[Fri31Aug]

Just to be sure, "path" must be understood as "trajectory" here? If the hiker doesn't know the starting position then it cannot be "path" as in "line between point A and point B" since there is no point A or B.

So the solution would be something like: "go ahead 10 meters, then turn 45° right, then go ahead 50 meters, then take a Bézier curve left with such parameters, etc"

> The best path is taken to be the one that minimizes the worst-case distance to travel before reaching the edge of the forest.

Again, just to be sure, the "worst-case distance to travel" is the longest distance achieved by the "trajectory" when you apply it starting from any point of the forest?

So basically (assuming you walk at constant speed):

1. Determine a trajectory to follow that guaranties that you would get out of the forest under N seconds (easy).

2. What is smallest possible N and the associated trajectory under which #1 is true? (hard)