Al Zimmermann's Programming Contests match this description. The name includes "programming" but does not require it:
You can enter whether you use a computer, manual calculations, or tea
leaves to solve the problems. You send me solutions, not programs.
The current contest ends on July 18.
At OP's request, consolidating main steps of @Deusovi's solution with my part into a single solution. Personally, I think Deusovi's part was much more challenging than mine, so if you're inclined to upvote, please upvote both.
Summary of Deusovi's work (recommend reading his whole description, which is excellent):
Deusovi's key observation: