There are four dogs, each at the counter of a large square. Each of the dogs begins chasing the dog clockwise from it. All of the dogs run at the same speed. All continuously adjust their direction so that they are always heading straight towards their clockwise neighbor. How long does it take for the dogs to catch each other? Where does this happen? (Hint: Dog's are moving in a symmetrical fashion, not along the edges of the square).
+ в центре, за время a/v, где a - сторона квадрата, а v - скорость собаки. суть в том, что их скорости перпендикулярны в любой момент времени (из соображений симметрии)
