Chapter 5.1, Problem 70E

pose there arenpeople in a group, each aware of a scandal no one else in the group knows about. These people communicate by telephone; when two people in the group talk, they share information about all scandals each knows about. For example, on the first call, two people share information, so by the end of the call, each of these people knows about two scandals, Thegossip problemasks forG(n), the minimum number of telephone calls that are needed for allnpeople to learn about all the scandals. Exercises 69-71 deal with the gossip problem.

70.Use mathematical induction to prove that G(n)< 2n-4 for n >4. [Hint: In the inductive step, have a new person call a particular person at the start and at the end.]