Three ants are arranged on vertices of a triangle, one ant to a vertex. At some moment, all the ants begin crawiling along the sides of the triangel. Each one crawls along one of the two sides that connect to the vertex it is sitting on, with an equal probability of picking either.

Assuming that all the ants move with an equal speed, and that they keep crawling forever in the same direction along the triangle, what are the odds that no two will collide?

(In reply to Just picking at the words =P by Aeternus)

Not really. A triangle is a closed circuit of segments, and as such itis possible to travel forever even on a small (or finite) triangle. The lack of directional change only means that an ant going clockwise will not turn around and start going counterclockqise at any point.

Posted by levik on 2002-11-21 05:38:10