Can you talk about your most challenging technical problem?

While I appreciate that the context of technical problems is vitally important... the examples given are product and team management problems, not technical. I have had technical problems where I discovered bugs in a 3rd party core product, even notably show-stopper bugs on their major releases, and had to work in tandem with their devs while leadership from both companies lurked on the conference calls. That is the kind of context I think of when I am thinking of difficult technical problems.

The danger of thinking of your own product management as the context that caused the problem is that instead of telling a story of high-pressure but successful collaboration, it is easy to fall into the trap of bitching about how your former bosses handled things. That is never a good move in an interview.