It could. But for the reason of "that's just how most Germans say it", choose Duolingo's phrasing. Just as in English you could say "They like visitors not" or "They like no visitors" - they're not technically incorrect... it's just that people usually don't say it that way. There are different patterns of expression in German as compared to English sometimes.
Does "keinen Besucher" work as a translation of "no visitors" (even though it is literally singular)?
As TheDidact said, use the conjugation of the verb to distinguish between "they" and "she" for sie.
Disregard what TheDidact said regarding capitalization: when sie is the first word of the sentence (as it is here) it is capitalized regardless of meaning. When sie is not the first word in a sentence, but is still capitalized, it means "you" in a formal/unfamiliar/polite sense. The formal Sie is used for both singular and plural "you" (one person or several--perhaps a group of diners in a restaurant) and in both cases the verb is conjugated for the plural.
- if the verb is conjugated for singular, sie must mean "she" (regardless of capitalization)
- if the verb is conjugated for a plural subject AND sie is uncapitalized, it must mean "they"
- if Sie is in the middle of a sentence and still capitalized, then it is the "polite you" (and the verb must be conjugated for the plural)
- if Sie is the first word of the sentence, look to the verb to see if it means "she"; look to context to distinguish between "they" and "formal you".
NB: All of the above presumes you've already determined that sie is the subject (Nominativ), and not an object (Akkusativ). If used as the object, disregard the conjugation of the verb and use context to distinguish between "her" and "them".
Maaaaybe you could have Sie haben keine Besucher gern. But I think that sounds more like that they do have visitors, but they personally don't like the visitors. The original sentence is more like they prefer not to have visitors in the first place.
That's also using gernhaben as a separable verb, rather than using gern as an adverb, strictly speaking.
Except that the German sentence you were asked to translate did not concern
the visitors, but rather just visitors in general.
Sometimes you may need to add the definite article to the German (e.g., "die Zeit" oder "die Natur" when we wouldn't normally use it in English. Rarely (if ever) should you insert "the" where you don't see "der/die/das/den/dem".
Hi can anyone shed some light on the difference between "der Besucher" and "das Gast"?
das Gast doesn't exist; der Gast is the guest while der Besucher is the visitor.
If a door-to-door salesman or one of Jehovah's Witnesses comes to your door, they're a visitor, but you may or may not consider them your guest.
As for the use of nicht instead of keine, is there something in az_p's answer to jaime.jara2's exact same question that is unclear? If so, please elaborate and someone will certainly try to explain.