Its an interview question, so no-one is expecting you to solve the problem or think of everything in what should be a fairly short time.

What they want to see is how you work: do you ask questions if you don't know something? do you sketch everything out? do you start from model up, or from UI/UX? can you draw from previous experience to improve the design?

After you've done something there would most likely be a discussion about the design, which again is like how you work: how do you handle criticism, how you debate approaches, can you see areas which could be improved on etc