What were the impossible questions? (You're not really expected to keep them secret, so it's fine to list them.)
To your point, it's strange that there's a common set of knowledge we're expected to know which we don't use, ever. Not just "in 99% of cases," but literally ever: If it ever comes up in the field, you can look up what you need to know in a few minutes.
Few would think that's a sensible way to hire someone, so I've spent a long time wondering why this is the case. I think it's because the hiring process implicitly selects for whoever makes it through. Meaning, if someone is giving you a test, they're biased into thinking it's a good test: After all, they passed it. That's why they're in a position to give it to you.
So it almost doesn't matter whether it's a good test or a bad test. Just that it's a test that the interviewer happens to like. There's enough talent floating around that people are willing to do whatever strange rituals you demand they do, regardless of whether it's efficient for them to know that knowledge. Since it's ambiguous whether the knowledge actually helps anyone, you get the present situation.