Can a Lion catch a Christian in an enclosed ring? (v. Hard!)?

Question

If you have a lion and a christian in an enclosed, circular ring (like in a Roman amphitheatre), and they both have exactly the same maximum speed, instant acceleration, are both intellegent and have perfect reactions, can the Lion catch the Christian in a finite amount of time?

by the way it's not supposed to be realistic, it's a question i got in maths, so stop saying things like 'yes because the christian would get tired'. And also, you shouldn't assume that the christian will just run in a circle.

also, the only reason i said lion and christian was because some guy thought up the question while reading about gladiators and the such like, and in Roman times they used to set lions on christians. If you prefer, change it to cat & mouse which might be more politically correct.

Answer 1

Yes the lion will catch the Christian. The runner has three choices. Run less than 180* (* stands for degrees), run180*, or run more than 180*. We can rule out running less than 180* as follows: Imagine the lion and Christian as two points on a line, bisect the line, any direction less than 180* from the line will eventually intersect the line, the lion will run towards that point and the they will meet at the bisecting line. The only other option here is that the wall stops the man before he reaches the imaginary bisecting line. (I will deal with the situation where the man is at the wall last) If the man runs more than 180* he will eventually hit the wall (Just think about it or use a piece of paper for drawing) This leaves running at 180* ( or 90* from the line made by lion and man) At this point we have a right triangle. The farthest the man can run is to the wall and the lion will run along the hypotenuse of the triangle. The lion will not catch the man before he reaches the wall, but he will have closed the absolute distance between him and the man. Now we see that no matter which of the three options the man takes he will eventually end up at the wall. ( I understand that the man may make directional changes but any of them fall into one of the three covered options and eventually will lead to the same result) Now the only scenario left is the man at the wall. Because a tangent line to a circle is at 180*, any divergence from running along the wall would be less than 180* and the lion will catch him. Unfortunately for the man, a tangent is only for a single point on the circle so as he attempts to run along the wall the tangent at the new point will effectively "become" less than 180* from the lion's postion leading to his capture. I know this is not mathematically rigorous, but if you proved each of the above statements with geometric formulas, you will have proven that the lion will catch the man.

Answer 2

Yes, if the lion and Christian are not on the same circumferential plane. The inner plane will travel faster around the ring because it covers a lesser circumference. If the lion has the inner path, he can catch the Christian. Only if the circle were of infinite size could the Christian escape, because at some point, the lion will be able to get the inside track.

Answer 3

First of all whether it is a Christian or a Muslim or a jew the answer will be same. In any case lion does not understand these differences. Its reaction will be same who ever it is.(Thank God for it)
Now it is a circular ring. Hence there is no chance for any one being cornered and attacked. Since two objects have the ability to move at the same top speed or accelerate same amount and intelligence and reactions are given as same theoretically the distance between two objects will remain unaltered.Hence it is NOT POSSIBLE for the tiger to catch the Christian in a finite time.

Answer 4

The question does not state that the christian wants to avoid the lion and, having a perfect knowledge of the lion's common sense, logical reasoning, morals, and motive (and vice versa), would probably ask it to ceace and the lion, seeing the only way he could win was though sheer luck would stop, and they would work together for a means of escape, the human being the creator (having opposable thumbs), and the lion being the destroyer. They would wreak havoc upon the unsuspecting planet.
Or you could say no.
By the way, the lion could speak if the christian could, by your logic.

Answer 5

The lion will prevail, because he will always try to force the man (any religion) backwards as
a cat would stalk a mouse. The lion is just too fast and the man will stop occasionally and try to think what to do next, as the cat keeps charging.

Answer 6

Not if they have the same reactions, same speed, same intelligence, and neither tires. But your scenario is unrealistic.

In reality, the lion will catch any unarmed human you put him up against; likewise a strong, properly trained and armed gladiator will find a lion an easy target.

Answer 7

Just out ov interest. why a christian, i know the romans did it but then islam and other religons were har and few between, maybe u should change ur question to a human because i find that u use the word christian insulting

Answer 8

yes because the christian will get tired before the Lion

Answer 9

Yes because the moment the Christian has realised that he must run, the lion has already caught him, because of its perfect reaction.

Answer 10

Lion will get bored and go to sleep. and lions hunt at night anyway, so the lion will kill and eat the human during the night