You are trapped with a lion in a cage with 1 unit as its radius. Both you and the lion can run effortlessly at the speed of one unit.
1) The lion is quite hungry and all he wants is to catch you and eat you up. Will he be able to do that?
2) If yes, how long do you have till he does that?
Solution:
There can be two possibilities for the given situation.
One is if I run on the perimeter. Then, the lion will eventually catch me as the lion can follow my radius and then his trajectory will be half of the circle and not a spiral. Therefore, the lion will subsequently catch me in a finite amount of time.
Secondly if I don’t run on the perimeter, then clearly, I have an infinite amount of time before the lion catches me.