Bellman’s ‘Lost In A Forest’ Problem

This one might sound a little bit like the Rendezvous problem, but that's just because both of them involve a person attempting to flee a forest. Richard E. Bellman, a mathematician, first proposed the geometrical problem known as the "Lost in a Forest" problem in 1955.

In essence, it seeks to determine whether there is a method—or, to be more precise, an algorithm—by which a lost hiker may precisely determine the best route out of a forest in any specific location. Despite not knowing where they are beginning from or which direction they are facing, it is assumed that they are familiar with the forest's shape. Every time they try to leave the forest, they must be able to calculate the shortest worst-case distance from wherever they are in the forest to the closest edge.

Since no such method has been discovered as yet, the issue remains unsolved. The difficulty of the problem lies in the fact that while there are answers for a handful of the fundamental shapes we are familiar with, none of them apply to a forest of any particular shape.