IMO 2017 Shortlist C5
A hunter and an invisible rabbit play a game in the Eu lidean plane. The hunter's starting point H0 oin ides with the ra...
Category: Combinatorics
Problem
A hunter and an invisible rabbit play a game in the Eu lidean plane. The hunter's starting point H0 oin ides with the rabbit's starting point R0. In the nth round of the game (n ě 1), the following happens. (1) First the invisible rabbit moves se retly and unobserved from its urrent point Rn´1 to some new point Rn with Rn´1Rn “ 1. (2) The hunter has a tra king devi e (e.g. dog) that returns an approximate position R1 n of the rabbit, so that RnR1 n ď 1. (3) The hunter then visibly moves from point Hn´1 to a new point Hn with Hn´1Hn “ 1. Is there a strategy for the hunter that guarantees that after 109 su h rounds the distan e between the hunter and the rabbit is below 100? (Austria) Shortlisted problems 7