# Ants on a Log

Here’s a cool puzzle, from Mudd Fun Facts, which is a great website for finding lots of cool math problems, which appear to be mostly at the high school level and beyond (many either require calculus, or discuss connections to calculus):

One hundred ants are dropped on a meter stick. Each ant is traveling either to the left or the right with constant speed 1 meter per minute. When two ants meet, they bounce off each other and reverse direction. When an ant reaches an end of the stick, it falls off.

At some point all the ants will have fallen off. The time at which this happens will depend on the initial configuration of the ants.

Question: over ALL possible initial configurations, what is the longest amount of time that you would need to wait to guarantee that the stick has no more ants?

From: Su, Francis E., et al. “Ants on a Stick.”Mudd Math Fun Facts.

You can find the solution at the Mudd website. But think about it before you go read the solution. You’ll kick yourself if you give up too quickly. 🙂

What an excellent problem! I will have to ask this to my friends.

the answer is t=l/v

when the ants meet u can consider it as if they are both keeping the same direction (since they both reverse their direction).

so assuming an ant falls at the very start of the log it will take l/v time to reach the end