From pure entertainment I am interested in the following questions:
Let $N$ (particularly $N=1$ case is special) pursuers pursue running at max speed $u$ a runner running at max speed $v$.
What is the min $v/u$ with which the runner may be not "caught" by the pursuers (that is may not be in the same point as at least one of the pursuers) during infinite time?
The question may be asked for a circle or for a $A\times B$ rectangle in which movements of the runner and the pursuers are limited to be inside it.
Well, I guess that this problem may probably be hard for modern mathematics. Was it solved?