It was never my only question.. I vary through the years.
Another favourite of mine is basically "implement a very sparse 100Mx100M matrix". Thought process much more important than result. (important things to consider: access time, storage size, static vs. dynamic, use cases, adversarial coordinate selection).
I actually consider the "cycles in the input" question a bit of a trick question -- I calibrated the test on people I knew were good, and no one who didn't know it already was able to come up with "the trick" in reasonable-settings-for-interview-time, and not many were able to come up with any O(1)space O(n)time solution.
The discussion with those who don't know the solution is useful, of course.