"The cat is drinking its water."
Translation:Katten drikker sit vand.
Shouldn't "katten drikker sit vand" and "katten drikker dens/dets vand" both be correct? Because the second means "the cat is drinking its (something else's) water," right?
Yes, you're right, but in the context of this sentence by itself "it" has nothing else to refer to other than the cat. That's why "sit" is correct here.
That's what I thought, but I was told to mark all correct translations and I got confused (I'd quibble that I was actually right!)
Because of the gender of "vand".:
Vand - et vand - vandet - sit vand.
Hund - en hund - hunden - sin hund.
Correct; but only in the singular case. In the plural it is always "sine".
I believe common would be n-words (like pigen) and neuter is t-words (like vandet).
So does the sin/sit have to agree with the subject (cat in this example) or with the object (water in this example)?
It has to agree with the object. I think you would say "Katten drikker sit vand" and "Katten drikker sin mælk".