Friday, 3 November 2006

More maths

Just a quickie in between preparing for social choice theory midterm.

Guy Arie told me this one.

Suppose you throw a bunch of ants on to a one yard long stick. The ants run along the stick at one yard per minute. When an ant meets another ant, s/he changes direction and runs the other way.

How long before all of the ants run off the stick?

Answer

As Guy said, stop thinking that ants have personality.

If one ant goes on to the stick, he runs off within (at most) one minute.

But if lots of ants are bumping into each other and changing direction, the problem gets much more complex....

Until you stop thinking that ants have personality. When two ants meet, both change direction. So just swap the labels on the ants and imagine that they ran straight through each other. In other words, them meeting doesn't make any difference. All the ants still run off the stick in (at most) one minute.

This is a slightly more advanced version of the famous "what if your dog is running between Donegal and Kerry" question.