Here is a problem I came up with that is extremely easy, but when I posted it on another forum it took a while for someone to answer and the answer was much more complex than what was needed. Let's see if MHF has better mathematicians....I have faith!

Question: Find the largest $\displaystyle n$ in $\displaystyle \mathbb{R}^n$ such that every k-cell (denoted $\displaystyle E$) has finitely many points $\displaystyle p,q\in{E}$ such that $\displaystyle d(q,p)=\text{diam}\left(E\right)$. Prove that this is the largest $\displaystyle n$.