysivät hyvän ratkaisun.
Why does the verb löytää become löysivät in the past tense instead of keeping the "t"?
In certain Finnish verbs, the consonant t changes to s when it meets the past tense marker i. This is why the stem löytä- becomes löysi- in the past tense, similar to how tietää (to know) becomes tiesi. The -vät at the end simply shows it is the "they" form.
Why are hyvän and ratkaisun in the genitive-accusative case (ending in -n) instead of the partitive case?
The verb löytää (to find) almost always takes a total object because finding something is a complete, bounded action. Since they successfully found the entire solution, the object takes the -n ending. If the action were ongoing, like "searching" (etsiä), you would use the partitive case.
The word lopulta means "eventually", but it looks like a location case. How does that work?
It is formed from the noun loppu (end) plus the ablative case ending -lta (from). While it literally translates to "from the end", it has become a fixed adverb meaning "eventually" or "finally". Notice how the strong pp in loppu weakens to a single p due to consonant gradation when the ending is added.
If the sentence starts with an adverb (lopulta), why doesn't the verb switch places with the subject?