Originally posted by iraqi insurgent
It really depends on the starting position,
if the sheep are in a circle with the wolf in the middle of the circle and with the sheep spaced 3 metres apart then the wolf would never catch any sheep.
however if the wolf stays at the door he can eat them all as they're getting of the plane when it lands
Initially, I disagreed with you, but you're absolutely right. The circle clearly being the ideal starting position, as long as the sheep are sufficiently spaced, the wolf will be unable to catch them.
The way the wolf can catch a sheep is if he gets himself nearly colinear with two sheep and infinitely close to one of them. The closer sheep must run directly away from the wolf and straight into the other. How close to colinear do they have to be? Close enough that when a line is drawn between the wolf and his closer prey, the further sheep will be within 1 meter of that line.
Okay, so how does this fit in to the initial starting position? Well, the wolf starts running directly toward one sheep. (Running at the space between sheep wouldn't help as they are spaced far apart that the wolf could never have the potential to reach both in the same move.) For simplicity, let's say that the target sheep doesn't do anything until the wolf is infinitely close to it (this should be to the wolf's benefit, so it can be used to prove that the wolf can't catch any). At this point, the sheep moves directly away. Seeing that he will never catch this sheep by pursuing it in this manner, the wolf picks a new target. This time it's a little more complicated, but any target the wolf picks should be far enough away to position itself to be chased at such an angle that the path they take will not come within the aforementioned 1 meter limit of another sheep that would allow the wolf to catch a sheep. The more you space the sheep out to start with, the easier it is to observe this fact.