I guess if you give someone a puzzle, there's a possibility they might solve the puzzle from memory. If you give an unsolved problem, you know they won't have seen the solution before and can see their thought process better(since you know thinking will be required).

The exact phrasing matters too, I guess. There are lots of ways to find a good packing, and even good bounds on how far your good packing is from the global optimizer. So a reasonable question to your interviewer would have been "does it need to be the exact global optimizer, or can it be a good approximation ?". If they wanted a good approximation it might not be a bad question, and the question may have been designed to get you to ask for the distinction? Or maybe they were just dicks, who knows.

Reminds me of reading about at least one case where a problem was solved in a situation like that. Anyone recall what it was?

Dantzig solved an open problem in statistics which he thought was being causally assigned as homework:

https://en.wikipedia.org/wiki/George_Dantzig#Mathematical_st...

I think you mean "casually", not "causally" (even though it's kind the interesting Freudian slip, IMHO).

How did you answer?