There is a wolf in the centre of a square field, and four dogs in the corners. The wolf can easily kill one dog, but two dogs can kill the wolf. The wolf can run all over the field, and the dogs -- along the fence (border) only. Prove that if a dog's speed is 1.5 times more than the wolf's, then the dogs can prevent the wolf escaping.
(In reply to re: Okay, then prove this:
by Wallace North)
Thanks, I was thinking of this problem wrong. (As I am oft to do)
The problem I want to see is where any dog can kill a wolf and the dogs can run some nominal amount faster than the wolf. Can the wolf escape?
This seems to be what you are explaining except I don't think that all the dogs would follow the wolf. Say he ran for the corner where two other dogs approached and then moved clockwise. only one dog would match the wolf while the other two would hustle to cover the other sides until they reached their safe spots on all four sides forming perpendicular lines which intersect at the wolf's position.
I think I am making this more difficult than it actually is.
Posted by Eric
on 2006-02-23 23:11:16