Imagine a Quidditch match in which the Golden Snitch is completely invisible.
You know exactly the initial distance, but not the direction. You move faster than the Snitch, which moves at constant speed and always chooses the direction that takes it as far away from you as possible.
Is there a trajectory that allows you to catch the Snitch?
I made a video exploring the problem, the geometry, the differential equations, and a possible strategy. The proof is partially incomplete (but simulations work), so I'd genuinely love to hear your ideas, objections, or alternative approaches.
Video link: https://youtu.be/0xVusHRQePQ