Problem of the Week

As an icebreaker at a recent convention, the organizers came up with the following idea.  Each person was asked to introduce himself to someone else in the room and chat for one minute at the end of which time the two people shake hands.  This process was repeated with a new introduction and hand shake taking place every minute.  Sadly, one of the people in the room was infected with mathematitis, an incurable, highly infectious (and highly desirable!) disease that is spread through handshaking.   Anyone shaking the hand of a person suffering from mathematitis becomes instantly infected with the disease, as well as a new carrier of the disease.

(a) If there are n people in the room, what is the minimum number of iterations of the introduction process before everyone is infected?

(b)  With 10 people in the room, what is the average number of people infected after k iterations of the introduction process? 

You are visitor number 2532   to this page.
ã2004 Alberto L. Delgado