Initially, each of 50 Puzzling Stack Exchange users have a single distinct juicy bit of gossip not known to the others.
- If $A$ sends an email to $B$, that email can include all the bits of gossip $A$ currently knows. What are the fewest number of emails that need to be sent so that each of the 50 users knows all 50 bits of gossip? Why can't it be done with fewer emails? Assume multiple recipients / carbon copies are not allowed.
- If $A$ calls $B$, $A$ and $B$ can exchange all the bits of gossip that both know. What is the fewest number of calls required so that each of the 50 users knows all 50 pieces of gossip?
Note: Addressing why (2) can't be done with fewer calls is a little too difficult for a puzzle in my opinion. But then again I believe Bollobás included it in his puzzle book "Coffee Time in Memphis", so if you want to have a go at it knock yourself out =).