singular: 'Tochter', plural: 'Töchter'. Umlauts aren't a purely decorative feature of German, they actually carry meaning.
There is a choise
"Ich habe ... 1Tochter 2Töchter 3Töchtern"
how one can know one or more daughters have to choose?
As far as I know, if it was about one only daughter, the German sentence would necessarily include the indefinite article "eine" before "Tochter":
Ich habe eine Tochter.
Now, if it is about many daughters, there is no need for articles:
Ich habe Töchter.
nhaines's reply just below.)
You would expect "Ich habe eine Tochter", but because there is no plural for indefinite articles, this is another clue if you can't hear the Tochter/Töchter difference. (It takes a little practice until it's easy to hear.)
The pronunciation is not really clear to hear the difference. It should sound more of an u sound.
Agreed. The pronunciations on Forvo are far different from the Duolingo one.
I think they've corrected it. Can you confirm if it is okay now? I just want to get the pronunciation right - the subtle differences are very important.
Because you it an attempt construct a plural form of a plural word "Töchter". It is always good and very helpful to read the discussions from the top. If you do this here, you will see that https://www.duolingo.com/nhaines has already answered your questions nicely. Give him a Lingot if you like his explanation ;) I did
Can anyone tell me the difference between "ein", "eine" and "einen" ?
"ein" is masculine or neuter nominative case, "eine" is feminine nominative or accusative case, and "einen" is masculine accusative case.
Basically, you should check a grammatical guide for more information. I hope you like memorizing tables.
How should I find out what determines plural, not singular, in that exercise?
With a dictionary, to be honest, but with practice you start to gain intuition. In this exercise, "daughter" and "daughters" is die Tochter, die Töchter. Also, there's no indefinite article eine.
Ich habe eine Tochter (I have a daughter)
Ich habe Töchter (I have daughters)
Duo, when the question is asking to select a missing word for 'Ich habe...', both Tochter and Töchter are correct answers, not just plural form.