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.
I agree with Debbie. The speed of the dogs needs to be sqrt(2) of the wolfs speed.
If the dogs are smart, they come up with a plan ahead of time. They start in the corners and they guard the two borders that meet at that corner. Whenever the wolf moves, the dogs maintain a 45 degree angle in relationship to the wolf.
If the wolf heads for a corner, she will find three dogs to contend with. Turning around and heading for the opposite corner, two of these dogs plus one other will be able to prevent the escape.
If the dog heads toward the center of one side, two dogs will be attending that point, with the other two halfway down the perpendicular borders.
If the wolf is smart, she will start a poker game and invite the dogs to play.
Edited for formatting.
Edited on February 23, 2006, 1:11 pm
Posted by Leming
on 2006-02-23 12:57:11