To be honest, I think it’s far more interesting to set aside a real world problem that you have encountered at your company and see how a candidate would think through it (out loud, of course). Many issues you’ll need to solve on a day-to-day basis have nothing to do with programming — and instead have to do with knowing related technologies (like a TCP/IP network, or a database) and how they interact.
You might be shocked to discover how many developers have a deep understanding of algorithms but can’t troubleshoot/design/architect/solve their way out of a paper bag.
Also: the thought of you ACTUALLY chewing your arm off is morbidly humorous. Thanks for that. :-)