"You know how Einstein got bad grades? Well mine are even worse!" - Calvin

Not to brag, but some problems I haven't even started yet.

We were given a problem involving the movements of a chess knight over a weird non-chess board to try to reach a particular point from a particular start in 4th grade. At the time I ran it backward and believed this showed it to be unsolvable. But I also believed the teacher would not give us an unsolvable problem without somehow indicating that it couldn't be solved (as doing so would violate the implied rules of the classroom).

One student solved it in class, but the rest of us weren't told what the solution was. I tried solving it a bit in high school but still couldn't come up with a solution.

I really hope there is a solution that I couldn't find, and not that we were expected to discover that there is no solution. I expect that problems in the real world may not have a solution, but if you're going to pull that sort of thing in a 4th grade classroom (even a gifted one) I expect some setup so that the kids know this is a possibility.