Finding a hider by an unknown deadline

An object is hidden among several locations. Each search at the object’s location independently finds the object with some location-dependent probability. The goal is to find the object by a deadline, but the deadline is unknown. Assuming the worst-case scenario, where Nature knows the deadline and uses this knowledge to hide the object to hinder the search, this paper shows that there is a randomized search strategy that simultaneously maximizes the probability of finding the object by any deadline.