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?
For 16 people, it is possible to do it in 28 calls.
Let 4 people be named A, B, C, D and 12 people get numbers from 1 to 12.
Call 1 to 12: A calls all of the number people and A has now all the number information +A information.
Call 13 to 16: A, B, C and D exchange information according to my earlier post. A,B,C and D have all information.
Call 17 to 28: A calls all of the number people again.
Looking at it for 5 people: A will do 1 call + ABCD do 4 calls +A does one more call. The system seems to work for all values where n>4.
So the total will be (n4) + 4 + (n4)= 2n4

Posted by Hugo
on 20120727 13:02:43 