Let $C = \{(i, j)|i, j \in \mathbb Z,\; 0 ≤ i, j ≤ 24\}$.
How many squares can be formed in the plane all of whose vertices are in $C$ and whose sides are parallel to the $x$−axis and $y$−axis?
This question recently came up in the Mathematics chat. While it is a problem statement question, I think that it is an intrinsically interesting problem (at the very least, I got sucked in). I also think that this is the kind of problem which can be given to a clever high school student or undergraduate and that, as such, it deserves a place on the site.