Here’s a cute problem I heard from Moor Xu:
Let . has exactly three critical points. Find the parabola that passes through these critical points.
I’ve been doing a daily problem of the day for my physics camp students. Questions and answers are posted here the day after we give them to the students. I haven’t been copying them over to this blog because many are repeats, and none are original. They might still be entertaining if you’re in to that sort of thing.