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Suppose that there are n people in a group, each aware of a different secret no...

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Advance Math

Suppose that there are n people in a group, each aware of adifferent secret no one else in the group knows about. These peoplecommunicate by phone; when two people in the group talk, they shareinformation about all secretes each knows about. For example, onthe first call, two people share information, so by the end of thecall, each of them knows about two secretes. The gossip problemasks for the number of phone calls that are needed for all n peopleto learn about all the secrets.

(a) Find the smallest number of telephone calls when there are 3and 4 people respectively. [2 marks]

(b) Prove by induction that the total number of phone calls forall n people to learn about all secretes is not more than 2n−4 forany n ≥ 4.

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