IMO Shortlist 2017 problem C5
A hunter and an invisible rabbit play a game in the Eulidean plane. The hunter's starting point coincides with the rabbit's starting point . In the th round of the game (), the following happens.
(1) First the invisible rabbit moves secretly and unobserved from its current point to some new point with .
(2) The hunter has a tracking device (e.g. dog) that returns an approximate position of the rabbit, so that .
(3) The hunter then visibly moves from point to a new point with .
Is there a strategy for the hunter that guarantees that after such rounds the distance between the hunter and the rabbit is below 100?