I think this one fits the profile, since it computational in nature, understandable by an undergrad student and still an open problem:

> **The envy-free cake-cutting**: the problem of cutting a heterogeneous "cake" that satisfies the envy-free criterion, namely, that every partner feels that their allocated share is at least as good as any other share, according to their own subjective valuation.
>
> _How many_ queries are required for cutting this cake into $n$ slices?

Whether it is "not too famous" might be disputable. Please take it with a grain of salt (I have never heard of it until a while ago, but I am not a mathematician). According to [wikipedia](https://en.wikipedia.org/wiki/Envy-free_cake-cutting) and [this other question](https://mathoverflow.net/q/279700/93602):

> The continuous "moving knife" algorithms for envy free cake cutting into connected pieces is only mentioned for up to 4 players. The general case is still an open problem.