3. Suppose that each of $n$ people knows exactly one piece of information, and all $n$ pieces are different. Every time person $A$ phones person $B, A$ tells $B$ everything he knows, while $B$ tells $A$ nothing. What is the minimum of phone calls between pairs of people needed for everyone to know everything?
3. We claim that the minimum of calls needed is $2 n-2$. Let $A$ be a particular person, the $2 n-2$ calls made by $A$ to each of the persons and vice versa will leave everybody informed. Thus at most $2 n-2$ calls are needed.

Next we prove that we need at least $2 n-2$ calls. Suppose that there is a sequence of calls that leaves everybody informed. Let $B$ be the first person to be fully informed and that he receives his last piece of information at the pth call. Then each of the remaining $n-1$ people must have placed at least one call prior to $p$ so that $B$ can be fully informed. Also these people must received at least one call after $p$ since they were still not fully informed at the pth call. Thus we need at least $2(n-1)$ calls.