There are N people, numbered 0...(N-1).

One of them, chosen at random, "it".

Every day, each person touches (and possibly makes also "it") one other person.



1) Suppose people meet completely at random. 
How long until everyone is it?  
How long until the majority of the people are it?

3) Suppose people meet mostly their neighbors.  In particular, each day person x tags person normal(mean=x, std_dev = 10).  
How long until everyone is it?  
How long until the majority of the people are it?