by, _

[Tukanja]

Which of these are correct ones?

Have the children paid for it themselves?
Have the children paid for it by themselves?

Thanks

[Josef]

Both are possible but the 1st is more idiomatic.

Are you sure you don't mean:
Did the children pay for it themselves?

(It seems difficult to imagine a context where the present perfect would be used for this question, though perhaps you have an example.)

[Tukanja]

A CGE book by RC and MMcC .
Page 384
Pronouns.
Reflexive pronouns for emphasis.