The ants go marching.... 100 ants are placed along a one-meter-long stick in random places. The stick is exactly one ant wide. Each ant moves at one meter per minute. When two ants collide, they each reverse direction. When an ant comes to the end of the stick, it falls off into oblivion. What is the longest possible amount of time before all the ants meet their doom? Hint: One ant looks very much like another ant.