Is this correct?

[Lie.K.]

Hello :)

I happened to find the question which I think is strange.

Would you look at this? I should choose the words in the parenthesis.

#1 Children (are sleeping / sleep / will be sleeping ) by the time I get home.

I think there is not appropriate answer in the parenthesis because of " by the time I get home." Is that right?

If I use "will be sleeping", what should I change this part? Is #2 or #3 OK?
If it's not, would you give me some sentence that make sense?

#2 Children will be sleeping at the time I will get home.
#3 Children will be sleeping at the time I get home.

Thank you.

[Alan]

'Will be sleeping' is the correct choice. A future progressive is perfectly able to combine with a temporal by-phrase.