You must place 7 robot ants on a long rod and set each of them to move left or right starting at time 0. You can set any positive speed for each ant. When 2 or more ants meet, they turn around. When an ant reaches the end it falls off.
Show that you can place and set the ants in such a way that none of them ever falls off.
Bonus question: Can you do this for other odd numbers, too?