It hits a nerve with me. I do computer tech stuff, and one of the hardest things for people to learn, seemingly, is to admit they don't actually know something (and that they should therefore consider, oh, doing research, or experiment, or perhaps seek someone with experience). The concept of "Well - you certainly can narrrow it down in some way" is lovely - but you still don't actually know. The incorrect statement would be "I know nothing (about your number)" - but nobody actually says that.

I kinda flip it - we know nothing for sure (you could be hallucinating or mistaken) - but we are pretty confident about a great many things, and can become more confident. So long as we follow up "I don't know" with "... but I can think of some ways to try to find out", it strikes me as simple humility.

Amusingly - "I am thinking of a number" - was a lie. So - there's a good chance that however you narrowed it down, you were wrong. Fair's fair - you were given false information you based that on, but still thought you might know more than you actually did. Just something to ponder.