This is how I've conducted a few interviews at a startup. I take pains to emphasize that:

1. I'm just looking for pseudocode, nobody cares about whether you do length(items) or items.size(), etc. The code won't even be run.

2. Invent functions without necessarily defining them, I'll object if doAllTheWork() needs to be fleshed out.

3. The problem/docs presented are the whole thing for the interview. There might be bugs to uncover, but there's no secret second phase to the boss battle.

Ultimately, I'm looking for them to assemble the basic building blocks, and see what suggestions they have when I point out issues like error, handling, stale data, security, etc.