There are 1000 ants walking on a horizontal stick, 1m long. Each ant is walking at a constant rate of 1m/hour. The ants start out in random locations on the stick, some walking to the left and some to the right. Whenever two ants meet they reverse their direction, as follows:

Whenever an ant reaches one of the ends of the stick, it falls off (eventually all ants will fall).

What is the longest time it will take the last ant to fall off the stick?

The Ants riddle is one of my all time favorites. It requires an imaginative mind, but does not require any knowledge of mathematics.