n people know each a different piece of gossip.

They can phone each other and exchange all they know so that after the call the parties know anything that either of them knew before the call.

What is the smallest number of calls needed so that everyone knows everything and how is this number achieved?

(In reply to

re: solution, some doubts by Hugo)

That's pretty convincing, Hugo. I guess that it is less than 2n - 3, when n > 3

Using your approach,

2 people could do it in 1 phone call

4 people could do it in 2*1 + 4/2 = 4, which is less than 5

8 people could do it in 2*4 + 8/2 = 12, which is less than 13

16 people could do it in 2*12 + 16/2 = 32, which is more than 29

I guess we need to do some more work to get a general formula