For the mathematically inclined, EWD717 and EWD765 have two really cool problems.

A while back someone posed EWD765 for an alternate solution, I don't recall if any other solution was found. That was my introduction to these.

[717]: https://www.cs.utexas.edu/~EWD/ewd07xx/EWD717.PDF

[765]: https://www.cs.utexas.edu/~EWD/ewd07xx/EWD765.PDF