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.

Define North, South, East, and West to be in the direction of the four edges of the field.

Have the four dogs stay on the the boundary of the square, with one each Northwest, Northeast, Southwest, and Southeast of the Wolf. 

If the wolf is in the center of the square, then the dogs are on the corner.  If the wolf runs to an edge, he meets 2 dogs.  If the wolf runs to a corner, he meets 3 dogs.

Because 1.5 is greater than the the square root of 2, the wolves can always do this. 

Posted by Steve Herman on 2006-02-23 13:01:01