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.

The only possible way wolf can escape is to lure two dogs at the centre of a side and run to a point farthest away from two adjacent dogs.

Lets say if the sides of square is of unit size then the maximum distance that he can create between two dogs would be 1.5

The distance he needs to travel is 0.5 to reach the edge. Hence the speed of the dog should be maximum 1.5/.5/2 times the speed of the wolf. i.e. 1.5 times.

 

Posted by salil on 2006-02-24 10:18:17