‘Why are they chasing you?’
‘I don't know.’
‘Oh, come on! There must be a reason.’
‘Oh, there's plenty of reasons. I just don't know which one.’

– Terry Pratchett, ‘Sourcery’

I really, really wish that more people understood the difference between ‘I don't know what the answer is’ and ‘I don't believe there is an answer’.

If I ask, for example, ‘How are you going to do this?’, I don't mean ‘this is impossible so you would be ill-advised to even consider trying it’. At least, sometimes I mean that (and I'll usually make it clear), but just as often I mean ‘there are several ways to do this and it might make a difference which one you pick’, or ‘I would like to do this myself and would be interested in your opinion of which way is better’, or ‘I don't doubt that if you say you can do this then you know of a way, but I haven't managed to think of one myself yet, so I want to know what I missed’. A question is not necessarily a challenge. Sometimes it's just a question.

I remember an infuriating conversation I had once while in the grip of a painfully strong crush on someone. She had said something ambiguous and I wasn't sure what she'd meant by it; I was agonising about this to a friend. Well, said my friend, she might have meant <this>. Yes, I said, she might have. Or, said the friend, she might have meant <that>. Indeed, I said. Or perhaps, my friend added helpfully, she meant <something totally opposed to both of the above suggestions>. Yes, I said, she could perfectly well have meant that too. The friend looked puzzled. ‘Then,’ he asked, ‘what's the problem?’

Not knowing the answer to a question doesn't necessarily mean you lack any possible answers. It may equally well mean that you have too many possible answers and can't choose between them. Or, indeed, that you have exactly one possible answer but are unconvinced that there aren't others you haven't thought of.