Rabbit Hunting using Set Theory and Probability

Abstract

Imagine an invisible rabbit that starts at some unknown integer point $A$ on the number line. At each time step, it hops by a fixed but unknown integer stride $B$. Both $A$ and $B$ are fixed integers, but their values are unknown. Suppose you have a magic hammer that you can throw at any integer point on the number line at each time step. When the hammer strikes the rabbit, it instantly squeals, indicating you have hit it. The problem now is to devise a strategy that guarantees your hammer will hit the rabbit in finitely many steps. We will provide two algorithms to solve this problem. The first involves Cantor's diagonal trick from set theory, and the second is a probabilistic approach.