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.

 If the dogs aren't at least 1.41 times faster than the wolf, the wolf may be able to escape by simply charging the nearest corner. The lone dog there can't get reinforcements in time, so the wolf will kill that dog and escape -- provided the wolf is an efficient enough killer that the time needed to reach and kill the lone dog is less than the time needed for the two adjacent dogs to reach that corner. Even if the dogs are only a little slower than 1.41 times the wolf, for a sufficiently large field size the lag time should still be enough for the wolf to kill and escape.

Posted by Paul on 2006-02-25 00:02:40