There is a group of n people and each of these people has a secret. Each time tw

Question

There is a group of n people and each of these people has a secret. Each time two people have a phone conversation, they share all of the secrets they know with each other. For example, on the first call, the two people share secrets; so after the call both of those people know two secrets. In this problem we are interested in how many phone calls are necessary before all n people know all n secrets. We will call the minimum number of calls necessary C(n) (a) What are C(1), C(2), C(3), C(4)? (b) Prove that for all n4, C(n)2n-4 [Hint: have one person make the first and last call]

Explanation / Answer

n(n-1) conversations

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