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My favorite continues to be 'How would you make a binary tree persist?'. That is, suppose you had a binary tree with an integer at each node stored in a program. How would you store it in such a way that you could retrieve it the next time you ran your program.

Back in the day, this typically involved C and a flat file. Now, there are a lot more ways to do it. If I get the two-line Java answer, I'm quite happy, but then move to "ok, suppose you didn't have serialization..."

I've only had 2 out of about 50 nail it.