The arrogance here seems to be from misjudging the difficulty of the question. I see it as coming from a mindset that says it's OK to pull some "nifty" problem

The arrogance here seems to be from misjudging the difficulty of the question. I see it as coming from a mindset that says it's OK to pull some "nifty" problem out of his head at the last minute -- in this case, literally between lathering his toe jam and rinsing his buttcrack -- and feed it to candidates without having it properly vetted first. Or even, for that matter, sitting down and thinking about it for a couple of seconds. To me at least -- right off the bat, the core assumption they made about this problem was highly suspect, just from the fundamentals. In short - they didn't just make a mistake; they were throwing caution to the wind. On the basis of an apparent view that candidates are a dime a bushel, and their time is more or less infinitely expendable. That is - the mindset that so many companies following the current penchant for on-the-spot technical interviewing seem deeply beholden to.