I've been trying to get a robust answer to this question but I've unfortunately not been able to because people have different opinions on this.
I haven't a clue.
I haven't an idea.
This doesn't sound correct to me because based on my understanding, it should be written with "got" and I'm not pretty sure whether this is grammatically correct or not. This probably works okay with "have" but as "haven't" stands for "have not", this seems wrong.
Thanks in advance.
Best Answer
"I haven't a clue" is an idiomatic expression, probably more common in UK English, or at least in English outside of the US, but still recognizable here in the US. It means, "I don't have a clue" or "I haven't got a clue," both of which are also perfectly fine. "I have no clue" is also used.
However, "I haven't" is not generally used to express that you don't have something, at least in American English. If you said, "I haven't a girlfriend," that would be understandable but would sound extremely weird. Instead, you would say "I don't have a girlfriend" (most common formulation in the US) or "I haven't got a girlfriend" (might be more likely to be heard in the UK - someone from there would need to confirm).
"I haven't an idea" doesn't sound idiomatic to me. "I have no idea," "I've no idea," or "I've got no idea," however, are common ways to very strongly say "I don't know."