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 Solution by Hugo)

I missed the example you gave for 5 persons (actually no example was given, only the formula for n > 4. Sloane OEIS A058992 does indeed give the formula a(n) = 2n - 4 for n >=4.
To be more complete, as the sequence in Sloane provides the first three terms of the sequence as 0, 1, 3:
a(n) = 0 for n = 1
a(n) = 1 for n = 2
a(n) = 3 for n = 3
a(n) = 2n - 4 for n >=4.

Posted by Dej Mar on 2012-07-27 17:48:28