Project Euler problem 198 is a number theory problem that turns out to be almost entirely about continued fractions. The problem hides this - the statement talks about "ambiguous" real numbers - but the ambiguity has a clean characterization in terms of continued fraction expansions, and once you see it, the problem gets a lot smaller.

Wiki notes: Project Euler/198.

The Problem

Define a best approximation to a real number x with denominator bound d as a rational r/s in reduced form with s ≤ d, such that any other rational p/q closer to x than r/s has q …