Question: 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).

Solution: They all will meet at the center of square, and will follow a circular trajectory.

time = pi*L/(4*v)

where L is length of cube, and v is the speed with which dogs are running