Escaping from a circle of fat lions.

You are surrounded, by X fat lions equally spaced around a circle of radius 200 meters in an open field. While making your escape plan you note several things: they are slow, they can only travel at one tenth of your speed, they are stupid,
they can only move directly at your current position, and they can’t cooperate with one another. If any lion gets within 1 meter of you, you will be eaten.

What is the maximum value of X for which you have a strategy to escape from them?




How do you define “a strategy to escape”?
– KonKan
Oct 21 at 0:31



Any path such that you escape.
– mtheorylord
Oct 21 at 1:11



D: This is like Calculus + 2D kinematics chase problem
– Simple Art
Oct 21 at 1:15



My best guess is that you should run straight towards the middle of two adjacent lions. Moving away from the center less than maximally possible will result in the circle enclosing on you without you escaping as much as possible i.e. backtracking/partial backtracking is a no-no. Then the rest is some problem I can’t imagine solving for exactly, but given XX is a discrete number…
– Simple Art
Oct 21 at 1:18



In more support of @SimpleArt’s strategy, I think it could be proved that the distance between each pair of lions decreases with time (given that they all move towards the same target inside the circle), so in a way the escape routes never get wider. Then the best chance would indeed seem to be to attempt a straight dash between two adjacent lions from the very beginning. Of course, formalizing this intuition is left as an exercise to the reader 😉 +1 for the question.
– dxiv
2 days ago