You are given a 4x4 square grid. It has 16 cells and 25 grid intersections. Can you place 10 points at grid intersections, such that no three points lie on the same straight line? Lines can be oriented in any direction. Bonus question: can you find multiple solutions that are not rotations/reflections of each other?
The answer to both main and bonus question is given by the following fact:
there are exactly five solutions, truly distinct even after rotations and reflections.
This is the $n=5$ case of the no-three-in-a-line problem (link contains spoilers, obviously). In general, one might ask whether it's always possible to get $2n$ dots on an $n\times n$ grid (the theoretical maximum is $2n$, since each row and column can contain at most 2 dots). The answer to this question for general $n$ is unknown. The number of possible solutions, distinct even after rotations and reflections, is given by this OEIS sequence (again, link contains spoilers).
I'm not sure if there's a short and neat way to prove that this problem has exactly five solutions and no more, but it's been done by a direct case-bashing approach by Alberto Cid on Quora. Certainly it's easily verified that all five of the solutions shown above do work.
just two of the five solutions (the first and last ones, according to the order I've put them in above) have any nice symmetry properties.