This is a terrible interviewer, it has nothing to do with you. They know what they want, but they don't know how to find it properly.

Don't be afraid to use you're own notebook/laptop to Google a solution, or keep asking questions about the desired solution.

Be free in not having all the answers either, be confident you can find the answers. An interview shouldn't be about vague technical hurdles you have to jump through.

It's about proving competence & compatibility of character.

If your interviewer is willing to end the interview because of one dropped ball, call them on it.