"The eighth, ninth, and tenth turns are ours."
Translation:La oka, la naŭa, kaj la deka vicoj estas la niaj.
It's essentially short for "the one(s) that is/are ours" (notice that la niaj doesn't have a noun attached)--"the ours-one".
Same idea as languages, where you say, for instance, "Li parolas la francan", where la francan also doesn't have a noun because it's short for la francan lingvon.
Yes, you don't have to write "la nia" for "ours", you can also simply write "nia", some choose to do it, some don't.
I'm guessing you're not an Italian or a Frenchman, then :)
Some languages use the definite article in such a situation, some don't. I think Esperanto can go either way.
Because the oka vico is singular, the naŭa vico is singular, and the deka vico is singular.
Compare: "La blua kaj flava libroj" = the blue book and the yellow book; "La bluaj kaj flavaj libroj" = the blue books and the yellow books.
In the first case, there is one book of each colour, so the adjectives are singular, but "libroj" is plural because there are two books in total; in the second case, there are multiple books of each colour and so the adjectives are plural (and the noun is too, of course).
It also works the other way around: "La verdaj pordo kaj fenestro" (the green door and window) -- there is only one door and one window, so the nouns are singular, but there are two green objects, so the adjective is plural.
This kind of number agreement is unusual from the point of view of English or German, but it seems to be standard in Esperanto.
I have trouble with the word vico which seems to stand for row, sequence, queue and turn. That's way to unspecific for a nerd like me! For instance, how to differentiate between people in a row (shoulder-to-shoulder) and in a queue (chest-to-back)? Or do you use linio in the first case?
I play a computer game World of Tanks, which has a grid superimposed on a realistic looking map. There are a lot of players from Slavic-language speaking countries and they tend to refer the columns and rows of that grid with just lines. That is confusing to me. Perhaps there is just one vico in those languages, and therefore Z chose one word or he had limited spacial perception or...
"Vico" eblas signifi:
- linio: line
- rektvico: queue
- atendovico: waiting line
- aritmetika vico: aritmethic series
- ludovico: game turn
vicoj is plural because there are three turns - the eighth one, the ninth one, and the tenth one.
But there is only one eighth one, so oka is singular.
See also my comment to HeroRobb.