I've given plenty of interviews in my day. Almost all of them have been for highly technical positions; typically software development. Of all the interview questions I've ever asked, this one is my absolute favorite:
"Write a function that can take the derivative of a single variable polynomial of any order. Perform this operation using the smallest number of operations possible."
Now, normally the people freak - and that's okay. They hear "derivative" and start flailing around, their brain short circuiting from the stress of the interview situation, until they aren't entirely certain if a derivative is a mathematical construct or the pet name of a certain species of spotted owl. I would typically continue on to give them an example of a taking a derivative, just to refresh their memory. I also tell them that the function can take whatever input they feel is neccessary. I then give them 15 minutes to work on this.
No one has ever come close to answering the question right. Well, one guy did, and I hired him. Of the rest of the people that I hired, they all got close - but here's the trick. The question wasn't about finding the right answer. The question was about finding out how your brain worked by a) stressing you and b) requiring you to think logically under that stress.
Anyone care to take a stab at it? Brownie points for the first person to get it right. 🙂