The arrogance here seems to be from misjudging the difficulty of the question. That is, it seems largely rooted in ignorance.
As for reckless, there's a wide variety of how much time people will spend preparing a question before an interview. Some people will spend days preparing a question. Others will just pick something off a list and ask it. I don't think everyone would agree that just thinking of a question is reckless. We also don't know how much time sethammons's coworker was given to prepare. Maybe he was told about the interview Monday evening, and had to conduct it Tuesday morning.
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.
As for reckless, there's a wide variety of how much time people will spend preparing a question before an interview. Some people will spend days preparing a question. Others will just pick something off a list and ask it. I don't think everyone would agree that just thinking of a question is reckless. We also don't know how much time sethammons's coworker was given to prepare. Maybe he was told about the interview Monday evening, and had to conduct it Tuesday morning.