Hi, and welcome to Using English.
Usually (usually, not always!), a simple statement about not having something uses a plural. That's the general rule.
I don't have any bananas to sell you. (Yes, we have no bananas... if you're really an old student, you can sing along.)
I don't see any pens in the drawer where you told me to look. .
She doesn't have any brothers or sisters.
However, the phrase "I don't have a clue!" takes the singular - it's an idiom. You don't have any clue, do you? He just doesn't have a clue.
So the child not having any clue, versus any clues, works.
I vaguely recall a similar issue popped up sometime last year.
One teacher, I can't remember who, said that there's actually no practical differenct between
There is no book here and
There are no books here. In both cases, no one can find any books here.
I can't help thinking if this is also the case here? Either
I don't have any bananas or
I don't have any banana can convey the same idea, i.e., I have none.
Therefore, I assume by
usually, not always, you don't only refer to idioms like
I don't have a clue, but also mean they're both right while the plural form is much more popular. I don't get what you meant by
So the child not having any clue, versus any clues, works but I assume it's just like what I said.
Am I right in thinking so?
Thanks
Richard