[kernelbandwidth]

Strictly technical? Determining the existence of metastable states for the T-cell receptor protein in solution (PhD Dissertation topic). Sort of difficult science, though it seems quite easy in retrospect now; the project wasn't so much hard, as it just cut across a lot of disciplines. Poor developer interview answer though, as it didn't involve a lot of software development (lots of TCL scripting for data extraction and ML with Python instead).

The answer I used to use was a problem I had working as an R&D intern: determine when the speed limits posted on a street have changed from measurements of driver behavior. Interesting and fairly tricky ML problem (weather is a big confounder). Ended up writing a lot of C to get high enough performance to make the solution reasonable which was educational (I didn't know a lot of C at the time), but almost certainly not the right approach to the performance problem. Still more science than development, so it depends on who's asking.

Probably the hardest business-type technical problem I've encountered is database restructuring. We moved (a subset of our data) from a NoSQL database to SQL as part of larger architectural changes, and mapping, migrating, and maintaining compatibility has been non-trivial.

The hardest problem I've encountered has been helping to rescue a project with a severely dysfunctional development history. Much more project management and people than technical (it was just a CRUD app) but I came into a project that had been in development for a year or so and stalled out. The development was outsourced and I fell into a position as a liaison between the internal folks at the university that wanted the product and the dev team that had been hired to build it. Sort of a classic issue where the dev team and the stakeholders would talk right past one another. It drove me crazy at the time, but an excellent experience in retrospect. And it has a happy ending; the project went on to be successful after that, at least when I last heard.